From fc43a488ccf87dfc23272ea6d7b6cc04a84682a3 Mon Sep 17 00:00:00 2001
From: Matt Johnston <matt@ucc.asn.au>
Date: Sun, 19 Dec 2004 11:33:56 +0000
Subject: [PATCH] import of libtommath 0.32
--HG--
branch : libtommath-orig
extra : convert_revision : 0dc5b2d6d8c18b7e32b077cd8051bd63835afa1e
---
bn.ind | 156 +-
bn.pdf | Bin 320564 -> 335593 bytes
bn.tex | 123 +-
bn_error.c | 4 +-
bn_fast_mp_invmod.c | 6 +-
bn_fast_mp_montgomery_reduce.c | 6 +-
bn_fast_s_mp_mul_digs.c | 95 +-
bn_fast_s_mp_mul_high_digs.c | 103 +-
bn_fast_s_mp_sqr.c | 160 +-
bn_mp_2expt.c | 6 +-
bn_mp_abs.c | 4 +-
bn_mp_add.c | 4 +-
bn_mp_add_d.c | 4 +-
bn_mp_addmod.c | 4 +-
bn_mp_and.c | 4 +-
bn_mp_clamp.c | 4 +-
bn_mp_clear.c | 10 +-
bn_mp_clear_multi.c | 4 +-
bn_mp_cmp.c | 4 +-
bn_mp_cmp_d.c | 4 +-
bn_mp_cmp_mag.c | 4 +-
bn_mp_cnt_lsb.c | 4 +-
bn_mp_copy.c | 4 +-
bn_mp_count_bits.c | 4 +-
bn_mp_div.c | 81 +-
bn_mp_div_2.c | 4 +-
bn_mp_div_2d.c | 4 +-
bn_mp_div_3.c | 4 +-
bn_mp_div_d.c | 8 +-
bn_mp_dr_is_modulus.c | 4 +-
bn_mp_dr_reduce.c | 4 +-
bn_mp_dr_setup.c | 4 +-
bn_mp_exch.c | 4 +-
bn_mp_expt_d.c | 4 +-
bn_mp_exptmod.c | 24 +-
bn_mp_exptmod_fast.c | 39 +-
bn_mp_exteuclid.c | 4 +-
bn_mp_fread.c | 4 +-
bn_mp_fwrite.c | 4 +-
bn_mp_gcd.c | 4 +-
bn_mp_get_int.c | 4 +-
bn_mp_grow.c | 4 +-
bn_mp_init.c | 15 +-
bn_mp_init_copy.c | 4 +-
bn_mp_init_multi.c | 4 +-
bn_mp_init_set.c | 4 +-
bn_mp_init_set_int.c | 4 +-
bn_mp_init_size.c | 15 +-
bn_mp_invmod.c | 153 +-
bn_mp_invmod_slow.c | 171 +
bn_mp_is_square.c | 6 +-
bn_mp_jacobi.c | 4 +-
bn_mp_karatsuba_mul.c | 7 +-
bn_mp_karatsuba_sqr.c | 6 +-
bn_mp_lcm.c | 4 +-
bn_mp_lshd.c | 4 +-
bn_mp_mod.c | 4 +-
bn_mp_mod_2d.c | 4 +-
bn_mp_mod_d.c | 4 +-
bn_mp_montgomery_calc_normalization.c | 25 +-
bn_mp_montgomery_reduce.c | 8 +-
bn_mp_montgomery_setup.c | 6 +-
bn_mp_mul.c | 28 +-
bn_mp_mul_2.c | 4 +-
bn_mp_mul_2d.c | 4 +-
bn_mp_mul_d.c | 4 +-
bn_mp_mulmod.c | 4 +-
bn_mp_n_root.c | 4 +-
bn_mp_neg.c | 4 +-
bn_mp_or.c | 4 +-
bn_mp_prime_fermat.c | 4 +-
bn_mp_prime_is_divisible.c | 4 +-
bn_mp_prime_is_prime.c | 6 +-
bn_mp_prime_miller_rabin.c | 4 +-
bn_mp_prime_next_prime.c | 4 +-
...tab.c => bn_mp_prime_rabin_miller_trials.c | 17 +-
bn_mp_prime_random_ex.c | 7 +-
bn_mp_radix_size.c | 4 +-
bn_mp_radix_smap.c | 4 +-
bn_mp_rand.c | 4 +-
bn_mp_read_radix.c | 4 +-
bn_mp_read_signed_bin.c | 4 +-
bn_mp_read_unsigned_bin.c | 4 +-
bn_mp_reduce.c | 15 +-
bn_mp_reduce_2k.c | 4 +-
bn_mp_reduce_2k_setup.c | 4 +-
bn_mp_reduce_is_2k.c | 9 +-
bn_mp_reduce_setup.c | 7 +-
bn_mp_rshd.c | 4 +-
bn_mp_set.c | 4 +-
bn_mp_set_int.c | 4 +-
bn_mp_shrink.c | 4 +-
bn_mp_signed_bin_size.c | 4 +-
bn_mp_sqr.c | 23 +-
bn_mp_sqrmod.c | 4 +-
bn_mp_sqrt.c | 4 +-
bn_mp_sub.c | 4 +-
bn_mp_sub_d.c | 4 +-
bn_mp_submod.c | 4 +-
bn_mp_to_signed_bin.c | 4 +-
bn_mp_to_unsigned_bin.c | 4 +-
bn_mp_toom_mul.c | 11 +-
bn_mp_toom_sqr.c | 4 +-
bn_mp_toradix.c | 4 +-
bn_mp_toradix_n.c | 4 +-
bn_mp_unsigned_bin_size.c | 4 +-
bn_mp_xor.c | 6 +-
bn_mp_zero.c | 4 +-
bn_prime_tab.c | 4 +-
bn_reverse.c | 4 +-
bn_s_mp_add.c | 4 +-
bn_s_mp_exptmod.c | 4 +-
bn_s_mp_mul_digs.c | 4 +-
bn_s_mp_mul_high_digs.c | 6 +-
bn_s_mp_sqr.c | 4 +-
bn_s_mp_sub.c | 4 +-
bncore.c | 14 +-
booker.pl | 3 +-
callgraph.txt | 10168 ++++++++++++++++
changes.txt | 24 +
demo/demo.c | 296 +-
demo/timing.c | 291 +
dep.pl | 121 +
etc/makefile | 3 +-
etc/makefile.icc | 67 +
etc/tune.c | 167 +-
logs/add.log | 32 +-
logs/addsub.png | Bin 7084 -> 6254 bytes
logs/expt.log | 7 -
logs/expt.png | Bin 7439 -> 6605 bytes
logs/expt_2k.log | 6 -
logs/expt_dr.log | 7 -
logs/graphs.dem | 34 +-
logs/invmod.log | 32 -
logs/invmod.png | Bin 5735 -> 4918 bytes
logs/k7/README | 13 -
logs/k7/add.log | 16 -
logs/k7/addsub.png | Bin 6933 -> 0 bytes
logs/k7/expt.log | 7 -
logs/k7/expt.png | Bin 6490 -> 0 bytes
logs/k7/expt_dr.log | 7 -
logs/k7/graphs.dem | 17 -
logs/k7/index.html | 24 -
logs/k7/invmod.log | 32 -
logs/k7/invmod.png | Bin 5730 -> 0 bytes
logs/k7/mult.log | 17 -
logs/k7/mult.png | Bin 8263 -> 0 bytes
logs/k7/mult_kara.log | 17 -
logs/k7/sqr.log | 17 -
logs/k7/sqr_kara.log | 17 -
logs/k7/sub.log | 16 -
logs/mult.log | 176 +-
logs/mult.png | Bin 8100 -> 6770 bytes
logs/mult_kara.log | 66 +-
logs/p4/README | 13 -
logs/p4/add.log | 16 -
logs/p4/addsub.png | Bin 6898 -> 0 bytes
logs/p4/expt.log | 7 -
logs/p4/expt.png | Bin 6587 -> 0 bytes
logs/p4/expt_dr.log | 7 -
logs/p4/graphs.dem | 17 -
logs/p4/index.html | 24 -
logs/p4/invmod.log | 32 -
logs/p4/invmod.png | Bin 5596 -> 0 bytes
logs/p4/mult.log | 17 -
logs/p4/mult.png | Bin 8100 -> 0 bytes
logs/p4/mult_kara.log | 17 -
logs/p4/sqr.log | 17 -
logs/p4/sqr_kara.log | 17 -
logs/p4/sub.log | 16 -
logs/sqr.log | 176 +-
logs/sqr_kara.log | 66 +-
logs/sub.log | 32 +-
makefile | 45 +-
makefile.bcc | 5 +-
makefile.cygwin_dll | 5 +-
makefile.icc | 110 +
makefile.msvc | 5 +-
makefile.shared | 74 +
mtest/mtest.c | 5 +-
poster.pdf | Bin 40819 -> 40822 bytes
pre_gen/mpi.c | 1225 +-
pretty.build | 66 +
tommath.h | 15 +-
tommath.pdf | Bin 1153705 -> 1158962 bytes
tommath.src | 167 +-
tommath.tex | 2516 ++--
tommath_class.h | 951 ++
tommath_superclass.h | 72 +
189 files changed, 15775 insertions(+), 3362 deletions(-)
create mode 100644 bn_mp_invmod_slow.c
rename bn_prime_sizes_tab.c => bn_mp_prime_rabin_miller_trials.c (82%)
create mode 100644 callgraph.txt
create mode 100644 demo/timing.c
create mode 100644 dep.pl
create mode 100644 etc/makefile.icc
delete mode 100644 logs/k7/README
delete mode 100644 logs/k7/add.log
delete mode 100644 logs/k7/addsub.png
delete mode 100644 logs/k7/expt.log
delete mode 100644 logs/k7/expt.png
delete mode 100644 logs/k7/expt_dr.log
delete mode 100644 logs/k7/graphs.dem
delete mode 100644 logs/k7/index.html
delete mode 100644 logs/k7/invmod.log
delete mode 100644 logs/k7/invmod.png
delete mode 100644 logs/k7/mult.log
delete mode 100644 logs/k7/mult.png
delete mode 100644 logs/k7/mult_kara.log
delete mode 100644 logs/k7/sqr.log
delete mode 100644 logs/k7/sqr_kara.log
delete mode 100644 logs/k7/sub.log
delete mode 100644 logs/p4/README
delete mode 100644 logs/p4/add.log
delete mode 100644 logs/p4/addsub.png
delete mode 100644 logs/p4/expt.log
delete mode 100644 logs/p4/expt.png
delete mode 100644 logs/p4/expt_dr.log
delete mode 100644 logs/p4/graphs.dem
delete mode 100644 logs/p4/index.html
delete mode 100644 logs/p4/invmod.log
delete mode 100644 logs/p4/invmod.png
delete mode 100644 logs/p4/mult.log
delete mode 100644 logs/p4/mult.png
delete mode 100644 logs/p4/mult_kara.log
delete mode 100644 logs/p4/sqr.log
delete mode 100644 logs/p4/sqr_kara.log
delete mode 100644 logs/p4/sub.log
create mode 100644 makefile.icc
create mode 100644 makefile.shared
create mode 100644 pretty.build
create mode 100644 tommath_class.h
create mode 100644 tommath_superclass.h
diff --git a/bn.ind b/bn.ind
index ae1dcdea..e5f7d4a5 100644
--- a/bn.ind
+++ b/bn.ind
@@ -1,82 +1,82 @@
\begin{theindex}
- \item mp\_add, \hyperpage{25}
- \item mp\_add\_d, \hyperpage{48}
- \item mp\_and, \hyperpage{25}
- \item mp\_clear, \hyperpage{7}
- \item mp\_clear\_multi, \hyperpage{8}
- \item mp\_cmp, \hyperpage{20}
- \item mp\_cmp\_d, \hyperpage{21}
- \item mp\_cmp\_mag, \hyperpage{19}
- \item mp\_div, \hyperpage{26}
- \item mp\_div\_2, \hyperpage{22}
- \item mp\_div\_2d, \hyperpage{24}
- \item mp\_div\_d, \hyperpage{48}
- \item mp\_dr\_reduce, \hyperpage{36}
- \item mp\_dr\_setup, \hyperpage{36}
- \item MP\_EQ, \hyperpage{18}
- \item mp\_error\_to\_string, \hyperpage{6}
- \item mp\_expt\_d, \hyperpage{39}
- \item mp\_exptmod, \hyperpage{39}
- \item mp\_exteuclid, \hyperpage{47}
- \item mp\_gcd, \hyperpage{47}
- \item mp\_get\_int, \hyperpage{16}
- \item mp\_grow, \hyperpage{12}
- \item MP\_GT, \hyperpage{18}
- \item mp\_init, \hyperpage{7}
- \item mp\_init\_copy, \hyperpage{9}
- \item mp\_init\_multi, \hyperpage{8}
- \item mp\_init\_set, \hyperpage{17}
- \item mp\_init\_set\_int, \hyperpage{17}
- \item mp\_init\_size, \hyperpage{10}
- \item mp\_int, \hyperpage{6}
- \item mp\_invmod, \hyperpage{48}
- \item mp\_jacobi, \hyperpage{48}
- \item mp\_lcm, \hyperpage{47}
- \item mp\_lshd, \hyperpage{24}
- \item MP\_LT, \hyperpage{18}
- \item MP\_MEM, \hyperpage{5}
- \item mp\_mod, \hyperpage{31}
- \item mp\_mod\_d, \hyperpage{48}
- \item mp\_montgomery\_calc\_normalization, \hyperpage{34}
- \item mp\_montgomery\_reduce, \hyperpage{33}
- \item mp\_montgomery\_setup, \hyperpage{33}
- \item mp\_mul, \hyperpage{27}
- \item mp\_mul\_2, \hyperpage{22}
- \item mp\_mul\_2d, \hyperpage{24}
- \item mp\_mul\_d, \hyperpage{48}
- \item mp\_n\_root, \hyperpage{40}
- \item mp\_neg, \hyperpage{25}
- \item MP\_NO, \hyperpage{5}
- \item MP\_OKAY, \hyperpage{5}
- \item mp\_or, \hyperpage{25}
- \item mp\_prime\_fermat, \hyperpage{41}
- \item mp\_prime\_is\_divisible, \hyperpage{41}
- \item mp\_prime\_is\_prime, \hyperpage{42}
- \item mp\_prime\_miller\_rabin, \hyperpage{41}
- \item mp\_prime\_next\_prime, \hyperpage{42}
- \item mp\_prime\_rabin\_miller\_trials, \hyperpage{42}
- \item mp\_prime\_random, \hyperpage{43}
- \item mp\_prime\_random\_ex, \hyperpage{43}
- \item mp\_radix\_size, \hyperpage{45}
- \item mp\_read\_radix, \hyperpage{45}
- \item mp\_read\_unsigned\_bin, \hyperpage{46}
- \item mp\_reduce, \hyperpage{32}
- \item mp\_reduce\_2k, \hyperpage{37}
- \item mp\_reduce\_2k\_setup, \hyperpage{37}
- \item mp\_reduce\_setup, \hyperpage{32}
- \item mp\_rshd, \hyperpage{24}
- \item mp\_set, \hyperpage{15}
- \item mp\_set\_int, \hyperpage{16}
- \item mp\_shrink, \hyperpage{11}
- \item mp\_sqr, \hyperpage{29}
- \item mp\_sub, \hyperpage{25}
- \item mp\_sub\_d, \hyperpage{48}
- \item mp\_to\_unsigned\_bin, \hyperpage{46}
- \item mp\_toradix, \hyperpage{45}
- \item mp\_unsigned\_bin\_size, \hyperpage{46}
- \item MP\_VAL, \hyperpage{5}
- \item mp\_xor, \hyperpage{25}
- \item MP\_YES, \hyperpage{5}
+ \item mp\_add, \hyperpage{29}
+ \item mp\_add\_d, \hyperpage{52}
+ \item mp\_and, \hyperpage{29}
+ \item mp\_clear, \hyperpage{11}
+ \item mp\_clear\_multi, \hyperpage{12}
+ \item mp\_cmp, \hyperpage{24}
+ \item mp\_cmp\_d, \hyperpage{25}
+ \item mp\_cmp\_mag, \hyperpage{23}
+ \item mp\_div, \hyperpage{30}
+ \item mp\_div\_2, \hyperpage{26}
+ \item mp\_div\_2d, \hyperpage{28}
+ \item mp\_div\_d, \hyperpage{52}
+ \item mp\_dr\_reduce, \hyperpage{40}
+ \item mp\_dr\_setup, \hyperpage{40}
+ \item MP\_EQ, \hyperpage{22}
+ \item mp\_error\_to\_string, \hyperpage{10}
+ \item mp\_expt\_d, \hyperpage{43}
+ \item mp\_exptmod, \hyperpage{43}
+ \item mp\_exteuclid, \hyperpage{51}
+ \item mp\_gcd, \hyperpage{51}
+ \item mp\_get\_int, \hyperpage{20}
+ \item mp\_grow, \hyperpage{16}
+ \item MP\_GT, \hyperpage{22}
+ \item mp\_init, \hyperpage{11}
+ \item mp\_init\_copy, \hyperpage{13}
+ \item mp\_init\_multi, \hyperpage{12}
+ \item mp\_init\_set, \hyperpage{21}
+ \item mp\_init\_set\_int, \hyperpage{21}
+ \item mp\_init\_size, \hyperpage{14}
+ \item mp\_int, \hyperpage{10}
+ \item mp\_invmod, \hyperpage{52}
+ \item mp\_jacobi, \hyperpage{52}
+ \item mp\_lcm, \hyperpage{51}
+ \item mp\_lshd, \hyperpage{28}
+ \item MP\_LT, \hyperpage{22}
+ \item MP\_MEM, \hyperpage{9}
+ \item mp\_mod, \hyperpage{35}
+ \item mp\_mod\_d, \hyperpage{52}
+ \item mp\_montgomery\_calc\_normalization, \hyperpage{38}
+ \item mp\_montgomery\_reduce, \hyperpage{37}
+ \item mp\_montgomery\_setup, \hyperpage{37}
+ \item mp\_mul, \hyperpage{31}
+ \item mp\_mul\_2, \hyperpage{26}
+ \item mp\_mul\_2d, \hyperpage{28}
+ \item mp\_mul\_d, \hyperpage{52}
+ \item mp\_n\_root, \hyperpage{44}
+ \item mp\_neg, \hyperpage{29}
+ \item MP\_NO, \hyperpage{9}
+ \item MP\_OKAY, \hyperpage{9}
+ \item mp\_or, \hyperpage{29}
+ \item mp\_prime\_fermat, \hyperpage{45}
+ \item mp\_prime\_is\_divisible, \hyperpage{45}
+ \item mp\_prime\_is\_prime, \hyperpage{46}
+ \item mp\_prime\_miller\_rabin, \hyperpage{45}
+ \item mp\_prime\_next\_prime, \hyperpage{46}
+ \item mp\_prime\_rabin\_miller\_trials, \hyperpage{46}
+ \item mp\_prime\_random, \hyperpage{47}
+ \item mp\_prime\_random\_ex, \hyperpage{47}
+ \item mp\_radix\_size, \hyperpage{49}
+ \item mp\_read\_radix, \hyperpage{49}
+ \item mp\_read\_unsigned\_bin, \hyperpage{50}
+ \item mp\_reduce, \hyperpage{36}
+ \item mp\_reduce\_2k, \hyperpage{41}
+ \item mp\_reduce\_2k\_setup, \hyperpage{41}
+ \item mp\_reduce\_setup, \hyperpage{36}
+ \item mp\_rshd, \hyperpage{28}
+ \item mp\_set, \hyperpage{19}
+ \item mp\_set\_int, \hyperpage{20}
+ \item mp\_shrink, \hyperpage{15}
+ \item mp\_sqr, \hyperpage{33}
+ \item mp\_sub, \hyperpage{29}
+ \item mp\_sub\_d, \hyperpage{52}
+ \item mp\_to\_unsigned\_bin, \hyperpage{50}
+ \item mp\_toradix, \hyperpage{49}
+ \item mp\_unsigned\_bin\_size, \hyperpage{50}
+ \item MP\_VAL, \hyperpage{9}
+ \item mp\_xor, \hyperpage{29}
+ \item MP\_YES, \hyperpage{9}
\end{theindex}
diff --git a/bn.pdf b/bn.pdf
index 52421fd5981b12f134d6f2352d6c7d978f6ffb32..fbd5b2adc106eacf9ae64849d42aa15100c676c4 100644
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diff --git a/bn.tex b/bn.tex
index a2545862..74a4f017 100644
--- a/bn.tex
+++ b/bn.tex
@@ -49,7 +49,7 @@
\begin{document}
\frontmatter
\pagestyle{empty}
-\title{LibTomMath User Manual \\ v0.30}
+\title{LibTomMath User Manual \\ v0.32}
\author{Tom St Denis \\ tomstdenis@iahu.ca}
\maketitle
This text, the library and the accompanying textbook are all hereby placed in the public domain. This book has been
@@ -96,27 +96,34 @@ LibTomMath is meant to be very ``GCC friendly'' as it comes with a makefile well
also build in MSVC, Borland C out of the box. For any other ISO C compiler a makefile will have to be made by the end
developer.
-To build the library for GCC simply issue the
-
+\subsection{Static Libraries}
+To build as a static library for GCC issue the following
\begin{alltt}
make
\end{alltt}
-command. This will build the library and archive the object files in ``libtommath.a''. Now you simply link against that
-and include ``tommath.h'' within your programs.
-
-Alternatively to build with MSVC type
-
+command. This will build the library and archive the object files in ``libtommath.a''. Now you link against
+that and include ``tommath.h'' within your programs. Alternatively to build with MSVC issue the following
\begin{alltt}
nmake -f makefile.msvc
\end{alltt}
-This will build the library and archive the object files in ``tommath.lib''. This has been tested with MSVC version 6.00
-with service pack 5.
+This will build the library and archive the object files in ``tommath.lib''. This has been tested with MSVC
+version 6.00 with service pack 5.
+
+\subsection{Shared Libraries}
+To build as a shared library for GCC issue the following
+\begin{alltt}
+make -f makefile.shared
+\end{alltt}
+This requires the ``libtool'' package (common on most Linux/BSD systems). It will build LibTomMath as both shared
+and static then install (by default) into /usr/lib as well as install the header files in /usr/include. The shared
+library (resource) will be called ``libtommath.la'' while the static library called ``libtommath.a''. Generally
+you use libtool to link your application against the shared object.
-There is limited support for making a ``DLL'' in windows via the ``makefile.cygwin\_dll'' makefile. It requires Cygwin
-to work with since it requires the auto-export/import functionality. The resulting DLL and imprt library ``libtomcrypt.dll.a''
-can be used to link LibTomMath dynamically to any Windows program using Cygwin.
+There is limited support for making a ``DLL'' in windows via the ``makefile.cygwin\_dll'' makefile. It requires
+Cygwin to work with since it requires the auto-export/import functionality. The resulting DLL and import library
+``libtommath.dll.a'' can be used to link LibTomMath dynamically to any Windows program using Cygwin.
\subsection{Testing}
To build the library and the test harness type
@@ -144,6 +151,96 @@ This will output a row of numbers that are increasing. Each column is a differe
that is being performed. The numbers represent how many times the test was invoked. If an error is detected the program
will exit with a dump of the relevent numbers it was working with.
+\section{Build Configuration}
+LibTomMath can configured at build time in three phases we shall call ``depends'', ``tweaks'' and ``trims''.
+Each phase changes how the library is built and they are applied one after another respectively.
+
+To make the system more powerful you can tweak the build process. Classes are defined in the file
+``tommath\_superclass.h''. By default, the symbol ``LTM\_ALL'' shall be defined which simply
+instructs the system to build all of the functions. This is how LibTomMath used to be packaged. This will give you
+access to every function LibTomMath offers.
+
+However, there are cases where such a build is not optional. For instance, you want to perform RSA operations. You
+don't need the vast majority of the library to perform these operations. Aside from LTM\_ALL there is
+another pre--defined class ``SC\_RSA\_1'' which works in conjunction with the RSA from LibTomCrypt. Additional
+classes can be defined base on the need of the user.
+
+\subsection{Build Depends}
+In the file tommath\_class.h you will see a large list of C ``defines'' followed by a series of ``ifdefs''
+which further define symbols. All of the symbols (technically they're macros $\ldots$) represent a given C source
+file. For instance, BN\_MP\_ADD\_C represents the file ``bn\_mp\_add.c''. When a define has been enabled the
+function in the respective file will be compiled and linked into the library. Accordingly when the define
+is absent the file will not be compiled and not contribute any size to the library.
+
+You will also note that the header tommath\_class.h is actually recursively included (it includes itself twice).
+This is to help resolve as many dependencies as possible. In the last pass the symbol LTM\_LAST will be defined.
+This is useful for ``trims''.
+
+\subsection{Build Tweaks}
+A tweak is an algorithm ``alternative''. For example, to provide tradeoffs (usually between size and space).
+They can be enabled at any pass of the configuration phase.
+
+\begin{small}
+\begin{center}
+\begin{tabular}{|l|l|}
+\hline \textbf{Define} & \textbf{Purpose} \\
+\hline BN\_MP\_DIV\_SMALL & Enables a slower, smaller and equally \\
+ & functional mp\_div() function \\
+\hline
+\end{tabular}
+\end{center}
+\end{small}
+
+\subsection{Build Trims}
+A trim is a manner of removing functionality from a function that is not required. For instance, to perform
+RSA cryptography you only require exponentiation with odd moduli so even moduli support can be safely removed.
+Build trims are meant to be defined on the last pass of the configuration which means they are to be defined
+only if LTM\_LAST has been defined.
+
+\subsubsection{Moduli Related}
+\begin{small}
+\begin{center}
+\begin{tabular}{|l|l|}
+\hline \textbf{Restriction} & \textbf{Undefine} \\
+\hline Exponentiation with odd moduli only & BN\_S\_MP\_EXPTMOD\_C \\
+ & BN\_MP\_REDUCE\_C \\
+ & BN\_MP\_REDUCE\_SETUP\_C \\
+ & BN\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
+ & BN\_FAST\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
+\hline Exponentiation with random odd moduli & (The above plus the following) \\
+ & BN\_MP\_REDUCE\_2K\_C \\
+ & BN\_MP\_REDUCE\_2K\_SETUP\_C \\
+ & BN\_MP\_REDUCE\_IS\_2K\_C \\
+ & BN\_MP\_DR\_IS\_MODULUS\_C \\
+ & BN\_MP\_DR\_REDUCE\_C \\
+ & BN\_MP\_DR\_SETUP\_C \\
+\hline Modular inverse odd moduli only & BN\_MP\_INVMOD\_SLOW\_C \\
+\hline Modular inverse (both, smaller/slower) & BN\_FAST\_MP\_INVMOD\_C \\
+\hline
+\end{tabular}
+\end{center}
+\end{small}
+
+\subsubsection{Operand Size Related}
+\begin{small}
+\begin{center}
+\begin{tabular}{|l|l|}
+\hline \textbf{Restriction} & \textbf{Undefine} \\
+\hline Moduli $\le 2560$ bits & BN\_MP\_MONTGOMERY\_REDUCE\_C \\
+ & BN\_S\_MP\_MUL\_DIGS\_C \\
+ & BN\_S\_MP\_MUL\_HIGH\_DIGS\_C \\
+ & BN\_S\_MP\_SQR\_C \\
+\hline Polynomial Schmolynomial & BN\_MP\_KARATSUBA\_MUL\_C \\
+ & BN\_MP\_KARATSUBA\_SQR\_C \\
+ & BN\_MP\_TOOM\_MUL\_C \\
+ & BN\_MP\_TOOM\_SQR\_C \\
+
+\hline
+\end{tabular}
+\end{center}
+\end{small}
+
+
\section{Purpose of LibTomMath}
Unlike GNU MP (GMP) Library, LIP, OpenSSL or various other commercial kits (Miracl), LibTomMath was not written with
bleeding edge performance in mind. First and foremost LibTomMath was written to be entirely open. Not only is the
diff --git a/bn_error.c b/bn_error.c
index 7cac6497..15467841 100644
--- a/bn_error.c
+++ b/bn_error.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_ERROR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
static const struct {
int code;
@@ -39,3 +40,4 @@ char *mp_error_to_string(int code)
return "Invalid error code";
}
+#endif
diff --git a/bn_fast_mp_invmod.c b/bn_fast_mp_invmod.c
index c9a94598..492a3f1f 100644
--- a/bn_fast_mp_invmod.c
+++ b/bn_fast_mp_invmod.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_FAST_MP_INVMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,12 +14,11 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes the modular inverse via binary extended euclidean algorithm,
* that is c = 1/a mod b
*
- * Based on mp_invmod except this is optimized for the case where b is
+ * Based on slow invmod except this is optimized for the case where b is
* odd as per HAC Note 14.64 on pp. 610
*/
int
@@ -141,3 +142,4 @@ top:
__ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
return res;
}
+#endif
diff --git a/bn_fast_mp_montgomery_reduce.c b/bn_fast_mp_montgomery_reduce.c
index c7a3413e..7373ae6b 100644
--- a/bn_fast_mp_montgomery_reduce.c
+++ b/bn_fast_mp_montgomery_reduce.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,11 +14,10 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes xR**-1 == x (mod N) via Montgomery Reduction
*
- * This is an optimized implementation of mp_montgomery_reduce
+ * This is an optimized implementation of montgomery_reduce
* which uses the comba method to quickly calculate the columns of the
* reduction.
*
@@ -165,3 +166,4 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
}
return MP_OKAY;
}
+#endif
diff --git a/bn_fast_s_mp_mul_digs.c b/bn_fast_s_mp_mul_digs.c
index 75fa706e..92b50bb7 100644
--- a/bn_fast_s_mp_mul_digs.c
+++ b/bn_fast_s_mp_mul_digs.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_MUL_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Fast (comba) multiplier
*
@@ -33,8 +34,9 @@
int
fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
- int olduse, res, pa, ix;
- mp_word W[MP_WARRAY];
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY];
+ register mp_word _W;
/* grow the destination as required */
if (c->alloc < digs) {
@@ -43,82 +45,52 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
}
}
- /* clear temp buf (the columns) */
- memset (W, 0, sizeof (mp_word) * digs);
+ /* number of output digits to produce */
+ pa = MIN(digs, a->used + b->used);
- /* calculate the columns */
- pa = a->used;
- for (ix = 0; ix < pa; ix++) {
- /* this multiplier has been modified to allow you to
- * control how many digits of output are produced.
- * So at most we want to make upto "digs" digits of output.
- *
- * this adds products to distinct columns (at ix+iy) of W
- * note that each step through the loop is not dependent on
- * the previous which means the compiler can easily unroll
- * the loop without scheduling problems
- */
- {
- register mp_digit tmpx, *tmpy;
- register mp_word *_W;
- register int iy, pb;
+ /* clear the carry */
+ _W = 0;
+ for (ix = 0; ix <= pa; ix++) {
+ int tx, ty;
+ int iy;
+ mp_digit *tmpx, *tmpy;
- /* alias for the the word on the left e.g. A[ix] * A[iy] */
- tmpx = a->dp[ix];
+ /* get offsets into the two bignums */
+ ty = MIN(b->used-1, ix);
+ tx = ix - ty;
- /* alias for the right side */
- tmpy = b->dp;
-
- /* alias for the columns, each step through the loop adds a new
- term to each column
- */
- _W = W + ix;
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = b->dp + ty;
- /* the number of digits is limited by their placement. E.g.
- we avoid multiplying digits that will end up above the # of
- digits of precision requested
+ /* this is the number of times the loop will iterrate, essentially its
+ while (tx++ < a->used && ty-- >= 0) { ... }
*/
- pb = MIN (b->used, digs - ix);
+ iy = MIN(a->used-tx, ty+1);
- for (iy = 0; iy < pb; iy++) {
- *_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++);
+ /* execute loop */
+ for (iz = 0; iz < iy; ++iz) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
}
- }
+ /* store term */
+ W[ix] = ((mp_digit)_W) & MP_MASK;
+
+ /* make next carry */
+ _W = _W >> ((mp_word)DIGIT_BIT);
}
/* setup dest */
- olduse = c->used;
+ olduse = c->used;
c->used = digs;
{
register mp_digit *tmpc;
-
- /* At this point W[] contains the sums of each column. To get the
- * correct result we must take the extra bits from each column and
- * carry them down
- *
- * Note that while this adds extra code to the multiplier it
- * saves time since the carry propagation is removed from the
- * above nested loop.This has the effect of reducing the work
- * from N*(N+N*c)==N**2 + c*N**2 to N**2 + N*c where c is the
- * cost of the shifting. On very small numbers this is slower
- * but on most cryptographic size numbers it is faster.
- *
- * In this particular implementation we feed the carries from
- * behind which means when the loop terminates we still have one
- * last digit to copy
- */
tmpc = c->dp;
- for (ix = 1; ix < digs; ix++) {
- /* forward the carry from the previous temp */
- W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
-
+ for (ix = 0; ix < digs; ix++) {
/* now extract the previous digit [below the carry] */
- *tmpc++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
+ *tmpc++ = W[ix];
}
- /* fetch the last digit */
- *tmpc++ = (mp_digit) (W[digs - 1] & ((mp_word) MP_MASK));
/* clear unused digits [that existed in the old copy of c] */
for (; ix < olduse; ix++) {
@@ -128,3 +100,4 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
mp_clamp (c);
return MP_OKAY;
}
+#endif
diff --git a/bn_fast_s_mp_mul_high_digs.c b/bn_fast_s_mp_mul_high_digs.c
index 779aa140..9e0cf55a 100644
--- a/bn_fast_s_mp_mul_high_digs.c
+++ b/bn_fast_s_mp_mul_high_digs.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,10 +14,9 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
- #include <tommath.h>
-/* this is a modified version of fast_s_mp_mul_digs that only produces
- * output digits *above* digs. See the comments for fast_s_mp_mul_digs
+/* this is a modified version of fast_s_mul_digs that only produces
+ * output digits *above* digs. See the comments for fast_s_mul_digs
* to see how it works.
*
* This is used in the Barrett reduction since for one of the multiplications
@@ -26,73 +27,69 @@
int
fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
- int oldused, newused, res, pa, pb, ix;
- mp_word W[MP_WARRAY];
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY];
+ mp_word _W;
- /* calculate size of product and allocate more space if required */
- newused = a->used + b->used + 1;
- if (c->alloc < newused) {
- if ((res = mp_grow (c, newused)) != MP_OKAY) {
+ /* grow the destination as required */
+ pa = a->used + b->used;
+ if (c->alloc < pa) {
+ if ((res = mp_grow (c, pa)) != MP_OKAY) {
return res;
}
}
- /* like the other comba method we compute the columns first */
- pa = a->used;
- pb = b->used;
- memset (W + digs, 0, (pa + pb + 1 - digs) * sizeof (mp_word));
- for (ix = 0; ix < pa; ix++) {
- {
- register mp_digit tmpx, *tmpy;
- register int iy;
- register mp_word *_W;
+ /* number of output digits to produce */
+ pa = a->used + b->used;
+ _W = 0;
+ for (ix = digs; ix <= pa; ix++) {
+ int tx, ty, iy;
+ mp_digit *tmpx, *tmpy;
- /* work todo, that is we only calculate digits that are at "digs" or above */
- iy = digs - ix;
+ /* get offsets into the two bignums */
+ ty = MIN(b->used-1, ix);
+ tx = ix - ty;
- /* copy of word on the left of A[ix] * B[iy] */
- tmpx = a->dp[ix];
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = b->dp + ty;
- /* alias for right side */
- tmpy = b->dp + iy;
-
- /* alias for the columns of output. Offset to be equal to or above the
- * smallest digit place requested
+ /* this is the number of times the loop will iterrate, essentially its
+ while (tx++ < a->used && ty-- >= 0) { ... }
*/
- _W = W + digs;
-
- /* skip cases below zero where ix > digs */
- if (iy < 0) {
- iy = abs(iy);
- tmpy += iy;
- _W += iy;
- iy = 0;
- }
+ iy = MIN(a->used-tx, ty+1);
- /* compute column products for digits above the minimum */
- for (; iy < pb; iy++) {
- *_W++ += ((mp_word) tmpx) * ((mp_word)*tmpy++);
+ /* execute loop */
+ for (iz = 0; iz < iy; iz++) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
}
- }
+
+ /* store term */
+ W[ix] = ((mp_digit)_W) & MP_MASK;
+
+ /* make next carry */
+ _W = _W >> ((mp_word)DIGIT_BIT);
}
/* setup dest */
- oldused = c->used;
- c->used = newused;
+ olduse = c->used;
+ c->used = pa;
- /* now convert the array W downto what we need
- *
- * See comments in bn_fast_s_mp_mul_digs.c
- */
- for (ix = digs + 1; ix < newused; ix++) {
- W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
- c->dp[ix - 1] = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
- }
- c->dp[newused - 1] = (mp_digit) (W[newused - 1] & ((mp_word) MP_MASK));
+ {
+ register mp_digit *tmpc;
+
+ tmpc = c->dp + digs;
+ for (ix = digs; ix <= pa; ix++) {
+ /* now extract the previous digit [below the carry] */
+ *tmpc++ = W[ix];
+ }
- for (; ix < oldused; ix++) {
- c->dp[ix] = 0;
+ /* clear unused digits [that existed in the old copy of c] */
+ for (; ix < olduse; ix++) {
+ *tmpc++ = 0;
+ }
}
mp_clamp (c);
return MP_OKAY;
}
+#endif
diff --git a/bn_fast_s_mp_sqr.c b/bn_fast_s_mp_sqr.c
index f62ae54e..9f6962dc 100644
--- a/bn_fast_s_mp_sqr.c
+++ b/bn_fast_s_mp_sqr.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* fast squaring
*
@@ -31,109 +32,98 @@
* Based on Algorithm 14.16 on pp.597 of HAC.
*
*/
+/* the jist of squaring...
+
+you do like mult except the offset of the tmpx [one that starts closer to zero]
+can't equal the offset of tmpy. So basically you set up iy like before then you min it with
+(ty-tx) so that it never happens. You double all those you add in the inner loop
+
+After that loop you do the squares and add them in.
+
+Remove W2 and don't memset W
+
+*/
+
int fast_s_mp_sqr (mp_int * a, mp_int * b)
{
- int olduse, newused, res, ix, pa;
- mp_word W2[MP_WARRAY], W[MP_WARRAY];
-
- /* calculate size of product and allocate as required */
- pa = a->used;
- newused = pa + pa + 1;
- if (b->alloc < newused) {
- if ((res = mp_grow (b, newused)) != MP_OKAY) {
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY], *tmpx;
+ mp_word W1;
+
+ /* grow the destination as required */
+ pa = a->used + a->used;
+ if (b->alloc < pa) {
+ if ((res = mp_grow (b, pa)) != MP_OKAY) {
return res;
}
}
- /* zero temp buffer (columns)
- * Note that there are two buffers. Since squaring requires
- * a outer and inner product and the inner product requires
- * computing a product and doubling it (a relatively expensive
- * op to perform n**2 times if you don't have to) the inner and
- * outer products are computed in different buffers. This way
- * the inner product can be doubled using n doublings instead of
- * n**2
- */
- memset (W, 0, newused * sizeof (mp_word));
- memset (W2, 0, newused * sizeof (mp_word));
-
- /* This computes the inner product. To simplify the inner N**2 loop
- * the multiplication by two is done afterwards in the N loop.
- */
- for (ix = 0; ix < pa; ix++) {
- /* compute the outer product
- *
- * Note that every outer product is computed
- * for a particular column only once which means that
- * there is no need todo a double precision addition
- * into the W2[] array.
- */
- W2[ix + ix] = ((mp_word)a->dp[ix]) * ((mp_word)a->dp[ix]);
-
- {
- register mp_digit tmpx, *tmpy;
- register mp_word *_W;
- register int iy;
-
- /* copy of left side */
- tmpx = a->dp[ix];
-
- /* alias for right side */
- tmpy = a->dp + (ix + 1);
-
- /* the column to store the result in */
- _W = W + (ix + ix + 1);
-
- /* inner products */
- for (iy = ix + 1; iy < pa; iy++) {
- *_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++);
+ /* number of output digits to produce */
+ W1 = 0;
+ for (ix = 0; ix <= pa; ix++) {
+ int tx, ty, iy;
+ mp_word _W;
+ mp_digit *tmpy;
+
+ /* clear counter */
+ _W = 0;
+
+ /* get offsets into the two bignums */
+ ty = MIN(a->used-1, ix);
+ tx = ix - ty;
+
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = a->dp + ty;
+
+ /* this is the number of times the loop will iterrate, essentially its
+ while (tx++ < a->used && ty-- >= 0) { ... }
+ */
+ iy = MIN(a->used-tx, ty+1);
+
+ /* now for squaring tx can never equal ty
+ * we halve the distance since they approach at a rate of 2x
+ * and we have to round because odd cases need to be executed
+ */
+ iy = MIN(iy, (ty-tx+1)>>1);
+
+ /* execute loop */
+ for (iz = 0; iz < iy; iz++) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
}
- }
+
+ /* double the inner product and add carry */
+ _W = _W + _W + W1;
+
+ /* even columns have the square term in them */
+ if ((ix&1) == 0) {
+ _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
+ }
+
+ /* store it */
+ W[ix] = _W;
+
+ /* make next carry */
+ W1 = _W >> ((mp_word)DIGIT_BIT);
}
/* setup dest */
olduse = b->used;
- b->used = newused;
-
- /* now compute digits
- *
- * We have to double the inner product sums, add in the
- * outer product sums, propagate carries and convert
- * to single precision.
- */
- {
- register mp_digit *tmpb;
-
- /* double first value, since the inner products are
- * half of what they should be
- */
- W[0] += W[0] + W2[0];
+ b->used = a->used+a->used;
+ {
+ mp_digit *tmpb;
tmpb = b->dp;
- for (ix = 1; ix < newused; ix++) {
- /* double/add next digit */
- W[ix] += W[ix] + W2[ix];
-
- /* propagate carry forwards [from the previous digit] */
- W[ix] = W[ix] + (W[ix - 1] >> ((mp_word) DIGIT_BIT));
-
- /* store the current digit now that the carry isn't
- * needed
- */
- *tmpb++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
+ for (ix = 0; ix < pa; ix++) {
+ *tmpb++ = W[ix] & MP_MASK;
}
- /* set the last value. Note even if the carry is zero
- * this is required since the next step will not zero
- * it if b originally had a value at b->dp[2*a.used]
- */
- *tmpb++ = (mp_digit) (W[(newused) - 1] & ((mp_word) MP_MASK));
- /* clear high digits of b if there were any originally */
+ /* clear unused digits [that existed in the old copy of c] */
for (; ix < olduse; ix++) {
*tmpb++ = 0;
}
}
-
mp_clamp (b);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_2expt.c b/bn_mp_2expt.c
index 5c4e2564..45a68184 100644
--- a/bn_mp_2expt.c
+++ b/bn_mp_2expt.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_2EXPT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes a = 2**b
*
@@ -36,7 +37,8 @@ mp_2expt (mp_int * a, int b)
a->used = b / DIGIT_BIT + 1;
/* put the single bit in its place */
- a->dp[b / DIGIT_BIT] = 1 << (b % DIGIT_BIT);
+ a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_abs.c b/bn_mp_abs.c
index a5e9ab02..34f810fd 100644
--- a/bn_mp_abs.c
+++ b/bn_mp_abs.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_ABS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* b = |a|
*
@@ -35,3 +36,4 @@ mp_abs (mp_int * a, mp_int * b)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_add.c b/bn_mp_add.c
index f6251953..554b7f74 100644
--- a/bn_mp_add.c
+++ b/bn_mp_add.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_ADD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* high level addition (handles signs) */
int mp_add (mp_int * a, mp_int * b, mp_int * c)
@@ -45,3 +46,4 @@ int mp_add (mp_int * a, mp_int * b, mp_int * c)
return res;
}
+#endif
diff --git a/bn_mp_add_d.c b/bn_mp_add_d.c
index edc93c1f..bdd02809 100644
--- a/bn_mp_add_d.c
+++ b/bn_mp_add_d.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_ADD_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* single digit addition */
int
@@ -101,3 +102,4 @@ mp_add_d (mp_int * a, mp_digit b, mp_int * c)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_addmod.c b/bn_mp_addmod.c
index 691dc508..13eb33f5 100644
--- a/bn_mp_addmod.c
+++ b/bn_mp_addmod.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_ADDMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* d = a + b (mod c) */
int
@@ -33,3 +34,4 @@ mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
mp_clear (&t);
return res;
}
+#endif
diff --git a/bn_mp_and.c b/bn_mp_and.c
index 9abb6184..61dc3868 100644
--- a/bn_mp_and.c
+++ b/bn_mp_and.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_AND_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* AND two ints together */
int
@@ -49,3 +50,4 @@ mp_and (mp_int * a, mp_int * b, mp_int * c)
mp_clear (&t);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_clamp.c b/bn_mp_clamp.c
index c6285cea..c1726111 100644
--- a/bn_mp_clamp.c
+++ b/bn_mp_clamp.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_CLAMP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* trim unused digits
*
@@ -36,3 +37,4 @@ mp_clamp (mp_int * a)
a->sign = MP_ZPOS;
}
}
+#endif
diff --git a/bn_mp_clear.c b/bn_mp_clear.c
index afe9b263..53426480 100644
--- a/bn_mp_clear.c
+++ b/bn_mp_clear.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_CLEAR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,16 +14,19 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* clear one (frees) */
void
mp_clear (mp_int * a)
{
+ int i;
+
/* only do anything if a hasn't been freed previously */
if (a->dp != NULL) {
/* first zero the digits */
- memset (a->dp, 0, sizeof (mp_digit) * a->used);
+ for (i = 0; i < a->used; i++) {
+ a->dp[i] = 0;
+ }
/* free ram */
XFREE(a->dp);
@@ -32,3 +37,4 @@ mp_clear (mp_int * a)
a->sign = MP_ZPOS;
}
}
+#endif
diff --git a/bn_mp_clear_multi.c b/bn_mp_clear_multi.c
index d262b2ff..24cbe732 100644
--- a/bn_mp_clear_multi.c
+++ b/bn_mp_clear_multi.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_CLEAR_MULTI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
#include <stdarg.h>
void mp_clear_multi(mp_int *mp, ...)
@@ -26,3 +27,4 @@ void mp_clear_multi(mp_int *mp, ...)
}
va_end(args);
}
+#endif
diff --git a/bn_mp_cmp.c b/bn_mp_cmp.c
index ed27d21f..583b5f86 100644
--- a/bn_mp_cmp.c
+++ b/bn_mp_cmp.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_CMP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* compare two ints (signed)*/
int
@@ -35,3 +36,4 @@ mp_cmp (mp_int * a, mp_int * b)
return mp_cmp_mag(a, b);
}
}
+#endif
diff --git a/bn_mp_cmp_d.c b/bn_mp_cmp_d.c
index 6baa172c..882b1c93 100644
--- a/bn_mp_cmp_d.c
+++ b/bn_mp_cmp_d.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_CMP_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* compare a digit */
int mp_cmp_d(mp_int * a, mp_digit b)
@@ -36,3 +37,4 @@ int mp_cmp_d(mp_int * a, mp_digit b)
return MP_EQ;
}
}
+#endif
diff --git a/bn_mp_cmp_mag.c b/bn_mp_cmp_mag.c
index b50f769d..a0f351c7 100644
--- a/bn_mp_cmp_mag.c
+++ b/bn_mp_cmp_mag.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_CMP_MAG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* compare maginitude of two ints (unsigned) */
int mp_cmp_mag (mp_int * a, mp_int * b)
@@ -47,3 +48,4 @@ int mp_cmp_mag (mp_int * a, mp_int * b)
}
return MP_EQ;
}
+#endif
diff --git a/bn_mp_cnt_lsb.c b/bn_mp_cnt_lsb.c
index 07cb709c..571f03f9 100644
--- a/bn_mp_cnt_lsb.c
+++ b/bn_mp_cnt_lsb.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_CNT_LSB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
static const int lnz[16] = {
4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
@@ -45,3 +46,4 @@ int mp_cnt_lsb(mp_int *a)
return x;
}
+#endif
diff --git a/bn_mp_copy.c b/bn_mp_copy.c
index 1c45f3e0..183ec9b6 100644
--- a/bn_mp_copy.c
+++ b/bn_mp_copy.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_COPY_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* copy, b = a */
int
@@ -60,3 +61,4 @@ mp_copy (mp_int * a, mp_int * b)
b->sign = a->sign;
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_count_bits.c b/bn_mp_count_bits.c
index 33b971bd..f3f85ac6 100644
--- a/bn_mp_count_bits.c
+++ b/bn_mp_count_bits.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_COUNT_BITS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* returns the number of bits in an int */
int
@@ -37,3 +38,4 @@ mp_count_bits (mp_int * a)
}
return r;
}
+#endif
diff --git a/bn_mp_div.c b/bn_mp_div.c
index 652a0944..39d921a2 100644
--- a/bn_mp_div.c
+++ b/bn_mp_div.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_DIV_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,78 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
+
+#ifdef BN_MP_DIV_SMALL
+
+/* slower bit-bang division... also smaller */
+int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ mp_int ta, tb, tq, q;
+ int res, n, n2;
+
+ /* is divisor zero ? */
+ if (mp_iszero (b) == 1) {
+ return MP_VAL;
+ }
+
+ /* if a < b then q=0, r = a */
+ if (mp_cmp_mag (a, b) == MP_LT) {
+ if (d != NULL) {
+ res = mp_copy (a, d);
+ } else {
+ res = MP_OKAY;
+ }
+ if (c != NULL) {
+ mp_zero (c);
+ }
+ return res;
+ }
+
+ /* init our temps */
+ if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
+ return res;
+ }
+
+
+ mp_set(&tq, 1);
+ n = mp_count_bits(a) - mp_count_bits(b);
+ if (((res = mp_copy(a, &ta)) != MP_OKAY) ||
+ ((res = mp_copy(b, &tb)) != MP_OKAY) ||
+ ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
+ ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
+ goto __ERR;
+ }
+
+ while (n-- >= 0) {
+ if (mp_cmp(&tb, &ta) != MP_GT) {
+ if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
+ ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
+ goto __ERR;
+ }
+ }
+ if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
+ ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
+ goto __ERR;
+ }
+ }
+
+ /* now q == quotient and ta == remainder */
+ n = a->sign;
+ n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
+ if (c != NULL) {
+ mp_exch(c, &q);
+ c->sign = n2;
+ }
+ if (d != NULL) {
+ mp_exch(d, &ta);
+ d->sign = n;
+ }
+__ERR:
+ mp_clear_multi(&ta, &tb, &tq, &q, NULL);
+ return res;
+}
+
+#else
/* integer signed division.
* c*b + d == a [e.g. a/b, c=quotient, d=remainder]
@@ -187,7 +260,7 @@ int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
*/
/* get sign before writing to c */
- x.sign = a->sign;
+ x.sign = x.used == 0 ? MP_ZPOS : a->sign;
if (c != NULL) {
mp_clamp (&q);
@@ -209,3 +282,7 @@ __T1:mp_clear (&t1);
__Q:mp_clear (&q);
return res;
}
+
+#endif
+
+#endif
diff --git a/bn_mp_div_2.c b/bn_mp_div_2.c
index ebad7ae4..57779971 100644
--- a/bn_mp_div_2.c
+++ b/bn_mp_div_2.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_DIV_2_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* b = a/2 */
int mp_div_2(mp_int * a, mp_int * b)
@@ -60,3 +61,4 @@ int mp_div_2(mp_int * a, mp_int * b)
mp_clamp (b);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_div_2d.c b/bn_mp_div_2d.c
index 75f090ce..cf103f2b 100644
--- a/bn_mp_div_2d.c
+++ b/bn_mp_div_2d.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_DIV_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
@@ -89,3 +90,4 @@ int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
mp_clear (&t);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_div_3.c b/bn_mp_div_3.c
index 3bc2bd2f..7cbafc14 100644
--- a/bn_mp_div_3.c
+++ b/bn_mp_div_3.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_DIV_3_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* divide by three (based on routine from MPI and the GMP manual) */
int
@@ -71,3 +72,4 @@ mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
return res;
}
+#endif
diff --git a/bn_mp_div_d.c b/bn_mp_div_d.c
index f8caf836..9b58aa66 100644
--- a/bn_mp_div_d.c
+++ b/bn_mp_div_d.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_DIV_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
static int s_is_power_of_two(mp_digit b, int *p)
{
@@ -54,7 +55,7 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
/* power of two ? */
if (s_is_power_of_two(b, &ix) == 1) {
if (d != NULL) {
- *d = a->dp[0] & ((1<<ix) - 1);
+ *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
}
if (c != NULL) {
return mp_div_2d(a, ix, c, NULL);
@@ -62,10 +63,12 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
return MP_OKAY;
}
+#ifdef BN_MP_DIV_3_C
/* three? */
if (b == 3) {
return mp_div_3(a, c, d);
}
+#endif
/* no easy answer [c'est la vie]. Just division */
if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
@@ -100,3 +103,4 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
return res;
}
+#endif
diff --git a/bn_mp_dr_is_modulus.c b/bn_mp_dr_is_modulus.c
index 0206e0ed..5ef78a39 100644
--- a/bn_mp_dr_is_modulus.c
+++ b/bn_mp_dr_is_modulus.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_DR_IS_MODULUS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* determines if a number is a valid DR modulus */
int mp_dr_is_modulus(mp_int *a)
@@ -35,3 +36,4 @@ int mp_dr_is_modulus(mp_int *a)
return 1;
}
+#endif
diff --git a/bn_mp_dr_reduce.c b/bn_mp_dr_reduce.c
index bad240aa..308b80a1 100644
--- a/bn_mp_dr_reduce.c
+++ b/bn_mp_dr_reduce.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_DR_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
*
@@ -86,3 +87,4 @@ top:
}
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_dr_setup.c b/bn_mp_dr_setup.c
index f269436c..029d3108 100644
--- a/bn_mp_dr_setup.c
+++ b/bn_mp_dr_setup.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_DR_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* determines the setup value */
void mp_dr_setup(mp_int *a, mp_digit *d)
@@ -24,3 +25,4 @@ void mp_dr_setup(mp_int *a, mp_digit *d)
((mp_word)a->dp[0]));
}
+#endif
diff --git a/bn_mp_exch.c b/bn_mp_exch.c
index b0f1cd00..0ef485ad 100644
--- a/bn_mp_exch.c
+++ b/bn_mp_exch.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_EXCH_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* swap the elements of two integers, for cases where you can't simply swap the
* mp_int pointers around
@@ -26,3 +27,4 @@ mp_exch (mp_int * a, mp_int * b)
*a = *b;
*b = t;
}
+#endif
diff --git a/bn_mp_expt_d.c b/bn_mp_expt_d.c
index 6ec12a49..fdb8bd91 100644
--- a/bn_mp_expt_d.c
+++ b/bn_mp_expt_d.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_EXPT_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* calculate c = a**b using a square-multiply algorithm */
int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
@@ -49,3 +50,4 @@ int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
mp_clear (&g);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_exptmod.c b/bn_mp_exptmod.c
index 21d0cc50..da88feca 100644
--- a/bn_mp_exptmod.c
+++ b/bn_mp_exptmod.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_EXPTMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* this is a shell function that calls either the normal or Montgomery
@@ -31,6 +32,7 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
/* if exponent X is negative we have to recurse */
if (X->sign == MP_NEG) {
+#ifdef BN_MP_INVMOD_C
mp_int tmpG, tmpX;
int err;
@@ -57,22 +59,42 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
err = mp_exptmod(&tmpG, &tmpX, P, Y);
mp_clear_multi(&tmpG, &tmpX, NULL);
return err;
+#else
+ /* no invmod */
+ return MP_VAL
+#endif
}
+#ifdef BN_MP_DR_IS_MODULUS_C
/* is it a DR modulus? */
dr = mp_dr_is_modulus(P);
+#else
+ dr = 0;
+#endif
+#ifdef BN_MP_REDUCE_IS_2K_C
/* if not, is it a uDR modulus? */
if (dr == 0) {
dr = mp_reduce_is_2k(P) << 1;
}
+#endif
/* if the modulus is odd or dr != 0 use the fast method */
+#ifdef BN_MP_EXPTMOD_FAST_C
if (mp_isodd (P) == 1 || dr != 0) {
return mp_exptmod_fast (G, X, P, Y, dr);
} else {
+#endif
+#ifdef BN_S_MP_EXPTMOD_C
/* otherwise use the generic Barrett reduction technique */
return s_mp_exptmod (G, X, P, Y);
+#else
+ /* no exptmod for evens */
+ return MP_VAL;
+#endif
+#ifdef BN_MP_EXPTMOD_FAST_C
}
+#endif
}
+#endif
diff --git a/bn_mp_exptmod_fast.c b/bn_mp_exptmod_fast.c
index c2817339..4351e60f 100644
--- a/bn_mp_exptmod_fast.c
+++ b/bn_mp_exptmod_fast.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_EXPTMOD_FAST_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
*
@@ -84,29 +85,52 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
/* determine and setup reduction code */
if (redmode == 0) {
+#ifdef BN_MP_MONTGOMERY_SETUP_C
/* now setup montgomery */
if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
goto __M;
}
+#else
+ err = MP_VAL;
+ goto __M;
+#endif
/* automatically pick the comba one if available (saves quite a few calls/ifs) */
+#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
if (((P->used * 2 + 1) < MP_WARRAY) &&
P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
redux = fast_mp_montgomery_reduce;
- } else {
+ } else
+#endif
+ {
+#ifdef BN_MP_MONTGOMERY_REDUCE_C
/* use slower baseline Montgomery method */
redux = mp_montgomery_reduce;
+#else
+ err = MP_VAL;
+ goto __M;
+#endif
}
} else if (redmode == 1) {
+#if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
/* setup DR reduction for moduli of the form B**k - b */
mp_dr_setup(P, &mp);
redux = mp_dr_reduce;
+#else
+ err = MP_VAL;
+ goto __M;
+#endif
} else {
+#if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
/* setup DR reduction for moduli of the form 2**k - b */
if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
goto __M;
}
redux = mp_reduce_2k;
+#else
+ err = MP_VAL;
+ goto __M;
+#endif
}
/* setup result */
@@ -116,16 +140,21 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
/* create M table
*
- * The M table contains powers of the input base, e.g. M[x] = G^x mod P
+
*
* The first half of the table is not computed though accept for M[0] and M[1]
*/
if (redmode == 0) {
+#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
/* now we need R mod m */
if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
goto __RES;
}
+#else
+ err = MP_VAL;
+ goto __RES;
+#endif
/* now set M[1] to G * R mod m */
if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
@@ -269,7 +298,7 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
* to reduce one more time to cancel out the factor
* of R.
*/
- if ((err = mp_montgomery_reduce (&res, P, mp)) != MP_OKAY) {
+ if ((err = redux(&res, P, mp)) != MP_OKAY) {
goto __RES;
}
}
@@ -285,3 +314,5 @@ __M:
}
return err;
}
+#endif
+
diff --git a/bn_mp_exteuclid.c b/bn_mp_exteuclid.c
index cb3f7872..545450bb 100644
--- a/bn_mp_exteuclid.c
+++ b/bn_mp_exteuclid.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_EXTEUCLID_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Extended euclidean algorithm of (a, b) produces
a*u1 + b*u2 = u3
@@ -67,3 +68,4 @@ int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
_ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
return err;
}
+#endif
diff --git a/bn_mp_fread.c b/bn_mp_fread.c
index ef665e5f..293df3fa 100644
--- a/bn_mp_fread.c
+++ b/bn_mp_fread.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_FREAD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* read a bigint from a file stream in ASCII */
int mp_fread(mp_int *a, int radix, FILE *stream)
@@ -59,3 +60,4 @@ int mp_fread(mp_int *a, int radix, FILE *stream)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_fwrite.c b/bn_mp_fwrite.c
index 2853ec1b..8fa3129b 100644
--- a/bn_mp_fwrite.c
+++ b/bn_mp_fwrite.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_FWRITE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
int mp_fwrite(mp_int *a, int radix, FILE *stream)
{
@@ -44,3 +45,4 @@ int mp_fwrite(mp_int *a, int radix, FILE *stream)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_gcd.c b/bn_mp_gcd.c
index 78ddda22..1cd21fcd 100644
--- a/bn_mp_gcd.c
+++ b/bn_mp_gcd.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_GCD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Greatest Common Divisor using the binary method */
int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
@@ -105,3 +106,4 @@ __V:mp_clear (&u);
__U:mp_clear (&v);
return res;
}
+#endif
diff --git a/bn_mp_get_int.c b/bn_mp_get_int.c
index 41df6e11..034467b7 100644
--- a/bn_mp_get_int.c
+++ b/bn_mp_get_int.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_GET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* get the lower 32-bits of an mp_int */
unsigned long mp_get_int(mp_int * a)
@@ -37,3 +38,4 @@ unsigned long mp_get_int(mp_int * a)
/* force result to 32-bits always so it is consistent on non 32-bit platforms */
return res & 0xFFFFFFFFUL;
}
+#endif
diff --git a/bn_mp_grow.c b/bn_mp_grow.c
index 43a30284..12a78a86 100644
--- a/bn_mp_grow.c
+++ b/bn_mp_grow.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_GROW_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* grow as required */
int mp_grow (mp_int * a, int size)
@@ -49,3 +50,4 @@ int mp_grow (mp_int * a, int size)
}
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_init.c b/bn_mp_init.c
index 5c5c1adf..9d705541 100644
--- a/bn_mp_init.c
+++ b/bn_mp_init.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_INIT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,17 +14,23 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* init a new bigint */
+/* init a new mp_int */
int mp_init (mp_int * a)
{
+ int i;
+
/* allocate memory required and clear it */
- a->dp = OPT_CAST(mp_digit) XCALLOC (sizeof (mp_digit), MP_PREC);
+ a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC);
if (a->dp == NULL) {
return MP_MEM;
}
+ /* set the digits to zero */
+ for (i = 0; i < MP_PREC; i++) {
+ a->dp[i] = 0;
+ }
+
/* set the used to zero, allocated digits to the default precision
* and sign to positive */
a->used = 0;
@@ -31,3 +39,4 @@ int mp_init (mp_int * a)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_init_copy.c b/bn_mp_init_copy.c
index 1c5da4d1..b1b0fa2a 100644
--- a/bn_mp_init_copy.c
+++ b/bn_mp_init_copy.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_INIT_COPY_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* creates "a" then copies b into it */
int mp_init_copy (mp_int * a, mp_int * b)
@@ -24,3 +25,4 @@ int mp_init_copy (mp_int * a, mp_int * b)
}
return mp_copy (b, a);
}
+#endif
diff --git a/bn_mp_init_multi.c b/bn_mp_init_multi.c
index 99ce3310..8cb123a9 100644
--- a/bn_mp_init_multi.c
+++ b/bn_mp_init_multi.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_INIT_MULTI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
#include <stdarg.h>
int mp_init_multi(mp_int *mp, ...)
@@ -51,3 +52,4 @@ int mp_init_multi(mp_int *mp, ...)
return res; /* Assumed ok, if error flagged above. */
}
+#endif
diff --git a/bn_mp_init_set.c b/bn_mp_init_set.c
index c8d8bf82..0251e611 100644
--- a/bn_mp_init_set.c
+++ b/bn_mp_init_set.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_INIT_SET_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* initialize and set a digit */
int mp_init_set (mp_int * a, mp_digit b)
@@ -24,3 +25,4 @@ int mp_init_set (mp_int * a, mp_digit b)
mp_set(a, b);
return err;
}
+#endif
diff --git a/bn_mp_init_set_int.c b/bn_mp_init_set_int.c
index 2d6628d5..f59fd190 100644
--- a/bn_mp_init_set_int.c
+++ b/bn_mp_init_set_int.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_INIT_SET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* initialize and set a digit */
int mp_init_set_int (mp_int * a, unsigned long b)
@@ -23,3 +24,4 @@ int mp_init_set_int (mp_int * a, unsigned long b)
}
return mp_set_int(a, b);
}
+#endif
diff --git a/bn_mp_init_size.c b/bn_mp_init_size.c
index c763ee0f..845ce2c0 100644
--- a/bn_mp_init_size.c
+++ b/bn_mp_init_size.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_INIT_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,22 +14,31 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* init an mp_init for a given size */
int mp_init_size (mp_int * a, int size)
{
+ int x;
+
/* pad size so there are always extra digits */
size += (MP_PREC * 2) - (size % MP_PREC);
/* alloc mem */
- a->dp = OPT_CAST(mp_digit) XCALLOC (sizeof (mp_digit), size);
+ a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
if (a->dp == NULL) {
return MP_MEM;
}
+
+ /* set the members */
a->used = 0;
a->alloc = size;
a->sign = MP_ZPOS;
+ /* zero the digits */
+ for (x = 0; x < size; x++) {
+ a->dp[x] = 0;
+ }
+
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_invmod.c b/bn_mp_invmod.c
index 4ac5b2f6..46118ad8 100644
--- a/bn_mp_invmod.c
+++ b/bn_mp_invmod.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_INVMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,163 +14,26 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* hac 14.61, pp608 */
int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
{
- mp_int x, y, u, v, A, B, C, D;
- int res;
-
/* b cannot be negative */
if (b->sign == MP_NEG || mp_iszero(b) == 1) {
return MP_VAL;
}
+#ifdef BN_FAST_MP_INVMOD_C
/* if the modulus is odd we can use a faster routine instead */
if (mp_isodd (b) == 1) {
return fast_mp_invmod (a, b, c);
}
-
- /* init temps */
- if ((res = mp_init_multi(&x, &y, &u, &v,
- &A, &B, &C, &D, NULL)) != MP_OKAY) {
- return res;
- }
-
- /* x = a, y = b */
- if ((res = mp_copy (a, &x)) != MP_OKAY) {
- goto __ERR;
- }
- if ((res = mp_copy (b, &y)) != MP_OKAY) {
- goto __ERR;
- }
+#endif
- /* 2. [modified] if x,y are both even then return an error! */
- if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
- res = MP_VAL;
- goto __ERR;
- }
-
- /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
- if ((res = mp_copy (&x, &u)) != MP_OKAY) {
- goto __ERR;
- }
- if ((res = mp_copy (&y, &v)) != MP_OKAY) {
- goto __ERR;
- }
- mp_set (&A, 1);
- mp_set (&D, 1);
+#ifdef BN_MP_INVMOD_SLOW_C
+ return mp_invmod_slow(a, b, c);
+#endif
-top:
- /* 4. while u is even do */
- while (mp_iseven (&u) == 1) {
- /* 4.1 u = u/2 */
- if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
- goto __ERR;
- }
- /* 4.2 if A or B is odd then */
- if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
- /* A = (A+y)/2, B = (B-x)/2 */
- if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
- goto __ERR;
- }
- if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
- goto __ERR;
- }
- }
- /* A = A/2, B = B/2 */
- if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
- goto __ERR;
- }
- if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
- goto __ERR;
- }
- }
-
- /* 5. while v is even do */
- while (mp_iseven (&v) == 1) {
- /* 5.1 v = v/2 */
- if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
- goto __ERR;
- }
- /* 5.2 if C or D is odd then */
- if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
- /* C = (C+y)/2, D = (D-x)/2 */
- if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
- goto __ERR;
- }
- if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
- goto __ERR;
- }
- }
- /* C = C/2, D = D/2 */
- if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
- goto __ERR;
- }
- if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
- goto __ERR;
- }
- }
-
- /* 6. if u >= v then */
- if (mp_cmp (&u, &v) != MP_LT) {
- /* u = u - v, A = A - C, B = B - D */
- if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
- goto __ERR;
- }
-
- if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
- goto __ERR;
- }
-
- if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
- goto __ERR;
- }
- } else {
- /* v - v - u, C = C - A, D = D - B */
- if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
- goto __ERR;
- }
-
- if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
- goto __ERR;
- }
-
- if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
- goto __ERR;
- }
- }
-
- /* if not zero goto step 4 */
- if (mp_iszero (&u) == 0)
- goto top;
-
- /* now a = C, b = D, gcd == g*v */
-
- /* if v != 1 then there is no inverse */
- if (mp_cmp_d (&v, 1) != MP_EQ) {
- res = MP_VAL;
- goto __ERR;
- }
-
- /* if its too low */
- while (mp_cmp_d(&C, 0) == MP_LT) {
- if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
- goto __ERR;
- }
- }
-
- /* too big */
- while (mp_cmp_mag(&C, b) != MP_LT) {
- if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
- goto __ERR;
- }
- }
-
- /* C is now the inverse */
- mp_exch (&C, c);
- res = MP_OKAY;
-__ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
- return res;
+ return MP_VAL;
}
+#endif
diff --git a/bn_mp_invmod_slow.c b/bn_mp_invmod_slow.c
new file mode 100644
index 00000000..8ecb0094
--- /dev/null
+++ b/bn_mp_invmod_slow.c
@@ -0,0 +1,171 @@
+#include <tommath.h>
+#ifdef BN_MP_INVMOD_SLOW_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* hac 14.61, pp608 */
+int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int x, y, u, v, A, B, C, D;
+ int res;
+
+ /* b cannot be negative */
+ if (b->sign == MP_NEG || mp_iszero(b) == 1) {
+ return MP_VAL;
+ }
+
+ /* init temps */
+ if ((res = mp_init_multi(&x, &y, &u, &v,
+ &A, &B, &C, &D, NULL)) != MP_OKAY) {
+ return res;
+ }
+
+ /* x = a, y = b */
+ if ((res = mp_copy (a, &x)) != MP_OKAY) {
+ goto __ERR;
+ }
+ if ((res = mp_copy (b, &y)) != MP_OKAY) {
+ goto __ERR;
+ }
+
+ /* 2. [modified] if x,y are both even then return an error! */
+ if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
+ res = MP_VAL;
+ goto __ERR;
+ }
+
+ /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
+ if ((res = mp_copy (&x, &u)) != MP_OKAY) {
+ goto __ERR;
+ }
+ if ((res = mp_copy (&y, &v)) != MP_OKAY) {
+ goto __ERR;
+ }
+ mp_set (&A, 1);
+ mp_set (&D, 1);
+
+top:
+ /* 4. while u is even do */
+ while (mp_iseven (&u) == 1) {
+ /* 4.1 u = u/2 */
+ if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
+ goto __ERR;
+ }
+ /* 4.2 if A or B is odd then */
+ if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
+ /* A = (A+y)/2, B = (B-x)/2 */
+ if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
+ goto __ERR;
+ }
+ if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
+ goto __ERR;
+ }
+ }
+ /* A = A/2, B = B/2 */
+ if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
+ goto __ERR;
+ }
+ if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
+ goto __ERR;
+ }
+ }
+
+ /* 5. while v is even do */
+ while (mp_iseven (&v) == 1) {
+ /* 5.1 v = v/2 */
+ if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
+ goto __ERR;
+ }
+ /* 5.2 if C or D is odd then */
+ if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
+ /* C = (C+y)/2, D = (D-x)/2 */
+ if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
+ goto __ERR;
+ }
+ if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
+ goto __ERR;
+ }
+ }
+ /* C = C/2, D = D/2 */
+ if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
+ goto __ERR;
+ }
+ if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
+ goto __ERR;
+ }
+ }
+
+ /* 6. if u >= v then */
+ if (mp_cmp (&u, &v) != MP_LT) {
+ /* u = u - v, A = A - C, B = B - D */
+ if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
+ goto __ERR;
+ }
+
+ if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
+ goto __ERR;
+ }
+
+ if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
+ goto __ERR;
+ }
+ } else {
+ /* v - v - u, C = C - A, D = D - B */
+ if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
+ goto __ERR;
+ }
+
+ if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
+ goto __ERR;
+ }
+
+ if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
+ goto __ERR;
+ }
+ }
+
+ /* if not zero goto step 4 */
+ if (mp_iszero (&u) == 0)
+ goto top;
+
+ /* now a = C, b = D, gcd == g*v */
+
+ /* if v != 1 then there is no inverse */
+ if (mp_cmp_d (&v, 1) != MP_EQ) {
+ res = MP_VAL;
+ goto __ERR;
+ }
+
+ /* if its too low */
+ while (mp_cmp_d(&C, 0) == MP_LT) {
+ if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
+ goto __ERR;
+ }
+ }
+
+ /* too big */
+ while (mp_cmp_mag(&C, b) != MP_LT) {
+ if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
+ goto __ERR;
+ }
+ }
+
+ /* C is now the inverse */
+ mp_exch (&C, c);
+ res = MP_OKAY;
+__ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
+ return res;
+}
+#endif
diff --git a/bn_mp_is_square.c b/bn_mp_is_square.c
index 1f01bca5..969d2377 100644
--- a/bn_mp_is_square.c
+++ b/bn_mp_is_square.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_IS_SQUARE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Check if remainders are possible squares - fast exclude non-squares */
static const char rem_128[128] = {
@@ -69,7 +70,7 @@ int mp_is_square(mp_int *arg,int *ret)
return MP_OKAY;
}
- /* product of primes less than 2^31 */
+
if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) {
return res;
}
@@ -101,3 +102,4 @@ int mp_is_square(mp_int *arg,int *ret)
ERR:mp_clear(&t);
return res;
}
+#endif
diff --git a/bn_mp_jacobi.c b/bn_mp_jacobi.c
index 634370f2..1c69cfde 100644
--- a/bn_mp_jacobi.c
+++ b/bn_mp_jacobi.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_JACOBI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes the jacobi c = (a | n) (or Legendre if n is prime)
* HAC pp. 73 Algorithm 2.149
@@ -97,3 +98,4 @@ __P1:mp_clear (&p1);
__A1:mp_clear (&a1);
return res;
}
+#endif
diff --git a/bn_mp_karatsuba_mul.c b/bn_mp_karatsuba_mul.c
index 169dacf9..daa78c71 100644
--- a/bn_mp_karatsuba_mul.c
+++ b/bn_mp_karatsuba_mul.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_KARATSUBA_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* c = |a| * |b| using Karatsuba Multiplication using
* three half size multiplications
@@ -76,9 +77,6 @@ int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c)
goto X0Y0;
/* now shift the digits */
- x0.sign = x1.sign = a->sign;
- y0.sign = y1.sign = b->sign;
-
x0.used = y0.used = B;
x1.used = a->used - B;
y1.used = b->used - B;
@@ -162,3 +160,4 @@ X0:mp_clear (&x0);
ERR:
return err;
}
+#endif
diff --git a/bn_mp_karatsuba_sqr.c b/bn_mp_karatsuba_sqr.c
index c3356135..315ceabf 100644
--- a/bn_mp_karatsuba_sqr.c
+++ b/bn_mp_karatsuba_sqr.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_KARATSUBA_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,12 +14,11 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Karatsuba squaring, computes b = a*a using three
* half size squarings
*
- * See comments of mp_karatsuba_mul for details. It
+ * See comments of karatsuba_mul for details. It
* is essentially the same algorithm but merely
* tuned to perform recursive squarings.
*/
@@ -113,3 +114,4 @@ X0:mp_clear (&x0);
ERR:
return err;
}
+#endif
diff --git a/bn_mp_lcm.c b/bn_mp_lcm.c
index 4aa57490..340d757b 100644
--- a/bn_mp_lcm.c
+++ b/bn_mp_lcm.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_LCM_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes least common multiple as |a*b|/(a, b) */
int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
@@ -52,3 +53,4 @@ __T:
mp_clear_multi (&t1, &t2, NULL);
return res;
}
+#endif
diff --git a/bn_mp_lshd.c b/bn_mp_lshd.c
index f1702376..398b6482 100644
--- a/bn_mp_lshd.c
+++ b/bn_mp_lshd.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_LSHD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shift left a certain amount of digits */
int mp_lshd (mp_int * a, int b)
@@ -59,3 +60,4 @@ int mp_lshd (mp_int * a, int b)
}
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_mod.c b/bn_mp_mod.c
index ad963a97..75779bb0 100644
--- a/bn_mp_mod.c
+++ b/bn_mp_mod.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_MOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* c = a mod b, 0 <= c < b */
int
@@ -40,3 +41,4 @@ mp_mod (mp_int * a, mp_int * b, mp_int * c)
mp_clear (&t);
return res;
}
+#endif
diff --git a/bn_mp_mod_2d.c b/bn_mp_mod_2d.c
index 89e9081c..f81a0d41 100644
--- a/bn_mp_mod_2d.c
+++ b/bn_mp_mod_2d.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_MOD_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* calc a value mod 2**b */
int
@@ -47,3 +48,4 @@ mp_mod_2d (mp_int * a, int b, mp_int * c)
mp_clamp (c);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_mod_d.c b/bn_mp_mod_d.c
index c5dbe46a..8a2ad242 100644
--- a/bn_mp_mod_d.c
+++ b/bn_mp_mod_d.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_MOD_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,10 +14,10 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
int
mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
{
return mp_div_d(a, b, NULL, c);
}
+#endif
diff --git a/bn_mp_montgomery_calc_normalization.c b/bn_mp_montgomery_calc_normalization.c
index a38555ce..0a760cfe 100644
--- a/bn_mp_montgomery_calc_normalization.c
+++ b/bn_mp_montgomery_calc_normalization.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,31 +14,31 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* calculates a = B^n mod b for Montgomery reduction
- * Where B is the base [e.g. 2^DIGIT_BIT].
- * B^n mod b is computed by first computing
- * A = B^(n-1) which doesn't require a reduction but a simple OR.
- * then C = A * B = B^n is computed by performing upto DIGIT_BIT
+/*
* shifts with subtractions when the result is greater than b.
*
* The method is slightly modified to shift B unconditionally upto just under
* the leading bit of b. This saves alot of multiple precision shifting.
*/
-int
-mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
+int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
{
int x, bits, res;
/* how many bits of last digit does b use */
bits = mp_count_bits (b) % DIGIT_BIT;
- /* compute A = B^(n-1) * 2^(bits-1) */
- if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
- return res;
+
+ if (b->used > 1) {
+ if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
+ return res;
+ }
+ } else {
+ mp_set(a, 1);
+ bits = 1;
}
+
/* now compute C = A * B mod b */
for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
@@ -51,3 +53,4 @@ mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_montgomery_reduce.c b/bn_mp_montgomery_reduce.c
index 52b98cdb..3095fa76 100644
--- a/bn_mp_montgomery_reduce.c
+++ b/bn_mp_montgomery_reduce.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes xR**-1 == x (mod N) via Montgomery Reduction */
int
@@ -23,7 +24,7 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
/* can the fast reduction [comba] method be used?
*
- * Note that unlike in mp_mul you're safely allowed *less*
+ * Note that unlike in mul you're safely allowed *less*
* than the available columns [255 per default] since carries
* are fixed up in the inner loop.
*/
@@ -46,7 +47,7 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
/* mu = ai * rho mod b
*
* The value of rho must be precalculated via
- * bn_mp_montgomery_setup() such that
+ * montgomery_setup() such that
* it equals -1/n0 mod b this allows the
* following inner loop to reduce the
* input one digit at a time
@@ -110,3 +111,4 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_montgomery_setup.c b/bn_mp_montgomery_setup.c
index 36253afb..9dfc0878 100644
--- a/bn_mp_montgomery_setup.c
+++ b/bn_mp_montgomery_setup.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* setups the montgomery reduction stuff */
int
@@ -47,7 +48,8 @@ mp_montgomery_setup (mp_int * n, mp_digit * rho)
#endif
/* rho = -1/m mod b */
- *rho = (((mp_digit) 1 << ((mp_digit) DIGIT_BIT)) - x) & MP_MASK;
+ *rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_mul.c b/bn_mp_mul.c
index 6f3c4911..f9cfa09e 100644
--- a/bn_mp_mul.c
+++ b/bn_mp_mul.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* high level multiplication (handles sign) */
int mp_mul (mp_int * a, mp_int * b, mp_int * c)
@@ -21,12 +22,18 @@ int mp_mul (mp_int * a, mp_int * b, mp_int * c)
neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
/* use Toom-Cook? */
+#ifdef BN_MP_TOOM_MUL_C
if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) {
res = mp_toom_mul(a, b, c);
+ } else
+#endif
+#ifdef BN_MP_KARATSUBA_MUL_C
/* use Karatsuba? */
- } else if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
+ if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
res = mp_karatsuba_mul (a, b, c);
- } else {
+ } else
+#endif
+ {
/* can we use the fast multiplier?
*
* The fast multiplier can be used if the output will
@@ -35,14 +42,21 @@ int mp_mul (mp_int * a, mp_int * b, mp_int * c)
*/
int digs = a->used + b->used + 1;
+#ifdef BN_FAST_S_MP_MUL_DIGS_C
if ((digs < MP_WARRAY) &&
MIN(a->used, b->used) <=
(1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
res = fast_s_mp_mul_digs (a, b, c, digs);
- } else {
- res = s_mp_mul (a, b, c);
- }
+ } else
+#endif
+#ifdef BN_S_MP_MUL_DIGS_C
+ res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
+#else
+ res = MP_VAL;
+#endif
+
}
- c->sign = neg;
+ c->sign = (c->used > 0) ? neg : MP_ZPOS;
return res;
}
+#endif
diff --git a/bn_mp_mul_2.c b/bn_mp_mul_2.c
index f947d754..6936681f 100644
--- a/bn_mp_mul_2.c
+++ b/bn_mp_mul_2.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_MUL_2_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* b = a*2 */
int mp_mul_2(mp_int * a, mp_int * b)
@@ -74,3 +75,4 @@ int mp_mul_2(mp_int * a, mp_int * b)
b->sign = a->sign;
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_mul_2d.c b/bn_mp_mul_2d.c
index f5fa1d07..04cb8dd9 100644
--- a/bn_mp_mul_2d.c
+++ b/bn_mp_mul_2d.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_MUL_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shift left by a certain bit count */
int mp_mul_2d (mp_int * a, int b, mp_int * c)
@@ -77,3 +78,4 @@ int mp_mul_2d (mp_int * a, int b, mp_int * c)
mp_clamp (c);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_mul_d.c b/bn_mp_mul_d.c
index 658fe01c..f9363619 100644
--- a/bn_mp_mul_d.c
+++ b/bn_mp_mul_d.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_MUL_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* multiply by a digit */
int
@@ -70,3 +71,4 @@ mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_mulmod.c b/bn_mp_mulmod.c
index 77f84592..d34e90ac 100644
--- a/bn_mp_mulmod.c
+++ b/bn_mp_mulmod.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_MULMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* d = a * b (mod c) */
int
@@ -33,3 +34,4 @@ mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
mp_clear (&t);
return res;
}
+#endif
diff --git a/bn_mp_n_root.c b/bn_mp_n_root.c
index a79af174..94899037 100644
--- a/bn_mp_n_root.c
+++ b/bn_mp_n_root.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_N_ROOT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* find the n'th root of an integer
*
@@ -124,3 +125,4 @@ __T2:mp_clear (&t2);
__T1:mp_clear (&t1);
return res;
}
+#endif
diff --git a/bn_mp_neg.c b/bn_mp_neg.c
index f9de6e43..3a991db5 100644
--- a/bn_mp_neg.c
+++ b/bn_mp_neg.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_NEG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* b = -a */
int mp_neg (mp_int * a, mp_int * b)
@@ -26,3 +27,4 @@ int mp_neg (mp_int * a, mp_int * b)
}
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_or.c b/bn_mp_or.c
index 793e8e9a..dccee7e1 100644
--- a/bn_mp_or.c
+++ b/bn_mp_or.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_OR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* OR two ints together */
int mp_or (mp_int * a, mp_int * b, mp_int * c)
@@ -42,3 +43,4 @@ int mp_or (mp_int * a, mp_int * b, mp_int * c)
mp_clear (&t);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_prime_fermat.c b/bn_mp_prime_fermat.c
index 7d587856..fe17aaab 100644
--- a/bn_mp_prime_fermat.c
+++ b/bn_mp_prime_fermat.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_PRIME_FERMAT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* performs one Fermat test.
*
@@ -54,3 +55,4 @@ int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
__T:mp_clear (&t);
return err;
}
+#endif
diff --git a/bn_mp_prime_is_divisible.c b/bn_mp_prime_is_divisible.c
index 86392d17..22ec1aea 100644
--- a/bn_mp_prime_is_divisible.c
+++ b/bn_mp_prime_is_divisible.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_PRIME_IS_DIVISIBLE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* determines if an integers is divisible by one
* of the first PRIME_SIZE primes or not
@@ -42,3 +43,4 @@ int mp_prime_is_divisible (mp_int * a, int *result)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_prime_is_prime.c b/bn_mp_prime_is_prime.c
index 88a777b4..c2354d2f 100644
--- a/bn_mp_prime_is_prime.c
+++ b/bn_mp_prime_is_prime.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_PRIME_IS_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,12 +14,11 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* performs a variable number of rounds of Miller-Rabin
*
* Probability of error after t rounds is no more than
- * (1/4)^t when 1 <= t <= PRIME_SIZE
+
*
* Sets result to 1 if probably prime, 0 otherwise
*/
@@ -75,3 +76,4 @@ int mp_prime_is_prime (mp_int * a, int t, int *result)
__B:mp_clear (&b);
return err;
}
+#endif
diff --git a/bn_mp_prime_miller_rabin.c b/bn_mp_prime_miller_rabin.c
index 0c55d9c7..22dec2f2 100644
--- a/bn_mp_prime_miller_rabin.c
+++ b/bn_mp_prime_miller_rabin.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_PRIME_MILLER_RABIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Miller-Rabin test of "a" to the base of "b" as described in
* HAC pp. 139 Algorithm 4.24
@@ -95,3 +96,4 @@ __R:mp_clear (&r);
__N1:mp_clear (&n1);
return err;
}
+#endif
diff --git a/bn_mp_prime_next_prime.c b/bn_mp_prime_next_prime.c
index f45af81e..c478ce5a 100644
--- a/bn_mp_prime_next_prime.c
+++ b/bn_mp_prime_next_prime.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_PRIME_NEXT_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* finds the next prime after the number "a" using "t" trials
* of Miller-Rabin.
@@ -162,3 +163,4 @@ __ERR:
return err;
}
+#endif
diff --git a/bn_prime_sizes_tab.c b/bn_mp_prime_rabin_miller_trials.c
similarity index 82%
rename from bn_prime_sizes_tab.c
rename to bn_mp_prime_rabin_miller_trials.c
index c6e1dadf..d1d08671 100644
--- a/bn_prime_sizes_tab.c
+++ b/bn_mp_prime_rabin_miller_trials.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,9 +14,8 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* this table gives the # of rabin miller trials for a prob of failure lower than 2^-96 */
+
static const struct {
int k, t;
} sizes[] = {
@@ -25,13 +26,8 @@ static const struct {
{ 640, 6 },
{ 768, 5 },
{ 896, 4 },
-{ 1024, 4 },
-{ 1152, 3 },
-{ 1280, 3 },
-{ 1408, 3 },
-{ 1536, 3 },
-{ 1664, 3 },
-{ 1792, 2 } };
+{ 1024, 4 }
+};
/* returns # of RM trials required for a given bit size */
int mp_prime_rabin_miller_trials(int size)
@@ -45,7 +41,8 @@ int mp_prime_rabin_miller_trials(int size)
return (x == 0) ? sizes[0].t : sizes[x - 1].t;
}
}
- return 1;
+ return sizes[x-1].t + 1;
}
+#endif
diff --git a/bn_mp_prime_random_ex.c b/bn_mp_prime_random_ex.c
index 147721bd..2c4f4f07 100644
--- a/bn_mp_prime_random_ex.c
+++ b/bn_mp_prime_random_ex.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_PRIME_RANDOM_EX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* makes a truly random prime of a given size (bits),
*
@@ -92,6 +93,9 @@ int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback
/* is it prime? */
if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { goto error; }
+ if (res == MP_NO) {
+ continue;
+ }
if (flags & LTM_PRIME_SAFE) {
/* see if (a-1)/2 is prime */
@@ -116,3 +120,4 @@ error:
}
+#endif
diff --git a/bn_mp_radix_size.c b/bn_mp_radix_size.c
index ae2d09a7..30b78d99 100644
--- a/bn_mp_radix_size.c
+++ b/bn_mp_radix_size.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_RADIX_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* returns size of ASCII reprensentation */
int mp_radix_size (mp_int * a, int radix, int *size)
@@ -63,3 +64,4 @@ int mp_radix_size (mp_int * a, int radix, int *size)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_radix_smap.c b/bn_mp_radix_smap.c
index 2c4d9663..bc7517da 100644
--- a/bn_mp_radix_smap.c
+++ b/bn_mp_radix_smap.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_RADIX_SMAP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,7 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* chars used in radix conversions */
const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
+#endif
diff --git a/bn_mp_rand.c b/bn_mp_rand.c
index c7449947..1cc47f19 100644
--- a/bn_mp_rand.c
+++ b/bn_mp_rand.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_RAND_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* makes a pseudo-random int of a given size */
int
@@ -47,3 +48,4 @@ mp_rand (mp_int * a, int digits)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_read_radix.c b/bn_mp_read_radix.c
index 653a891c..704bd0fe 100644
--- a/bn_mp_read_radix.c
+++ b/bn_mp_read_radix.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_READ_RADIX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* read a string [ASCII] in a given radix */
int mp_read_radix (mp_int * a, char *str, int radix)
@@ -74,3 +75,4 @@ int mp_read_radix (mp_int * a, char *str, int radix)
}
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_read_signed_bin.c b/bn_mp_read_signed_bin.c
index 39d86183..814d6c12 100644
--- a/bn_mp_read_signed_bin.c
+++ b/bn_mp_read_signed_bin.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_READ_SIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* read signed bin, big endian, first byte is 0==positive or 1==negative */
int
@@ -34,3 +35,4 @@ mp_read_signed_bin (mp_int * a, unsigned char *b, int c)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_read_unsigned_bin.c b/bn_mp_read_unsigned_bin.c
index cb11d873..946457de 100644
--- a/bn_mp_read_unsigned_bin.c
+++ b/bn_mp_read_unsigned_bin.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_READ_UNSIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reads a unsigned char array, assumes the msb is stored first [big endian] */
int
@@ -48,3 +49,4 @@ mp_read_unsigned_bin (mp_int * a, unsigned char *b, int c)
mp_clamp (a);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_reduce.c b/bn_mp_reduce.c
index d4c5b107..cfcb55a7 100644
--- a/bn_mp_reduce.c
+++ b/bn_mp_reduce.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reduces x mod m, assumes 0 < x < m**2, mu is
* precomputed via mp_reduce_setup.
@@ -38,9 +39,20 @@ mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
goto CLEANUP;
}
} else {
+#ifdef BN_S_MP_MUL_HIGH_DIGS_C
if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) {
goto CLEANUP;
}
+#elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
+ if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+#else
+ {
+ res = MP_VAL;
+ goto CLEANUP;
+ }
+#endif
}
/* q3 = q2 / b**(k+1) */
@@ -82,3 +94,4 @@ CLEANUP:
return res;
}
+#endif
diff --git a/bn_mp_reduce_2k.c b/bn_mp_reduce_2k.c
index f6b40cf1..a5a9c743 100644
--- a/bn_mp_reduce_2k.c
+++ b/bn_mp_reduce_2k.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reduces a modulo n where n is of the form 2**p - d */
int
@@ -54,3 +55,4 @@ ERR:
return res;
}
+#endif
diff --git a/bn_mp_reduce_2k_setup.c b/bn_mp_reduce_2k_setup.c
index 6bdfe7f2..5e1fb6e8 100644
--- a/bn_mp_reduce_2k_setup.c
+++ b/bn_mp_reduce_2k_setup.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* determines the setup value */
int
@@ -40,3 +41,4 @@ mp_reduce_2k_setup(mp_int *a, mp_digit *d)
mp_clear(&tmp);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_reduce_is_2k.c b/bn_mp_reduce_is_2k.c
index d43b9ffb..fc81397b 100644
--- a/bn_mp_reduce_is_2k.c
+++ b/bn_mp_reduce_is_2k.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_IS_2K_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,12 +14,12 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* determines if mp_reduce_2k can be used */
int mp_reduce_is_2k(mp_int *a)
{
- int ix, iy, iz, iw;
+ int ix, iy, iw;
+ mp_digit iz;
if (a->used == 0) {
return 0;
@@ -34,7 +36,7 @@ int mp_reduce_is_2k(mp_int *a)
return 0;
}
iz <<= 1;
- if (iz > (int)MP_MASK) {
+ if (iz > (mp_digit)MP_MASK) {
++iw;
iz = 1;
}
@@ -43,3 +45,4 @@ int mp_reduce_is_2k(mp_int *a)
return 1;
}
+#endif
diff --git a/bn_mp_reduce_setup.c b/bn_mp_reduce_setup.c
index 1ba69e96..99f158a5 100644
--- a/bn_mp_reduce_setup.c
+++ b/bn_mp_reduce_setup.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,13 +14,11 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* pre-calculate the value required for Barrett reduction
* For a given modulus "b" it calulates the value required in "a"
*/
-int
-mp_reduce_setup (mp_int * a, mp_int * b)
+int mp_reduce_setup (mp_int * a, mp_int * b)
{
int res;
@@ -27,3 +27,4 @@ mp_reduce_setup (mp_int * a, mp_int * b)
}
return mp_div (a, b, a, NULL);
}
+#endif
diff --git a/bn_mp_rshd.c b/bn_mp_rshd.c
index 87d6e3b0..913dda6d 100644
--- a/bn_mp_rshd.c
+++ b/bn_mp_rshd.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_RSHD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shift right a certain amount of digits */
void mp_rshd (mp_int * a, int b)
@@ -64,3 +65,4 @@ void mp_rshd (mp_int * a, int b)
/* remove excess digits */
a->used -= b;
}
+#endif
diff --git a/bn_mp_set.c b/bn_mp_set.c
index 25ccf64e..078fd5fb 100644
--- a/bn_mp_set.c
+++ b/bn_mp_set.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_SET_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* set to a digit */
void mp_set (mp_int * a, mp_digit b)
@@ -21,3 +22,4 @@ void mp_set (mp_int * a, mp_digit b)
a->dp[0] = b & MP_MASK;
a->used = (a->dp[0] != 0) ? 1 : 0;
}
+#endif
diff --git a/bn_mp_set_int.c b/bn_mp_set_int.c
index 64f1aed5..bd47136c 100644
--- a/bn_mp_set_int.c
+++ b/bn_mp_set_int.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_SET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* set a 32-bit const */
int mp_set_int (mp_int * a, unsigned long b)
@@ -40,3 +41,4 @@ int mp_set_int (mp_int * a, unsigned long b)
mp_clamp (a);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_shrink.c b/bn_mp_shrink.c
index daefed2b..b31f9d22 100644
--- a/bn_mp_shrink.c
+++ b/bn_mp_shrink.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_SHRINK_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shrink a bignum */
int mp_shrink (mp_int * a)
@@ -27,3 +28,4 @@ int mp_shrink (mp_int * a)
}
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_signed_bin_size.c b/bn_mp_signed_bin_size.c
index 76d085cb..30048cb8 100644
--- a/bn_mp_signed_bin_size.c
+++ b/bn_mp_signed_bin_size.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_SIGNED_BIN_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,10 +14,10 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* get the size for an signed equivalent */
int mp_signed_bin_size (mp_int * a)
{
return 1 + mp_unsigned_bin_size (a);
}
+#endif
diff --git a/bn_mp_sqr.c b/bn_mp_sqr.c
index 4857994d..b1fdb57c 100644
--- a/bn_mp_sqr.c
+++ b/bn_mp_sqr.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes b = a*a */
int
@@ -20,22 +21,34 @@ mp_sqr (mp_int * a, mp_int * b)
{
int res;
+#ifdef BN_MP_TOOM_SQR_C
/* use Toom-Cook? */
if (a->used >= TOOM_SQR_CUTOFF) {
res = mp_toom_sqr(a, b);
/* Karatsuba? */
- } else if (a->used >= KARATSUBA_SQR_CUTOFF) {
+ } else
+#endif
+#ifdef BN_MP_KARATSUBA_SQR_C
+if (a->used >= KARATSUBA_SQR_CUTOFF) {
res = mp_karatsuba_sqr (a, b);
- } else {
+ } else
+#endif
+ {
+#ifdef BN_FAST_S_MP_SQR_C
/* can we use the fast comba multiplier? */
if ((a->used * 2 + 1) < MP_WARRAY &&
a->used <
(1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
res = fast_s_mp_sqr (a, b);
- } else {
+ } else
+#endif
+#ifdef BN_S_MP_SQR_C
res = s_mp_sqr (a, b);
- }
+#else
+ res = MP_VAL;
+#endif
}
b->sign = MP_ZPOS;
return res;
}
+#endif
diff --git a/bn_mp_sqrmod.c b/bn_mp_sqrmod.c
index 778b68e8..1923be43 100644
--- a/bn_mp_sqrmod.c
+++ b/bn_mp_sqrmod.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_SQRMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* c = a * a (mod b) */
int
@@ -33,3 +34,4 @@ mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
mp_clear (&t);
return res;
}
+#endif
diff --git a/bn_mp_sqrt.c b/bn_mp_sqrt.c
index ec9d1026..76cec878 100644
--- a/bn_mp_sqrt.c
+++ b/bn_mp_sqrt.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_SQRT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* this function is less generic than mp_n_root, simpler and faster */
int mp_sqrt(mp_int *arg, mp_int *ret)
@@ -73,3 +74,4 @@ E2: mp_clear(&t1);
return res;
}
+#endif
diff --git a/bn_mp_sub.c b/bn_mp_sub.c
index eb99583f..97495f42 100644
--- a/bn_mp_sub.c
+++ b/bn_mp_sub.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_SUB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* high level subtraction (handles signs) */
int
@@ -51,3 +52,4 @@ mp_sub (mp_int * a, mp_int * b, mp_int * c)
return res;
}
+#endif
diff --git a/bn_mp_sub_d.c b/bn_mp_sub_d.c
index 6368970f..4923ddeb 100644
--- a/bn_mp_sub_d.c
+++ b/bn_mp_sub_d.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_SUB_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* single digit subtraction */
int
@@ -81,3 +82,4 @@ mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_submod.c b/bn_mp_submod.c
index 868dd2f4..b999c854 100644
--- a/bn_mp_submod.c
+++ b/bn_mp_submod.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_SUBMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* d = a - b (mod c) */
int
@@ -34,3 +35,4 @@ mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
mp_clear (&t);
return res;
}
+#endif
diff --git a/bn_mp_to_signed_bin.c b/bn_mp_to_signed_bin.c
index 1e21667e..0e40d0fa 100644
--- a/bn_mp_to_signed_bin.c
+++ b/bn_mp_to_signed_bin.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_TO_SIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* store in signed [big endian] format */
int
@@ -26,3 +27,4 @@ mp_to_signed_bin (mp_int * a, unsigned char *b)
b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_to_unsigned_bin.c b/bn_mp_to_unsigned_bin.c
index f7cae691..763e3461 100644
--- a/bn_mp_to_unsigned_bin.c
+++ b/bn_mp_to_unsigned_bin.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_TO_UNSIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* store in unsigned [big endian] format */
int
@@ -41,3 +42,4 @@ mp_to_unsigned_bin (mp_int * a, unsigned char *b)
mp_clear (&t);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_toom_mul.c b/bn_mp_toom_mul.c
index 50660ffd..2d66779c 100644
--- a/bn_mp_toom_mul.c
+++ b/bn_mp_toom_mul.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_TOOM_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,9 +14,13 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* multiplication using the Toom-Cook 3-way algorithm */
+/* multiplication using the Toom-Cook 3-way algorithm
+ *
+ * Much more complicated than Karatsuba but has a lower asymptotic running time of
+ * O(N**1.464). This algorithm is only particularly useful on VERY large
+ * inputs (we're talking 1000s of digits here...).
+*/
int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
{
mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
@@ -270,3 +276,4 @@ ERR:
return res;
}
+#endif
diff --git a/bn_mp_toom_sqr.c b/bn_mp_toom_sqr.c
index de3094aa..8c46fead 100644
--- a/bn_mp_toom_sqr.c
+++ b/bn_mp_toom_sqr.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_TOOM_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* squaring using Toom-Cook 3-way algorithm */
int
@@ -218,3 +219,4 @@ ERR:
return res;
}
+#endif
diff --git a/bn_mp_toradix.c b/bn_mp_toradix.c
index c605867e..a206d5ee 100644
--- a/bn_mp_toradix.c
+++ b/bn_mp_toradix.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_TORADIX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* stores a bignum as a ASCII string in a given radix (2..64) */
int mp_toradix (mp_int * a, char *str, int radix)
@@ -67,3 +68,4 @@ int mp_toradix (mp_int * a, char *str, int radix)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_toradix_n.c b/bn_mp_toradix_n.c
index d2f6ec20..7d435587 100644
--- a/bn_mp_toradix_n.c
+++ b/bn_mp_toradix_n.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_TORADIX_N_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* stores a bignum as a ASCII string in a given radix (2..64)
*
@@ -81,3 +82,4 @@ int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_unsigned_bin_size.c b/bn_mp_unsigned_bin_size.c
index 47bbc648..80da415a 100644
--- a/bn_mp_unsigned_bin_size.c
+++ b/bn_mp_unsigned_bin_size.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_UNSIGNED_BIN_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* get the size for an unsigned equivalent */
int
@@ -21,3 +22,4 @@ mp_unsigned_bin_size (mp_int * a)
int size = mp_count_bits (a);
return (size / 8 + ((size & 7) != 0 ? 1 : 0));
}
+#endif
diff --git a/bn_mp_xor.c b/bn_mp_xor.c
index 36e6733e..192aacc4 100644
--- a/bn_mp_xor.c
+++ b/bn_mp_xor.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_XOR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* XOR two ints together */
int
@@ -36,10 +37,11 @@ mp_xor (mp_int * a, mp_int * b, mp_int * c)
}
for (ix = 0; ix < px; ix++) {
- t.dp[ix] ^= x->dp[ix];
+
}
mp_clamp (&t);
mp_exch (c, &t);
mp_clear (&t);
return MP_OKAY;
}
+#endif
diff --git a/bn_mp_zero.c b/bn_mp_zero.c
index a888589f..0097598c 100644
--- a/bn_mp_zero.c
+++ b/bn_mp_zero.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_MP_ZERO_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* set to zero */
void
@@ -22,3 +23,4 @@ mp_zero (mp_int * a)
a->used = 0;
memset (a->dp, 0, sizeof (mp_digit) * a->alloc);
}
+#endif
diff --git a/bn_prime_tab.c b/bn_prime_tab.c
index 7dfdc8ce..18ecc47a 100644
--- a/bn_prime_tab.c
+++ b/bn_prime_tab.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_PRIME_TAB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
const mp_digit __prime_tab[] = {
0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
@@ -53,3 +54,4 @@ const mp_digit __prime_tab[] = {
0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
#endif
};
+#endif
diff --git a/bn_reverse.c b/bn_reverse.c
index 89cbbb7c..851a6e8b 100644
--- a/bn_reverse.c
+++ b/bn_reverse.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_REVERSE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reverse an array, used for radix code */
void
@@ -31,3 +32,4 @@ bn_reverse (unsigned char *s, int len)
--iy;
}
}
+#endif
diff --git a/bn_s_mp_add.c b/bn_s_mp_add.c
index e07931ab..2b378ae6 100644
--- a/bn_s_mp_add.c
+++ b/bn_s_mp_add.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_S_MP_ADD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* low level addition, based on HAC pp.594, Algorithm 14.7 */
int
@@ -101,3 +102,4 @@ s_mp_add (mp_int * a, mp_int * b, mp_int * c)
mp_clamp (c);
return MP_OKAY;
}
+#endif
diff --git a/bn_s_mp_exptmod.c b/bn_s_mp_exptmod.c
index 28c14fd9..4f1032a9 100644
--- a/bn_s_mp_exptmod.c
+++ b/bn_s_mp_exptmod.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_S_MP_EXPTMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
#ifdef MP_LOW_MEM
#define TAB_SIZE 32
@@ -232,3 +233,4 @@ __M:
}
return err;
}
+#endif
diff --git a/bn_s_mp_mul_digs.c b/bn_s_mp_mul_digs.c
index a5b10675..d9f0a56e 100644
--- a/bn_s_mp_mul_digs.c
+++ b/bn_s_mp_mul_digs.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_S_MP_MUL_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* multiplies |a| * |b| and only computes upto digs digits of result
* HAC pp. 595, Algorithm 14.12 Modified so you can control how
@@ -83,3 +84,4 @@ s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
mp_clear (&t);
return MP_OKAY;
}
+#endif
diff --git a/bn_s_mp_mul_high_digs.c b/bn_s_mp_mul_high_digs.c
index 84cc7d0a..a060248b 100644
--- a/bn_s_mp_mul_high_digs.c
+++ b/bn_s_mp_mul_high_digs.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_S_MP_MUL_HIGH_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* multiplies |a| * |b| and does not compute the lower digs digits
* [meant to get the higher part of the product]
@@ -27,10 +28,12 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
mp_digit tmpx, *tmpt, *tmpy;
/* can we use the fast multiplier? */
+#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
if (((a->used + b->used + 1) < MP_WARRAY)
&& MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
return fast_s_mp_mul_high_digs (a, b, c, digs);
}
+#endif
if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
return res;
@@ -71,3 +74,4 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
mp_clear (&t);
return MP_OKAY;
}
+#endif
diff --git a/bn_s_mp_sqr.c b/bn_s_mp_sqr.c
index 3a00a4ed..4d128047 100644
--- a/bn_s_mp_sqr.c
+++ b/bn_s_mp_sqr.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_S_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
int
@@ -77,3 +78,4 @@ s_mp_sqr (mp_int * a, mp_int * b)
mp_clear (&t);
return MP_OKAY;
}
+#endif
diff --git a/bn_s_mp_sub.c b/bn_s_mp_sub.c
index 4381af89..5b7aef9d 100644
--- a/bn_s_mp_sub.c
+++ b/bn_s_mp_sub.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BN_S_MP_SUB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,7 +14,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
int
@@ -81,3 +82,4 @@ s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
return MP_OKAY;
}
+#endif
diff --git a/bncore.c b/bncore.c
index acb78a0a..cf8a15a1 100644
--- a/bncore.c
+++ b/bncore.c
@@ -1,3 +1,5 @@
+#include <tommath.h>
+#ifdef BNCORE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -12,20 +14,18 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Known optimal configurations
CPU /Compiler /MUL CUTOFF/SQR CUTOFF
-------------------------------------------------------------
- Intel P4 /GCC v3.2 / 70/ 108
- AMD Athlon XP /GCC v3.2 / 109/ 127
-
+ Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-)
+
*/
-/* configured for a AMD XP Thoroughbred core with etc/tune.c */
-int KARATSUBA_MUL_CUTOFF = 109, /* Min. number of digits before Karatsuba multiplication is used. */
- KARATSUBA_SQR_CUTOFF = 127, /* Min. number of digits before Karatsuba squaring is used. */
+int KARATSUBA_MUL_CUTOFF = 88, /* Min. number of digits before Karatsuba multiplication is used. */
+ KARATSUBA_SQR_CUTOFF = 128, /* Min. number of digits before Karatsuba squaring is used. */
TOOM_MUL_CUTOFF = 350, /* no optimal values of these are known yet so set em high */
TOOM_SQR_CUTOFF = 400;
+#endif
diff --git a/booker.pl b/booker.pl
index 4f4231f2..5c77e538 100644
--- a/booker.pl
+++ b/booker.pl
@@ -82,8 +82,9 @@ while (<IN>) {
# scan till next end of comment, e.g. skip license
while (<SRC>) {
$text[$line++] = $_;
- last if ($_ =~ /tommath\.h/);
+ last if ($_ =~ /math\.libtomcrypt\.org/);
}
+ <SRC>;
}
$inline = 0;
diff --git a/callgraph.txt b/callgraph.txt
new file mode 100644
index 00000000..56d4f8bb
--- /dev/null
+++ b/callgraph.txt
@@ -0,0 +1,10168 @@
+BN_PRIME_TAB_C
+
+
+BN_MP_SQRT_C
++--->BN_MP_N_ROOT_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_SET_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_EXPT_D_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_SQR_C
+| | | +--->BN_MP_TOOM_SQR_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_FAST_S_MP_SQR_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_MUL_C
+| | | +--->BN_MP_TOOM_MUL_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| +--->BN_MP_MUL_C
+| | +--->BN_MP_TOOM_MUL_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_3_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_KARATSUBA_MUL_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_MUL_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_CMP_C
+| | +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_SUB_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_ZERO_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_RSHD_C
++--->BN_MP_DIV_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_SET_C
+| +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_MUL_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_ADD_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_2_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_MAG_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_CMP_D_C
+
+
+BN_MP_EXCH_C
+
+
+BN_MP_IS_SQUARE_C
++--->BN_MP_MOD_D_C
+| +--->BN_MP_DIV_D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_INIT_SET_INT_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_SET_INT_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_MOD_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_SET_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
++--->BN_MP_GET_INT_C
++--->BN_MP_SQRT_C
+| +--->BN_MP_N_ROOT_C
+| | +--->BN_MP_INIT_C
+| | +--->BN_MP_SET_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_EXPT_D_C
+| | | +--->BN_MP_INIT_COPY_C
+| | | +--->BN_MP_SQR_C
+| | | | +--->BN_MP_TOOM_SQR_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_CLEAR_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_CLEAR_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_FAST_S_MP_SQR_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_MUL_C
+| | | | +--->BN_MP_TOOM_MUL_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_MUL_C
+| | | +--->BN_MP_TOOM_MUL_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_COUNT_BITS_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2D_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_COPY_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_CMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_SUB_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_SET_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_2_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_SQR_C
+| +--->BN_MP_TOOM_SQR_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_KARATSUBA_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_SQR_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_CMP_MAG_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_NEG_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
+
+
+BN_MP_EXPTMOD_C
++--->BN_MP_INIT_C
++--->BN_MP_INVMOD_C
+| +--->BN_FAST_MP_INVMOD_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ABS_C
+| | +--->BN_MP_SET_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_CMP_D_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INVMOD_SLOW_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_SET_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_CMP_D_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
++--->BN_MP_ABS_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_CLEAR_MULTI_C
++--->BN_MP_DR_IS_MODULUS_C
++--->BN_MP_REDUCE_IS_2K_C
+| +--->BN_MP_REDUCE_2K_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_COUNT_BITS_C
++--->BN_MP_EXPTMOD_FAST_C
+| +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_MONTGOMERY_SETUP_C
+| +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| +--->BN_MP_MONTGOMERY_REDUCE_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| +--->BN_MP_DR_SETUP_C
+| +--->BN_MP_DR_REDUCE_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| +--->BN_MP_REDUCE_2K_SETUP_C
+| | +--->BN_MP_2EXPT_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_REDUCE_2K_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+| | +--->BN_MP_2EXPT_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_SET_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_MULMOD_C
+| | +--->BN_MP_MUL_C
+| | | +--->BN_MP_TOOM_MUL_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_MOD_C
+| | | +--->BN_MP_DIV_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2D_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_COPY_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| +--->BN_MP_SET_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_MOD_C
+| | +--->BN_MP_DIV_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2D_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_COPY_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_SQR_C
+| | +--->BN_MP_TOOM_SQR_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_3_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_KARATSUBA_SQR_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | +--->BN_FAST_S_MP_SQR_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SQR_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| +--->BN_MP_MUL_C
+| | +--->BN_MP_TOOM_MUL_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_3_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_KARATSUBA_MUL_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| +--->BN_MP_EXCH_C
++--->BN_S_MP_EXPTMOD_C
+| +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_REDUCE_SETUP_C
+| | +--->BN_MP_2EXPT_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_DIV_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_SET_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2D_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_COPY_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_MOD_C
+| | +--->BN_MP_DIV_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_SET_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2D_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_COPY_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_SQR_C
+| | +--->BN_MP_TOOM_SQR_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_3_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_KARATSUBA_SQR_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | +--->BN_FAST_S_MP_SQR_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SQR_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| +--->BN_MP_REDUCE_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_C
+| | | +--->BN_MP_TOOM_MUL_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_S_MP_MUL_HIGH_DIGS_C
+| | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_MUL_DIGS_C
+| | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_D_C
+| | +--->BN_MP_SET_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_MUL_C
+| | +--->BN_MP_TOOM_MUL_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_3_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_KARATSUBA_MUL_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| +--->BN_MP_SET_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_EXCH_C
+
+
+BN_MP_OR_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_ZERO_C
+
+
+BN_MP_GROW_C
+
+
+BN_MP_COUNT_BITS_C
+
+
+BN_MP_PRIME_FERMAT_C
++--->BN_MP_CMP_D_C
++--->BN_MP_INIT_C
++--->BN_MP_EXPTMOD_C
+| +--->BN_MP_INVMOD_C
+| | +--->BN_FAST_MP_INVMOD_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ABS_C
+| | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INVMOD_SLOW_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_ABS_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_DR_IS_MODULUS_C
+| +--->BN_MP_REDUCE_IS_2K_C
+| | +--->BN_MP_REDUCE_2K_C
+| | | +--->BN_MP_COUNT_BITS_C
+| | | +--->BN_MP_DIV_2D_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_EXPTMOD_FAST_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_MONTGOMERY_SETUP_C
+| | +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | +--->BN_MP_MONTGOMERY_REDUCE_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | +--->BN_MP_DR_SETUP_C
+| | +--->BN_MP_DR_REDUCE_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | +--->BN_MP_REDUCE_2K_SETUP_C
+| | | +--->BN_MP_2EXPT_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_REDUCE_2K_C
+| | | +--->BN_MP_DIV_2D_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+| | | +--->BN_MP_2EXPT_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MULMOD_C
+| | | +--->BN_MP_MUL_C
+| | | | +--->BN_MP_TOOM_MUL_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_COPY_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_MOD_C
+| | | | +--->BN_MP_DIV_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_SET_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2D_C
+| | | | | | +--->BN_MP_MOD_2D_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_INIT_COPY_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_SET_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MOD_C
+| | | +--->BN_MP_DIV_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2D_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_COPY_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_SQR_C
+| | | +--->BN_MP_TOOM_SQR_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | +--->BN_FAST_S_MP_SQR_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_MUL_C
+| | | +--->BN_MP_TOOM_MUL_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_S_MP_EXPTMOD_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_REDUCE_SETUP_C
+| | | +--->BN_MP_2EXPT_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_DIV_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2D_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_COPY_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MOD_C
+| | | +--->BN_MP_DIV_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2D_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_COPY_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_SQR_C
+| | | +--->BN_MP_TOOM_SQR_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | +--->BN_FAST_S_MP_SQR_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_REDUCE_C
+| | | +--->BN_MP_INIT_COPY_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_C
+| | | | +--->BN_MP_TOOM_MUL_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_S_MP_MUL_HIGH_DIGS_C
+| | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_MUL_DIGS_C
+| | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_C
+| | | +--->BN_MP_TOOM_MUL_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_SET_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_EXCH_C
++--->BN_MP_CMP_C
+| +--->BN_MP_CMP_MAG_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_SUBMOD_C
++--->BN_MP_INIT_C
++--->BN_MP_SUB_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
++--->BN_MP_MOD_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_SET_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+
+
+BN_MP_MOD_2D_C
++--->BN_MP_ZERO_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_TORADIX_N_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_DIV_D_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_DIV_3_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_CMP_C
++--->BN_MP_CMP_MAG_C
+
+
+BNCORE_C
+
+
+BN_MP_TORADIX_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_DIV_D_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_DIV_3_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_ADD_D_C
++--->BN_MP_GROW_C
++--->BN_MP_SUB_D_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_DIV_3_C
++--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_INIT_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_FAST_S_MP_MUL_DIGS_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_SQRMOD_C
++--->BN_MP_INIT_C
++--->BN_MP_SQR_C
+| +--->BN_MP_TOOM_SQR_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_KARATSUBA_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_SQR_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
++--->BN_MP_MOD_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_SET_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+
+
+BN_MP_INVMOD_C
++--->BN_FAST_MP_INVMOD_C
+| +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_ABS_C
+| +--->BN_MP_SET_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_DIV_2_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_C
+| | +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_CMP_D_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_INVMOD_SLOW_C
+| +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_SET_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_DIV_2_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_C
+| | +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_CMP_D_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_CLEAR_C
+
+
+BN_MP_AND_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_MUL_D_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
+
+
+BN_FAST_MP_INVMOD_C
++--->BN_MP_INIT_MULTI_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_ABS_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_DIV_2_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_SUB_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_C
+| +--->BN_MP_CMP_MAG_C
++--->BN_MP_CMP_D_C
++--->BN_MP_ADD_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_MP_FWRITE_C
++--->BN_MP_RADIX_SIZE_C
+| +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_DIV_D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_TORADIX_C
+| +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_DIV_D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_S_MP_SQR_C
++--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_INIT_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_N_ROOT_C
++--->BN_MP_INIT_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_EXPT_D_C
+| +--->BN_MP_INIT_COPY_C
+| +--->BN_MP_SQR_C
+| | +--->BN_MP_TOOM_SQR_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_3_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_KARATSUBA_SQR_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_FAST_S_MP_SQR_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SQR_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_MUL_C
+| | +--->BN_MP_TOOM_MUL_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_3_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_KARATSUBA_MUL_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
++--->BN_MP_MUL_C
+| +--->BN_MP_TOOM_MUL_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_KARATSUBA_MUL_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_MUL_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_MUL_DIGS_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_SUB_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_INIT_COPY_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_CMP_C
+| +--->BN_MP_CMP_MAG_C
++--->BN_MP_SUB_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_ADD_D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_PRIME_RABIN_MILLER_TRIALS_C
+
+
+BN_MP_RADIX_SIZE_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_DIV_D_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_DIV_3_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_READ_SIGNED_BIN_C
++--->BN_MP_READ_UNSIGNED_BIN_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
+
+
+BN_MP_PRIME_RANDOM_EX_C
++--->BN_MP_READ_UNSIGNED_BIN_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_PRIME_IS_PRIME_C
+| +--->BN_MP_CMP_D_C
+| +--->BN_MP_PRIME_IS_DIVISIBLE_C
+| | +--->BN_MP_MOD_D_C
+| | | +--->BN_MP_DIV_D_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_DIV_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_INIT_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_INIT_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_INIT_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_SET_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_PRIME_MILLER_RABIN_C
+| | +--->BN_MP_INIT_COPY_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_SUB_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CNT_LSB_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXPTMOD_C
+| | | +--->BN_MP_INVMOD_C
+| | | | +--->BN_FAST_MP_INVMOD_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_CLEAR_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ABS_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_INVMOD_SLOW_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_CLEAR_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_ABS_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_DR_IS_MODULUS_C
+| | | +--->BN_MP_REDUCE_IS_2K_C
+| | | | +--->BN_MP_REDUCE_2K_C
+| | | | | +--->BN_MP_COUNT_BITS_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_COUNT_BITS_C
+| | | +--->BN_MP_EXPTMOD_FAST_C
+| | | | +--->BN_MP_COUNT_BITS_C
+| | | | +--->BN_MP_MONTGOMERY_SETUP_C
+| | | | +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_MONTGOMERY_REDUCE_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_DR_SETUP_C
+| | | | +--->BN_MP_DR_REDUCE_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_REDUCE_2K_SETUP_C
+| | | | | +--->BN_MP_2EXPT_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_REDUCE_2K_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+| | | | | +--->BN_MP_2EXPT_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MULMOD_C
+| | | | | +--->BN_MP_MUL_C
+| | | | | | +--->BN_MP_TOOM_MUL_C
+| | | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | | +--->BN_MP_MOD_2D_C
+| | | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | | +--->BN_MP_COPY_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_COPY_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | +--->BN_MP_MUL_2_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_ADD_C
+| | | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_SUB_C
+| | | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_DIV_2_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_DIV_3_C
+| | | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | | +--->BN_MP_EXCH_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_SUB_C
+| | | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_ADD_C
+| | | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_MOD_C
+| | | | | | +--->BN_MP_DIV_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_MP_COPY_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_C
+| | | | | | | +--->BN_MP_SUB_C
+| | | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_ADD_C
+| | | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_EXCH_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_MOD_C
+| | | | | +--->BN_MP_DIV_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_MP_COPY_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_SQR_C
+| | | | | +--->BN_MP_TOOM_SQR_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MOD_2D_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_MUL_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_3_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_FAST_S_MP_SQR_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SQR_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_MUL_C
+| | | | | +--->BN_MP_TOOM_MUL_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MOD_2D_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_MUL_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_3_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_S_MP_EXPTMOD_C
+| | | | +--->BN_MP_COUNT_BITS_C
+| | | | +--->BN_MP_REDUCE_SETUP_C
+| | | | | +--->BN_MP_2EXPT_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_DIV_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_MP_COPY_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MOD_C
+| | | | | +--->BN_MP_DIV_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_MP_COPY_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_SQR_C
+| | | | | +--->BN_MP_TOOM_SQR_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MOD_2D_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_MUL_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_3_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_FAST_S_MP_SQR_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SQR_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_REDUCE_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_C
+| | | | | | +--->BN_MP_TOOM_MUL_C
+| | | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | | +--->BN_MP_MOD_2D_C
+| | | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_MUL_2_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_ADD_C
+| | | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_SUB_C
+| | | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_DIV_2_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_DIV_3_C
+| | | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | | +--->BN_MP_EXCH_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_SUB_C
+| | | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_ADD_C
+| | | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_S_MP_MUL_HIGH_DIGS_C
+| | | | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_C
+| | | | | +--->BN_MP_TOOM_MUL_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MOD_2D_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_MUL_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_3_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_SQRMOD_C
+| | | +--->BN_MP_SQR_C
+| | | | +--->BN_MP_TOOM_SQR_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_CLEAR_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_COPY_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_CLEAR_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_FAST_S_MP_SQR_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_MOD_C
+| | | | +--->BN_MP_DIV_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_COUNT_BITS_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_SUB_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_ADD_D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_2_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_2_C
+| +--->BN_MP_GROW_C
++--->BN_MP_ADD_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
+
+
+BN_MP_KARATSUBA_SQR_C
++--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_INIT_C
++--->BN_MP_CLAMP_C
++--->BN_MP_SQR_C
+| +--->BN_MP_TOOM_SQR_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_SQR_C
+| | +--->BN_MP_GROW_C
+| +--->BN_S_MP_SQR_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_SUB_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
++--->BN_S_MP_ADD_C
+| +--->BN_MP_GROW_C
++--->BN_MP_LSHD_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_RSHD_C
+| | +--->BN_MP_ZERO_C
++--->BN_MP_ADD_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_INIT_COPY_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
+
+
+BN_MP_CLAMP_C
+
+
+BN_MP_TOOM_SQR_C
++--->BN_MP_INIT_MULTI_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_MOD_2D_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_RSHD_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_SQR_C
+| +--->BN_MP_KARATSUBA_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_SQR_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_MUL_2_C
+| +--->BN_MP_GROW_C
++--->BN_MP_ADD_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_SUB_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_2_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_2D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_LSHD_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_3_C
+| +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_LSHD_C
+| +--->BN_MP_GROW_C
++--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_MP_MOD_C
++--->BN_MP_INIT_C
++--->BN_MP_DIV_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_SET_C
+| +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_INIT_COPY_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_MUL_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
++--->BN_MP_ADD_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
+
+
+BN_MP_INIT_C
+
+
+BN_MP_TOOM_MUL_C
++--->BN_MP_INIT_MULTI_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_MOD_2D_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_RSHD_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_MUL_C
+| +--->BN_MP_KARATSUBA_MUL_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_MUL_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_MUL_DIGS_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_MUL_2_C
+| +--->BN_MP_GROW_C
++--->BN_MP_ADD_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_SUB_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_2_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_2D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_LSHD_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_3_C
+| +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_LSHD_C
+| +--->BN_MP_GROW_C
++--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_MP_PRIME_IS_PRIME_C
++--->BN_MP_CMP_D_C
++--->BN_MP_PRIME_IS_DIVISIBLE_C
+| +--->BN_MP_MOD_D_C
+| | +--->BN_MP_DIV_D_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_DIV_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_INIT_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_DIV_3_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_INIT_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
++--->BN_MP_INIT_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_PRIME_MILLER_RABIN_C
+| +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_SUB_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CNT_LSB_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_EXPTMOD_C
+| | +--->BN_MP_INVMOD_C
+| | | +--->BN_FAST_MP_INVMOD_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ABS_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_INVMOD_SLOW_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_ABS_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_DR_IS_MODULUS_C
+| | +--->BN_MP_REDUCE_IS_2K_C
+| | | +--->BN_MP_REDUCE_2K_C
+| | | | +--->BN_MP_COUNT_BITS_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_EXPTMOD_FAST_C
+| | | +--->BN_MP_COUNT_BITS_C
+| | | +--->BN_MP_MONTGOMERY_SETUP_C
+| | | +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_MONTGOMERY_REDUCE_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_DR_SETUP_C
+| | | +--->BN_MP_DR_REDUCE_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_REDUCE_2K_SETUP_C
+| | | | +--->BN_MP_2EXPT_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_REDUCE_2K_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+| | | | +--->BN_MP_2EXPT_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MULMOD_C
+| | | | +--->BN_MP_MUL_C
+| | | | | +--->BN_MP_TOOM_MUL_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MOD_2D_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | +--->BN_MP_COPY_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_COPY_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_MUL_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_3_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_MOD_C
+| | | | | +--->BN_MP_DIV_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_MP_COPY_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_MOD_C
+| | | | +--->BN_MP_DIV_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_SQR_C
+| | | | +--->BN_MP_TOOM_SQR_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_FAST_S_MP_SQR_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_MUL_C
+| | | | +--->BN_MP_TOOM_MUL_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_S_MP_EXPTMOD_C
+| | | +--->BN_MP_COUNT_BITS_C
+| | | +--->BN_MP_REDUCE_SETUP_C
+| | | | +--->BN_MP_2EXPT_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_DIV_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MOD_C
+| | | | +--->BN_MP_DIV_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_SQR_C
+| | | | +--->BN_MP_TOOM_SQR_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_FAST_S_MP_SQR_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_REDUCE_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_C
+| | | | | +--->BN_MP_TOOM_MUL_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MOD_2D_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_3_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_S_MP_MUL_HIGH_DIGS_C
+| | | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_C
+| | | | +--->BN_MP_TOOM_MUL_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_EXCH_C
+| +--->BN_MP_CMP_C
+| | +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_SQRMOD_C
+| | +--->BN_MP_SQR_C
+| | | +--->BN_MP_TOOM_SQR_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_FAST_S_MP_SQR_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_MOD_C
+| | | +--->BN_MP_DIV_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_COUNT_BITS_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_COPY_C
++--->BN_MP_GROW_C
+
+
+BN_S_MP_SUB_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_READ_UNSIGNED_BIN_C
++--->BN_MP_GROW_C
++--->BN_MP_ZERO_C
++--->BN_MP_MUL_2D_C
+| +--->BN_MP_COPY_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_EXPTMOD_FAST_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_INIT_C
++--->BN_MP_CLEAR_C
++--->BN_MP_MONTGOMERY_SETUP_C
++--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_RSHD_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
++--->BN_MP_MONTGOMERY_REDUCE_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_RSHD_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
++--->BN_MP_DR_SETUP_C
++--->BN_MP_DR_REDUCE_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
++--->BN_MP_REDUCE_2K_SETUP_C
+| +--->BN_MP_2EXPT_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_GROW_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_REDUCE_2K_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_MUL_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+| +--->BN_MP_2EXPT_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_SET_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_MUL_2_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_MULMOD_C
+| +--->BN_MP_MUL_C
+| | +--->BN_MP_TOOM_MUL_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_3_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_KARATSUBA_MUL_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| +--->BN_MP_MOD_C
+| | +--->BN_MP_DIV_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_SET_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2D_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_COPY_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_MOD_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_SQR_C
+| +--->BN_MP_TOOM_SQR_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_KARATSUBA_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| +--->BN_FAST_S_MP_SQR_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
++--->BN_MP_MUL_C
+| +--->BN_MP_TOOM_MUL_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_KARATSUBA_MUL_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| +--->BN_FAST_S_MP_MUL_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_MUL_DIGS_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
++--->BN_MP_EXCH_C
+
+
+BN_MP_TO_UNSIGNED_BIN_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_DIV_2D_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_MOD_2D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_SET_INT_C
++--->BN_MP_ZERO_C
++--->BN_MP_MUL_2D_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_MOD_D_C
++--->BN_MP_DIV_D_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_DIV_3_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_MP_SQR_C
++--->BN_MP_TOOM_SQR_C
+| +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_MOD_2D_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_RSHD_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_MUL_2_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_2_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_MUL_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_3_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_KARATSUBA_SQR_C
+| +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| +--->BN_MP_ADD_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_CLEAR_C
++--->BN_FAST_S_MP_SQR_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_S_MP_SQR_C
+| +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_MP_MULMOD_C
++--->BN_MP_INIT_C
++--->BN_MP_MUL_C
+| +--->BN_MP_TOOM_MUL_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_KARATSUBA_MUL_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_MUL_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_MUL_DIGS_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
++--->BN_MP_MOD_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_SET_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+
+
+BN_MP_DIV_2D_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_ZERO_C
++--->BN_MP_INIT_C
++--->BN_MP_MOD_2D_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
++--->BN_MP_RSHD_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
+
+
+BN_S_MP_ADD_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
+
+
+BN_FAST_S_MP_SQR_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
+
+
+BN_S_MP_MUL_DIGS_C
++--->BN_FAST_S_MP_MUL_DIGS_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_INIT_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_XOR_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_RADIX_SMAP_C
+
+
+BN_MP_DR_IS_MODULUS_C
+
+
+BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_2EXPT_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_GROW_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_MUL_2_C
+| +--->BN_MP_GROW_C
++--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
+
+
+BN_MP_SUB_C
++--->BN_S_MP_ADD_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
+
+
+BN_MP_INIT_MULTI_C
++--->BN_MP_INIT_C
++--->BN_MP_CLEAR_C
+
+
+BN_S_MP_MUL_HIGH_DIGS_C
++--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_INIT_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_PRIME_NEXT_PRIME_C
++--->BN_MP_CMP_D_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_SUB_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_ADD_D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_MOD_D_C
+| +--->BN_MP_DIV_D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_INIT_C
++--->BN_MP_ADD_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_PRIME_MILLER_RABIN_C
+| +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_CNT_LSB_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_EXPTMOD_C
+| | +--->BN_MP_INVMOD_C
+| | | +--->BN_FAST_MP_INVMOD_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ABS_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_INVMOD_SLOW_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_ABS_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_DR_IS_MODULUS_C
+| | +--->BN_MP_REDUCE_IS_2K_C
+| | | +--->BN_MP_REDUCE_2K_C
+| | | | +--->BN_MP_COUNT_BITS_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_EXPTMOD_FAST_C
+| | | +--->BN_MP_COUNT_BITS_C
+| | | +--->BN_MP_MONTGOMERY_SETUP_C
+| | | +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_MONTGOMERY_REDUCE_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_DR_SETUP_C
+| | | +--->BN_MP_DR_REDUCE_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_REDUCE_2K_SETUP_C
+| | | | +--->BN_MP_2EXPT_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_REDUCE_2K_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+| | | | +--->BN_MP_2EXPT_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MULMOD_C
+| | | | +--->BN_MP_MUL_C
+| | | | | +--->BN_MP_TOOM_MUL_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MOD_2D_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | +--->BN_MP_COPY_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_COPY_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_MUL_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_3_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_MOD_C
+| | | | | +--->BN_MP_DIV_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_MP_COPY_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_MOD_C
+| | | | +--->BN_MP_DIV_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_SQR_C
+| | | | +--->BN_MP_TOOM_SQR_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_FAST_S_MP_SQR_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_MUL_C
+| | | | +--->BN_MP_TOOM_MUL_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_S_MP_EXPTMOD_C
+| | | +--->BN_MP_COUNT_BITS_C
+| | | +--->BN_MP_REDUCE_SETUP_C
+| | | | +--->BN_MP_2EXPT_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_DIV_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MOD_C
+| | | | +--->BN_MP_DIV_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_SQR_C
+| | | | +--->BN_MP_TOOM_SQR_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_FAST_S_MP_SQR_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SQR_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_REDUCE_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_C
+| | | | | +--->BN_MP_TOOM_MUL_C
+| | | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | | +--->BN_MP_MOD_2D_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_2_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_2D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_MUL_D_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_DIV_3_C
+| | | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | | +--->BN_MP_EXCH_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_SUB_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_ADD_C
+| | | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_S_MP_MUL_HIGH_DIGS_C
+| | | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_C
+| | | | +--->BN_MP_TOOM_MUL_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_EXCH_C
+| +--->BN_MP_CMP_C
+| | +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_SQRMOD_C
+| | +--->BN_MP_SQR_C
+| | | +--->BN_MP_TOOM_SQR_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_FAST_S_MP_SQR_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_MOD_C
+| | | +--->BN_MP_DIV_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_COUNT_BITS_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_MULTI_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_SIGNED_BIN_SIZE_C
++--->BN_MP_UNSIGNED_BIN_SIZE_C
+| +--->BN_MP_COUNT_BITS_C
+
+
+BN_MP_INVMOD_SLOW_C
++--->BN_MP_INIT_MULTI_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_DIV_2_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_ADD_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_SUB_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_C
+| +--->BN_MP_CMP_MAG_C
++--->BN_MP_CMP_D_C
++--->BN_MP_CMP_MAG_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_MP_LCM_C
++--->BN_MP_INIT_MULTI_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_GCD_C
+| +--->BN_MP_ABS_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_CNT_LSB_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_EXCH_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_CMP_MAG_C
++--->BN_MP_DIV_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_SET_C
+| +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_INIT_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_INIT_COPY_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_MUL_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_MUL_C
+| +--->BN_MP_TOOM_MUL_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_KARATSUBA_MUL_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_MUL_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_MUL_DIGS_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_REVERSE_C
+
+
+BN_MP_PRIME_IS_DIVISIBLE_C
++--->BN_MP_MOD_D_C
+| +--->BN_MP_DIV_D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
+
+
+BN_MP_SET_C
++--->BN_MP_ZERO_C
+
+
+BN_MP_GCD_C
++--->BN_MP_ABS_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_ZERO_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_CNT_LSB_C
++--->BN_MP_DIV_2D_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_MOD_2D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
++--->BN_MP_CMP_MAG_C
++--->BN_MP_EXCH_C
++--->BN_S_MP_SUB_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_2D_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_READ_RADIX_C
++--->BN_MP_ZERO_C
++--->BN_MP_MUL_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_ADD_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_SUB_D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
+
+
+BN_FAST_S_MP_MUL_HIGH_DIGS_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
+
+
+BN_FAST_MP_MONTGOMERY_REDUCE_C
++--->BN_MP_GROW_C
++--->BN_MP_RSHD_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_CLAMP_C
++--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+
+
+BN_MP_DIV_D_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_DIV_2D_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_MOD_2D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
++--->BN_MP_DIV_3_C
+| +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_INIT_C
++--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_REDUCE_2K_SETUP_C
++--->BN_MP_INIT_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_2EXPT_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_GROW_C
++--->BN_MP_CLEAR_C
++--->BN_S_MP_SUB_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
+
+
+BN_MP_INIT_SET_C
++--->BN_MP_INIT_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
+
+
+BN_MP_REDUCE_2K_C
++--->BN_MP_INIT_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_DIV_2D_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_MOD_2D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
++--->BN_MP_MUL_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_S_MP_ADD_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
+
+
+BN_ERROR_C
+
+
+BN_MP_EXPT_D_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_SQR_C
+| +--->BN_MP_TOOM_SQR_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_KARATSUBA_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_SQR_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_CLEAR_C
++--->BN_MP_MUL_C
+| +--->BN_MP_TOOM_MUL_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_KARATSUBA_MUL_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| +--->BN_FAST_S_MP_MUL_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_MUL_DIGS_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+
+
+BN_S_MP_EXPTMOD_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_INIT_C
++--->BN_MP_CLEAR_C
++--->BN_MP_REDUCE_SETUP_C
+| +--->BN_MP_2EXPT_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_SET_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_MOD_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_SET_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_SQR_C
+| +--->BN_MP_TOOM_SQR_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_KARATSUBA_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| +--->BN_FAST_S_MP_SQR_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_SQR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
++--->BN_MP_REDUCE_C
+| +--->BN_MP_INIT_COPY_C
+| +--->BN_MP_RSHD_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_MUL_C
+| | +--->BN_MP_TOOM_MUL_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_3_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_KARATSUBA_MUL_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| +--->BN_S_MP_MUL_HIGH_DIGS_C
+| | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_MOD_2D_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_MUL_DIGS_C
+| | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_D_C
+| +--->BN_MP_SET_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_C
+| | +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_MUL_C
+| +--->BN_MP_TOOM_MUL_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_KARATSUBA_MUL_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| +--->BN_FAST_S_MP_MUL_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_MUL_DIGS_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_EXCH_C
+
+
+BN_MP_ABS_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
+
+
+BN_MP_INIT_SET_INT_C
++--->BN_MP_INIT_C
++--->BN_MP_SET_INT_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
+
+
+BN_MP_SUB_D_C
++--->BN_MP_GROW_C
++--->BN_MP_ADD_D_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_TO_SIGNED_BIN_C
++--->BN_MP_TO_UNSIGNED_BIN_C
+| +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_MP_DIV_2_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_REDUCE_IS_2K_C
++--->BN_MP_REDUCE_2K_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_MUL_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_COUNT_BITS_C
+
+
+BN_MP_INIT_SIZE_C
++--->BN_MP_INIT_C
+
+
+BN_MP_DIV_C
++--->BN_MP_CMP_MAG_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_ZERO_C
++--->BN_MP_INIT_MULTI_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_SET_C
++--->BN_MP_COUNT_BITS_C
++--->BN_MP_MUL_2D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_C
++--->BN_MP_SUB_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_ADD_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_DIV_2D_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_MOD_2D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_INIT_C
++--->BN_MP_INIT_C
++--->BN_MP_INIT_COPY_C
++--->BN_MP_LSHD_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_RSHD_C
++--->BN_MP_RSHD_C
++--->BN_MP_MUL_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_CLEAR_C
+
+
+BN_MP_MONTGOMERY_REDUCE_C
++--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_RSHD_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
++--->BN_MP_RSHD_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+
+
+BN_MP_MUL_2_C
++--->BN_MP_GROW_C
+
+
+BN_MP_UNSIGNED_BIN_SIZE_C
++--->BN_MP_COUNT_BITS_C
+
+
+BN_MP_ADDMOD_C
++--->BN_MP_INIT_C
++--->BN_MP_ADD_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
++--->BN_MP_MOD_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_SET_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+
+
+BN_MP_ADD_C
++--->BN_S_MP_ADD_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
+
+
+BN_MP_RAND_C
++--->BN_MP_ZERO_C
++--->BN_MP_ADD_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_SUB_D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_LSHD_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_RSHD_C
+
+
+BN_MP_CNT_LSB_C
+
+
+BN_MP_2EXPT_C
++--->BN_MP_ZERO_C
++--->BN_MP_GROW_C
+
+
+BN_MP_RSHD_C
++--->BN_MP_ZERO_C
+
+
+BN_MP_SHRINK_C
+
+
+BN_MP_REDUCE_C
++--->BN_MP_REDUCE_SETUP_C
+| +--->BN_MP_2EXPT_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_SET_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2D_C
+| | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_INIT_C
+| | +--->BN_MP_INIT_COPY_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_RSHD_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_MUL_C
+| +--->BN_MP_TOOM_MUL_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_KARATSUBA_MUL_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_MUL_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_MUL_DIGS_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_S_MP_MUL_HIGH_DIGS_C
+| +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_MOD_2D_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_S_MP_MUL_DIGS_C
+| +--->BN_FAST_S_MP_MUL_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_SUB_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_D_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_LSHD_C
+| +--->BN_MP_GROW_C
++--->BN_MP_ADD_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_C
+| +--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_MUL_2D_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_GROW_C
++--->BN_MP_LSHD_C
+| +--->BN_MP_RSHD_C
+| | +--->BN_MP_ZERO_C
++--->BN_MP_CLAMP_C
+
+
+BN_MP_GET_INT_C
+
+
+BN_MP_JACOBI_C
++--->BN_MP_CMP_D_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_CNT_LSB_C
++--->BN_MP_DIV_2D_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_MOD_2D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
++--->BN_MP_MOD_C
+| +--->BN_MP_DIV_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_SET_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_CLEAR_MULTI_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_MUL_C
++--->BN_MP_TOOM_MUL_C
+| +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_MOD_2D_C
+| | +--->BN_MP_ZERO_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_RSHD_C
+| | +--->BN_MP_ZERO_C
+| +--->BN_MP_MUL_2_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_2_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_MUL_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_3_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_KARATSUBA_MUL_C
+| +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CMP_MAG_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| +--->BN_MP_CLEAR_C
++--->BN_FAST_S_MP_MUL_DIGS_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_S_MP_MUL_DIGS_C
+| +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_MP_EXTEUCLID_C
++--->BN_MP_INIT_MULTI_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_SET_C
+| +--->BN_MP_ZERO_C
++--->BN_MP_COPY_C
+| +--->BN_MP_GROW_C
++--->BN_MP_DIV_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_INIT_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_INIT_COPY_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_MUL_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
++--->BN_MP_MUL_C
+| +--->BN_MP_TOOM_MUL_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_KARATSUBA_MUL_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_MUL_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_MUL_DIGS_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_SUB_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
++--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_MP_DR_REDUCE_C
++--->BN_MP_GROW_C
++--->BN_MP_CLAMP_C
++--->BN_MP_CMP_MAG_C
++--->BN_S_MP_SUB_C
+
+
+BN_MP_FREAD_C
++--->BN_MP_ZERO_C
++--->BN_MP_MUL_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_ADD_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_SUB_D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CMP_D_C
+
+
+BN_MP_REDUCE_SETUP_C
++--->BN_MP_2EXPT_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_GROW_C
++--->BN_MP_DIV_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_INIT_MULTI_C
+| | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_SET_C
+| +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_MUL_2D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CMP_C
+| +--->BN_MP_SUB_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_ADD_C
+| | +--->BN_S_MP_ADD_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SUB_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| +--->BN_MP_DIV_2D_C
+| | +--->BN_MP_INIT_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_RSHD_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_MP_EXCH_C
+| +--->BN_MP_CLEAR_MULTI_C
+| | +--->BN_MP_CLEAR_C
+| +--->BN_MP_INIT_SIZE_C
+| | +--->BN_MP_INIT_C
+| +--->BN_MP_INIT_C
+| +--->BN_MP_INIT_COPY_C
+| +--->BN_MP_LSHD_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_MUL_D_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
+
+
+BN_MP_MONTGOMERY_SETUP_C
+
+
+BN_MP_KARATSUBA_MUL_C
++--->BN_MP_MUL_C
+| +--->BN_MP_TOOM_MUL_C
+| | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_MOD_2D_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MUL_2_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_SUB_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_2_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_2D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_D_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_DIV_3_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_INIT_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_LSHD_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_FAST_S_MP_MUL_DIGS_C
+| | +--->BN_MP_GROW_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_S_MP_MUL_DIGS_C
+| | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_INIT_C
+| | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
+| | +--->BN_MP_CLEAR_C
++--->BN_MP_INIT_SIZE_C
+| +--->BN_MP_INIT_C
++--->BN_MP_CLAMP_C
++--->BN_MP_SUB_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_ADD_C
+| +--->BN_S_MP_ADD_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_CMP_MAG_C
+| +--->BN_S_MP_SUB_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_LSHD_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_RSHD_C
+| | +--->BN_MP_ZERO_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_LSHD_C
++--->BN_MP_GROW_C
++--->BN_MP_RSHD_C
+| +--->BN_MP_ZERO_C
+
+
+BN_MP_PRIME_MILLER_RABIN_C
++--->BN_MP_CMP_D_C
++--->BN_MP_INIT_COPY_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
++--->BN_MP_SUB_D_C
+| +--->BN_MP_GROW_C
+| +--->BN_MP_ADD_D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLAMP_C
++--->BN_MP_CNT_LSB_C
++--->BN_MP_DIV_2D_C
+| +--->BN_MP_COPY_C
+| | +--->BN_MP_GROW_C
+| +--->BN_MP_ZERO_C
+| +--->BN_MP_MOD_2D_C
+| | +--->BN_MP_CLAMP_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_RSHD_C
+| +--->BN_MP_CLAMP_C
+| +--->BN_MP_EXCH_C
++--->BN_MP_EXPTMOD_C
+| +--->BN_MP_INVMOD_C
+| | +--->BN_FAST_MP_INVMOD_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ABS_C
+| | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_INVMOD_SLOW_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_ABS_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| +--->BN_MP_CLEAR_MULTI_C
+| +--->BN_MP_DR_IS_MODULUS_C
+| +--->BN_MP_REDUCE_IS_2K_C
+| | +--->BN_MP_REDUCE_2K_C
+| | | +--->BN_MP_COUNT_BITS_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_COUNT_BITS_C
+| +--->BN_MP_EXPTMOD_FAST_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_MONTGOMERY_SETUP_C
+| | +--->BN_FAST_MP_MONTGOMERY_REDUCE_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | +--->BN_MP_MONTGOMERY_REDUCE_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | +--->BN_MP_DR_SETUP_C
+| | +--->BN_MP_DR_REDUCE_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | +--->BN_MP_REDUCE_2K_SETUP_C
+| | | +--->BN_MP_2EXPT_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_REDUCE_2K_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+| | | +--->BN_MP_2EXPT_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MULMOD_C
+| | | +--->BN_MP_MUL_C
+| | | | +--->BN_MP_TOOM_MUL_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_COPY_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_MOD_C
+| | | | +--->BN_MP_DIV_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_MP_COPY_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_SET_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_SET_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_MOD_C
+| | | +--->BN_MP_DIV_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_SQR_C
+| | | +--->BN_MP_TOOM_SQR_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | +--->BN_FAST_S_MP_SQR_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_MUL_C
+| | | +--->BN_MP_TOOM_MUL_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_EXCH_C
+| +--->BN_S_MP_EXPTMOD_C
+| | +--->BN_MP_COUNT_BITS_C
+| | +--->BN_MP_REDUCE_SETUP_C
+| | | +--->BN_MP_2EXPT_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_DIV_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MOD_C
+| | | +--->BN_MP_DIV_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_COPY_C
+| | | +--->BN_MP_GROW_C
+| | +--->BN_MP_SQR_C
+| | | +--->BN_MP_TOOM_SQR_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_KARATSUBA_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | +--->BN_FAST_S_MP_SQR_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_SQR_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_REDUCE_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_C
+| | | | +--->BN_MP_TOOM_MUL_C
+| | | | | +--->BN_MP_INIT_MULTI_C
+| | | | | +--->BN_MP_MOD_2D_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_2_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_2D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_MUL_D_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_DIV_3_C
+| | | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | | +--->BN_MP_EXCH_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_SUB_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_ADD_C
+| | | | | | +--->BN_S_MP_ADD_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CMP_MAG_C
+| | | | | | +--->BN_S_MP_SUB_C
+| | | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | +--->BN_S_MP_MUL_HIGH_DIGS_C
+| | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_MUL_DIGS_C
+| | | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SET_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_MUL_C
+| | | +--->BN_MP_TOOM_MUL_C
+| | | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_MOD_2D_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_MUL_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_2_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_2D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_MUL_D_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_DIV_3_C
+| | | | | +--->BN_MP_INIT_SIZE_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_KARATSUBA_MUL_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_SUB_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_ADD_C
+| | | | | +--->BN_S_MP_ADD_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CMP_MAG_C
+| | | | | +--->BN_S_MP_SUB_C
+| | | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | | | +--->BN_MP_ZERO_C
+| | | +--->BN_FAST_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_S_MP_MUL_DIGS_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | +--->BN_MP_SET_C
+| | | +--->BN_MP_ZERO_C
+| | +--->BN_MP_EXCH_C
++--->BN_MP_CMP_C
+| +--->BN_MP_CMP_MAG_C
++--->BN_MP_SQRMOD_C
+| +--->BN_MP_SQR_C
+| | +--->BN_MP_TOOM_SQR_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_MOD_2D_C
+| | | | +--->BN_MP_ZERO_C
+| | | | +--->BN_MP_COPY_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_MUL_2_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_2_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_DIV_3_C
+| | | | +--->BN_MP_INIT_SIZE_C
+| | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_MP_EXCH_C
+| | | | +--->BN_MP_CLEAR_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | | | +--->BN_MP_CLEAR_C
+| | +--->BN_MP_KARATSUBA_SQR_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_MP_CMP_MAG_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLEAR_C
+| | +--->BN_FAST_S_MP_SQR_C
+| | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_S_MP_SQR_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_C
+| +--->BN_MP_CLEAR_C
+| +--->BN_MP_MOD_C
+| | +--->BN_MP_DIV_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_MP_COPY_C
+| | | | +--->BN_MP_GROW_C
+| | | +--->BN_MP_ZERO_C
+| | | +--->BN_MP_INIT_MULTI_C
+| | | +--->BN_MP_SET_C
+| | | +--->BN_MP_COUNT_BITS_C
+| | | +--->BN_MP_MUL_2D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_LSHD_C
+| | | | | +--->BN_MP_RSHD_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_SUB_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_ADD_C
+| | | | +--->BN_S_MP_ADD_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | | +--->BN_S_MP_SUB_C
+| | | | | +--->BN_MP_GROW_C
+| | | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_EXCH_C
+| | | +--->BN_MP_CLEAR_MULTI_C
+| | | +--->BN_MP_INIT_SIZE_C
+| | | +--->BN_MP_LSHD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_RSHD_C
+| | | +--->BN_MP_MUL_D_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_ADD_C
+| | | +--->BN_S_MP_ADD_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | | +--->BN_MP_CMP_MAG_C
+| | | +--->BN_S_MP_SUB_C
+| | | | +--->BN_MP_GROW_C
+| | | | +--->BN_MP_CLAMP_C
+| | +--->BN_MP_EXCH_C
++--->BN_MP_CLEAR_C
+
+
+BN_MP_DR_SETUP_C
+
+
+BN_MP_CMP_MAG_C
+
+
diff --git a/changes.txt b/changes.txt
index 63e9d617..6a862096 100644
--- a/changes.txt
+++ b/changes.txt
@@ -1,3 +1,27 @@
+October 29th, 2004
+v0.32 -- Added "makefile.shared" for shared object support
+ -- Added more to the build options/configs in the manual
+ -- Started the Depends framework, wrote dep.pl to scan deps and
+ produce "callgraph.txt" ;-)
+ -- Wrote SC_RSA_1 which will enable close to the minimum required to perform
+ RSA on 32-bit [or 64-bit] platforms with LibTomCrypt
+ -- Merged in the small/slower mp_div replacement. You can now toggle which
+ you want to use as your mp_div() at build time. Saves roughly 8KB or so.
+ -- Renamed a few files and changed some comments to make depends system work better.
+ (No changes to function names)
+ -- Merged in new Combas that perform 2 reads per inner loop instead of the older
+ 3reads/2writes per inner loop of the old code. Really though if you want speed
+ learn to use TomsFastMath ;-)
+
+August 9th, 2004
+v0.31 -- "profiled" builds now :-) new timings for Intel Northwoods
+ -- Added "pretty" build target
+ -- Update mp_init() to actually assign 0's instead of relying on calloc()
+ -- "Wolfgang Ehrhardt" <Wolfgang.Ehrhardt@munich.netsurf.de> found a bug in mp_mul() where if
+ you multiply a negative by zero you get negative zero as the result. Oops.
+ -- J Harper from PeerSec let me toy with his AMD64 and I got 60-bit digits working properly
+ [this also means that I fixed a bug where if sizeof(int) < sizeof(mp_digit) it would bug]
+
April 11th, 2004
v0.30 -- Added "mp_toradix_n" which stores upto "n-1" least significant digits of an mp_int
-- Johan Lindh sent a patch so MSVC wouldn't whine about redefining malloc [in weird dll modes]
diff --git a/demo/demo.c b/demo/demo.c
index 8014ea82..53eb3cfc 100644
--- a/demo/demo.c
+++ b/demo/demo.c
@@ -1,7 +1,5 @@
#include <time.h>
-#define TESTING
-
#ifdef IOWNANATHLON
#include <unistd.h>
#define SLEEP sleep(4)
@@ -11,49 +9,6 @@
#include "tommath.h"
-#ifdef TIMER
-ulong64 _tt;
-
-#if defined(__i386__) || defined(_M_IX86) || defined(_M_AMD64)
-/* RDTSC from Scott Duplichan */
-static ulong64 TIMFUNC (void)
- {
- #if defined __GNUC__
- #ifdef __i386__
- ulong64 a;
- __asm__ __volatile__ ("rdtsc ":"=A" (a));
- return a;
- #else /* gcc-IA64 version */
- unsigned long result;
- __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory");
- while (__builtin_expect ((int) result == -1, 0))
- __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory");
- return result;
- #endif
-
- // Microsoft and Intel Windows compilers
- #elif defined _M_IX86
- __asm rdtsc
- #elif defined _M_AMD64
- return __rdtsc ();
- #elif defined _M_IA64
- #if defined __INTEL_COMPILER
- #include <ia64intrin.h>
- #endif
- return __getReg (3116);
- #else
- #error need rdtsc function for this build
- #endif
- }
-#else
-#define TIMFUNC clock
-#endif
-
-ulong64 rdtsc(void) { return TIMFUNC() - _tt; }
-void reset(void) { _tt = TIMFUNC(); }
-
-#endif
-
void ndraw(mp_int *a, char *name)
{
char buf[4096];
@@ -89,10 +44,6 @@ int myrng(unsigned char *dst, int len, void *dat)
}
-#define DO2(x) x; x;
-#define DO4(x) DO2(x); DO2(x);
-#define DO8(x) DO4(x); DO4(x);
-#define DO(x) DO8(x); DO8(x);
char cmd[4096], buf[4096];
int main(void)
@@ -103,10 +54,6 @@ int main(void)
unsigned rr;
int i, n, err, cnt, ix, old_kara_m, old_kara_s;
-#ifdef TIMER
- ulong64 tt, CLK_PER_SEC;
- FILE *log, *logb, *logc;
-#endif
mp_init(&a);
mp_init(&b);
@@ -117,11 +64,11 @@ int main(void)
srand(time(NULL));
-#ifdef TESTING
+#if 0
// test mp_get_int
printf("Testing: mp_get_int\n");
for(i=0;i<1000;++i) {
- t = (unsigned long)rand()*rand()+1;
+ t = ((unsigned long)rand()*rand()+1)&0xFFFFFFFF;
mp_set_int(&a,t);
if (t!=mp_get_int(&a)) {
printf("mp_get_int() bad result!\n");
@@ -141,7 +88,7 @@ int main(void)
// test mp_sqrt
printf("Testing: mp_sqrt\n");
- for (i=0;i<10000;++i) {
+ for (i=0;i<1000;++i) {
printf("%6d\r", i); fflush(stdout);
n = (rand()&15)+1;
mp_rand(&a,n);
@@ -157,7 +104,7 @@ int main(void)
}
printf("\nTesting: mp_is_square\n");
- for (i=0;i<100000;++i) {
+ for (i=0;i<1000;++i) {
printf("%6d\r", i); fflush(stdout);
/* test mp_is_square false negatives */
@@ -186,11 +133,9 @@ int main(void)
}
printf("\n\n");
-#endif
-#ifdef TESTING
/* test for size */
- for (ix = 16; ix < 512; ix++) {
+ for (ix = 10; ix < 256; ix++) {
printf("Testing (not safe-prime): %9d bits \r", ix); fflush(stdout);
err = mp_prime_random_ex(&a, 8, ix, (rand()&1)?LTM_PRIME_2MSB_OFF:LTM_PRIME_2MSB_ON, myrng, NULL);
if (err != MP_OKAY) {
@@ -203,7 +148,7 @@ int main(void)
}
}
- for (ix = 16; ix < 512; ix++) {
+ for (ix = 16; ix < 256; ix++) {
printf("Testing ( safe-prime): %9d bits \r", ix); fflush(stdout);
err = mp_prime_random_ex(&a, 8, ix, ((rand()&1)?LTM_PRIME_2MSB_OFF:LTM_PRIME_2MSB_ON)|LTM_PRIME_SAFE, myrng, NULL);
if (err != MP_OKAY) {
@@ -225,9 +170,7 @@ int main(void)
}
printf("\n\n");
-#endif
-#ifdef TESTING
mp_read_radix(&a, "123456", 10);
mp_toradix_n(&a, buf, 10, 3);
printf("a == %s\n", buf);
@@ -235,7 +178,6 @@ int main(void)
printf("a == %s\n", buf);
mp_toradix_n(&a, buf, 10, 30);
printf("a == %s\n", buf);
-#endif
#if 0
@@ -248,22 +190,6 @@ int main(void)
}
#endif
-#if 0
-{
- mp_word aa, bb;
-
- for (;;) {
- aa = abs(rand()) & MP_MASK;
- bb = abs(rand()) & MP_MASK;
- if (MULT(aa,bb) != (aa*bb)) {
- printf("%llu * %llu == %llu or %llu?\n", aa, bb, (ulong64)MULT(aa,bb), (ulong64)(aa*bb));
- return 0;
- }
- }
-}
-#endif
-
-#ifdef TESTING
/* test mp_cnt_lsb */
printf("testing mp_cnt_lsb...\n");
mp_set(&a, 1);
@@ -274,12 +200,10 @@ int main(void)
}
mp_mul_2(&a, &a);
}
-#endif
/* test mp_reduce_2k */
-#ifdef TESTING
printf("Testing mp_reduce_2k...\n");
- for (cnt = 3; cnt <= 384; ++cnt) {
+ for (cnt = 3; cnt <= 128; ++cnt) {
mp_digit tmp;
mp_2expt(&a, cnt);
mp_sub_d(&a, 2, &a); /* a = 2**cnt - 2 */
@@ -289,7 +213,7 @@ int main(void)
printf("(%d)", mp_reduce_is_2k(&a));
mp_reduce_2k_setup(&a, &tmp);
printf("(%d)", tmp);
- for (ix = 0; ix < 10000; ix++) {
+ for (ix = 0; ix < 1000; ix++) {
if (!(ix & 127)) {printf("."); fflush(stdout); }
mp_rand(&b, (cnt/DIGIT_BIT + 1) * 2);
mp_copy(&c, &b);
@@ -301,14 +225,11 @@ int main(void)
}
}
}
-#endif
-
/* test mp_div_3 */
-#ifdef TESTING
printf("Testing mp_div_3...\n");
mp_set(&d, 3);
- for (cnt = 0; cnt < 1000000; ) {
+ for (cnt = 0; cnt < 10000; ) {
mp_digit r1, r2;
if (!(++cnt & 127)) printf("%9d\r", cnt);
@@ -321,12 +242,10 @@ int main(void)
}
}
printf("\n\nPassed div_3 testing\n");
-#endif
/* test the DR reduction */
-#ifdef TESTING
printf("testing mp_dr_reduce...\n");
- for (cnt = 2; cnt < 128; cnt++) {
+ for (cnt = 2; cnt < 32; cnt++) {
printf("%d digit modulus\n", cnt);
mp_grow(&a, cnt);
mp_zero(&a);
@@ -334,7 +253,7 @@ int main(void)
a.dp[ix] = MP_MASK;
}
a.used = cnt;
- mp_prime_next_prime(&a, 3, 0);
+ a.dp[0] = 3;
mp_rand(&b, cnt - 1);
mp_copy(&b, &c);
@@ -346,204 +265,15 @@ int main(void)
mp_copy(&b, &c);
mp_mod(&b, &a, &b);
- mp_dr_reduce(&c, &a, (1<<DIGIT_BIT)-a.dp[0]);
+ mp_dr_reduce(&c, &a, (((mp_digit)1)<<DIGIT_BIT)-a.dp[0]);
if (mp_cmp(&b, &c) != MP_EQ) {
printf("Failed on trial %lu\n", rr); exit(-1);
}
- } while (++rr < 100000);
+ } while (++rr < 500);
printf("Passed DR test for %d digits\n", cnt);
}
-#endif
-
-#ifdef TIMER
- /* temp. turn off TOOM */
- TOOM_MUL_CUTOFF = TOOM_SQR_CUTOFF = 100000;
-
- reset();
- sleep(1);
- CLK_PER_SEC = rdtsc();
-
- printf("CLK_PER_SEC == %lu\n", CLK_PER_SEC);
-
-
- log = fopen("logs/add.log", "w");
- for (cnt = 8; cnt <= 128; cnt += 8) {
- SLEEP;
- mp_rand(&a, cnt);
- mp_rand(&b, cnt);
- reset();
- rr = 0;
- do {
- DO(mp_add(&a,&b,&c));
- rr += 16;
- } while (rdtsc() < (CLK_PER_SEC * 2));
- tt = rdtsc();
- printf("Adding\t\t%4d-bit => %9llu/sec, %9llu ticks\n", mp_count_bits(&a), (((ulong64)rr)*CLK_PER_SEC)/tt, tt);
- fprintf(log, "%d %9llu\n", cnt*DIGIT_BIT, (((ulong64)rr)*CLK_PER_SEC)/tt); fflush(log);
- }
- fclose(log);
-
- log = fopen("logs/sub.log", "w");
- for (cnt = 8; cnt <= 128; cnt += 8) {
- SLEEP;
- mp_rand(&a, cnt);
- mp_rand(&b, cnt);
- reset();
- rr = 0;
- do {
- DO(mp_sub(&a,&b,&c));
- rr += 16;
- } while (rdtsc() < (CLK_PER_SEC * 2));
- tt = rdtsc();
- printf("Subtracting\t\t%4d-bit => %9llu/sec, %9llu ticks\n", mp_count_bits(&a), (((ulong64)rr)*CLK_PER_SEC)/tt, tt);
- fprintf(log, "%d %9llu\n", cnt*DIGIT_BIT, (((ulong64)rr)*CLK_PER_SEC)/tt); fflush(log);
- }
- fclose(log);
-
- /* do mult/square twice, first without karatsuba and second with */
-mult_test:
- old_kara_m = KARATSUBA_MUL_CUTOFF;
- old_kara_s = KARATSUBA_SQR_CUTOFF;
- for (ix = 0; ix < 2; ix++) {
- printf("With%s Karatsuba\n", (ix==0)?"out":"");
-
- KARATSUBA_MUL_CUTOFF = (ix==0)?9999:old_kara_m;
- KARATSUBA_SQR_CUTOFF = (ix==0)?9999:old_kara_s;
-
- log = fopen((ix==0)?"logs/mult.log":"logs/mult_kara.log", "w");
- for (cnt = 32; cnt <= 288; cnt += 8) {
- SLEEP;
- mp_rand(&a, cnt);
- mp_rand(&b, cnt);
- reset();
- rr = 0;
- do {
- DO(mp_mul(&a, &b, &c));
- rr += 16;
- } while (rdtsc() < (CLK_PER_SEC * 2));
- tt = rdtsc();
- printf("Multiplying\t%4d-bit => %9llu/sec, %9llu ticks\n", mp_count_bits(&a), (((ulong64)rr)*CLK_PER_SEC)/tt, tt);
- fprintf(log, "%d %9llu\n", mp_count_bits(&a), (((ulong64)rr)*CLK_PER_SEC)/tt); fflush(log);
- }
- fclose(log);
-
- log = fopen((ix==0)?"logs/sqr.log":"logs/sqr_kara.log", "w");
- for (cnt = 32; cnt <= 288; cnt += 8) {
- SLEEP;
- mp_rand(&a, cnt);
- reset();
- rr = 0;
- do {
- DO(mp_sqr(&a, &b));
- rr += 16;
- } while (rdtsc() < (CLK_PER_SEC * 2));
- tt = rdtsc();
- printf("Squaring\t%4d-bit => %9llu/sec, %9llu ticks\n", mp_count_bits(&a), (((ulong64)rr)*CLK_PER_SEC)/tt, tt);
- fprintf(log, "%d %9llu\n", mp_count_bits(&a), (((ulong64)rr)*CLK_PER_SEC)/tt); fflush(log);
- }
- fclose(log);
-
- }
-expt_test:
- {
- char *primes[] = {
- /* 2K moduli mersenne primes */
- "6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151",
- "531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728127",
- "10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729087",
- "1475979915214180235084898622737381736312066145333169775147771216478570297878078949377407337049389289382748507531496480477281264838760259191814463365330269540496961201113430156902396093989090226259326935025281409614983499388222831448598601834318536230923772641390209490231836446899608210795482963763094236630945410832793769905399982457186322944729636418890623372171723742105636440368218459649632948538696905872650486914434637457507280441823676813517852099348660847172579408422316678097670224011990280170474894487426924742108823536808485072502240519452587542875349976558572670229633962575212637477897785501552646522609988869914013540483809865681250419497686697771007",
- "259117086013202627776246767922441530941818887553125427303974923161874019266586362086201209516800483406550695241733194177441689509238807017410377709597512042313066624082916353517952311186154862265604547691127595848775610568757931191017711408826252153849035830401185072116424747461823031471398340229288074545677907941037288235820705892351068433882986888616658650280927692080339605869308790500409503709875902119018371991620994002568935113136548829739112656797303241986517250116412703509705427773477972349821676443446668383119322540099648994051790241624056519054483690809616061625743042361721863339415852426431208737266591962061753535748892894599629195183082621860853400937932839420261866586142503251450773096274235376822938649407127700846077124211823080804139298087057504713825264571448379371125032081826126566649084251699453951887789613650248405739378594599444335231188280123660406262468609212150349937584782292237144339628858485938215738821232393687046160677362909315071",
- "190797007524439073807468042969529173669356994749940177394741882673528979787005053706368049835514900244303495954950709725762186311224148828811920216904542206960744666169364221195289538436845390250168663932838805192055137154390912666527533007309292687539092257043362517857366624699975402375462954490293259233303137330643531556539739921926201438606439020075174723029056838272505051571967594608350063404495977660656269020823960825567012344189908927956646011998057988548630107637380993519826582389781888135705408653045219655801758081251164080554609057468028203308718724654081055323215860189611391296030471108443146745671967766308925858547271507311563765171008318248647110097614890313562856541784154881743146033909602737947385055355960331855614540900081456378659068370317267696980001187750995491090350108417050917991562167972281070161305972518044872048331306383715094854938415738549894606070722584737978176686422134354526989443028353644037187375385397838259511833166416134323695660367676897722287918773420968982326089026150031515424165462111337527431154890666327374921446276833564519776797633875503548665093914556482031482248883127023777039667707976559857333357013727342079099064400455741830654320379350833236245819348824064783585692924881021978332974949906122664421376034687815350484991",
-
- /* DR moduli */
- "14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368612079",
- "101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411688900243039",
- "736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140821797602431",
- "38564998830736521417281865696453025806593491967131023221754800625044118265468851210705360385717536794615180260494208076605798671660719333199513807806252394423283413430106003596332513246682903994829528690198205120921557533726473585751382193953592127439965050261476810842071573684505878854588706623484573925925903505747545471088867712185004135201289273405614415899438276535626346098904241020877974002916168099951885406379295536200413493190419727789712076165162175783",
- "542189391331696172661670440619180536749994166415993334151601745392193484590296600979602378676624808129613777993466242203025054573692562689251250471628358318743978285860720148446448885701001277560572526947619392551574490839286458454994488665744991822837769918095117129546414124448777033941223565831420390846864429504774477949153794689948747680362212954278693335653935890352619041936727463717926744868338358149568368643403037768649616778526013610493696186055899318268339432671541328195724261329606699831016666359440874843103020666106568222401047720269951530296879490444224546654729111504346660859907296364097126834834235287147",
- "1487259134814709264092032648525971038895865645148901180585340454985524155135260217788758027400478312256339496385275012465661575576202252063145698732079880294664220579764848767704076761853197216563262660046602703973050798218246170835962005598561669706844469447435461092542265792444947706769615695252256130901271870341005768912974433684521436211263358097522726462083917939091760026658925757076733484173202927141441492573799914240222628795405623953109131594523623353044898339481494120112723445689647986475279242446083151413667587008191682564376412347964146113898565886683139407005941383669325997475076910488086663256335689181157957571445067490187939553165903773554290260531009121879044170766615232300936675369451260747671432073394867530820527479172464106442450727640226503746586340279816318821395210726268291535648506190714616083163403189943334431056876038286530365757187367147446004855912033137386225053275419626102417236133948503",
- "1095121115716677802856811290392395128588168592409109494900178008967955253005183831872715423151551999734857184538199864469605657805519106717529655044054833197687459782636297255219742994736751541815269727940751860670268774903340296040006114013971309257028332849679096824800250742691718610670812374272414086863715763724622797509437062518082383056050144624962776302147890521249477060215148275163688301275847155316042279405557632639366066847442861422164832655874655824221577849928863023018366835675399949740429332468186340518172487073360822220449055340582568461568645259954873303616953776393853174845132081121976327462740354930744487429617202585015510744298530101547706821590188733515880733527449780963163909830077616357506845523215289297624086914545378511082534229620116563260168494523906566709418166011112754529766183554579321224940951177394088465596712620076240067370589036924024728375076210477267488679008016579588696191194060127319035195370137160936882402244399699172017835144537488486396906144217720028992863941288217185353914991583400421682751000603596655790990815525126154394344641336397793791497068253936771017031980867706707490224041075826337383538651825493679503771934836094655802776331664261631740148281763487765852746577808019633679",
-
- /* generic unrestricted moduli */
- "17933601194860113372237070562165128350027320072176844226673287945873370751245439587792371960615073855669274087805055507977323024886880985062002853331424203",
- "2893527720709661239493896562339544088620375736490408468011883030469939904368086092336458298221245707898933583190713188177399401852627749210994595974791782790253946539043962213027074922559572312141181787434278708783207966459019479487",
- "347743159439876626079252796797422223177535447388206607607181663903045907591201940478223621722118173270898487582987137708656414344685816179420855160986340457973820182883508387588163122354089264395604796675278966117567294812714812796820596564876450716066283126720010859041484786529056457896367683122960411136319",
- "47266428956356393164697365098120418976400602706072312735924071745438532218237979333351774907308168340693326687317443721193266215155735814510792148768576498491199122744351399489453533553203833318691678263241941706256996197460424029012419012634671862283532342656309677173602509498417976091509154360039893165037637034737020327399910409885798185771003505320583967737293415979917317338985837385734747478364242020380416892056650841470869294527543597349250299539682430605173321029026555546832473048600327036845781970289288898317888427517364945316709081173840186150794397479045034008257793436817683392375274635794835245695887",
- "436463808505957768574894870394349739623346440601945961161254440072143298152040105676491048248110146278752857839930515766167441407021501229924721335644557342265864606569000117714935185566842453630868849121480179691838399545644365571106757731317371758557990781880691336695584799313313687287468894148823761785582982549586183756806449017542622267874275103877481475534991201849912222670102069951687572917937634467778042874315463238062009202992087620963771759666448266532858079402669920025224220613419441069718482837399612644978839925207109870840278194042158748845445131729137117098529028886770063736487420613144045836803985635654192482395882603511950547826439092832800532152534003936926017612446606135655146445620623395788978726744728503058670046885876251527122350275750995227",
- "11424167473351836398078306042624362277956429440521137061889702611766348760692206243140413411077394583180726863277012016602279290144126785129569474909173584789822341986742719230331946072730319555984484911716797058875905400999504305877245849119687509023232790273637466821052576859232452982061831009770786031785669030271542286603956118755585683996118896215213488875253101894663403069677745948305893849505434201763745232895780711972432011344857521691017896316861403206449421332243658855453435784006517202894181640562433575390821384210960117518650374602256601091379644034244332285065935413233557998331562749140202965844219336298970011513882564935538704289446968322281451907487362046511461221329799897350993370560697505809686438782036235372137015731304779072430260986460269894522159103008260495503005267165927542949439526272736586626709581721032189532726389643625590680105784844246152702670169304203783072275089194754889511973916207",
- "1214855636816562637502584060163403830270705000634713483015101384881871978446801224798536155406895823305035467591632531067547890948695117172076954220727075688048751022421198712032848890056357845974246560748347918630050853933697792254955890439720297560693579400297062396904306270145886830719309296352765295712183040773146419022875165382778007040109957609739589875590885701126197906063620133954893216612678838507540777138437797705602453719559017633986486649523611975865005712371194067612263330335590526176087004421363598470302731349138773205901447704682181517904064735636518462452242791676541725292378925568296858010151852326316777511935037531017413910506921922450666933202278489024521263798482237150056835746454842662048692127173834433089016107854491097456725016327709663199738238442164843147132789153725513257167915555162094970853584447993125488607696008169807374736711297007473812256272245489405898470297178738029484459690836250560495461579533254473316340608217876781986188705928270735695752830825527963838355419762516246028680280988020401914551825487349990306976304093109384451438813251211051597392127491464898797406789175453067960072008590614886532333015881171367104445044718144312416815712216611576221546455968770801413440778423979",
- NULL
- };
- log = fopen("logs/expt.log", "w");
- logb = fopen("logs/expt_dr.log", "w");
- logc = fopen("logs/expt_2k.log", "w");
- for (n = 0; primes[n]; n++) {
- SLEEP;
- mp_read_radix(&a, primes[n], 10);
- mp_zero(&b);
- for (rr = 0; rr < mp_count_bits(&a); rr++) {
- mp_mul_2(&b, &b);
- b.dp[0] |= lbit();
- b.used += 1;
- }
- mp_sub_d(&a, 1, &c);
- mp_mod(&b, &c, &b);
- mp_set(&c, 3);
- reset();
- rr = 0;
- do {
- DO(mp_exptmod(&c, &b, &a, &d));
- rr += 16;
- } while (rdtsc() < (CLK_PER_SEC * 2));
- tt = rdtsc();
- mp_sub_d(&a, 1, &e);
- mp_sub(&e, &b, &b);
- mp_exptmod(&c, &b, &a, &e); /* c^(p-1-b) mod a */
- mp_mulmod(&e, &d, &a, &d); /* c^b * c^(p-1-b) == c^p-1 == 1 */
- if (mp_cmp_d(&d, 1)) {
- printf("Different (%d)!!!\n", mp_count_bits(&a));
- draw(&d);
- exit(0);
- }
- printf("Exponentiating\t%4d-bit => %9llu/sec, %9llu ticks\n", mp_count_bits(&a), (((ulong64)rr)*CLK_PER_SEC)/tt, tt);
- fprintf((n < 6) ? logc : (n < 13) ? logb : log, "%d %9llu\n", mp_count_bits(&a), (((ulong64)rr)*CLK_PER_SEC)/tt);
- }
- }
- fclose(log);
- fclose(logb);
- fclose(logc);
-
- log = fopen("logs/invmod.log", "w");
- for (cnt = 4; cnt <= 128; cnt += 4) {
- SLEEP;
- mp_rand(&a, cnt);
- mp_rand(&b, cnt);
-
- do {
- mp_add_d(&b, 1, &b);
- mp_gcd(&a, &b, &c);
- } while (mp_cmp_d(&c, 1) != MP_EQ);
-
- reset();
- rr = 0;
- do {
- DO(mp_invmod(&b, &a, &c));
- rr += 16;
- } while (rdtsc() < (CLK_PER_SEC * 2));
- tt = rdtsc();
- mp_mulmod(&b, &c, &a, &d);
- if (mp_cmp_d(&d, 1) != MP_EQ) {
- printf("Failed to invert\n");
- return 0;
- }
- printf("Inverting mod\t%4d-bit => %9llu/sec, %9llu ticks\n", mp_count_bits(&a), (((ulong64)rr)*CLK_PER_SEC)/tt, tt);
- fprintf(log, "%d %9llu\n", cnt*DIGIT_BIT, (((ulong64)rr)*CLK_PER_SEC)/tt);
- }
- fclose(log);
-
- return 0;
#endif
diff --git a/demo/timing.c b/demo/timing.c
new file mode 100644
index 00000000..865c444a
--- /dev/null
+++ b/demo/timing.c
@@ -0,0 +1,291 @@
+#include <tommath.h>
+#include <time.h>
+
+ulong64 _tt;
+
+#ifdef IOWNANATHLON
+#include <unistd.h>
+#define SLEEP sleep(4)
+#else
+#define SLEEP
+#endif
+
+
+void ndraw(mp_int *a, char *name)
+{
+ char buf[4096];
+ printf("%s: ", name);
+ mp_toradix(a, buf, 64);
+ printf("%s\n", buf);
+}
+
+static void draw(mp_int *a)
+{
+ ndraw(a, "");
+}
+
+
+unsigned long lfsr = 0xAAAAAAAAUL;
+
+int lbit(void)
+{
+ if (lfsr & 0x80000000UL) {
+ lfsr = ((lfsr << 1) ^ 0x8000001BUL) & 0xFFFFFFFFUL;
+ return 1;
+ } else {
+ lfsr <<= 1;
+ return 0;
+ }
+}
+
+#if defined(__i386__) || defined(_M_IX86) || defined(_M_AMD64)
+/* RDTSC from Scott Duplichan */
+static ulong64 TIMFUNC (void)
+ {
+ #if defined __GNUC__
+ #ifdef __i386__
+ ulong64 a;
+ __asm__ __volatile__ ("rdtsc ":"=A" (a));
+ return a;
+ #else /* gcc-IA64 version */
+ unsigned long result;
+ __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory");
+ while (__builtin_expect ((int) result == -1, 0))
+ __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory");
+ return result;
+ #endif
+
+ // Microsoft and Intel Windows compilers
+ #elif defined _M_IX86
+ __asm rdtsc
+ #elif defined _M_AMD64
+ return __rdtsc ();
+ #elif defined _M_IA64
+ #if defined __INTEL_COMPILER
+ #include <ia64intrin.h>
+ #endif
+ return __getReg (3116);
+ #else
+ #error need rdtsc function for this build
+ #endif
+ }
+#else
+#define TIMFUNC clock
+#endif
+
+#define DO(x) x; x;
+//#define DO4(x) DO2(x); DO2(x);
+//#define DO8(x) DO4(x); DO4(x);
+//#define DO(x) DO8(x); DO8(x);
+
+int main(void)
+{
+ ulong64 tt, gg, CLK_PER_SEC;
+ FILE *log, *logb, *logc;
+ mp_int a, b, c, d, e, f;
+ int n, cnt, ix, old_kara_m, old_kara_s;
+ unsigned rr;
+
+ mp_init(&a);
+ mp_init(&b);
+ mp_init(&c);
+ mp_init(&d);
+ mp_init(&e);
+ mp_init(&f);
+
+ srand(time(NULL));
+
+
+ /* temp. turn off TOOM */
+ TOOM_MUL_CUTOFF = TOOM_SQR_CUTOFF = 100000;
+
+ CLK_PER_SEC = TIMFUNC();
+ sleep(1);
+ CLK_PER_SEC = TIMFUNC() - CLK_PER_SEC;
+
+ printf("CLK_PER_SEC == %llu\n", CLK_PER_SEC);
+
+ log = fopen("logs/add.log", "w");
+ for (cnt = 8; cnt <= 128; cnt += 8) {
+ SLEEP;
+ mp_rand(&a, cnt);
+ mp_rand(&b, cnt);
+ rr = 0;
+ tt = -1;
+ do {
+ gg = TIMFUNC();
+ DO(mp_add(&a,&b,&c));
+ gg = (TIMFUNC() - gg)>>1;
+ if (tt > gg) tt = gg;
+ } while (++rr < 100000);
+ printf("Adding\t\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt);
+ fprintf(log, "%d %9llu\n", cnt*DIGIT_BIT, tt); fflush(log);
+ }
+ fclose(log);
+
+ log = fopen("logs/sub.log", "w");
+ for (cnt = 8; cnt <= 128; cnt += 8) {
+ SLEEP;
+ mp_rand(&a, cnt);
+ mp_rand(&b, cnt);
+ rr = 0;
+ tt = -1;
+ do {
+ gg = TIMFUNC();
+ DO(mp_sub(&a,&b,&c));
+ gg = (TIMFUNC() - gg)>>1;
+ if (tt > gg) tt = gg;
+ } while (++rr < 100000);
+
+ printf("Subtracting\t\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt);
+ fprintf(log, "%d %9llu\n", cnt*DIGIT_BIT, tt); fflush(log);
+ }
+ fclose(log);
+
+ /* do mult/square twice, first without karatsuba and second with */
+ old_kara_m = KARATSUBA_MUL_CUTOFF;
+ old_kara_s = KARATSUBA_SQR_CUTOFF;
+ for (ix = 0; ix < 1; ix++) {
+ printf("With%s Karatsuba\n", (ix==0)?"out":"");
+
+ KARATSUBA_MUL_CUTOFF = (ix==0)?9999:old_kara_m;
+ KARATSUBA_SQR_CUTOFF = (ix==0)?9999:old_kara_s;
+
+ log = fopen((ix==0)?"logs/mult.log":"logs/mult_kara.log", "w");
+ for (cnt = 4; cnt <= 288; cnt += 2) {
+ SLEEP;
+ mp_rand(&a, cnt);
+ mp_rand(&b, cnt);
+ rr = 0;
+ tt = -1;
+ do {
+ gg = TIMFUNC();
+ DO(mp_mul(&a, &b, &c));
+ gg = (TIMFUNC() - gg)>>1;
+ if (tt > gg) tt = gg;
+ } while (++rr < 100);
+ printf("Multiplying\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt);
+ fprintf(log, "%d %9llu\n", mp_count_bits(&a), tt); fflush(log);
+ }
+ fclose(log);
+
+ log = fopen((ix==0)?"logs/sqr.log":"logs/sqr_kara.log", "w");
+ for (cnt = 4; cnt <= 288; cnt += 2) {
+ SLEEP;
+ mp_rand(&a, cnt);
+ rr = 0;
+ tt = -1;
+ do {
+ gg = TIMFUNC();
+ DO(mp_sqr(&a, &b));
+ gg = (TIMFUNC() - gg)>>1;
+ if (tt > gg) tt = gg;
+ } while (++rr < 100);
+ printf("Squaring\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt);
+ fprintf(log, "%d %9llu\n", mp_count_bits(&a), tt); fflush(log);
+ }
+ fclose(log);
+
+ }
+
+ {
+ char *primes[] = {
+ /* 2K moduli mersenne primes */
+ "6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151",
+ "531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728127",
+ "10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729087",
+ "1475979915214180235084898622737381736312066145333169775147771216478570297878078949377407337049389289382748507531496480477281264838760259191814463365330269540496961201113430156902396093989090226259326935025281409614983499388222831448598601834318536230923772641390209490231836446899608210795482963763094236630945410832793769905399982457186322944729636418890623372171723742105636440368218459649632948538696905872650486914434637457507280441823676813517852099348660847172579408422316678097670224011990280170474894487426924742108823536808485072502240519452587542875349976558572670229633962575212637477897785501552646522609988869914013540483809865681250419497686697771007",
+ "259117086013202627776246767922441530941818887553125427303974923161874019266586362086201209516800483406550695241733194177441689509238807017410377709597512042313066624082916353517952311186154862265604547691127595848775610568757931191017711408826252153849035830401185072116424747461823031471398340229288074545677907941037288235820705892351068433882986888616658650280927692080339605869308790500409503709875902119018371991620994002568935113136548829739112656797303241986517250116412703509705427773477972349821676443446668383119322540099648994051790241624056519054483690809616061625743042361721863339415852426431208737266591962061753535748892894599629195183082621860853400937932839420261866586142503251450773096274235376822938649407127700846077124211823080804139298087057504713825264571448379371125032081826126566649084251699453951887789613650248405739378594599444335231188280123660406262468609212150349937584782292237144339628858485938215738821232393687046160677362909315071",
+ "190797007524439073807468042969529173669356994749940177394741882673528979787005053706368049835514900244303495954950709725762186311224148828811920216904542206960744666169364221195289538436845390250168663932838805192055137154390912666527533007309292687539092257043362517857366624699975402375462954490293259233303137330643531556539739921926201438606439020075174723029056838272505051571967594608350063404495977660656269020823960825567012344189908927956646011998057988548630107637380993519826582389781888135705408653045219655801758081251164080554609057468028203308718724654081055323215860189611391296030471108443146745671967766308925858547271507311563765171008318248647110097614890313562856541784154881743146033909602737947385055355960331855614540900081456378659068370317267696980001187750995491090350108417050917991562167972281070161305972518044872048331306383715094854938415738549894606070722584737978176686422134354526989443028353644037187375385397838259511833166416134323695660367676897722287918773420968982326089026150031515424165462111337527431154890666327374921446276833564519776797633875503548665093914556482031482248883127023777039667707976559857333357013727342079099064400455741830654320379350833236245819348824064783585692924881021978332974949906122664421376034687815350484991",
+
+ /* DR moduli */
+ "14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368612079",
+ "101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411688900243039",
+ "736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140821797602431",
+ "38564998830736521417281865696453025806593491967131023221754800625044118265468851210705360385717536794615180260494208076605798671660719333199513807806252394423283413430106003596332513246682903994829528690198205120921557533726473585751382193953592127439965050261476810842071573684505878854588706623484573925925903505747545471088867712185004135201289273405614415899438276535626346098904241020877974002916168099951885406379295536200413493190419727789712076165162175783",
+ "542189391331696172661670440619180536749994166415993334151601745392193484590296600979602378676624808129613777993466242203025054573692562689251250471628358318743978285860720148446448885701001277560572526947619392551574490839286458454994488665744991822837769918095117129546414124448777033941223565831420390846864429504774477949153794689948747680362212954278693335653935890352619041936727463717926744868338358149568368643403037768649616778526013610493696186055899318268339432671541328195724261329606699831016666359440874843103020666106568222401047720269951530296879490444224546654729111504346660859907296364097126834834235287147",
+ "1487259134814709264092032648525971038895865645148901180585340454985524155135260217788758027400478312256339496385275012465661575576202252063145698732079880294664220579764848767704076761853197216563262660046602703973050798218246170835962005598561669706844469447435461092542265792444947706769615695252256130901271870341005768912974433684521436211263358097522726462083917939091760026658925757076733484173202927141441492573799914240222628795405623953109131594523623353044898339481494120112723445689647986475279242446083151413667587008191682564376412347964146113898565886683139407005941383669325997475076910488086663256335689181157957571445067490187939553165903773554290260531009121879044170766615232300936675369451260747671432073394867530820527479172464106442450727640226503746586340279816318821395210726268291535648506190714616083163403189943334431056876038286530365757187367147446004855912033137386225053275419626102417236133948503",
+ "1095121115716677802856811290392395128588168592409109494900178008967955253005183831872715423151551999734857184538199864469605657805519106717529655044054833197687459782636297255219742994736751541815269727940751860670268774903340296040006114013971309257028332849679096824800250742691718610670812374272414086863715763724622797509437062518082383056050144624962776302147890521249477060215148275163688301275847155316042279405557632639366066847442861422164832655874655824221577849928863023018366835675399949740429332468186340518172487073360822220449055340582568461568645259954873303616953776393853174845132081121976327462740354930744487429617202585015510744298530101547706821590188733515880733527449780963163909830077616357506845523215289297624086914545378511082534229620116563260168494523906566709418166011112754529766183554579321224940951177394088465596712620076240067370589036924024728375076210477267488679008016579588696191194060127319035195370137160936882402244399699172017835144537488486396906144217720028992863941288217185353914991583400421682751000603596655790990815525126154394344641336397793791497068253936771017031980867706707490224041075826337383538651825493679503771934836094655802776331664261631740148281763487765852746577808019633679",
+
+ /* generic unrestricted moduli */
+ "17933601194860113372237070562165128350027320072176844226673287945873370751245439587792371960615073855669274087805055507977323024886880985062002853331424203",
+ "2893527720709661239493896562339544088620375736490408468011883030469939904368086092336458298221245707898933583190713188177399401852627749210994595974791782790253946539043962213027074922559572312141181787434278708783207966459019479487",
+ "347743159439876626079252796797422223177535447388206607607181663903045907591201940478223621722118173270898487582987137708656414344685816179420855160986340457973820182883508387588163122354089264395604796675278966117567294812714812796820596564876450716066283126720010859041484786529056457896367683122960411136319",
+ "47266428956356393164697365098120418976400602706072312735924071745438532218237979333351774907308168340693326687317443721193266215155735814510792148768576498491199122744351399489453533553203833318691678263241941706256996197460424029012419012634671862283532342656309677173602509498417976091509154360039893165037637034737020327399910409885798185771003505320583967737293415979917317338985837385734747478364242020380416892056650841470869294527543597349250299539682430605173321029026555546832473048600327036845781970289288898317888427517364945316709081173840186150794397479045034008257793436817683392375274635794835245695887",
+ "436463808505957768574894870394349739623346440601945961161254440072143298152040105676491048248110146278752857839930515766167441407021501229924721335644557342265864606569000117714935185566842453630868849121480179691838399545644365571106757731317371758557990781880691336695584799313313687287468894148823761785582982549586183756806449017542622267874275103877481475534991201849912222670102069951687572917937634467778042874315463238062009202992087620963771759666448266532858079402669920025224220613419441069718482837399612644978839925207109870840278194042158748845445131729137117098529028886770063736487420613144045836803985635654192482395882603511950547826439092832800532152534003936926017612446606135655146445620623395788978726744728503058670046885876251527122350275750995227",
+ "11424167473351836398078306042624362277956429440521137061889702611766348760692206243140413411077394583180726863277012016602279290144126785129569474909173584789822341986742719230331946072730319555984484911716797058875905400999504305877245849119687509023232790273637466821052576859232452982061831009770786031785669030271542286603956118755585683996118896215213488875253101894663403069677745948305893849505434201763745232895780711972432011344857521691017896316861403206449421332243658855453435784006517202894181640562433575390821384210960117518650374602256601091379644034244332285065935413233557998331562749140202965844219336298970011513882564935538704289446968322281451907487362046511461221329799897350993370560697505809686438782036235372137015731304779072430260986460269894522159103008260495503005267165927542949439526272736586626709581721032189532726389643625590680105784844246152702670169304203783072275089194754889511973916207",
+ "1214855636816562637502584060163403830270705000634713483015101384881871978446801224798536155406895823305035467591632531067547890948695117172076954220727075688048751022421198712032848890056357845974246560748347918630050853933697792254955890439720297560693579400297062396904306270145886830719309296352765295712183040773146419022875165382778007040109957609739589875590885701126197906063620133954893216612678838507540777138437797705602453719559017633986486649523611975865005712371194067612263330335590526176087004421363598470302731349138773205901447704682181517904064735636518462452242791676541725292378925568296858010151852326316777511935037531017413910506921922450666933202278489024521263798482237150056835746454842662048692127173834433089016107854491097456725016327709663199738238442164843147132789153725513257167915555162094970853584447993125488607696008169807374736711297007473812256272245489405898470297178738029484459690836250560495461579533254473316340608217876781986188705928270735695752830825527963838355419762516246028680280988020401914551825487349990306976304093109384451438813251211051597392127491464898797406789175453067960072008590614886532333015881171367104445044718144312416815712216611576221546455968770801413440778423979",
+ NULL
+ };
+ log = fopen("logs/expt.log", "w");
+ logb = fopen("logs/expt_dr.log", "w");
+ logc = fopen("logs/expt_2k.log", "w");
+ for (n = 0; primes[n]; n++) {
+ SLEEP;
+ mp_read_radix(&a, primes[n], 10);
+ mp_zero(&b);
+ for (rr = 0; rr < (unsigned)mp_count_bits(&a); rr++) {
+ mp_mul_2(&b, &b);
+ b.dp[0] |= lbit();
+ b.used += 1;
+ }
+ mp_sub_d(&a, 1, &c);
+ mp_mod(&b, &c, &b);
+ mp_set(&c, 3);
+ rr = 0;
+ tt = -1;
+ do {
+ gg = TIMFUNC();
+ DO(mp_exptmod(&c, &b, &a, &d));
+ gg = (TIMFUNC() - gg)>>1;
+ if (tt > gg) tt = gg;
+ } while (++rr < 10);
+ mp_sub_d(&a, 1, &e);
+ mp_sub(&e, &b, &b);
+ mp_exptmod(&c, &b, &a, &e); /* c^(p-1-b) mod a */
+ mp_mulmod(&e, &d, &a, &d); /* c^b * c^(p-1-b) == c^p-1 == 1 */
+ if (mp_cmp_d(&d, 1)) {
+ printf("Different (%d)!!!\n", mp_count_bits(&a));
+ draw(&d);
+ exit(0);
+ }
+ printf("Exponentiating\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt);
+ fprintf((n < 6) ? logc : (n < 13) ? logb : log, "%d %9llu\n", mp_count_bits(&a), tt);
+ }
+ }
+ fclose(log);
+ fclose(logb);
+ fclose(logc);
+
+ log = fopen("logs/invmod.log", "w");
+ for (cnt = 4; cnt <= 128; cnt += 4) {
+ SLEEP;
+ mp_rand(&a, cnt);
+ mp_rand(&b, cnt);
+
+ do {
+ mp_add_d(&b, 1, &b);
+ mp_gcd(&a, &b, &c);
+ } while (mp_cmp_d(&c, 1) != MP_EQ);
+
+ rr = 0;
+ tt = -1;
+ do {
+ gg = TIMFUNC();
+ DO(mp_invmod(&b, &a, &c));
+ gg = (TIMFUNC() - gg)>>1;
+ if (tt > gg) tt = gg;
+ } while (++rr < 1000);
+ mp_mulmod(&b, &c, &a, &d);
+ if (mp_cmp_d(&d, 1) != MP_EQ) {
+ printf("Failed to invert\n");
+ return 0;
+ }
+ printf("Inverting mod\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt);
+ fprintf(log, "%d %9llu\n", cnt*DIGIT_BIT, tt);
+ }
+ fclose(log);
+
+ return 0;
+}
+
diff --git a/dep.pl b/dep.pl
new file mode 100644
index 00000000..22266e38
--- /dev/null
+++ b/dep.pl
@@ -0,0 +1,121 @@
+#!/usr/bin/perl
+#
+# Walk through source, add labels and make classes
+#
+#use strict;
+
+my %deplist;
+
+#open class file and write preamble
+open(CLASS, ">tommath_class.h") or die "Couldn't open tommath_class.h for writing\n";
+print CLASS "#if !(defined(LTM1) && defined(LTM2) && defined(LTM3))\n#if defined(LTM2)\n#define LTM3\n#endif\n#if defined(LTM1)\n#define LTM2\n#endif\n#define LTM1\n\n#if defined(LTM_ALL)\n";
+
+foreach my $filename (glob "bn*.c") {
+ my $define = $filename;
+
+ # convert filename to upper case so we can use it as a define
+ $define =~ tr/[a-z]/[A-Z]/;
+ $define =~ tr/\./_/;
+ print CLASS "#define $define\n";
+
+ # now copy text and apply #ifdef as required
+ my $apply = 0;
+ open(SRC, "<$filename");
+ open(OUT, ">tmp");
+
+ # first line will be the #ifdef
+ my $line = <SRC>;
+ if ($line =~ /include/) {
+ print OUT $line;
+ } else {
+ print OUT "#include <tommath.h>\n#ifdef $define\n$line";
+ $apply = 1;
+ }
+ while (<SRC>) {
+ if (!($_ =~ /tommath\.h/)) {
+ print OUT $_;
+ }
+ }
+ if ($apply == 1) {
+ print OUT "#endif\n";
+ }
+ close SRC;
+ close OUT;
+
+ unlink($filename);
+ rename("tmp", $filename);
+}
+print CLASS "#endif\n\n";
+
+# now do classes
+
+foreach my $filename (glob "bn*.c") {
+ open(SRC, "<$filename") or die "Can't open source file!\n";
+
+ # convert filename to upper case so we can use it as a define
+ $filename =~ tr/[a-z]/[A-Z]/;
+ $filename =~ tr/\./_/;
+
+ print CLASS "#if defined($filename)\n";
+ my $list = $filename;
+
+ # scan for mp_* and make classes
+ while (<SRC>) {
+ my $line = $_;
+ while ($line =~ m/(fast_)*(s_)*mp\_[a-z_0-9]*/) {
+ $line = $';
+ # now $& is the match, we want to skip over LTM keywords like
+ # mp_int, mp_word, mp_digit
+ if (!($& eq "mp_digit") && !($& eq "mp_word") && !($& eq "mp_int")) {
+ my $a = $&;
+ $a =~ tr/[a-z]/[A-Z]/;
+ $a = "BN_" . $a . "_C";
+ if (!($list =~ /$a/)) {
+ print CLASS " #define $a\n";
+ }
+ $list = $list . "," . $a;
+ }
+ }
+ }
+ @deplist{$filename} = $list;
+
+ print CLASS "#endif\n\n";
+ close SRC;
+}
+
+print CLASS "#ifdef LTM3\n#define LTM_LAST\n#endif\n#include <tommath_superclass.h>\n#include <tommath_class.h>\n#else\n#define LTM_LAST\n#endif\n";
+close CLASS;
+
+#now let's make a cool call graph...
+
+open(OUT,">callgraph.txt");
+$indent = 0;
+foreach (keys %deplist) {
+ $list = "";
+ draw_func(@deplist{$_});
+ print OUT "\n\n";
+}
+close(OUT);
+
+sub draw_func()
+{
+ my @funcs = split(",", $_[0]);
+ if ($list =~ /@funcs[0]/) {
+ return;
+ } else {
+ $list = $list . @funcs[0];
+ }
+ if ($indent == 0) { }
+ elsif ($indent >= 1) { print OUT "| " x ($indent - 1) . "+--->"; }
+ print OUT @funcs[0] . "\n";
+ shift @funcs;
+ my $temp = $list;
+ foreach my $i (@funcs) {
+ ++$indent;
+ draw_func(@deplist{$i});
+ --$indent;
+ }
+ $list = $temp;
+}
+
+
diff --git a/etc/makefile b/etc/makefile
index 98ddb1ce..99154d86 100644
--- a/etc/makefile
+++ b/etc/makefile
@@ -46,4 +46,5 @@ mont: mont.o
clean:
- rm -f *.log *.o *.obj *.exe pprime tune mersenne drprime tune86 tune86l mont 2kprime pprime.dat
+ rm -f *.log *.o *.obj *.exe pprime tune mersenne drprime tune86 tune86l mont 2kprime pprime.dat \
+ *.da *.dyn *.dpi *~
diff --git a/etc/makefile.icc b/etc/makefile.icc
new file mode 100644
index 00000000..0a507282
--- /dev/null
+++ b/etc/makefile.icc
@@ -0,0 +1,67 @@
+CC = icc
+
+CFLAGS += -I../
+
+# optimize for SPEED
+#
+# -mcpu= can be pentium, pentiumpro (covers PII through PIII) or pentium4
+# -ax? specifies make code specifically for ? but compatible with IA-32
+# -x? specifies compile solely for ? [not specifically IA-32 compatible]
+#
+# where ? is
+# K - PIII
+# W - first P4 [Williamette]
+# N - P4 Northwood
+# P - P4 Prescott
+# B - Blend of P4 and PM [mobile]
+#
+# Default to just generic max opts
+CFLAGS += -O3 -xN -ip
+
+# default lib name (requires install with root)
+# LIBNAME=-ltommath
+
+# libname when you can't install the lib with install
+LIBNAME=../libtommath.a
+
+#provable primes
+pprime: pprime.o
+ $(CC) pprime.o $(LIBNAME) -o pprime
+
+# portable [well requires clock()] tuning app
+tune: tune.o
+ $(CC) tune.o $(LIBNAME) -o tune
+
+# same app but using RDTSC for higher precision [requires 80586+], coff based gcc installs [e.g. ming, cygwin, djgpp]
+tune86: tune.c
+ nasm -f coff timer.asm
+ $(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86
+
+# for cygwin
+tune86c: tune.c
+ nasm -f gnuwin32 timer.asm
+ $(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86
+
+#make tune86 for linux or any ELF format
+tune86l: tune.c
+ nasm -f elf -DUSE_ELF timer.asm
+ $(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86l
+
+# spits out mersenne primes
+mersenne: mersenne.o
+ $(CC) mersenne.o $(LIBNAME) -o mersenne
+
+# fines DR safe primes for the given config
+drprime: drprime.o
+ $(CC) drprime.o $(LIBNAME) -o drprime
+
+# fines 2k safe primes for the given config
+2kprime: 2kprime.o
+ $(CC) 2kprime.o $(LIBNAME) -o 2kprime
+
+mont: mont.o
+ $(CC) mont.o $(LIBNAME) -o mont
+
+
+clean:
+ rm -f *.log *.o *.obj *.exe pprime tune mersenne drprime tune86 tune86l mont 2kprime pprime.dat *.il
diff --git a/etc/tune.c b/etc/tune.c
index 11ce2104..bc101be9 100644
--- a/etc/tune.c
+++ b/etc/tune.c
@@ -8,7 +8,7 @@
/* how many times todo each size mult. Depends on your computer. For slow computers
* this can be low like 5 or 10. For fast [re: Athlon] should be 25 - 50 or so
*/
-#define TIMES 50
+#define TIMES (1UL<<14UL)
#ifndef X86_TIMER
@@ -23,154 +23,85 @@ extern void t_start(void);
extern ulong64 t_read(void);
#endif
-ulong64
-time_mult (int max)
+ulong64 time_mult(int size, int s)
{
- int x, y;
+ unsigned long x;
mp_int a, b, c;
+ ulong64 t1;
mp_init (&a);
mp_init (&b);
mp_init (&c);
+ mp_rand (&a, size);
+ mp_rand (&b, size);
+
+ if (s == 1) {
+ KARATSUBA_MUL_CUTOFF = size;
+ } else {
+ KARATSUBA_MUL_CUTOFF = 100000;
+ }
+
t_start();
- for (x = 32; x <= max; x += 4) {
- mp_rand (&a, x);
- mp_rand (&b, x);
- for (y = 0; y < TIMES; y++) {
- mp_mul (&a, &b, &c);
- }
+ for (x = 0; x < TIMES; x++) {
+ mp_mul(&a,&b,&c);
}
+ t1 = t_read();
mp_clear (&a);
mp_clear (&b);
mp_clear (&c);
- return t_read();
+ return t1;
}
-ulong64
-time_sqr (int max)
+ulong64 time_sqr(int size, int s)
{
- int x, y;
+ unsigned long x;
mp_int a, b;
+ ulong64 t1;
mp_init (&a);
mp_init (&b);
+ mp_rand (&a, size);
+
+ if (s == 1) {
+ KARATSUBA_SQR_CUTOFF = size;
+ } else {
+ KARATSUBA_SQR_CUTOFF = 100000;
+ }
+
t_start();
- for (x = 32; x <= max; x += 4) {
- mp_rand (&a, x);
- for (y = 0; y < TIMES; y++) {
- mp_sqr (&a, &b);
- }
+ for (x = 0; x < TIMES; x++) {
+ mp_sqr(&a,&b);
}
+ t1 = t_read();
mp_clear (&a);
mp_clear (&b);
- return t_read();
+ return t1;
}
int
main (void)
{
- int best_kmult, best_tmult, best_ksquare, best_tsquare, counter;
- ulong64 best, ti;
- FILE *log;
-
- best_kmult = best_ksquare = best_tmult = best_tsquare = 0;
- /* tune multiplication first */
-
- /* effectively turn TOOM off */
- TOOM_SQR_CUTOFF = TOOM_MUL_CUTOFF = 100000;
-
- log = fopen ("mult.log", "w");
- best = -1;
- counter = 16;
- for (KARATSUBA_MUL_CUTOFF = 8; KARATSUBA_MUL_CUTOFF <= 200; KARATSUBA_MUL_CUTOFF++) {
- ti = time_mult (300);
- printf ("%4d : %9llu \r", KARATSUBA_MUL_CUTOFF, ti);
- fprintf (log, "%d, %llu\n", KARATSUBA_MUL_CUTOFF, ti);
- fflush (stdout);
- if (ti < best) {
- printf ("New best: %llu, %d \r", ti, KARATSUBA_MUL_CUTOFF);
- best = ti;
- best_kmult = KARATSUBA_MUL_CUTOFF;
- counter = 16;
- } else if (--counter == 0) {
- printf("No better found in 16 trials.\n");
- break;
- }
- }
- fclose (log);
- printf("Karatsuba Multiplier Cutoff (KARATSUBA_MUL_CUTOFF) == %d\n", best_kmult);
-
- /* tune squaring */
- log = fopen ("sqr.log", "w");
- best = -1;
- counter = 16;
- for (KARATSUBA_SQR_CUTOFF = 8; KARATSUBA_SQR_CUTOFF <= 200; KARATSUBA_SQR_CUTOFF++) {
- ti = time_sqr (300);
- printf ("%4d : %9llu \r", KARATSUBA_SQR_CUTOFF, ti);
- fprintf (log, "%d, %llu\n", KARATSUBA_SQR_CUTOFF, ti);
- fflush (stdout);
- if (ti < best) {
- printf ("New best: %llu, %d \r", ti, KARATSUBA_SQR_CUTOFF);
- best = ti;
- best_ksquare = KARATSUBA_SQR_CUTOFF;
- counter = 16;
- } else if (--counter == 0) {
- printf("No better found in 16 trials.\n");
- break;
- }
- }
- fclose (log);
- printf("Karatsuba Squaring Cutoff (KARATSUBA_SQR_CUTOFF) == %d\n", best_ksquare);
-
- KARATSUBA_MUL_CUTOFF = best_kmult;
- KARATSUBA_SQR_CUTOFF = best_ksquare;
-
- /* tune TOOM mult */
- counter = 16;
- log = fopen ("tmult.log", "w");
- best = -1;
- for (TOOM_MUL_CUTOFF = best_kmult*5; TOOM_MUL_CUTOFF <= 800; TOOM_MUL_CUTOFF++) {
- ti = time_mult (1200);
- printf ("%4d : %9llu \r", TOOM_MUL_CUTOFF, ti);
- fprintf (log, "%d, %llu\n", TOOM_MUL_CUTOFF, ti);
- fflush (stdout);
- if (ti < best) {
- printf ("New best: %llu, %d \r", ti, TOOM_MUL_CUTOFF);
- best = ti;
- best_tmult = TOOM_MUL_CUTOFF;
- counter = 16;
- } else if (--counter == 0) {
- printf("No better found in 16 trials.\n");
- break;
- }
- }
- fclose (log);
- printf("Toom-Cook Multiplier Cutoff (TOOM_MUL_CUTOFF) == %d\n", best_tmult);
-
- /* tune TOOM sqr */
- log = fopen ("tsqr.log", "w");
- best = -1;
- counter = 16;
- for (TOOM_SQR_CUTOFF = best_ksquare*3; TOOM_SQR_CUTOFF <= 800; TOOM_SQR_CUTOFF++) {
- ti = time_sqr (1200);
- printf ("%4d : %9llu \r", TOOM_SQR_CUTOFF, ti);
- fprintf (log, "%d, %llu\n", TOOM_SQR_CUTOFF, ti);
- fflush (stdout);
- if (ti < best) {
- printf ("New best: %llu, %d \r", ti, TOOM_SQR_CUTOFF);
- best = ti;
- best_tsquare = TOOM_SQR_CUTOFF;
- counter = 16;
- } else if (--counter == 0) {
- printf("No better found in 16 trials.\n");
- break;
- }
+ ulong64 t1, t2;
+ int x, y;
+
+ for (x = 8; ; x += 2) {
+ t1 = time_mult(x, 0);
+ t2 = time_mult(x, 1);
+ printf("%d: %9llu %9llu, %9llu\n", x, t1, t2, t2 - t1);
+ if (t2 < t1) break;
}
- fclose (log);
- printf("Toom-Cook Squaring Cutoff (TOOM_SQR_CUTOFF) == %d\n", best_tsquare);
+ y = x;
+ for (x = 8; ; x += 2) {
+ t1 = time_sqr(x, 0);
+ t2 = time_sqr(x, 1);
+ printf("%d: %9llu %9llu, %9llu\n", x, t1, t2, t2 - t1);
+ if (t2 < t1) break;
+ }
+ printf("KARATSUBA_MUL_CUTOFF = %d\n", y);
+ printf("KARATSUBA_SQR_CUTOFF = %d\n", x);
return 0;
}
diff --git a/logs/add.log b/logs/add.log
index e53b415d..d44c4cde 100644
--- a/logs/add.log
+++ b/logs/add.log
@@ -1,16 +1,16 @@
-224 20297071
-448 15151383
-672 13088682
-896 11111587
-1120 9240621
-1344 8221878
-1568 7227434
-1792 6718051
-2016 6042524
-2240 5685200
-2464 5240465
-2688 4818032
-2912 4412794
-3136 4155883
-3360 3927078
-3584 3722138
+224 222
+448 330
+672 436
+896 520
+1120 612
+1344 696
+1568 810
+1792 912
+2016 1006
+2240 1116
+2464 1152
+2688 1284
+2912 1348
+3136 1486
+3360 1580
+3584 1636
diff --git a/logs/addsub.png b/logs/addsub.png
index e733f8d7622be239c70d1708c6ef8c79ec12576d..a5679ac563e6cf347bccc70fb4694ef684375ffc 100644
GIT binary patch
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diff --git a/logs/expt.log b/logs/expt.log
index 2597b486..e69de29b 100644
--- a/logs/expt.log
+++ b/logs/expt.log
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diff --git a/logs/expt.png b/logs/expt.png
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diff --git a/logs/expt_2k.log b/logs/expt_2k.log
index f4c282c2..e69de29b 100644
--- a/logs/expt_2k.log
+++ b/logs/expt_2k.log
@@ -1,6 +0,0 @@
-521 783
-607 585
-1279 138
-2203 39
-3217 15
-4253 6
diff --git a/logs/expt_dr.log b/logs/expt_dr.log
index c552e127..e69de29b 100644
--- a/logs/expt_dr.log
+++ b/logs/expt_dr.log
@@ -1,7 +0,0 @@
-532 1296
-784 551
-1036 283
-1540 109
-2072 52
-3080 18
-4116 7
diff --git a/logs/graphs.dem b/logs/graphs.dem
index d5c9b8ad..dfaf6138 100644
--- a/logs/graphs.dem
+++ b/logs/graphs.dem
@@ -1,17 +1,17 @@
-set terminal png
-set size 1.75
-set ylabel "Operations per Second"
-set xlabel "Operand size (bits)"
-
-set output "addsub.png"
-plot 'add.log' smooth bezier title "Addition", 'sub.log' smooth bezier title "Subtraction"
-
-set output "mult.png"
-plot 'sqr.log' smooth bezier title "Squaring (without Karatsuba)", 'sqr_kara.log' smooth bezier title "Squaring (Karatsuba)", 'mult.log' smooth bezier title "Multiplication (without Karatsuba)", 'mult_kara.log' smooth bezier title "Multiplication (Karatsuba)"
-
-set output "expt.png"
-plot 'expt.log' smooth bezier title "Exptmod (Montgomery)", 'expt_dr.log' smooth bezier title "Exptmod (Dimminished Radix)", 'expt_2k.log' smooth bezier title "Exptmod (2k Reduction)"
-
-set output "invmod.png"
-plot 'invmod.log' smooth bezier title "Modular Inverse"
-
+set terminal png
+set size 1.75
+set ylabel "Cycles per Operation"
+set xlabel "Operand size (bits)"
+
+set output "addsub.png"
+plot 'add.log' smooth bezier title "Addition", 'sub.log' smooth bezier title "Subtraction"
+
+set output "mult.png"
+plot 'sqr.log' smooth bezier title "Squaring (without Karatsuba)", 'sqr_kara.log' smooth bezier title "Squaring (Karatsuba)", 'mult.log' smooth bezier title "Multiplication (without Karatsuba)", 'mult_kara.log' smooth bezier title "Multiplication (Karatsuba)"
+
+set output "expt.png"
+plot 'expt.log' smooth bezier title "Exptmod (Montgomery)", 'expt_dr.log' smooth bezier title "Exptmod (Dimminished Radix)", 'expt_2k.log' smooth bezier title "Exptmod (2k Reduction)"
+
+set output "invmod.png"
+plot 'invmod.log' smooth bezier title "Modular Inverse"
+
diff --git a/logs/invmod.log b/logs/invmod.log
index c9294ef6..e69de29b 100644
--- a/logs/invmod.log
+++ b/logs/invmod.log
@@ -1,32 +0,0 @@
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-2464 469
-2576 263
-2688 247
-2800 227
-2912 354
-3024 336
-3136 312
-3248 296
-3360 166
-3472 155
-3584 248
diff --git a/logs/invmod.png b/logs/invmod.png
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diff --git a/logs/k7/README b/logs/k7/README
deleted file mode 100644
index ea20c813..00000000
--- a/logs/k7/README
+++ /dev/null
@@ -1,13 +0,0 @@
-To use the pretty graphs you have to first build/run the ltmtest from the root directory of the package.
-Todo this type
-
-make timing ; ltmtest
-
-in the root. It will run for a while [about ten minutes on most PCs] and produce a series of .log files in logs/.
-
-After doing that run "gnuplot graphs.dem" to make the PNGs. If you managed todo that all so far just open index.html to view
-them all :-)
-
-Have fun
-
-Tom
\ No newline at end of file
diff --git a/logs/k7/add.log b/logs/k7/add.log
deleted file mode 100644
index 796ab485..00000000
--- a/logs/k7/add.log
+++ /dev/null
@@ -1,16 +0,0 @@
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diff --git a/logs/k7/addsub.png b/logs/k7/addsub.png
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deleted file mode 100644
index 46bb50be..00000000
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diff --git a/logs/k7/expt.png b/logs/k7/expt.png
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diff --git a/logs/k7/expt_dr.log b/logs/k7/expt_dr.log
deleted file mode 100644
index 7df658fc..00000000
--- a/logs/k7/expt_dr.log
+++ /dev/null
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diff --git a/logs/k7/graphs.dem b/logs/k7/graphs.dem
deleted file mode 100644
index c580495c..00000000
--- a/logs/k7/graphs.dem
+++ /dev/null
@@ -1,17 +0,0 @@
-set terminal png color
-set size 1.75
-set ylabel "Operations per Second"
-set xlabel "Operand size (bits)"
-
-set output "addsub.png"
-plot 'add.log' smooth bezier title "Addition", 'sub.log' smooth bezier title "Subtraction"
-
-set output "mult.png"
-plot 'sqr.log' smooth bezier title "Squaring (without Karatsuba)", 'sqr_kara.log' smooth bezier title "Squaring (Karatsuba)", 'mult.log' smooth bezier title "Multiplication (without Karatsuba)", 'mult_kara.log' smooth bezier title "Multiplication (Karatsuba)"
-
-set output "expt.png"
-plot 'expt.log' smooth bezier title "Exptmod (Montgomery)", 'expt_dr.log' smooth bezier title "Exptmod (Dimminished Radix)"
-
-set output "invmod.png"
-plot 'invmod.log' smooth bezier title "Modular Inverse"
-
diff --git a/logs/k7/index.html b/logs/k7/index.html
deleted file mode 100644
index 19fe403e..00000000
--- a/logs/k7/index.html
+++ /dev/null
@@ -1,24 +0,0 @@
-<html>
-<head>
-<title>LibTomMath Log Plots</title>
-</head>
-<body>
-
-<h1>Addition and Subtraction</h1>
-<center><img src=addsub.png></center>
-<hr>
-
-<h1>Multipliers</h1>
-<center><img src=mult.png></center>
-<hr>
-
-<h1>Exptmod</h1>
-<center><img src=expt.png></center>
-<hr>
-
-<h1>Modular Inverse</h1>
-<center><img src=invmod.png></center>
-<hr>
-
-</body>
-</html>
\ No newline at end of file
diff --git a/logs/k7/invmod.log b/logs/k7/invmod.log
deleted file mode 100644
index d1198fb9..00000000
--- a/logs/k7/invmod.log
+++ /dev/null
@@ -1,32 +0,0 @@
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-224 8192
-336 5320
-448 3560
-560 2728
-672 2064
-784 1704
-896 2176
-1008 1184
-1120 976
-1232 1280
-1344 1176
-1456 624
-1568 912
-1680 504
-1792 452
-1904 658
-2016 608
-2128 336
-2240 312
-2352 288
-2464 264
-2576 408
-2688 376
-2800 354
-2912 198
-3024 307
-3136 173
-3248 162
-3360 256
-3472 145
-3584 226
diff --git a/logs/k7/invmod.png b/logs/k7/invmod.png
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diff --git a/logs/k7/mult.log b/logs/k7/mult.log
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diff --git a/logs/mult_kara.log b/logs/mult_kara.log
index 6edc4394..086feaff 100644
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diff --git a/logs/p4/README b/logs/p4/README
deleted file mode 100644
index ea20c813..00000000
--- a/logs/p4/README
+++ /dev/null
@@ -1,13 +0,0 @@
-To use the pretty graphs you have to first build/run the ltmtest from the root directory of the package.
-Todo this type
-
-make timing ; ltmtest
-
-in the root. It will run for a while [about ten minutes on most PCs] and produce a series of .log files in logs/.
-
-After doing that run "gnuplot graphs.dem" to make the PNGs. If you managed todo that all so far just open index.html to view
-them all :-)
-
-Have fun
-
-Tom
\ No newline at end of file
diff --git a/logs/p4/add.log b/logs/p4/add.log
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diff --git a/logs/p4/expt_dr.log b/logs/p4/expt_dr.log
deleted file mode 100644
index 2f5f6a3a..00000000
--- a/logs/p4/expt_dr.log
+++ /dev/null
@@ -1,7 +0,0 @@
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-784 158
-1036 79
-1540 27
-2072 12
-3080 4
-4116 1
diff --git a/logs/p4/graphs.dem b/logs/p4/graphs.dem
deleted file mode 100644
index c580495c..00000000
--- a/logs/p4/graphs.dem
+++ /dev/null
@@ -1,17 +0,0 @@
-set terminal png color
-set size 1.75
-set ylabel "Operations per Second"
-set xlabel "Operand size (bits)"
-
-set output "addsub.png"
-plot 'add.log' smooth bezier title "Addition", 'sub.log' smooth bezier title "Subtraction"
-
-set output "mult.png"
-plot 'sqr.log' smooth bezier title "Squaring (without Karatsuba)", 'sqr_kara.log' smooth bezier title "Squaring (Karatsuba)", 'mult.log' smooth bezier title "Multiplication (without Karatsuba)", 'mult_kara.log' smooth bezier title "Multiplication (Karatsuba)"
-
-set output "expt.png"
-plot 'expt.log' smooth bezier title "Exptmod (Montgomery)", 'expt_dr.log' smooth bezier title "Exptmod (Dimminished Radix)"
-
-set output "invmod.png"
-plot 'invmod.log' smooth bezier title "Modular Inverse"
-
diff --git a/logs/p4/index.html b/logs/p4/index.html
deleted file mode 100644
index 19fe403e..00000000
--- a/logs/p4/index.html
+++ /dev/null
@@ -1,24 +0,0 @@
-<html>
-<head>
-<title>LibTomMath Log Plots</title>
-</head>
-<body>
-
-<h1>Addition and Subtraction</h1>
-<center><img src=addsub.png></center>
-<hr>
-
-<h1>Multipliers</h1>
-<center><img src=mult.png></center>
-<hr>
-
-<h1>Exptmod</h1>
-<center><img src=expt.png></center>
-<hr>
-
-<h1>Modular Inverse</h1>
-<center><img src=invmod.png></center>
-<hr>
-
-</body>
-</html>
\ No newline at end of file
diff --git a/logs/p4/invmod.log b/logs/p4/invmod.log
deleted file mode 100644
index 096087b0..00000000
--- a/logs/p4/invmod.log
+++ /dev/null
@@ -1,32 +0,0 @@
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diff --git a/logs/p4/invmod.png b/logs/p4/invmod.png
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diff --git a/logs/p4/mult_kara.log b/logs/p4/mult_kara.log
deleted file mode 100644
index e1d50a65..00000000
--- a/logs/p4/mult_kara.log
+++ /dev/null
@@ -1,17 +0,0 @@
-896 77752
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-2240 14704
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diff --git a/logs/p4/sqr.log b/logs/p4/sqr.log
deleted file mode 100644
index b133fb3d..00000000
--- a/logs/p4/sqr.log
+++ /dev/null
@@ -1,17 +0,0 @@
-896 128088
-1344 63640
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diff --git a/logs/p4/sqr_kara.log b/logs/p4/sqr_kara.log
deleted file mode 100644
index 13e4f3e5..00000000
--- a/logs/p4/sqr_kara.log
+++ /dev/null
@@ -1,17 +0,0 @@
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diff --git a/logs/p4/sub.log b/logs/p4/sub.log
deleted file mode 100644
index 424de325..00000000
--- a/logs/p4/sub.log
+++ /dev/null
@@ -1,16 +0,0 @@
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diff --git a/logs/sqr.log b/logs/sqr.log
index 81fa612f..3e175acd 100644
--- a/logs/sqr.log
+++ b/logs/sqr.log
@@ -1,33 +1,143 @@
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diff --git a/logs/sqr_kara.log b/logs/sqr_kara.log
index 3b547cf3..cafe4582 100644
--- a/logs/sqr_kara.log
+++ b/logs/sqr_kara.log
@@ -1,33 +1,33 @@
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diff --git a/logs/sub.log b/logs/sub.log
index f1ade94b..cf2bcd6a 100644
--- a/logs/sub.log
+++ b/logs/sub.log
@@ -1,16 +1,16 @@
-224 16370431
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diff --git a/makefile b/makefile
index 07b7842b..4fe22569 100644
--- a/makefile
+++ b/makefile
@@ -12,7 +12,10 @@ CFLAGS += -O3 -funroll-loops
#x86 optimizations [should be valid for any GCC install though]
CFLAGS += -fomit-frame-pointer
-VERSION=0.30
+#debug
+#CFLAGS += -g3
+
+VERSION=0.32
default: libtommath.a
@@ -20,7 +23,7 @@ default: libtommath.a
LIBNAME=libtommath.a
HEADERS=tommath.h
-#LIBPATH-The directory for libtomcrypt to be installed to.
+#LIBPATH-The directory for libtommath to be installed to.
#INCPATH-The directory to install the header files for libtommath.
#DATAPATH-The directory to install the pdf docs.
DESTDIR=
@@ -50,14 +53,38 @@ bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
-bn_mp_init_multi.o bn_mp_clear_multi.o bn_prime_sizes_tab.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
+bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \
-bn_mp_init_set_int.o
+bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o
libtommath.a: $(OBJECTS)
$(AR) $(ARFLAGS) libtommath.a $(OBJECTS)
ranlib libtommath.a
+
+#make a profiled library (takes a while!!!)
+#
+# This will build the library with profile generation
+# then run the test demo and rebuild the library.
+#
+# So far I've seen improvements in the MP math
+profiled:
+ make CFLAGS="$(CFLAGS) -fprofile-arcs -DTESTING" timing
+ ./ltmtest
+ rm -f *.a *.o ltmtest
+ make CFLAGS="$(CFLAGS) -fbranch-probabilities"
+
+#make a single object profiled library
+profiled_single:
+ perl gen.pl
+ $(CC) $(CFLAGS) -fprofile-arcs -DTESTING -c mpi.c -o mpi.o
+ $(CC) $(CFLAGS) -DTESTING -DTIMER demo/timing.c mpi.o -o ltmtest
+ ./ltmtest
+ rm -f *.o ltmtest
+ $(CC) $(CFLAGS) -fbranch-probabilities -DTESTING -c mpi.c -o mpi.o
+ $(AR) $(ARFLAGS) libtommath.a mpi.o
+ ranlib libtommath.a
+
install: libtommath.a
install -d -g root -o root $(DESTDIR)$(LIBPATH)
install -d -g root -o root $(DESTDIR)$(INCPATH)
@@ -71,7 +98,7 @@ mtest: test
cd mtest ; $(CC) $(CFLAGS) mtest.c -o mtest -s
timing: libtommath.a
- $(CC) $(CFLAGS) -DTIMER demo/demo.c libtommath.a -o ltmtest -s
+ $(CC) $(CFLAGS) -DTIMER demo/timing.c libtommath.a -o ltmtest -s
# makes the LTM book DVI file, requires tetex, perl and makeindex [part of tetex I think]
docdvi: tommath.src
@@ -106,10 +133,14 @@ mandvi: bn.tex
manual: mandvi
pdflatex bn >/dev/null
rm -f bn.aux bn.dvi bn.log bn.idx bn.lof bn.out bn.toc
-
+
+pretty:
+ perl pretty.build
+
clean:
rm -f *.bat *.pdf *.o *.a *.obj *.lib *.exe *.dll etclib/*.o demo/demo.o test ltmtest mpitest mtest/mtest mtest/mtest.exe \
- *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c
+ *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c *.da *.dyn *.dpi tommath.tex `find -type f | grep [~] | xargs` *.lo *.la
+ rm -rf .libs
cd etc ; make clean
cd pics ; make clean
diff --git a/makefile.bcc b/makefile.bcc
index 6874d2f3..775e9ff2 100644
--- a/makefile.bcc
+++ b/makefile.bcc
@@ -29,8 +29,9 @@ bn_mp_toom_mul.obj bn_mp_toom_sqr.obj bn_mp_div_3.obj bn_s_mp_exptmod.obj \
bn_mp_reduce_2k.obj bn_mp_reduce_is_2k.obj bn_mp_reduce_2k_setup.obj \
bn_mp_radix_smap.obj bn_mp_read_radix.obj bn_mp_toradix.obj bn_mp_radix_size.obj \
bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_cnt_lsb.obj bn_error.obj \
-bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_prime_sizes_tab.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \
-bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj
+bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \
+bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj \
+bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj
TARGET = libtommath.lib
diff --git a/makefile.cygwin_dll b/makefile.cygwin_dll
index e5ab814c..c90e5d99 100644
--- a/makefile.cygwin_dll
+++ b/makefile.cygwin_dll
@@ -34,8 +34,9 @@ bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
-bn_mp_init_multi.o bn_mp_clear_multi.o bn_prime_sizes_tab.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
-bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o
+bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
+bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \
+bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o
# make a Windows DLL via Cygwin
windll: $(OBJECTS)
diff --git a/makefile.icc b/makefile.icc
new file mode 100644
index 00000000..09117b74
--- /dev/null
+++ b/makefile.icc
@@ -0,0 +1,110 @@
+#Makefile for ICC
+#
+#Tom St Denis
+CC=icc
+
+CFLAGS += -I./
+
+# optimize for SPEED
+#
+# -mcpu= can be pentium, pentiumpro (covers PII through PIII) or pentium4
+# -ax? specifies make code specifically for ? but compatible with IA-32
+# -x? specifies compile solely for ? [not specifically IA-32 compatible]
+#
+# where ? is
+# K - PIII
+# W - first P4 [Williamette]
+# N - P4 Northwood
+# P - P4 Prescott
+# B - Blend of P4 and PM [mobile]
+#
+# Default to just generic max opts
+CFLAGS += -O3 -xN
+
+default: libtommath.a
+
+#default files to install
+LIBNAME=libtommath.a
+HEADERS=tommath.h
+
+#LIBPATH-The directory for libtomcrypt to be installed to.
+#INCPATH-The directory to install the header files for libtommath.
+#DATAPATH-The directory to install the pdf docs.
+DESTDIR=
+LIBPATH=/usr/lib
+INCPATH=/usr/include
+DATAPATH=/usr/share/doc/libtommath/pdf
+
+OBJECTS=bncore.o bn_mp_init.o bn_mp_clear.o bn_mp_exch.o bn_mp_grow.o bn_mp_shrink.o \
+bn_mp_clamp.o bn_mp_zero.o bn_mp_set.o bn_mp_set_int.o bn_mp_init_size.o bn_mp_copy.o \
+bn_mp_init_copy.o bn_mp_abs.o bn_mp_neg.o bn_mp_cmp_mag.o bn_mp_cmp.o bn_mp_cmp_d.o \
+bn_mp_rshd.o bn_mp_lshd.o bn_mp_mod_2d.o bn_mp_div_2d.o bn_mp_mul_2d.o bn_mp_div_2.o \
+bn_mp_mul_2.o bn_s_mp_add.o bn_s_mp_sub.o bn_fast_s_mp_mul_digs.o bn_s_mp_mul_digs.o \
+bn_fast_s_mp_mul_high_digs.o bn_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_s_mp_sqr.o \
+bn_mp_add.o bn_mp_sub.o bn_mp_karatsuba_mul.o bn_mp_mul.o bn_mp_karatsuba_sqr.o \
+bn_mp_sqr.o bn_mp_div.o bn_mp_mod.o bn_mp_add_d.o bn_mp_sub_d.o bn_mp_mul_d.o \
+bn_mp_div_d.o bn_mp_mod_d.o bn_mp_expt_d.o bn_mp_addmod.o bn_mp_submod.o \
+bn_mp_mulmod.o bn_mp_sqrmod.o bn_mp_gcd.o bn_mp_lcm.o bn_fast_mp_invmod.o bn_mp_invmod.o \
+bn_mp_reduce.o bn_mp_montgomery_setup.o bn_fast_mp_montgomery_reduce.o bn_mp_montgomery_reduce.o \
+bn_mp_exptmod_fast.o bn_mp_exptmod.o bn_mp_2expt.o bn_mp_n_root.o bn_mp_jacobi.o bn_reverse.o \
+bn_mp_count_bits.o bn_mp_read_unsigned_bin.o bn_mp_read_signed_bin.o bn_mp_to_unsigned_bin.o \
+bn_mp_to_signed_bin.o bn_mp_unsigned_bin_size.o bn_mp_signed_bin_size.o \
+bn_mp_xor.o bn_mp_and.o bn_mp_or.o bn_mp_rand.o bn_mp_montgomery_calc_normalization.o \
+bn_mp_prime_is_divisible.o bn_prime_tab.o bn_mp_prime_fermat.o bn_mp_prime_miller_rabin.o \
+bn_mp_prime_is_prime.o bn_mp_prime_next_prime.o bn_mp_dr_reduce.o \
+bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \
+bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
+bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
+bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
+bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
+bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
+bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \
+bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o
+
+libtommath.a: $(OBJECTS)
+ $(AR) $(ARFLAGS) libtommath.a $(OBJECTS)
+ ranlib libtommath.a
+
+#make a profiled library (takes a while!!!)
+#
+# This will build the library with profile generation
+# then run the test demo and rebuild the library.
+#
+# So far I've seen improvements in the MP math
+profiled:
+ make -f makefile.icc CFLAGS="$(CFLAGS) -prof_gen -DTESTING" timing
+ ./ltmtest
+ rm -f *.a *.o ltmtest
+ make -f makefile.icc CFLAGS="$(CFLAGS) -prof_use"
+
+#make a single object profiled library
+profiled_single:
+ perl gen.pl
+ $(CC) $(CFLAGS) -prof_gen -DTESTING -c mpi.c -o mpi.o
+ $(CC) $(CFLAGS) -DTESTING -DTIMER demo/demo.c mpi.o -o ltmtest
+ ./ltmtest
+ rm -f *.o ltmtest
+ $(CC) $(CFLAGS) -prof_use -ip -DTESTING -c mpi.c -o mpi.o
+ $(AR) $(ARFLAGS) libtommath.a mpi.o
+ ranlib libtommath.a
+
+install: libtommath.a
+ install -d -g root -o root $(DESTDIR)$(LIBPATH)
+ install -d -g root -o root $(DESTDIR)$(INCPATH)
+ install -g root -o root $(LIBNAME) $(DESTDIR)$(LIBPATH)
+ install -g root -o root $(HEADERS) $(DESTDIR)$(INCPATH)
+
+test: libtommath.a demo/demo.o
+ $(CC) demo/demo.o libtommath.a -o test
+
+mtest: test
+ cd mtest ; $(CC) $(CFLAGS) mtest.c -o mtest
+
+timing: libtommath.a
+ $(CC) $(CFLAGS) -DTIMER demo/timing.c libtommath.a -o ltmtest
+
+clean:
+ rm -f *.bat *.pdf *.o *.a *.obj *.lib *.exe *.dll etclib/*.o demo/demo.o test ltmtest mpitest mtest/mtest mtest/mtest.exe \
+ *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c *.il etc/*.il *.dyn
+ cd etc ; make clean
+ cd pics ; make clean
diff --git a/makefile.msvc b/makefile.msvc
index beeb77e4..cf599438 100644
--- a/makefile.msvc
+++ b/makefile.msvc
@@ -28,8 +28,9 @@ bn_mp_toom_mul.obj bn_mp_toom_sqr.obj bn_mp_div_3.obj bn_s_mp_exptmod.obj \
bn_mp_reduce_2k.obj bn_mp_reduce_is_2k.obj bn_mp_reduce_2k_setup.obj \
bn_mp_radix_smap.obj bn_mp_read_radix.obj bn_mp_toradix.obj bn_mp_radix_size.obj \
bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_cnt_lsb.obj bn_error.obj \
-bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_prime_sizes_tab.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \
-bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj
+bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \
+bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj \
+bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj
library: $(OBJECTS)
lib /out:tommath.lib $(OBJECTS)
diff --git a/makefile.shared b/makefile.shared
new file mode 100644
index 00000000..96bbf329
--- /dev/null
+++ b/makefile.shared
@@ -0,0 +1,74 @@
+#Makefile for GCC
+#
+#Tom St Denis
+VERSION=0:32
+
+CC = libtool --mode=compile gcc
+
+CFLAGS += -I./ -Wall -W -Wshadow -Wsign-compare
+
+#for speed
+CFLAGS += -O3 -funroll-loops
+
+#for size
+#CFLAGS += -Os
+
+#x86 optimizations [should be valid for any GCC install though]
+CFLAGS += -fomit-frame-pointer
+
+default: libtommath.la
+
+#default files to install
+LIBNAME=libtommath.la
+HEADERS=tommath.h
+
+#LIBPATH-The directory for libtommath to be installed to.
+#INCPATH-The directory to install the header files for libtommath.
+#DATAPATH-The directory to install the pdf docs.
+DESTDIR=
+LIBPATH=/usr/lib
+INCPATH=/usr/include
+DATAPATH=/usr/share/doc/libtommath/pdf
+
+OBJECTS=bncore.o bn_mp_init.o bn_mp_clear.o bn_mp_exch.o bn_mp_grow.o bn_mp_shrink.o \
+bn_mp_clamp.o bn_mp_zero.o bn_mp_set.o bn_mp_set_int.o bn_mp_init_size.o bn_mp_copy.o \
+bn_mp_init_copy.o bn_mp_abs.o bn_mp_neg.o bn_mp_cmp_mag.o bn_mp_cmp.o bn_mp_cmp_d.o \
+bn_mp_rshd.o bn_mp_lshd.o bn_mp_mod_2d.o bn_mp_div_2d.o bn_mp_mul_2d.o bn_mp_div_2.o \
+bn_mp_mul_2.o bn_s_mp_add.o bn_s_mp_sub.o bn_fast_s_mp_mul_digs.o bn_s_mp_mul_digs.o \
+bn_fast_s_mp_mul_high_digs.o bn_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_s_mp_sqr.o \
+bn_mp_add.o bn_mp_sub.o bn_mp_karatsuba_mul.o bn_mp_mul.o bn_mp_karatsuba_sqr.o \
+bn_mp_sqr.o bn_mp_div.o bn_mp_mod.o bn_mp_add_d.o bn_mp_sub_d.o bn_mp_mul_d.o \
+bn_mp_div_d.o bn_mp_mod_d.o bn_mp_expt_d.o bn_mp_addmod.o bn_mp_submod.o \
+bn_mp_mulmod.o bn_mp_sqrmod.o bn_mp_gcd.o bn_mp_lcm.o bn_fast_mp_invmod.o bn_mp_invmod.o \
+bn_mp_reduce.o bn_mp_montgomery_setup.o bn_fast_mp_montgomery_reduce.o bn_mp_montgomery_reduce.o \
+bn_mp_exptmod_fast.o bn_mp_exptmod.o bn_mp_2expt.o bn_mp_n_root.o bn_mp_jacobi.o bn_reverse.o \
+bn_mp_count_bits.o bn_mp_read_unsigned_bin.o bn_mp_read_signed_bin.o bn_mp_to_unsigned_bin.o \
+bn_mp_to_signed_bin.o bn_mp_unsigned_bin_size.o bn_mp_signed_bin_size.o \
+bn_mp_xor.o bn_mp_and.o bn_mp_or.o bn_mp_rand.o bn_mp_montgomery_calc_normalization.o \
+bn_mp_prime_is_divisible.o bn_prime_tab.o bn_mp_prime_fermat.o bn_mp_prime_miller_rabin.o \
+bn_mp_prime_is_prime.o bn_mp_prime_next_prime.o bn_mp_dr_reduce.o \
+bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \
+bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \
+bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \
+bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \
+bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \
+bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \
+bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \
+bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o
+
+libtommath.la: $(OBJECTS)
+ libtool --mode=link gcc *.lo -o libtommath.la -rpath $(LIBPATH) -version-info $(VERSION)
+ libtool --mode=link gcc *.o -o libtommath.a
+ libtool --mode=install install -c libtommath.la $(LIBPATH)/libtommath.la
+ install -d -g root -o root $(DESTDIR)$(INCPATH)
+ install -g root -o root $(HEADERS) $(DESTDIR)$(INCPATH)
+
+test: libtommath.a demo/demo.o
+ gcc $(CFLAGS) -c demo/demo.c -o demo/demo.o
+ libtool --mode=link gcc -o test demo/demo.o libtommath.la
+
+mtest: test
+ cd mtest ; gcc $(CFLAGS) mtest.c -o mtest -s
+
+timing: libtommath.la
+ gcc $(CFLAGS) -DTIMER demo/timing.c libtommath.a -o ltmtest -s
diff --git a/mtest/mtest.c b/mtest/mtest.c
index 2c248256..ef0e0933 100644
--- a/mtest/mtest.c
+++ b/mtest/mtest.c
@@ -58,7 +58,7 @@ void rand_num2(mp_int *a)
int n, size;
unsigned char buf[2048];
- size = 1 + ((fgetc(rng)<<8) + fgetc(rng)) % 97;
+ size = 10 + ((fgetc(rng)<<8) + fgetc(rng)) % 97;
buf[0] = (fgetc(rng)&1)?1:0;
fread(buf+1, 1, size, rng);
while (buf[1] == 0) buf[1] = fgetc(rng);
@@ -109,11 +109,12 @@ int main(void)
t1 = clock();
for (;;) {
+#if 0
if (clock() - t1 > CLOCKS_PER_SEC) {
sleep(2);
t1 = clock();
}
-
+#endif
n = fgetc(rng) % 15;
if (n == 0) {
diff --git a/poster.pdf b/poster.pdf
index 3731bd2bdaa53bb2052ef8258e5d97368b1b413c..60999daef1a6991036d5a8836971cca7180f9aac 100644
GIT binary patch
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diff --git a/pre_gen/mpi.c b/pre_gen/mpi.c
index 1f9997f1..78a73f09 100644
--- a/pre_gen/mpi.c
+++ b/pre_gen/mpi.c
@@ -1,4 +1,6 @@
/* Start: bn_error.c */
+#include <tommath.h>
+#ifdef BN_ERROR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -13,7 +15,6 @@
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
static const struct {
int code;
@@ -40,10 +41,13 @@ char *mp_error_to_string(int code)
return "Invalid error code";
}
+#endif
/* End: bn_error.c */
/* Start: bn_fast_mp_invmod.c */
+#include <tommath.h>
+#ifdef BN_FAST_MP_INVMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -58,12 +62,11 @@ char *mp_error_to_string(int code)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes the modular inverse via binary extended euclidean algorithm,
* that is c = 1/a mod b
*
- * Based on mp_invmod except this is optimized for the case where b is
+ * Based on slow invmod except this is optimized for the case where b is
* odd as per HAC Note 14.64 on pp. 610
*/
int
@@ -187,10 +190,13 @@ top:
__ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
return res;
}
+#endif
/* End: bn_fast_mp_invmod.c */
/* Start: bn_fast_mp_montgomery_reduce.c */
+#include <tommath.h>
+#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -205,11 +211,10 @@ __ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes xR**-1 == x (mod N) via Montgomery Reduction
*
- * This is an optimized implementation of mp_montgomery_reduce
+ * This is an optimized implementation of montgomery_reduce
* which uses the comba method to quickly calculate the columns of the
* reduction.
*
@@ -358,10 +363,13 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
}
return MP_OKAY;
}
+#endif
/* End: bn_fast_mp_montgomery_reduce.c */
/* Start: bn_fast_s_mp_mul_digs.c */
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_MUL_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -376,7 +384,6 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Fast (comba) multiplier
*
@@ -397,8 +404,9 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
int
fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
- int olduse, res, pa, ix;
- mp_word W[MP_WARRAY];
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY];
+ register mp_word _W;
/* grow the destination as required */
if (c->alloc < digs) {
@@ -407,82 +415,52 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
}
}
- /* clear temp buf (the columns) */
- memset (W, 0, sizeof (mp_word) * digs);
-
- /* calculate the columns */
- pa = a->used;
- for (ix = 0; ix < pa; ix++) {
- /* this multiplier has been modified to allow you to
- * control how many digits of output are produced.
- * So at most we want to make upto "digs" digits of output.
- *
- * this adds products to distinct columns (at ix+iy) of W
- * note that each step through the loop is not dependent on
- * the previous which means the compiler can easily unroll
- * the loop without scheduling problems
- */
- {
- register mp_digit tmpx, *tmpy;
- register mp_word *_W;
- register int iy, pb;
+ /* number of output digits to produce */
+ pa = MIN(digs, a->used + b->used);
- /* alias for the the word on the left e.g. A[ix] * A[iy] */
- tmpx = a->dp[ix];
+ /* clear the carry */
+ _W = 0;
+ for (ix = 0; ix <= pa; ix++) {
+ int tx, ty;
+ int iy;
+ mp_digit *tmpx, *tmpy;
- /* alias for the right side */
- tmpy = b->dp;
+ /* get offsets into the two bignums */
+ ty = MIN(b->used-1, ix);
+ tx = ix - ty;
- /* alias for the columns, each step through the loop adds a new
- term to each column
- */
- _W = W + ix;
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = b->dp + ty;
- /* the number of digits is limited by their placement. E.g.
- we avoid multiplying digits that will end up above the # of
- digits of precision requested
+ /* this is the number of times the loop will iterrate, essentially its
+ while (tx++ < a->used && ty-- >= 0) { ... }
*/
- pb = MIN (b->used, digs - ix);
+ iy = MIN(a->used-tx, ty+1);
- for (iy = 0; iy < pb; iy++) {
- *_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++);
+ /* execute loop */
+ for (iz = 0; iz < iy; ++iz) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
}
- }
+ /* store term */
+ W[ix] = ((mp_digit)_W) & MP_MASK;
+
+ /* make next carry */
+ _W = _W >> ((mp_word)DIGIT_BIT);
}
/* setup dest */
- olduse = c->used;
+ olduse = c->used;
c->used = digs;
{
register mp_digit *tmpc;
-
- /* At this point W[] contains the sums of each column. To get the
- * correct result we must take the extra bits from each column and
- * carry them down
- *
- * Note that while this adds extra code to the multiplier it
- * saves time since the carry propagation is removed from the
- * above nested loop.This has the effect of reducing the work
- * from N*(N+N*c)==N**2 + c*N**2 to N**2 + N*c where c is the
- * cost of the shifting. On very small numbers this is slower
- * but on most cryptographic size numbers it is faster.
- *
- * In this particular implementation we feed the carries from
- * behind which means when the loop terminates we still have one
- * last digit to copy
- */
tmpc = c->dp;
- for (ix = 1; ix < digs; ix++) {
- /* forward the carry from the previous temp */
- W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
-
+ for (ix = 0; ix < digs; ix++) {
/* now extract the previous digit [below the carry] */
- *tmpc++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
+ *tmpc++ = W[ix];
}
- /* fetch the last digit */
- *tmpc++ = (mp_digit) (W[digs - 1] & ((mp_word) MP_MASK));
/* clear unused digits [that existed in the old copy of c] */
for (; ix < olduse; ix++) {
@@ -492,10 +470,13 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
mp_clamp (c);
return MP_OKAY;
}
+#endif
/* End: bn_fast_s_mp_mul_digs.c */
/* Start: bn_fast_s_mp_mul_high_digs.c */
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -510,10 +491,9 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
- #include <tommath.h>
-/* this is a modified version of fast_s_mp_mul_digs that only produces
- * output digits *above* digs. See the comments for fast_s_mp_mul_digs
+/* this is a modified version of fast_s_mul_digs that only produces
+ * output digits *above* digs. See the comments for fast_s_mul_digs
* to see how it works.
*
* This is used in the Barrett reduction since for one of the multiplications
@@ -524,80 +504,78 @@ fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
int
fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
{
- int oldused, newused, res, pa, pb, ix;
- mp_word W[MP_WARRAY];
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY];
+ mp_word _W;
- /* calculate size of product and allocate more space if required */
- newused = a->used + b->used + 1;
- if (c->alloc < newused) {
- if ((res = mp_grow (c, newused)) != MP_OKAY) {
+ /* grow the destination as required */
+ pa = a->used + b->used;
+ if (c->alloc < pa) {
+ if ((res = mp_grow (c, pa)) != MP_OKAY) {
return res;
}
}
- /* like the other comba method we compute the columns first */
- pa = a->used;
- pb = b->used;
- memset (W + digs, 0, (pa + pb + 1 - digs) * sizeof (mp_word));
- for (ix = 0; ix < pa; ix++) {
- {
- register mp_digit tmpx, *tmpy;
- register int iy;
- register mp_word *_W;
+ /* number of output digits to produce */
+ pa = a->used + b->used;
+ _W = 0;
+ for (ix = digs; ix <= pa; ix++) {
+ int tx, ty, iy;
+ mp_digit *tmpx, *tmpy;
- /* work todo, that is we only calculate digits that are at "digs" or above */
- iy = digs - ix;
+ /* get offsets into the two bignums */
+ ty = MIN(b->used-1, ix);
+ tx = ix - ty;
- /* copy of word on the left of A[ix] * B[iy] */
- tmpx = a->dp[ix];
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = b->dp + ty;
- /* alias for right side */
- tmpy = b->dp + iy;
-
- /* alias for the columns of output. Offset to be equal to or above the
- * smallest digit place requested
+ /* this is the number of times the loop will iterrate, essentially its
+ while (tx++ < a->used && ty-- >= 0) { ... }
*/
- _W = W + digs;
-
- /* skip cases below zero where ix > digs */
- if (iy < 0) {
- iy = abs(iy);
- tmpy += iy;
- _W += iy;
- iy = 0;
- }
+ iy = MIN(a->used-tx, ty+1);
- /* compute column products for digits above the minimum */
- for (; iy < pb; iy++) {
- *_W++ += ((mp_word) tmpx) * ((mp_word)*tmpy++);
+ /* execute loop */
+ for (iz = 0; iz < iy; iz++) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
}
- }
+
+ /* store term */
+ W[ix] = ((mp_digit)_W) & MP_MASK;
+
+ /* make next carry */
+ _W = _W >> ((mp_word)DIGIT_BIT);
}
/* setup dest */
- oldused = c->used;
- c->used = newused;
+ olduse = c->used;
+ c->used = pa;
- /* now convert the array W downto what we need
- *
- * See comments in bn_fast_s_mp_mul_digs.c
- */
- for (ix = digs + 1; ix < newused; ix++) {
- W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
- c->dp[ix - 1] = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
- }
- c->dp[newused - 1] = (mp_digit) (W[newused - 1] & ((mp_word) MP_MASK));
+ {
+ register mp_digit *tmpc;
+
+ tmpc = c->dp + digs;
+ for (ix = digs; ix <= pa; ix++) {
+ /* now extract the previous digit [below the carry] */
+ *tmpc++ = W[ix];
+ }
- for (; ix < oldused; ix++) {
- c->dp[ix] = 0;
+ /* clear unused digits [that existed in the old copy of c] */
+ for (; ix < olduse; ix++) {
+ *tmpc++ = 0;
+ }
}
mp_clamp (c);
return MP_OKAY;
}
+#endif
/* End: bn_fast_s_mp_mul_high_digs.c */
/* Start: bn_fast_s_mp_sqr.c */
+#include <tommath.h>
+#ifdef BN_FAST_S_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -612,7 +590,6 @@ fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* fast squaring
*
@@ -631,116 +608,107 @@ fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
* Based on Algorithm 14.16 on pp.597 of HAC.
*
*/
+/* the jist of squaring...
+
+you do like mult except the offset of the tmpx [one that starts closer to zero]
+can't equal the offset of tmpy. So basically you set up iy like before then you min it with
+(ty-tx) so that it never happens. You double all those you add in the inner loop
+
+After that loop you do the squares and add them in.
+
+Remove W2 and don't memset W
+
+*/
+
int fast_s_mp_sqr (mp_int * a, mp_int * b)
{
- int olduse, newused, res, ix, pa;
- mp_word W2[MP_WARRAY], W[MP_WARRAY];
+ int olduse, res, pa, ix, iz;
+ mp_digit W[MP_WARRAY], *tmpx;
+ mp_word W1;
- /* calculate size of product and allocate as required */
- pa = a->used;
- newused = pa + pa + 1;
- if (b->alloc < newused) {
- if ((res = mp_grow (b, newused)) != MP_OKAY) {
+ /* grow the destination as required */
+ pa = a->used + a->used;
+ if (b->alloc < pa) {
+ if ((res = mp_grow (b, pa)) != MP_OKAY) {
return res;
}
}
- /* zero temp buffer (columns)
- * Note that there are two buffers. Since squaring requires
- * a outer and inner product and the inner product requires
- * computing a product and doubling it (a relatively expensive
- * op to perform n**2 times if you don't have to) the inner and
- * outer products are computed in different buffers. This way
- * the inner product can be doubled using n doublings instead of
- * n**2
- */
- memset (W, 0, newused * sizeof (mp_word));
- memset (W2, 0, newused * sizeof (mp_word));
+ /* number of output digits to produce */
+ W1 = 0;
+ for (ix = 0; ix <= pa; ix++) {
+ int tx, ty, iy;
+ mp_word _W;
+ mp_digit *tmpy;
- /* This computes the inner product. To simplify the inner N**2 loop
- * the multiplication by two is done afterwards in the N loop.
- */
- for (ix = 0; ix < pa; ix++) {
- /* compute the outer product
- *
- * Note that every outer product is computed
- * for a particular column only once which means that
- * there is no need todo a double precision addition
- * into the W2[] array.
- */
- W2[ix + ix] = ((mp_word)a->dp[ix]) * ((mp_word)a->dp[ix]);
+ /* clear counter */
+ _W = 0;
- {
- register mp_digit tmpx, *tmpy;
- register mp_word *_W;
- register int iy;
+ /* get offsets into the two bignums */
+ ty = MIN(a->used-1, ix);
+ tx = ix - ty;
+
+ /* setup temp aliases */
+ tmpx = a->dp + tx;
+ tmpy = a->dp + ty;
- /* copy of left side */
- tmpx = a->dp[ix];
+ /* this is the number of times the loop will iterrate, essentially its
+ while (tx++ < a->used && ty-- >= 0) { ... }
+ */
+ iy = MIN(a->used-tx, ty+1);
+
+ /* now for squaring tx can never equal ty
+ * we halve the distance since they approach at a rate of 2x
+ * and we have to round because odd cases need to be executed
+ */
+ iy = MIN(iy, (ty-tx+1)>>1);
- /* alias for right side */
- tmpy = a->dp + (ix + 1);
+ /* execute loop */
+ for (iz = 0; iz < iy; iz++) {
+ _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
+ }
- /* the column to store the result in */
- _W = W + (ix + ix + 1);
+ /* double the inner product and add carry */
+ _W = _W + _W + W1;
- /* inner products */
- for (iy = ix + 1; iy < pa; iy++) {
- *_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++);
+ /* even columns have the square term in them */
+ if ((ix&1) == 0) {
+ _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
}
- }
+
+ /* store it */
+ W[ix] = _W;
+
+ /* make next carry */
+ W1 = _W >> ((mp_word)DIGIT_BIT);
}
/* setup dest */
olduse = b->used;
- b->used = newused;
+ b->used = a->used+a->used;
- /* now compute digits
- *
- * We have to double the inner product sums, add in the
- * outer product sums, propagate carries and convert
- * to single precision.
- */
{
- register mp_digit *tmpb;
-
- /* double first value, since the inner products are
- * half of what they should be
- */
- W[0] += W[0] + W2[0];
-
+ mp_digit *tmpb;
tmpb = b->dp;
- for (ix = 1; ix < newused; ix++) {
- /* double/add next digit */
- W[ix] += W[ix] + W2[ix];
-
- /* propagate carry forwards [from the previous digit] */
- W[ix] = W[ix] + (W[ix - 1] >> ((mp_word) DIGIT_BIT));
-
- /* store the current digit now that the carry isn't
- * needed
- */
- *tmpb++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
+ for (ix = 0; ix < pa; ix++) {
+ *tmpb++ = W[ix] & MP_MASK;
}
- /* set the last value. Note even if the carry is zero
- * this is required since the next step will not zero
- * it if b originally had a value at b->dp[2*a.used]
- */
- *tmpb++ = (mp_digit) (W[(newused) - 1] & ((mp_word) MP_MASK));
- /* clear high digits of b if there were any originally */
+ /* clear unused digits [that existed in the old copy of c] */
for (; ix < olduse; ix++) {
*tmpb++ = 0;
}
}
-
mp_clamp (b);
return MP_OKAY;
}
+#endif
/* End: bn_fast_s_mp_sqr.c */
/* Start: bn_mp_2expt.c */
+#include <tommath.h>
+#ifdef BN_MP_2EXPT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -755,7 +723,6 @@ int fast_s_mp_sqr (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes a = 2**b
*
@@ -779,14 +746,17 @@ mp_2expt (mp_int * a, int b)
a->used = b / DIGIT_BIT + 1;
/* put the single bit in its place */
- a->dp[b / DIGIT_BIT] = 1 << (b % DIGIT_BIT);
+ a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
return MP_OKAY;
}
+#endif
/* End: bn_mp_2expt.c */
/* Start: bn_mp_abs.c */
+#include <tommath.h>
+#ifdef BN_MP_ABS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -801,7 +771,6 @@ mp_2expt (mp_int * a, int b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* b = |a|
*
@@ -824,10 +793,13 @@ mp_abs (mp_int * a, mp_int * b)
return MP_OKAY;
}
+#endif
/* End: bn_mp_abs.c */
/* Start: bn_mp_add.c */
+#include <tommath.h>
+#ifdef BN_MP_ADD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -842,7 +814,6 @@ mp_abs (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* high level addition (handles signs) */
int mp_add (mp_int * a, mp_int * b, mp_int * c)
@@ -875,10 +846,13 @@ int mp_add (mp_int * a, mp_int * b, mp_int * c)
return res;
}
+#endif
/* End: bn_mp_add.c */
/* Start: bn_mp_add_d.c */
+#include <tommath.h>
+#ifdef BN_MP_ADD_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -893,7 +867,6 @@ int mp_add (mp_int * a, mp_int * b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* single digit addition */
int
@@ -982,10 +955,13 @@ mp_add_d (mp_int * a, mp_digit b, mp_int * c)
return MP_OKAY;
}
+#endif
/* End: bn_mp_add_d.c */
/* Start: bn_mp_addmod.c */
+#include <tommath.h>
+#ifdef BN_MP_ADDMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1000,7 +976,6 @@ mp_add_d (mp_int * a, mp_digit b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* d = a + b (mod c) */
int
@@ -1021,10 +996,13 @@ mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
mp_clear (&t);
return res;
}
+#endif
/* End: bn_mp_addmod.c */
/* Start: bn_mp_and.c */
+#include <tommath.h>
+#ifdef BN_MP_AND_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1039,7 +1017,6 @@ mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* AND two ints together */
int
@@ -1076,10 +1053,13 @@ mp_and (mp_int * a, mp_int * b, mp_int * c)
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_mp_and.c */
/* Start: bn_mp_clamp.c */
+#include <tommath.h>
+#ifdef BN_MP_CLAMP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1094,7 +1074,6 @@ mp_and (mp_int * a, mp_int * b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* trim unused digits
*
@@ -1118,10 +1097,13 @@ mp_clamp (mp_int * a)
a->sign = MP_ZPOS;
}
}
+#endif
/* End: bn_mp_clamp.c */
/* Start: bn_mp_clear.c */
+#include <tommath.h>
+#ifdef BN_MP_CLEAR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1136,16 +1118,19 @@ mp_clamp (mp_int * a)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* clear one (frees) */
void
mp_clear (mp_int * a)
{
+ int i;
+
/* only do anything if a hasn't been freed previously */
if (a->dp != NULL) {
/* first zero the digits */
- memset (a->dp, 0, sizeof (mp_digit) * a->used);
+ for (i = 0; i < a->used; i++) {
+ a->dp[i] = 0;
+ }
/* free ram */
XFREE(a->dp);
@@ -1156,10 +1141,13 @@ mp_clear (mp_int * a)
a->sign = MP_ZPOS;
}
}
+#endif
/* End: bn_mp_clear.c */
/* Start: bn_mp_clear_multi.c */
+#include <tommath.h>
+#ifdef BN_MP_CLEAR_MULTI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1174,7 +1162,6 @@ mp_clear (mp_int * a)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
#include <stdarg.h>
void mp_clear_multi(mp_int *mp, ...)
@@ -1188,10 +1175,13 @@ void mp_clear_multi(mp_int *mp, ...)
}
va_end(args);
}
+#endif
/* End: bn_mp_clear_multi.c */
/* Start: bn_mp_cmp.c */
+#include <tommath.h>
+#ifdef BN_MP_CMP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1206,7 +1196,6 @@ void mp_clear_multi(mp_int *mp, ...)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* compare two ints (signed)*/
int
@@ -1229,10 +1218,13 @@ mp_cmp (mp_int * a, mp_int * b)
return mp_cmp_mag(a, b);
}
}
+#endif
/* End: bn_mp_cmp.c */
/* Start: bn_mp_cmp_d.c */
+#include <tommath.h>
+#ifdef BN_MP_CMP_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1247,7 +1239,6 @@ mp_cmp (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* compare a digit */
int mp_cmp_d(mp_int * a, mp_digit b)
@@ -1271,10 +1262,13 @@ int mp_cmp_d(mp_int * a, mp_digit b)
return MP_EQ;
}
}
+#endif
/* End: bn_mp_cmp_d.c */
/* Start: bn_mp_cmp_mag.c */
+#include <tommath.h>
+#ifdef BN_MP_CMP_MAG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1289,7 +1283,6 @@ int mp_cmp_d(mp_int * a, mp_digit b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* compare maginitude of two ints (unsigned) */
int mp_cmp_mag (mp_int * a, mp_int * b)
@@ -1324,10 +1317,13 @@ int mp_cmp_mag (mp_int * a, mp_int * b)
}
return MP_EQ;
}
+#endif
/* End: bn_mp_cmp_mag.c */
/* Start: bn_mp_cnt_lsb.c */
+#include <tommath.h>
+#ifdef BN_MP_CNT_LSB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1342,7 +1338,6 @@ int mp_cmp_mag (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
static const int lnz[16] = {
4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
@@ -1375,10 +1370,13 @@ int mp_cnt_lsb(mp_int *a)
return x;
}
+#endif
/* End: bn_mp_cnt_lsb.c */
/* Start: bn_mp_copy.c */
+#include <tommath.h>
+#ifdef BN_MP_COPY_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1393,7 +1391,6 @@ int mp_cnt_lsb(mp_int *a)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* copy, b = a */
int
@@ -1441,10 +1438,13 @@ mp_copy (mp_int * a, mp_int * b)
b->sign = a->sign;
return MP_OKAY;
}
+#endif
/* End: bn_mp_copy.c */
/* Start: bn_mp_count_bits.c */
+#include <tommath.h>
+#ifdef BN_MP_COUNT_BITS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1459,7 +1459,6 @@ mp_copy (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* returns the number of bits in an int */
int
@@ -1484,10 +1483,13 @@ mp_count_bits (mp_int * a)
}
return r;
}
+#endif
/* End: bn_mp_count_bits.c */
/* Start: bn_mp_div.c */
+#include <tommath.h>
+#ifdef BN_MP_DIV_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1502,7 +1504,78 @@ mp_count_bits (mp_int * a)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
+
+#ifdef BN_MP_DIV_SMALL
+
+/* slower bit-bang division... also smaller */
+int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+ mp_int ta, tb, tq, q;
+ int res, n, n2;
+
+ /* is divisor zero ? */
+ if (mp_iszero (b) == 1) {
+ return MP_VAL;
+ }
+
+ /* if a < b then q=0, r = a */
+ if (mp_cmp_mag (a, b) == MP_LT) {
+ if (d != NULL) {
+ res = mp_copy (a, d);
+ } else {
+ res = MP_OKAY;
+ }
+ if (c != NULL) {
+ mp_zero (c);
+ }
+ return res;
+ }
+
+ /* init our temps */
+ if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
+ return res;
+ }
+
+
+ mp_set(&tq, 1);
+ n = mp_count_bits(a) - mp_count_bits(b);
+ if (((res = mp_copy(a, &ta)) != MP_OKAY) ||
+ ((res = mp_copy(b, &tb)) != MP_OKAY) ||
+ ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
+ ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
+ goto __ERR;
+ }
+
+ while (n-- >= 0) {
+ if (mp_cmp(&tb, &ta) != MP_GT) {
+ if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
+ ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
+ goto __ERR;
+ }
+ }
+ if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
+ ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
+ goto __ERR;
+ }
+ }
+
+ /* now q == quotient and ta == remainder */
+ n = a->sign;
+ n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
+ if (c != NULL) {
+ mp_exch(c, &q);
+ c->sign = n2;
+ }
+ if (d != NULL) {
+ mp_exch(d, &ta);
+ d->sign = n;
+ }
+__ERR:
+ mp_clear_multi(&ta, &tb, &tq, &q, NULL);
+ return res;
+}
+
+#else
/* integer signed division.
* c*b + d == a [e.g. a/b, c=quotient, d=remainder]
@@ -1677,7 +1750,7 @@ int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
*/
/* get sign before writing to c */
- x.sign = a->sign;
+ x.sign = x.used == 0 ? MP_ZPOS : a->sign;
if (c != NULL) {
mp_clamp (&q);
@@ -1700,9 +1773,15 @@ __Q:mp_clear (&q);
return res;
}
+#endif
+
+#endif
+
/* End: bn_mp_div.c */
/* Start: bn_mp_div_2.c */
+#include <tommath.h>
+#ifdef BN_MP_DIV_2_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1717,7 +1796,6 @@ __Q:mp_clear (&q);
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* b = a/2 */
int mp_div_2(mp_int * a, mp_int * b)
@@ -1765,10 +1843,13 @@ int mp_div_2(mp_int * a, mp_int * b)
mp_clamp (b);
return MP_OKAY;
}
+#endif
/* End: bn_mp_div_2.c */
/* Start: bn_mp_div_2d.c */
+#include <tommath.h>
+#ifdef BN_MP_DIV_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1783,7 +1864,6 @@ int mp_div_2(mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
@@ -1860,10 +1940,13 @@ int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_mp_div_2d.c */
/* Start: bn_mp_div_3.c */
+#include <tommath.h>
+#ifdef BN_MP_DIV_3_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1878,7 +1961,6 @@ int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* divide by three (based on routine from MPI and the GMP manual) */
int
@@ -1937,10 +2019,13 @@ mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
return res;
}
+#endif
/* End: bn_mp_div_3.c */
/* Start: bn_mp_div_d.c */
+#include <tommath.h>
+#ifdef BN_MP_DIV_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -1955,7 +2040,6 @@ mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
static int s_is_power_of_two(mp_digit b, int *p)
{
@@ -1997,7 +2081,7 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
/* power of two ? */
if (s_is_power_of_two(b, &ix) == 1) {
if (d != NULL) {
- *d = a->dp[0] & ((1<<ix) - 1);
+ *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
}
if (c != NULL) {
return mp_div_2d(a, ix, c, NULL);
@@ -2005,10 +2089,12 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
return MP_OKAY;
}
+#ifdef BN_MP_DIV_3_C
/* three? */
if (b == 3) {
return mp_div_3(a, c, d);
}
+#endif
/* no easy answer [c'est la vie]. Just division */
if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
@@ -2043,10 +2129,13 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
return res;
}
+#endif
/* End: bn_mp_div_d.c */
/* Start: bn_mp_dr_is_modulus.c */
+#include <tommath.h>
+#ifdef BN_MP_DR_IS_MODULUS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2061,7 +2150,6 @@ int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* determines if a number is a valid DR modulus */
int mp_dr_is_modulus(mp_int *a)
@@ -2084,10 +2172,13 @@ int mp_dr_is_modulus(mp_int *a)
return 1;
}
+#endif
/* End: bn_mp_dr_is_modulus.c */
/* Start: bn_mp_dr_reduce.c */
+#include <tommath.h>
+#ifdef BN_MP_DR_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2102,7 +2193,6 @@ int mp_dr_is_modulus(mp_int *a)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
*
@@ -2176,10 +2266,13 @@ top:
}
return MP_OKAY;
}
+#endif
/* End: bn_mp_dr_reduce.c */
/* Start: bn_mp_dr_setup.c */
+#include <tommath.h>
+#ifdef BN_MP_DR_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2194,7 +2287,6 @@ top:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* determines the setup value */
void mp_dr_setup(mp_int *a, mp_digit *d)
@@ -2206,10 +2298,13 @@ void mp_dr_setup(mp_int *a, mp_digit *d)
((mp_word)a->dp[0]));
}
+#endif
/* End: bn_mp_dr_setup.c */
/* Start: bn_mp_exch.c */
+#include <tommath.h>
+#ifdef BN_MP_EXCH_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2224,7 +2319,6 @@ void mp_dr_setup(mp_int *a, mp_digit *d)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* swap the elements of two integers, for cases where you can't simply swap the
* mp_int pointers around
@@ -2238,10 +2332,13 @@ mp_exch (mp_int * a, mp_int * b)
*a = *b;
*b = t;
}
+#endif
/* End: bn_mp_exch.c */
/* Start: bn_mp_expt_d.c */
+#include <tommath.h>
+#ifdef BN_MP_EXPT_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2256,7 +2353,6 @@ mp_exch (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* calculate c = a**b using a square-multiply algorithm */
int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
@@ -2293,10 +2389,13 @@ int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
mp_clear (&g);
return MP_OKAY;
}
+#endif
/* End: bn_mp_expt_d.c */
/* Start: bn_mp_exptmod.c */
+#include <tommath.h>
+#ifdef BN_MP_EXPTMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2311,7 +2410,6 @@ int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* this is a shell function that calls either the normal or Montgomery
@@ -2330,6 +2428,7 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
/* if exponent X is negative we have to recurse */
if (X->sign == MP_NEG) {
+#ifdef BN_MP_INVMOD_C
mp_int tmpG, tmpX;
int err;
@@ -2356,29 +2455,51 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
err = mp_exptmod(&tmpG, &tmpX, P, Y);
mp_clear_multi(&tmpG, &tmpX, NULL);
return err;
+#else
+ /* no invmod */
+ return MP_VAL
+#endif
}
+#ifdef BN_MP_DR_IS_MODULUS_C
/* is it a DR modulus? */
dr = mp_dr_is_modulus(P);
+#else
+ dr = 0;
+#endif
+#ifdef BN_MP_REDUCE_IS_2K_C
/* if not, is it a uDR modulus? */
if (dr == 0) {
dr = mp_reduce_is_2k(P) << 1;
}
+#endif
/* if the modulus is odd or dr != 0 use the fast method */
+#ifdef BN_MP_EXPTMOD_FAST_C
if (mp_isodd (P) == 1 || dr != 0) {
return mp_exptmod_fast (G, X, P, Y, dr);
} else {
+#endif
+#ifdef BN_S_MP_EXPTMOD_C
/* otherwise use the generic Barrett reduction technique */
return s_mp_exptmod (G, X, P, Y);
+#else
+ /* no exptmod for evens */
+ return MP_VAL;
+#endif
+#ifdef BN_MP_EXPTMOD_FAST_C
}
+#endif
}
+#endif
/* End: bn_mp_exptmod.c */
/* Start: bn_mp_exptmod_fast.c */
+#include <tommath.h>
+#ifdef BN_MP_EXPTMOD_FAST_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2393,7 +2514,6 @@ int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
*
@@ -2465,29 +2585,52 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
/* determine and setup reduction code */
if (redmode == 0) {
+#ifdef BN_MP_MONTGOMERY_SETUP_C
/* now setup montgomery */
if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
goto __M;
}
+#else
+ err = MP_VAL;
+ goto __M;
+#endif
/* automatically pick the comba one if available (saves quite a few calls/ifs) */
+#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
if (((P->used * 2 + 1) < MP_WARRAY) &&
P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
redux = fast_mp_montgomery_reduce;
- } else {
+ } else
+#endif
+ {
+#ifdef BN_MP_MONTGOMERY_REDUCE_C
/* use slower baseline Montgomery method */
redux = mp_montgomery_reduce;
+#else
+ err = MP_VAL;
+ goto __M;
+#endif
}
} else if (redmode == 1) {
+#if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
/* setup DR reduction for moduli of the form B**k - b */
mp_dr_setup(P, &mp);
redux = mp_dr_reduce;
+#else
+ err = MP_VAL;
+ goto __M;
+#endif
} else {
+#if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
/* setup DR reduction for moduli of the form 2**k - b */
if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
goto __M;
}
redux = mp_reduce_2k;
+#else
+ err = MP_VAL;
+ goto __M;
+#endif
}
/* setup result */
@@ -2497,16 +2640,21 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
/* create M table
*
- * The M table contains powers of the input base, e.g. M[x] = G^x mod P
+
*
* The first half of the table is not computed though accept for M[0] and M[1]
*/
if (redmode == 0) {
+#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
/* now we need R mod m */
if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
goto __RES;
}
+#else
+ err = MP_VAL;
+ goto __RES;
+#endif
/* now set M[1] to G * R mod m */
if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
@@ -2650,7 +2798,7 @@ mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
* to reduce one more time to cancel out the factor
* of R.
*/
- if ((err = mp_montgomery_reduce (&res, P, mp)) != MP_OKAY) {
+ if ((err = redux(&res, P, mp)) != MP_OKAY) {
goto __RES;
}
}
@@ -2666,10 +2814,14 @@ __M:
}
return err;
}
+#endif
+
/* End: bn_mp_exptmod_fast.c */
/* Start: bn_mp_exteuclid.c */
+#include <tommath.h>
+#ifdef BN_MP_EXTEUCLID_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2684,7 +2836,6 @@ __M:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Extended euclidean algorithm of (a, b) produces
a*u1 + b*u2 = u3
@@ -2739,10 +2890,13 @@ int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
_ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
return err;
}
+#endif
/* End: bn_mp_exteuclid.c */
/* Start: bn_mp_fread.c */
+#include <tommath.h>
+#ifdef BN_MP_FREAD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2757,7 +2911,6 @@ _ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* read a bigint from a file stream in ASCII */
int mp_fread(mp_int *a, int radix, FILE *stream)
@@ -2804,10 +2957,13 @@ int mp_fread(mp_int *a, int radix, FILE *stream)
return MP_OKAY;
}
+#endif
/* End: bn_mp_fread.c */
/* Start: bn_mp_fwrite.c */
+#include <tommath.h>
+#ifdef BN_MP_FWRITE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2822,7 +2978,6 @@ int mp_fread(mp_int *a, int radix, FILE *stream)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
int mp_fwrite(mp_int *a, int radix, FILE *stream)
{
@@ -2854,10 +3009,13 @@ int mp_fwrite(mp_int *a, int radix, FILE *stream)
return MP_OKAY;
}
+#endif
/* End: bn_mp_fwrite.c */
/* Start: bn_mp_gcd.c */
+#include <tommath.h>
+#ifdef BN_MP_GCD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2872,7 +3030,6 @@ int mp_fwrite(mp_int *a, int radix, FILE *stream)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Greatest Common Divisor using the binary method */
int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
@@ -2965,10 +3122,13 @@ __V:mp_clear (&u);
__U:mp_clear (&v);
return res;
}
+#endif
/* End: bn_mp_gcd.c */
/* Start: bn_mp_get_int.c */
+#include <tommath.h>
+#ifdef BN_MP_GET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -2983,7 +3143,6 @@ __U:mp_clear (&v);
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* get the lower 32-bits of an mp_int */
unsigned long mp_get_int(mp_int * a)
@@ -3008,10 +3167,13 @@ unsigned long mp_get_int(mp_int * a)
/* force result to 32-bits always so it is consistent on non 32-bit platforms */
return res & 0xFFFFFFFFUL;
}
+#endif
/* End: bn_mp_get_int.c */
/* Start: bn_mp_grow.c */
+#include <tommath.h>
+#ifdef BN_MP_GROW_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3026,7 +3188,6 @@ unsigned long mp_get_int(mp_int * a)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* grow as required */
int mp_grow (mp_int * a, int size)
@@ -3063,10 +3224,13 @@ int mp_grow (mp_int * a, int size)
}
return MP_OKAY;
}
+#endif
/* End: bn_mp_grow.c */
/* Start: bn_mp_init.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3081,17 +3245,23 @@ int mp_grow (mp_int * a, int size)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* init a new bigint */
+/* init a new mp_int */
int mp_init (mp_int * a)
{
+ int i;
+
/* allocate memory required and clear it */
- a->dp = OPT_CAST(mp_digit) XCALLOC (sizeof (mp_digit), MP_PREC);
+ a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC);
if (a->dp == NULL) {
return MP_MEM;
}
+ /* set the digits to zero */
+ for (i = 0; i < MP_PREC; i++) {
+ a->dp[i] = 0;
+ }
+
/* set the used to zero, allocated digits to the default precision
* and sign to positive */
a->used = 0;
@@ -3100,10 +3270,13 @@ int mp_init (mp_int * a)
return MP_OKAY;
}
+#endif
/* End: bn_mp_init.c */
/* Start: bn_mp_init_copy.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_COPY_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3118,7 +3291,6 @@ int mp_init (mp_int * a)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* creates "a" then copies b into it */
int mp_init_copy (mp_int * a, mp_int * b)
@@ -3130,10 +3302,13 @@ int mp_init_copy (mp_int * a, mp_int * b)
}
return mp_copy (b, a);
}
+#endif
/* End: bn_mp_init_copy.c */
/* Start: bn_mp_init_multi.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_MULTI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3148,7 +3323,6 @@ int mp_init_copy (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
#include <stdarg.h>
int mp_init_multi(mp_int *mp, ...)
@@ -3187,10 +3361,13 @@ int mp_init_multi(mp_int *mp, ...)
return res; /* Assumed ok, if error flagged above. */
}
+#endif
/* End: bn_mp_init_multi.c */
/* Start: bn_mp_init_set.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_SET_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3205,7 +3382,6 @@ int mp_init_multi(mp_int *mp, ...)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* initialize and set a digit */
int mp_init_set (mp_int * a, mp_digit b)
@@ -3217,10 +3393,13 @@ int mp_init_set (mp_int * a, mp_digit b)
mp_set(a, b);
return err;
}
+#endif
/* End: bn_mp_init_set.c */
/* Start: bn_mp_init_set_int.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_SET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3235,7 +3414,6 @@ int mp_init_set (mp_int * a, mp_digit b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* initialize and set a digit */
int mp_init_set_int (mp_int * a, unsigned long b)
@@ -3246,10 +3424,13 @@ int mp_init_set_int (mp_int * a, unsigned long b)
}
return mp_set_int(a, b);
}
+#endif
/* End: bn_mp_init_set_int.c */
/* Start: bn_mp_init_size.c */
+#include <tommath.h>
+#ifdef BN_MP_INIT_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3264,29 +3445,40 @@ int mp_init_set_int (mp_int * a, unsigned long b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* init an mp_init for a given size */
int mp_init_size (mp_int * a, int size)
{
+ int x;
+
/* pad size so there are always extra digits */
size += (MP_PREC * 2) - (size % MP_PREC);
/* alloc mem */
- a->dp = OPT_CAST(mp_digit) XCALLOC (sizeof (mp_digit), size);
+ a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
if (a->dp == NULL) {
return MP_MEM;
}
+
+ /* set the members */
a->used = 0;
a->alloc = size;
a->sign = MP_ZPOS;
+ /* zero the digits */
+ for (x = 0; x < size; x++) {
+ a->dp[x] = 0;
+ }
+
return MP_OKAY;
}
+#endif
/* End: bn_mp_init_size.c */
/* Start: bn_mp_invmod.c */
+#include <tommath.h>
+#ifdef BN_MP_INVMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3301,24 +3493,61 @@ int mp_init_size (mp_int * a, int size)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* hac 14.61, pp608 */
int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
{
- mp_int x, y, u, v, A, B, C, D;
- int res;
-
/* b cannot be negative */
if (b->sign == MP_NEG || mp_iszero(b) == 1) {
return MP_VAL;
}
+#ifdef BN_FAST_MP_INVMOD_C
/* if the modulus is odd we can use a faster routine instead */
if (mp_isodd (b) == 1) {
return fast_mp_invmod (a, b, c);
}
-
+#endif
+
+#ifdef BN_MP_INVMOD_SLOW_C
+ return mp_invmod_slow(a, b, c);
+#endif
+
+ return MP_VAL;
+}
+#endif
+
+/* End: bn_mp_invmod.c */
+
+/* Start: bn_mp_invmod_slow.c */
+#include <tommath.h>
+#ifdef BN_MP_INVMOD_SLOW_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+
+/* hac 14.61, pp608 */
+int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
+{
+ mp_int x, y, u, v, A, B, C, D;
+ int res;
+
+ /* b cannot be negative */
+ if (b->sign == MP_NEG || mp_iszero(b) == 1) {
+ return MP_VAL;
+ }
+
/* init temps */
if ((res = mp_init_multi(&x, &y, &u, &v,
&A, &B, &C, &D, NULL)) != MP_OKAY) {
@@ -3461,10 +3690,13 @@ top:
__ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
return res;
}
+#endif
-/* End: bn_mp_invmod.c */
+/* End: bn_mp_invmod_slow.c */
/* Start: bn_mp_is_square.c */
+#include <tommath.h>
+#ifdef BN_MP_IS_SQUARE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3479,7 +3711,6 @@ __ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Check if remainders are possible squares - fast exclude non-squares */
static const char rem_128[128] = {
@@ -3536,7 +3767,7 @@ int mp_is_square(mp_int *arg,int *ret)
return MP_OKAY;
}
- /* product of primes less than 2^31 */
+
if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) {
return res;
}
@@ -3568,10 +3799,13 @@ int mp_is_square(mp_int *arg,int *ret)
ERR:mp_clear(&t);
return res;
}
+#endif
/* End: bn_mp_is_square.c */
/* Start: bn_mp_jacobi.c */
+#include <tommath.h>
+#ifdef BN_MP_JACOBI_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3586,7 +3820,6 @@ ERR:mp_clear(&t);
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes the jacobi c = (a | n) (or Legendre if n is prime)
* HAC pp. 73 Algorithm 2.149
@@ -3671,10 +3904,13 @@ __P1:mp_clear (&p1);
__A1:mp_clear (&a1);
return res;
}
+#endif
/* End: bn_mp_jacobi.c */
/* Start: bn_mp_karatsuba_mul.c */
+#include <tommath.h>
+#ifdef BN_MP_KARATSUBA_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3689,7 +3925,6 @@ __A1:mp_clear (&a1);
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* c = |a| * |b| using Karatsuba Multiplication using
* three half size multiplications
@@ -3753,9 +3988,6 @@ int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c)
goto X0Y0;
/* now shift the digits */
- x0.sign = x1.sign = a->sign;
- y0.sign = y1.sign = b->sign;
-
x0.used = y0.used = B;
x1.used = a->used - B;
y1.used = b->used - B;
@@ -3839,10 +4071,13 @@ X0:mp_clear (&x0);
ERR:
return err;
}
+#endif
/* End: bn_mp_karatsuba_mul.c */
/* Start: bn_mp_karatsuba_sqr.c */
+#include <tommath.h>
+#ifdef BN_MP_KARATSUBA_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3857,12 +4092,11 @@ ERR:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Karatsuba squaring, computes b = a*a using three
* half size squarings
*
- * See comments of mp_karatsuba_mul for details. It
+ * See comments of karatsuba_mul for details. It
* is essentially the same algorithm but merely
* tuned to perform recursive squarings.
*/
@@ -3958,10 +4192,13 @@ X0:mp_clear (&x0);
ERR:
return err;
}
+#endif
/* End: bn_mp_karatsuba_sqr.c */
/* Start: bn_mp_lcm.c */
+#include <tommath.h>
+#ifdef BN_MP_LCM_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -3976,7 +4213,6 @@ ERR:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes least common multiple as |a*b|/(a, b) */
int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
@@ -4016,10 +4252,13 @@ __T:
mp_clear_multi (&t1, &t2, NULL);
return res;
}
+#endif
/* End: bn_mp_lcm.c */
/* Start: bn_mp_lshd.c */
+#include <tommath.h>
+#ifdef BN_MP_LSHD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4034,7 +4273,6 @@ __T:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shift left a certain amount of digits */
int mp_lshd (mp_int * a, int b)
@@ -4081,10 +4319,13 @@ int mp_lshd (mp_int * a, int b)
}
return MP_OKAY;
}
+#endif
/* End: bn_mp_lshd.c */
/* Start: bn_mp_mod.c */
+#include <tommath.h>
+#ifdef BN_MP_MOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4099,7 +4340,6 @@ int mp_lshd (mp_int * a, int b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* c = a mod b, 0 <= c < b */
int
@@ -4127,10 +4367,13 @@ mp_mod (mp_int * a, mp_int * b, mp_int * c)
mp_clear (&t);
return res;
}
+#endif
/* End: bn_mp_mod.c */
/* Start: bn_mp_mod_2d.c */
+#include <tommath.h>
+#ifdef BN_MP_MOD_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4145,7 +4388,6 @@ mp_mod (mp_int * a, mp_int * b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* calc a value mod 2**b */
int
@@ -4180,10 +4422,13 @@ mp_mod_2d (mp_int * a, int b, mp_int * c)
mp_clamp (c);
return MP_OKAY;
}
+#endif
/* End: bn_mp_mod_2d.c */
/* Start: bn_mp_mod_d.c */
+#include <tommath.h>
+#ifdef BN_MP_MOD_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4198,17 +4443,19 @@ mp_mod_2d (mp_int * a, int b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
int
mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
{
return mp_div_d(a, b, NULL, c);
}
+#endif
/* End: bn_mp_mod_d.c */
/* Start: bn_mp_montgomery_calc_normalization.c */
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4223,31 +4470,31 @@ mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* calculates a = B^n mod b for Montgomery reduction
- * Where B is the base [e.g. 2^DIGIT_BIT].
- * B^n mod b is computed by first computing
- * A = B^(n-1) which doesn't require a reduction but a simple OR.
- * then C = A * B = B^n is computed by performing upto DIGIT_BIT
+/*
* shifts with subtractions when the result is greater than b.
*
* The method is slightly modified to shift B unconditionally upto just under
* the leading bit of b. This saves alot of multiple precision shifting.
*/
-int
-mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
+int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
{
int x, bits, res;
/* how many bits of last digit does b use */
bits = mp_count_bits (b) % DIGIT_BIT;
- /* compute A = B^(n-1) * 2^(bits-1) */
- if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
- return res;
+
+ if (b->used > 1) {
+ if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
+ return res;
+ }
+ } else {
+ mp_set(a, 1);
+ bits = 1;
}
+
/* now compute C = A * B mod b */
for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
@@ -4262,10 +4509,13 @@ mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
return MP_OKAY;
}
+#endif
/* End: bn_mp_montgomery_calc_normalization.c */
/* Start: bn_mp_montgomery_reduce.c */
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4280,7 +4530,6 @@ mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes xR**-1 == x (mod N) via Montgomery Reduction */
int
@@ -4291,7 +4540,7 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
/* can the fast reduction [comba] method be used?
*
- * Note that unlike in mp_mul you're safely allowed *less*
+ * Note that unlike in mul you're safely allowed *less*
* than the available columns [255 per default] since carries
* are fixed up in the inner loop.
*/
@@ -4314,7 +4563,7 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
/* mu = ai * rho mod b
*
* The value of rho must be precalculated via
- * bn_mp_montgomery_setup() such that
+ * montgomery_setup() such that
* it equals -1/n0 mod b this allows the
* following inner loop to reduce the
* input one digit at a time
@@ -4378,10 +4627,13 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
return MP_OKAY;
}
+#endif
/* End: bn_mp_montgomery_reduce.c */
/* Start: bn_mp_montgomery_setup.c */
+#include <tommath.h>
+#ifdef BN_MP_MONTGOMERY_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4396,7 +4648,6 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* setups the montgomery reduction stuff */
int
@@ -4431,14 +4682,17 @@ mp_montgomery_setup (mp_int * n, mp_digit * rho)
#endif
/* rho = -1/m mod b */
- *rho = (((mp_digit) 1 << ((mp_digit) DIGIT_BIT)) - x) & MP_MASK;
+ *rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
return MP_OKAY;
}
+#endif
/* End: bn_mp_montgomery_setup.c */
/* Start: bn_mp_mul.c */
+#include <tommath.h>
+#ifdef BN_MP_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4453,7 +4707,6 @@ mp_montgomery_setup (mp_int * n, mp_digit * rho)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* high level multiplication (handles sign) */
int mp_mul (mp_int * a, mp_int * b, mp_int * c)
@@ -4462,12 +4715,18 @@ int mp_mul (mp_int * a, mp_int * b, mp_int * c)
neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
/* use Toom-Cook? */
+#ifdef BN_MP_TOOM_MUL_C
if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) {
res = mp_toom_mul(a, b, c);
+ } else
+#endif
+#ifdef BN_MP_KARATSUBA_MUL_C
/* use Karatsuba? */
- } else if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
+ if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
res = mp_karatsuba_mul (a, b, c);
- } else {
+ } else
+#endif
+ {
/* can we use the fast multiplier?
*
* The fast multiplier can be used if the output will
@@ -4476,21 +4735,30 @@ int mp_mul (mp_int * a, mp_int * b, mp_int * c)
*/
int digs = a->used + b->used + 1;
+#ifdef BN_FAST_S_MP_MUL_DIGS_C
if ((digs < MP_WARRAY) &&
MIN(a->used, b->used) <=
(1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
res = fast_s_mp_mul_digs (a, b, c, digs);
- } else {
- res = s_mp_mul (a, b, c);
- }
+ } else
+#endif
+#ifdef BN_S_MP_MUL_DIGS_C
+ res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
+#else
+ res = MP_VAL;
+#endif
+
}
- c->sign = neg;
+ c->sign = (c->used > 0) ? neg : MP_ZPOS;
return res;
}
+#endif
/* End: bn_mp_mul.c */
/* Start: bn_mp_mul_2.c */
+#include <tommath.h>
+#ifdef BN_MP_MUL_2_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4505,7 +4773,6 @@ int mp_mul (mp_int * a, mp_int * b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* b = a*2 */
int mp_mul_2(mp_int * a, mp_int * b)
@@ -4567,10 +4834,13 @@ int mp_mul_2(mp_int * a, mp_int * b)
b->sign = a->sign;
return MP_OKAY;
}
+#endif
/* End: bn_mp_mul_2.c */
/* Start: bn_mp_mul_2d.c */
+#include <tommath.h>
+#ifdef BN_MP_MUL_2D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4585,7 +4855,6 @@ int mp_mul_2(mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shift left by a certain bit count */
int mp_mul_2d (mp_int * a, int b, mp_int * c)
@@ -4650,10 +4919,13 @@ int mp_mul_2d (mp_int * a, int b, mp_int * c)
mp_clamp (c);
return MP_OKAY;
}
+#endif
/* End: bn_mp_mul_2d.c */
/* Start: bn_mp_mul_d.c */
+#include <tommath.h>
+#ifdef BN_MP_MUL_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4668,7 +4940,6 @@ int mp_mul_2d (mp_int * a, int b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* multiply by a digit */
int
@@ -4726,10 +4997,13 @@ mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
return MP_OKAY;
}
+#endif
/* End: bn_mp_mul_d.c */
/* Start: bn_mp_mulmod.c */
+#include <tommath.h>
+#ifdef BN_MP_MULMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4744,7 +5018,6 @@ mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* d = a * b (mod c) */
int
@@ -4765,10 +5038,13 @@ mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
mp_clear (&t);
return res;
}
+#endif
/* End: bn_mp_mulmod.c */
/* Start: bn_mp_n_root.c */
+#include <tommath.h>
+#ifdef BN_MP_N_ROOT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4783,7 +5059,6 @@ mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* find the n'th root of an integer
*
@@ -4895,10 +5170,13 @@ __T2:mp_clear (&t2);
__T1:mp_clear (&t1);
return res;
}
+#endif
/* End: bn_mp_n_root.c */
/* Start: bn_mp_neg.c */
+#include <tommath.h>
+#ifdef BN_MP_NEG_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4913,7 +5191,6 @@ __T1:mp_clear (&t1);
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* b = -a */
int mp_neg (mp_int * a, mp_int * b)
@@ -4927,10 +5204,13 @@ int mp_neg (mp_int * a, mp_int * b)
}
return MP_OKAY;
}
+#endif
/* End: bn_mp_neg.c */
/* Start: bn_mp_or.c */
+#include <tommath.h>
+#ifdef BN_MP_OR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4945,7 +5225,6 @@ int mp_neg (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* OR two ints together */
int mp_or (mp_int * a, mp_int * b, mp_int * c)
@@ -4975,10 +5254,13 @@ int mp_or (mp_int * a, mp_int * b, mp_int * c)
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_mp_or.c */
/* Start: bn_mp_prime_fermat.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_FERMAT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -4993,7 +5275,6 @@ int mp_or (mp_int * a, mp_int * b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* performs one Fermat test.
*
@@ -5035,10 +5316,13 @@ int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
__T:mp_clear (&t);
return err;
}
+#endif
/* End: bn_mp_prime_fermat.c */
/* Start: bn_mp_prime_is_divisible.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_IS_DIVISIBLE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5053,7 +5337,6 @@ __T:mp_clear (&t);
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* determines if an integers is divisible by one
* of the first PRIME_SIZE primes or not
@@ -5083,10 +5366,13 @@ int mp_prime_is_divisible (mp_int * a, int *result)
return MP_OKAY;
}
+#endif
/* End: bn_mp_prime_is_divisible.c */
/* Start: bn_mp_prime_is_prime.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_IS_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5101,12 +5387,11 @@ int mp_prime_is_divisible (mp_int * a, int *result)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* performs a variable number of rounds of Miller-Rabin
*
* Probability of error after t rounds is no more than
- * (1/4)^t when 1 <= t <= PRIME_SIZE
+
*
* Sets result to 1 if probably prime, 0 otherwise
*/
@@ -5164,10 +5449,13 @@ int mp_prime_is_prime (mp_int * a, int t, int *result)
__B:mp_clear (&b);
return err;
}
+#endif
/* End: bn_mp_prime_is_prime.c */
/* Start: bn_mp_prime_miller_rabin.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_MILLER_RABIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5182,7 +5470,6 @@ __B:mp_clear (&b);
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Miller-Rabin test of "a" to the base of "b" as described in
* HAC pp. 139 Algorithm 4.24
@@ -5265,10 +5552,13 @@ __R:mp_clear (&r);
__N1:mp_clear (&n1);
return err;
}
+#endif
/* End: bn_mp_prime_miller_rabin.c */
/* Start: bn_mp_prime_next_prime.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_NEXT_PRIME_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5283,7 +5573,6 @@ __N1:mp_clear (&n1);
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* finds the next prime after the number "a" using "t" trials
* of Miller-Rabin.
@@ -5433,10 +5722,13 @@ __ERR:
return err;
}
+#endif
/* End: bn_mp_prime_next_prime.c */
-/* Start: bn_mp_prime_random_ex.c */
+/* Start: bn_mp_prime_rabin_miller_trials.c */
+#include <tommath.h>
+#ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5451,7 +5743,58 @@ __ERR:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
+
+
+static const struct {
+ int k, t;
+} sizes[] = {
+{ 128, 28 },
+{ 256, 16 },
+{ 384, 10 },
+{ 512, 7 },
+{ 640, 6 },
+{ 768, 5 },
+{ 896, 4 },
+{ 1024, 4 }
+};
+
+/* returns # of RM trials required for a given bit size */
+int mp_prime_rabin_miller_trials(int size)
+{
+ int x;
+
+ for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) {
+ if (sizes[x].k == size) {
+ return sizes[x].t;
+ } else if (sizes[x].k > size) {
+ return (x == 0) ? sizes[0].t : sizes[x - 1].t;
+ }
+ }
+ return sizes[x-1].t + 1;
+}
+
+
+#endif
+
+/* End: bn_mp_prime_rabin_miller_trials.c */
+
+/* Start: bn_mp_prime_random_ex.c */
#include <tommath.h>
+#ifdef BN_MP_PRIME_RANDOM_EX_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
/* makes a truly random prime of a given size (bits),
*
@@ -5531,6 +5874,9 @@ int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback
/* is it prime? */
if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { goto error; }
+ if (res == MP_NO) {
+ continue;
+ }
if (flags & LTM_PRIME_SAFE) {
/* see if (a-1)/2 is prime */
@@ -5555,10 +5901,13 @@ error:
}
+#endif
/* End: bn_mp_prime_random_ex.c */
/* Start: bn_mp_radix_size.c */
+#include <tommath.h>
+#ifdef BN_MP_RADIX_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5573,7 +5922,6 @@ error:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* returns size of ASCII reprensentation */
int mp_radix_size (mp_int * a, int radix, int *size)
@@ -5624,10 +5972,13 @@ int mp_radix_size (mp_int * a, int radix, int *size)
return MP_OKAY;
}
+#endif
/* End: bn_mp_radix_size.c */
/* Start: bn_mp_radix_smap.c */
+#include <tommath.h>
+#ifdef BN_MP_RADIX_SMAP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5642,14 +5993,16 @@ int mp_radix_size (mp_int * a, int radix, int *size)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* chars used in radix conversions */
const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
+#endif
/* End: bn_mp_radix_smap.c */
/* Start: bn_mp_rand.c */
+#include <tommath.h>
+#ifdef BN_MP_RAND_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5664,7 +6017,6 @@ const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrs
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* makes a pseudo-random int of a given size */
int
@@ -5699,10 +6051,13 @@ mp_rand (mp_int * a, int digits)
return MP_OKAY;
}
+#endif
/* End: bn_mp_rand.c */
/* Start: bn_mp_read_radix.c */
+#include <tommath.h>
+#ifdef BN_MP_READ_RADIX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5717,7 +6072,6 @@ mp_rand (mp_int * a, int digits)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* read a string [ASCII] in a given radix */
int mp_read_radix (mp_int * a, char *str, int radix)
@@ -5779,10 +6133,13 @@ int mp_read_radix (mp_int * a, char *str, int radix)
}
return MP_OKAY;
}
+#endif
/* End: bn_mp_read_radix.c */
/* Start: bn_mp_read_signed_bin.c */
+#include <tommath.h>
+#ifdef BN_MP_READ_SIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5797,7 +6154,6 @@ int mp_read_radix (mp_int * a, char *str, int radix)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* read signed bin, big endian, first byte is 0==positive or 1==negative */
int
@@ -5819,10 +6175,13 @@ mp_read_signed_bin (mp_int * a, unsigned char *b, int c)
return MP_OKAY;
}
+#endif
/* End: bn_mp_read_signed_bin.c */
/* Start: bn_mp_read_unsigned_bin.c */
+#include <tommath.h>
+#ifdef BN_MP_READ_UNSIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5837,7 +6196,6 @@ mp_read_signed_bin (mp_int * a, unsigned char *b, int c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reads a unsigned char array, assumes the msb is stored first [big endian] */
int
@@ -5873,10 +6231,13 @@ mp_read_unsigned_bin (mp_int * a, unsigned char *b, int c)
mp_clamp (a);
return MP_OKAY;
}
+#endif
/* End: bn_mp_read_unsigned_bin.c */
/* Start: bn_mp_reduce.c */
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5891,7 +6252,6 @@ mp_read_unsigned_bin (mp_int * a, unsigned char *b, int c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reduces x mod m, assumes 0 < x < m**2, mu is
* precomputed via mp_reduce_setup.
@@ -5917,9 +6277,20 @@ mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
goto CLEANUP;
}
} else {
+#ifdef BN_S_MP_MUL_HIGH_DIGS_C
if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) {
goto CLEANUP;
}
+#elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
+ if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) {
+ goto CLEANUP;
+ }
+#else
+ {
+ res = MP_VAL;
+ goto CLEANUP;
+ }
+#endif
}
/* q3 = q2 / b**(k+1) */
@@ -5961,10 +6332,13 @@ CLEANUP:
return res;
}
+#endif
/* End: bn_mp_reduce.c */
/* Start: bn_mp_reduce_2k.c */
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -5979,7 +6353,6 @@ CLEANUP:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reduces a modulo n where n is of the form 2**p - d */
int
@@ -6021,10 +6394,13 @@ ERR:
return res;
}
+#endif
/* End: bn_mp_reduce_2k.c */
/* Start: bn_mp_reduce_2k_setup.c */
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_2K_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6039,7 +6415,6 @@ ERR:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* determines the setup value */
int
@@ -6067,10 +6442,13 @@ mp_reduce_2k_setup(mp_int *a, mp_digit *d)
mp_clear(&tmp);
return MP_OKAY;
}
+#endif
/* End: bn_mp_reduce_2k_setup.c */
/* Start: bn_mp_reduce_is_2k.c */
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_IS_2K_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6085,12 +6463,12 @@ mp_reduce_2k_setup(mp_int *a, mp_digit *d)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* determines if mp_reduce_2k can be used */
int mp_reduce_is_2k(mp_int *a)
{
- int ix, iy, iz, iw;
+ int ix, iy, iw;
+ mp_digit iz;
if (a->used == 0) {
return 0;
@@ -6107,7 +6485,7 @@ int mp_reduce_is_2k(mp_int *a)
return 0;
}
iz <<= 1;
- if (iz > (int)MP_MASK) {
+ if (iz > (mp_digit)MP_MASK) {
++iw;
iz = 1;
}
@@ -6116,10 +6494,13 @@ int mp_reduce_is_2k(mp_int *a)
return 1;
}
+#endif
/* End: bn_mp_reduce_is_2k.c */
/* Start: bn_mp_reduce_setup.c */
+#include <tommath.h>
+#ifdef BN_MP_REDUCE_SETUP_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6134,13 +6515,11 @@ int mp_reduce_is_2k(mp_int *a)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* pre-calculate the value required for Barrett reduction
* For a given modulus "b" it calulates the value required in "a"
*/
-int
-mp_reduce_setup (mp_int * a, mp_int * b)
+int mp_reduce_setup (mp_int * a, mp_int * b)
{
int res;
@@ -6149,10 +6528,13 @@ mp_reduce_setup (mp_int * a, mp_int * b)
}
return mp_div (a, b, a, NULL);
}
+#endif
/* End: bn_mp_reduce_setup.c */
/* Start: bn_mp_rshd.c */
+#include <tommath.h>
+#ifdef BN_MP_RSHD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6167,7 +6549,6 @@ mp_reduce_setup (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shift right a certain amount of digits */
void mp_rshd (mp_int * a, int b)
@@ -6219,10 +6600,13 @@ void mp_rshd (mp_int * a, int b)
/* remove excess digits */
a->used -= b;
}
+#endif
/* End: bn_mp_rshd.c */
/* Start: bn_mp_set.c */
+#include <tommath.h>
+#ifdef BN_MP_SET_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6237,7 +6621,6 @@ void mp_rshd (mp_int * a, int b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* set to a digit */
void mp_set (mp_int * a, mp_digit b)
@@ -6246,10 +6629,13 @@ void mp_set (mp_int * a, mp_digit b)
a->dp[0] = b & MP_MASK;
a->used = (a->dp[0] != 0) ? 1 : 0;
}
+#endif
/* End: bn_mp_set.c */
/* Start: bn_mp_set_int.c */
+#include <tommath.h>
+#ifdef BN_MP_SET_INT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6264,7 +6650,6 @@ void mp_set (mp_int * a, mp_digit b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* set a 32-bit const */
int mp_set_int (mp_int * a, unsigned long b)
@@ -6292,10 +6677,13 @@ int mp_set_int (mp_int * a, unsigned long b)
mp_clamp (a);
return MP_OKAY;
}
+#endif
/* End: bn_mp_set_int.c */
/* Start: bn_mp_shrink.c */
+#include <tommath.h>
+#ifdef BN_MP_SHRINK_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6310,7 +6698,6 @@ int mp_set_int (mp_int * a, unsigned long b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* shrink a bignum */
int mp_shrink (mp_int * a)
@@ -6325,10 +6712,13 @@ int mp_shrink (mp_int * a)
}
return MP_OKAY;
}
+#endif
/* End: bn_mp_shrink.c */
/* Start: bn_mp_signed_bin_size.c */
+#include <tommath.h>
+#ifdef BN_MP_SIGNED_BIN_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6343,17 +6733,19 @@ int mp_shrink (mp_int * a)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* get the size for an signed equivalent */
int mp_signed_bin_size (mp_int * a)
{
return 1 + mp_unsigned_bin_size (a);
}
+#endif
/* End: bn_mp_signed_bin_size.c */
/* Start: bn_mp_sqr.c */
+#include <tommath.h>
+#ifdef BN_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6368,7 +6760,6 @@ int mp_signed_bin_size (mp_int * a)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* computes b = a*a */
int
@@ -6376,29 +6767,43 @@ mp_sqr (mp_int * a, mp_int * b)
{
int res;
+#ifdef BN_MP_TOOM_SQR_C
/* use Toom-Cook? */
if (a->used >= TOOM_SQR_CUTOFF) {
res = mp_toom_sqr(a, b);
/* Karatsuba? */
- } else if (a->used >= KARATSUBA_SQR_CUTOFF) {
+ } else
+#endif
+#ifdef BN_MP_KARATSUBA_SQR_C
+if (a->used >= KARATSUBA_SQR_CUTOFF) {
res = mp_karatsuba_sqr (a, b);
- } else {
+ } else
+#endif
+ {
+#ifdef BN_FAST_S_MP_SQR_C
/* can we use the fast comba multiplier? */
if ((a->used * 2 + 1) < MP_WARRAY &&
a->used <
(1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
res = fast_s_mp_sqr (a, b);
- } else {
+ } else
+#endif
+#ifdef BN_S_MP_SQR_C
res = s_mp_sqr (a, b);
- }
+#else
+ res = MP_VAL;
+#endif
}
b->sign = MP_ZPOS;
return res;
}
+#endif
/* End: bn_mp_sqr.c */
/* Start: bn_mp_sqrmod.c */
+#include <tommath.h>
+#ifdef BN_MP_SQRMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6413,7 +6818,6 @@ mp_sqr (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* c = a * a (mod b) */
int
@@ -6434,10 +6838,13 @@ mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
mp_clear (&t);
return res;
}
+#endif
/* End: bn_mp_sqrmod.c */
/* Start: bn_mp_sqrt.c */
+#include <tommath.h>
+#ifdef BN_MP_SQRT_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6452,7 +6859,6 @@ mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* this function is less generic than mp_n_root, simpler and faster */
int mp_sqrt(mp_int *arg, mp_int *ret)
@@ -6513,10 +6919,13 @@ E2: mp_clear(&t1);
return res;
}
+#endif
/* End: bn_mp_sqrt.c */
/* Start: bn_mp_sub.c */
+#include <tommath.h>
+#ifdef BN_MP_SUB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6531,7 +6940,6 @@ E2: mp_clear(&t1);
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* high level subtraction (handles signs) */
int
@@ -6570,10 +6978,13 @@ mp_sub (mp_int * a, mp_int * b, mp_int * c)
return res;
}
+#endif
/* End: bn_mp_sub.c */
/* Start: bn_mp_sub_d.c */
+#include <tommath.h>
+#ifdef BN_MP_SUB_D_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6588,7 +6999,6 @@ mp_sub (mp_int * a, mp_int * b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* single digit subtraction */
int
@@ -6657,10 +7067,13 @@ mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
return MP_OKAY;
}
+#endif
/* End: bn_mp_sub_d.c */
/* Start: bn_mp_submod.c */
+#include <tommath.h>
+#ifdef BN_MP_SUBMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6675,7 +7088,6 @@ mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* d = a - b (mod c) */
int
@@ -6697,10 +7109,13 @@ mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
mp_clear (&t);
return res;
}
+#endif
/* End: bn_mp_submod.c */
/* Start: bn_mp_to_signed_bin.c */
+#include <tommath.h>
+#ifdef BN_MP_TO_SIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6715,7 +7130,6 @@ mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* store in signed [big endian] format */
int
@@ -6729,10 +7143,13 @@ mp_to_signed_bin (mp_int * a, unsigned char *b)
b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1);
return MP_OKAY;
}
+#endif
/* End: bn_mp_to_signed_bin.c */
/* Start: bn_mp_to_unsigned_bin.c */
+#include <tommath.h>
+#ifdef BN_MP_TO_UNSIGNED_BIN_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6747,7 +7164,6 @@ mp_to_signed_bin (mp_int * a, unsigned char *b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* store in unsigned [big endian] format */
int
@@ -6776,10 +7192,13 @@ mp_to_unsigned_bin (mp_int * a, unsigned char *b)
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_mp_to_unsigned_bin.c */
/* Start: bn_mp_toom_mul.c */
+#include <tommath.h>
+#ifdef BN_MP_TOOM_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -6794,9 +7213,13 @@ mp_to_unsigned_bin (mp_int * a, unsigned char *b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
-/* multiplication using the Toom-Cook 3-way algorithm */
+/* multiplication using the Toom-Cook 3-way algorithm
+ *
+ * Much more complicated than Karatsuba but has a lower asymptotic running time of
+ * O(N**1.464). This algorithm is only particularly useful on VERY large
+ * inputs (we're talking 1000s of digits here...).
+*/
int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
{
mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
@@ -7052,10 +7475,13 @@ ERR:
return res;
}
+#endif
/* End: bn_mp_toom_mul.c */
/* Start: bn_mp_toom_sqr.c */
+#include <tommath.h>
+#ifdef BN_MP_TOOM_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -7070,7 +7496,6 @@ ERR:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* squaring using Toom-Cook 3-way algorithm */
int
@@ -7276,10 +7701,13 @@ ERR:
return res;
}
+#endif
/* End: bn_mp_toom_sqr.c */
/* Start: bn_mp_toradix.c */
+#include <tommath.h>
+#ifdef BN_MP_TORADIX_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -7294,7 +7722,6 @@ ERR:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* stores a bignum as a ASCII string in a given radix (2..64) */
int mp_toradix (mp_int * a, char *str, int radix)
@@ -7349,10 +7776,13 @@ int mp_toradix (mp_int * a, char *str, int radix)
return MP_OKAY;
}
+#endif
/* End: bn_mp_toradix.c */
/* Start: bn_mp_toradix_n.c */
+#include <tommath.h>
+#ifdef BN_MP_TORADIX_N_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -7367,7 +7797,6 @@ int mp_toradix (mp_int * a, char *str, int radix)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* stores a bignum as a ASCII string in a given radix (2..64)
*
@@ -7436,10 +7865,13 @@ int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
return MP_OKAY;
}
+#endif
/* End: bn_mp_toradix_n.c */
/* Start: bn_mp_unsigned_bin_size.c */
+#include <tommath.h>
+#ifdef BN_MP_UNSIGNED_BIN_SIZE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -7454,7 +7886,6 @@ int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* get the size for an unsigned equivalent */
int
@@ -7463,10 +7894,13 @@ mp_unsigned_bin_size (mp_int * a)
int size = mp_count_bits (a);
return (size / 8 + ((size & 7) != 0 ? 1 : 0));
}
+#endif
/* End: bn_mp_unsigned_bin_size.c */
/* Start: bn_mp_xor.c */
+#include <tommath.h>
+#ifdef BN_MP_XOR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -7481,7 +7915,6 @@ mp_unsigned_bin_size (mp_int * a)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* XOR two ints together */
int
@@ -7505,17 +7938,20 @@ mp_xor (mp_int * a, mp_int * b, mp_int * c)
}
for (ix = 0; ix < px; ix++) {
- t.dp[ix] ^= x->dp[ix];
+
}
mp_clamp (&t);
mp_exch (c, &t);
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_mp_xor.c */
/* Start: bn_mp_zero.c */
+#include <tommath.h>
+#ifdef BN_MP_ZERO_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -7530,7 +7966,6 @@ mp_xor (mp_int * a, mp_int * b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* set to zero */
void
@@ -7540,65 +7975,13 @@ mp_zero (mp_int * a)
a->used = 0;
memset (a->dp, 0, sizeof (mp_digit) * a->alloc);
}
+#endif
/* End: bn_mp_zero.c */
-/* Start: bn_prime_sizes_tab.c */
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-#include <tommath.h>
-
-/* this table gives the # of rabin miller trials for a prob of failure lower than 2^-96 */
-static const struct {
- int k, t;
-} sizes[] = {
-{ 128, 28 },
-{ 256, 16 },
-{ 384, 10 },
-{ 512, 7 },
-{ 640, 6 },
-{ 768, 5 },
-{ 896, 4 },
-{ 1024, 4 },
-{ 1152, 3 },
-{ 1280, 3 },
-{ 1408, 3 },
-{ 1536, 3 },
-{ 1664, 3 },
-{ 1792, 2 } };
-
-/* returns # of RM trials required for a given bit size */
-int mp_prime_rabin_miller_trials(int size)
-{
- int x;
-
- for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) {
- if (sizes[x].k == size) {
- return sizes[x].t;
- } else if (sizes[x].k > size) {
- return (x == 0) ? sizes[0].t : sizes[x - 1].t;
- }
- }
- return 1;
-}
-
-
-
-/* End: bn_prime_sizes_tab.c */
-
/* Start: bn_prime_tab.c */
+#include <tommath.h>
+#ifdef BN_PRIME_TAB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -7613,7 +7996,6 @@ int mp_prime_rabin_miller_trials(int size)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
const mp_digit __prime_tab[] = {
0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
@@ -7654,10 +8036,13 @@ const mp_digit __prime_tab[] = {
0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
#endif
};
+#endif
/* End: bn_prime_tab.c */
/* Start: bn_reverse.c */
+#include <tommath.h>
+#ifdef BN_REVERSE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -7672,7 +8057,6 @@ const mp_digit __prime_tab[] = {
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* reverse an array, used for radix code */
void
@@ -7691,10 +8075,13 @@ bn_reverse (unsigned char *s, int len)
--iy;
}
}
+#endif
/* End: bn_reverse.c */
/* Start: bn_s_mp_add.c */
+#include <tommath.h>
+#ifdef BN_S_MP_ADD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -7709,7 +8096,6 @@ bn_reverse (unsigned char *s, int len)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* low level addition, based on HAC pp.594, Algorithm 14.7 */
int
@@ -7798,10 +8184,13 @@ s_mp_add (mp_int * a, mp_int * b, mp_int * c)
mp_clamp (c);
return MP_OKAY;
}
+#endif
/* End: bn_s_mp_add.c */
/* Start: bn_s_mp_exptmod.c */
+#include <tommath.h>
+#ifdef BN_S_MP_EXPTMOD_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -7816,7 +8205,6 @@ s_mp_add (mp_int * a, mp_int * b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
#ifdef MP_LOW_MEM
#define TAB_SIZE 32
@@ -8036,10 +8424,13 @@ __M:
}
return err;
}
+#endif
/* End: bn_s_mp_exptmod.c */
/* Start: bn_s_mp_mul_digs.c */
+#include <tommath.h>
+#ifdef BN_S_MP_MUL_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -8054,7 +8445,6 @@ __M:
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* multiplies |a| * |b| and only computes upto digs digits of result
* HAC pp. 595, Algorithm 14.12 Modified so you can control how
@@ -8125,10 +8515,13 @@ s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_s_mp_mul_digs.c */
/* Start: bn_s_mp_mul_high_digs.c */
+#include <tommath.h>
+#ifdef BN_S_MP_MUL_HIGH_DIGS_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -8143,7 +8536,6 @@ s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* multiplies |a| * |b| and does not compute the lower digs digits
* [meant to get the higher part of the product]
@@ -8158,10 +8550,12 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
mp_digit tmpx, *tmpt, *tmpy;
/* can we use the fast multiplier? */
+#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
if (((a->used + b->used + 1) < MP_WARRAY)
&& MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
return fast_s_mp_mul_high_digs (a, b, c, digs);
}
+#endif
if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
return res;
@@ -8202,10 +8596,13 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_s_mp_mul_high_digs.c */
/* Start: bn_s_mp_sqr.c */
+#include <tommath.h>
+#ifdef BN_S_MP_SQR_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -8220,7 +8617,6 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
int
@@ -8285,10 +8681,13 @@ s_mp_sqr (mp_int * a, mp_int * b)
mp_clear (&t);
return MP_OKAY;
}
+#endif
/* End: bn_s_mp_sqr.c */
/* Start: bn_s_mp_sub.c */
+#include <tommath.h>
+#ifdef BN_S_MP_SUB_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -8303,7 +8702,6 @@ s_mp_sqr (mp_int * a, mp_int * b)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
int
@@ -8372,10 +8770,13 @@ s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
return MP_OKAY;
}
+#endif
/* End: bn_s_mp_sub.c */
/* Start: bncore.c */
+#include <tommath.h>
+#ifdef BNCORE_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis
*
* LibTomMath is a library that provides multiple-precision
@@ -8390,23 +8791,21 @@ s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
*
* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
*/
-#include <tommath.h>
/* Known optimal configurations
CPU /Compiler /MUL CUTOFF/SQR CUTOFF
-------------------------------------------------------------
- Intel P4 /GCC v3.2 / 70/ 108
- AMD Athlon XP /GCC v3.2 / 109/ 127
-
+ Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-)
+
*/
-/* configured for a AMD XP Thoroughbred core with etc/tune.c */
-int KARATSUBA_MUL_CUTOFF = 109, /* Min. number of digits before Karatsuba multiplication is used. */
- KARATSUBA_SQR_CUTOFF = 127, /* Min. number of digits before Karatsuba squaring is used. */
+int KARATSUBA_MUL_CUTOFF = 88, /* Min. number of digits before Karatsuba multiplication is used. */
+ KARATSUBA_SQR_CUTOFF = 128, /* Min. number of digits before Karatsuba squaring is used. */
TOOM_MUL_CUTOFF = 350, /* no optimal values of these are known yet so set em high */
TOOM_SQR_CUTOFF = 400;
+#endif
/* End: bncore.c */
diff --git a/pretty.build b/pretty.build
new file mode 100644
index 00000000..a708b8af
--- /dev/null
+++ b/pretty.build
@@ -0,0 +1,66 @@
+#!/bin/perl -w
+#
+# Cute little builder for perl
+# Total waste of development time...
+#
+# This will build all the object files and then the archive .a file
+# requires GCC, GNU make and a sense of humour.
+#
+# Tom St Denis
+use strict;
+
+my $count = 0;
+my $starttime = time;
+my $rate = 0;
+print "Scanning for source files...\n";
+foreach my $filename (glob "*.c") {
+ ++$count;
+}
+print "Source files to build: $count\nBuilding...\n";
+my $i = 0;
+my $lines = 0;
+my $filesbuilt = 0;
+foreach my $filename (glob "*.c") {
+ printf("Building %3.2f%%, ", (++$i/$count)*100.0);
+ if ($i % 4 == 0) { print "/, "; }
+ if ($i % 4 == 1) { print "-, "; }
+ if ($i % 4 == 2) { print "\\, "; }
+ if ($i % 4 == 3) { print "|, "; }
+ if ($rate > 0) {
+ my $tleft = ($count - $i) / $rate;
+ my $tsec = $tleft%60;
+ my $tmin = ($tleft/60)%60;
+ my $thour = ($tleft/3600)%60;
+ printf("%2d:%02d:%02d left, ", $thour, $tmin, $tsec);
+ }
+ my $cnt = ($i/$count)*30.0;
+ my $x = 0;
+ print "[";
+ for (; $x < $cnt; $x++) { print "#"; }
+ for (; $x < 30; $x++) { print " "; }
+ print "]\r";
+ my $tmp = $filename;
+ $tmp =~ s/\.c/".o"/ge;
+ if (open(SRC, "<$tmp")) {
+ close SRC;
+ } else {
+ !system("make $tmp > /dev/null 2>/dev/null") or die "\nERROR: Failed to make $tmp!!!\n";
+ open( SRC, "<$filename" ) or die "Couldn't open $filename for reading: $!";
+ ++$lines while (<SRC>);
+ close SRC or die "Error closing $filename after reading: $!";
+ ++$filesbuilt;
+ }
+
+ # update timer
+ if (time != $starttime) {
+ my $delay = time - $starttime;
+ $rate = $i/$delay;
+ }
+}
+
+# finish building the library
+printf("\nFinished building source (%d seconds, %3.2f files per second).\n", time - $starttime, $rate);
+print "Compiled approximately $filesbuilt files and $lines lines of code.\n";
+print "Doing final make (building archive...)\n";
+!system("make > /dev/null 2>/dev/null") or die "\nERROR: Failed to perform last make command!!!\n";
+print "done.\n";
\ No newline at end of file
diff --git a/tommath.h b/tommath.h
index 00299947..896d389a 100644
--- a/tommath.h
+++ b/tommath.h
@@ -21,6 +21,8 @@
#include <ctype.h>
#include <limits.h>
+#include <tommath_class.h>
+
#undef MIN
#define MIN(x,y) ((x)<(y)?(x):(y))
#undef MAX
@@ -39,6 +41,14 @@ extern "C" {
#endif
+
+/* detect 64-bit mode if possible */
+#if defined(__x86_64__)
+ #if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT))
+ #define MP_64BIT
+ #endif
+#endif
+
/* some default configurations.
*
* A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
@@ -60,7 +70,7 @@ extern "C" {
typedef signed long long long64;
#endif
- typedef ulong64 mp_digit;
+ typedef unsigned long mp_digit;
typedef unsigned long mp_word __attribute__ ((mode(TI)));
#define DIGIT_BIT 60
@@ -153,7 +163,7 @@ extern int KARATSUBA_MUL_CUTOFF,
/* default precision */
#ifndef MP_PREC
- #ifdef MP_LOW_MEM
+ #ifndef MP_LOW_MEM
#define MP_PREC 64 /* default digits of precision */
#else
#define MP_PREC 8 /* default digits of precision */
@@ -541,6 +551,7 @@ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c);
int mp_karatsuba_sqr(mp_int *a, mp_int *b);
int mp_toom_sqr(mp_int *a, mp_int *b);
int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c);
+int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c);
int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode);
int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y);
diff --git a/tommath.pdf b/tommath.pdf
index fc3301a306fc0e63f9012d97b879bbed326ebf54..18cac6f2db318bf5fb3dae69c62855dfbce54bbe 100644
GIT binary patch
delta 755840
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diff --git a/tommath.src b/tommath.src
index 0389831c..6ee842d7 100644
--- a/tommath.src
+++ b/tommath.src
@@ -258,7 +258,7 @@ floating point is meant to be implemented in hardware the precision of the manti
a mantissa of much larger precision than hardware alone can efficiently support. This approach could be useful where
scientific applications must minimize the total output error over long calculations.
-Another use for large integers is within arithmetic on polynomials of large characteristic (i.e. $GF(p)[x]$ for large $p$).
+Yet another use for large integers is within arithmetic on polynomials of large characteristic (i.e. $GF(p)[x]$ for large $p$).
In fact the library discussed within this text has already been used to form a polynomial basis library\footnote{See \url{http://poly.libtomcrypt.org} for more details.}.
\subsection{Benefits of Multiple Precision Arithmetic}
@@ -316,7 +316,7 @@ the reader how the algorithms fit together as well as where to start on various
\section{Discussion and Notation}
\subsection{Notation}
-A multiple precision integer of $n$-digits shall be denoted as $x = (x_{n-1} ... x_1 x_0)_{ \beta }$ and represent
+A multiple precision integer of $n$-digits shall be denoted as $x = (x_{n-1}, \ldots, x_1, x_0)_{ \beta }$ and represent
the integer $x \equiv \sum_{i=0}^{n-1} x_i\beta^i$. The elements of the array $x$ are said to be the radix $\beta$ digits
of the integer. For example, $x = (1,2,3)_{10}$ would represent the integer
$1\cdot 10^2 + 2\cdot10^1 + 3\cdot10^0 = 123$.
@@ -339,12 +339,11 @@ algorithms will be used to establish the relevant theory which will subsequently
precision algorithm to solve the same problem.
\subsection{Precision Notation}
-For the purposes of this text a single precision variable must be able to represent integers in the range
-$0 \le x < q \beta$ while a double precision variable must be able to represent integers in the range
-$0 \le x < q \beta^2$. The variable $\beta$ represents the radix of a single digit of a multiple precision integer and
-must be of the form $q^p$ for $q, p \in \Z^+$. The extra radix-$q$ factor allows additions and subtractions to proceed
-without truncation of the carry. Since all modern computers are binary, it is assumed that $q$ is two, for all intents
-and purposes.
+The variable $\beta$ represents the radix of a single digit of a multiple precision integer and
+must be of the form $q^p$ for $q, p \in \Z^+$. A single precision variable must be able to represent integers in
+the range $0 \le x < q \beta$ while a double precision variable must be able to represent integers in the range
+$0 \le x < q \beta^2$. The extra radix-$q$ factor allows additions and subtractions to proceed without truncation of the
+carry. Since all modern computers are binary, it is assumed that $q$ is two.
\index{mp\_digit} \index{mp\_word}
Within the source code that will be presented for each algorithm, the data type \textbf{mp\_digit} will represent
@@ -376,7 +375,7 @@ the $/$ division symbol is used the intention is to perform an integer division
$5/2 = 2$ which will often be written as $\lfloor 5/2 \rfloor = 2$ for clarity. When an expression is written as a
fraction a real value division is implied, for example ${5 \over 2} = 2.5$.
-The norm of a multiple precision integer, for example, $\vert \vert x \vert \vert$ will be used to represent the number of digits in the representation
+The norm of a multiple precision integer, for example $\vert \vert x \vert \vert$, will be used to represent the number of digits in the representation
of the integer. For example, $\vert \vert 123 \vert \vert = 3$ and $\vert \vert 79452 \vert \vert = 5$.
\subsection{Work Effort}
@@ -569,7 +568,7 @@ By building outwards from a base foundation instead of using a parallel design m
highly modular. Being highly modular is a desirable property of any project as it often means the resulting product
has a small footprint and updates are easy to perform.
-Usually when I start a project I will begin with the header file. I define the data types I think I will need and
+Usually when I start a project I will begin with the header files. I define the data types I think I will need and
prototype the initial functions that are not dependent on other functions (within the library). After I
implement these base functions I prototype more dependent functions and implement them. The process repeats until
I implement all of the functions I require. For example, in the case of LibTomMath I implemented functions such as
@@ -619,14 +618,26 @@ any such data type but it does provide for making composite data types known as
used within LibTomMath.
\index{mp\_int}
-\begin{verbatim}
-typedef struct {
- int used, alloc, sign;
- mp_digit *dp;
-} mp_int;
-\end{verbatim}
+\begin{figure}[here]
+\begin{center}
+\begin{small}
+%\begin{verbatim}
+\begin{tabular}{|l|}
+\hline
+typedef struct \{ \\
+\hspace{3mm}int used, alloc, sign;\\
+\hspace{3mm}mp\_digit *dp;\\
+\} \textbf{mp\_int}; \\
+\hline
+\end{tabular}
+%\end{verbatim}
+\end{small}
+\caption{The mp\_int Structure}
+\label{fig:mpint}
+\end{center}
+\end{figure}
-The mp\_int structure can be broken down as follows.
+The mp\_int structure (fig. \ref{fig:mpint}) can be broken down as follows.
\begin{enumerate}
\item The \textbf{used} parameter denotes how many digits of the array \textbf{dp} contain the digits used to represent
@@ -701,9 +712,10 @@ fault by dereferencing memory not owned by the application.
In the case of LibTomMath the only errors that are checked for are related to inappropriate inputs (division by zero for
instance) and memory allocation errors. It will not check that the mp\_int passed to any function is valid nor
will it check pointers for validity. Any function that can cause a runtime error will return an error code as an
-\textbf{int} data type with one of the following values.
+\textbf{int} data type with one of the following values (fig \ref{fig:errcodes}).
\index{MP\_OKAY} \index{MP\_VAL} \index{MP\_MEM}
+\begin{figure}[here]
\begin{center}
\begin{tabular}{|l|l|}
\hline \textbf{Value} & \textbf{Meaning} \\
@@ -713,6 +725,9 @@ will it check pointers for validity. Any function that can cause a runtime erro
\hline
\end{tabular}
\end{center}
+\caption{LibTomMath Error Codes}
+\label{fig:errcodes}
+\end{figure}
When an error is detected within a function it should free any memory it allocated, often during the initialization of
temporary mp\_ints, and return as soon as possible. The goal is to leave the system in the same state it was when the
@@ -748,6 +763,7 @@ to zero. The \textbf{used} count set to zero and \textbf{sign} set to \textbf{M
An mp\_int is said to be initialized if it is set to a valid, preferably default, state such that all of the members of the
structure are set to valid values. The mp\_init algorithm will perform such an action.
+\index{mp\_init}
\begin{figure}[here]
\begin{center}
\begin{tabular}{l}
@@ -770,17 +786,23 @@ structure are set to valid values. The mp\_init algorithm will perform such an
\end{figure}
\textbf{Algorithm mp\_init.}
-The \textbf{MP\_PREC} name represents a constant\footnote{Defined in the ``tommath.h'' header file within LibTomMath.}
-used to dictate the minimum precision of allocated mp\_int integers. Ideally, it is at least equal to $32$ since for most
-purposes that will be more than enough.
+The purpose of this function is to initialize an mp\_int structure so that the rest of the library can properly
+manipulte it. It is assumed that the input may not have had any of its members previously initialized which is certainly
+a valid assumption if the input resides on the stack.
-Memory for the default number of digits is allocated first. If the allocation fails the algorithm returns immediately
-with the \textbf{MP\_MEM} error code. If the allocation succeeds the remaining members of the mp\_int structure
-must be initialized to reflect the default initial state.
+Before any of the members such as \textbf{sign}, \textbf{used} or \textbf{alloc} are initialized the memory for
+the digits is allocated. If this fails the function returns before setting any of the other members. The \textbf{MP\_PREC}
+name represents a constant\footnote{Defined in the ``tommath.h'' header file within LibTomMath.}
+used to dictate the minimum precision of newly initialized mp\_int integers. Ideally, it is at least equal to the smallest
+precision number you'll be working with.
-The allocated digits are all set to zero (step three) to ensure they are in a known state. The \textbf{sign}, \textbf{used}
-and \textbf{alloc} are subsequently initialized to represent the zero integer. By step seven the algorithm returns a success
-code and the mp\_int $a$ has been successfully initialized to a valid state representing the integer zero.
+Allocating a block of digits at first instead of a single digit has the benefit of lowering the number of usually slow
+heap operations later functions will have to perform in the future. If \textbf{MP\_PREC} is set correctly the slack
+memory and the number of heap operations will be trivial.
+
+Once the allocation has been made the digits have to be set to zero as well as the \textbf{used}, \textbf{sign} and
+\textbf{alloc} members initialized. This ensures that the mp\_int will always represent the default state of zero regardless
+of the original condition of the input.
\textbf{Remark.}
This function introduces the idiosyncrasy that all iterative loops, commonly initiated with the ``for'' keyword, iterate incrementally
@@ -796,19 +818,21 @@ One immediate observation of this initializtion function is that it does not ret
is assumed that the caller has already allocated memory for the mp\_int structure, typically on the application stack. The
call to mp\_init() is used only to initialize the members of the structure to a known default state.
-Before any of the other members of the structure are initialized memory from the application heap is allocated with
-the calloc() function (line @22,calloc@). The size of the allocated memory is large enough to hold \textbf{MP\_PREC}
-mp\_digit variables. The calloc() function is used instead\footnote{calloc() will allocate memory in the same
-manner as malloc() except that it also sets the contents to zero upon successfully allocating the memory.} of malloc()
-since digits have to be set to zero for the function to finish correctly. The \textbf{OPT\_CAST} token is a macro
-definition which will turn into a cast from void * to mp\_digit * for C++ compilers. It is not required for C compilers.
+Here we see (line @23,XMALLOC@) the memory allocation is performed first. This allows us to exit cleanly and quickly
+if there is an error. If the allocation fails the routine will return \textbf{MP\_MEM} to the caller to indicate there
+was a memory error. The function XMALLOC is what actually allocates the memory. Technically XMALLOC is not a function
+but a macro defined in ``tommath.h``. By default, XMALLOC will evaluate to malloc() which is the C library's built--in
+memory allocation routine.
-After the memory has been successfully allocated the remainder of the members are initialized
-(lines @29,used@ through @31,sign@) to their respective default states. At this point the algorithm has succeeded and
-a success code is returned to the calling function.
+In order to assure the mp\_int is in a known state the digits must be set to zero. On most platforms this could have been
+accomplished by using calloc() instead of malloc(). However, to correctly initialize a integer type to a given value in a
+portable fashion you have to actually assign the value. The for loop (line @28,for@) performs this required
+operation.
-If this function returns \textbf{MP\_OKAY} it is safe to assume the mp\_int structure has been properly initialized and
-is safe to use with other functions within the library.
+After the memory has been successfully initialized the remainder of the members are initialized
+(lines @29,used@ through @31,sign@) to their respective default states. At this point the algorithm has succeeded and
+a success code is returned to the calling function. If this function returns \textbf{MP\_OKAY} it is safe to assume the
+mp\_int structure has been properly initialized and is safe to use with other functions within the library.
\subsection{Clearing an mp\_int}
When an mp\_int is no longer required by the application, the memory that has been allocated for its digits must be
@@ -819,7 +843,7 @@ returned to the application's memory pool with the mp\_clear algorithm.
\begin{tabular}{l}
\hline Algorithm \textbf{mp\_clear}. \\
\textbf{Input}. An mp\_int $a$ \\
-\textbf{Output}. The memory for $a$ is freed for reuse. \\
+\textbf{Output}. The memory for $a$ shall be deallocated. \\
\hline \\
1. If $a$ has been previously freed then return(\textit{MP\_OKAY}). \\
2. for $n$ from 0 to $a.used - 1$ do \\
@@ -836,32 +860,31 @@ returned to the application's memory pool with the mp\_clear algorithm.
\end{figure}
\textbf{Algorithm mp\_clear.}
-This algorithm releases the memory allocated for an mp\_int back into the memory pool for reuse. It is designed
-such that a given mp\_int structure can be cleared multiple times between initializations without attempting to
-free the memory twice\footnote{In ISO C for example, calling free() twice on the same memory block causes undefinied
-behaviour.}.
-
-The first step determines if the mp\_int structure has been marked as free already. If it has, the algorithm returns
-success immediately as no further actions are required. Otherwise, the algorithm will proceed to put the structure
-in a known empty and otherwise invalid state. First the digits of the mp\_int are set to zero. The memory that has been allocated for the
-digits is then freed. The \textbf{used} and \textbf{alloc} counts are both set to zero and the \textbf{sign} set to
-\textbf{MP\_ZPOS}. This known fixed state for cleared mp\_int structures will make debuging easier for the end
-developer. That is, if they spot (via their debugger) an mp\_int they are using that is in this state it will be
-obvious that they erroneously and prematurely cleared the mp\_int structure.
-
-Note that once an mp\_int has been cleared the mp\_int structure is no longer in a valid state for any other algorithm
+This algorithm accomplishes two goals. First, it clears the digits and the other mp\_int members. This ensures that
+if a developer accidentally re-uses a cleared structure it is less likely to cause problems. The second goal
+is to free the allocated memory.
+
+The logic behind the algorithm is extended by marking cleared mp\_int structures so that subsequent calls to this
+algorithm will not try to free the memory multiple times. Cleared mp\_ints are detectable by having a pre-defined invalid
+digit pointer \textbf{dp} setting.
+
+Once an mp\_int has been cleared the mp\_int structure is no longer in a valid state for any other algorithm
with the exception of algorithms mp\_init, mp\_init\_copy, mp\_init\_size and mp\_clear.
EXAM,bn_mp_clear.c
-The ``if'' statement (line @21,a->dp != NULL@) prevents the heap from being corrupted if a user double-frees an
-mp\_int. This is because once the memory is freed the pointer is set to \textbf{NULL} (line @30,NULL@).
+The algorithm only operates on the mp\_int if it hasn't been previously cleared. The if statement (line @23,a->dp != NULL@)
+checks to see if the \textbf{dp} member is not \textbf{NULL}. If the mp\_int is a valid mp\_int then \textbf{dp} cannot be
+\textbf{NULL} in which case the if statement will evaluate to true.
+
+The digits of the mp\_int are cleared by the for loop (line @25,for@) which assigns a zero to every digit. Similar to mp\_init()
+the digits are assigned zero instead of using block memory operations (such as memset()) since this is more portable.
-Without the check, code that accidentally calls mp\_clear twice for a given mp\_int structure would try to free the memory
-allocated for the digits twice. This may cause some C libraries to signal a fault. By setting the pointer to
-\textbf{NULL} it helps debug code that may inadvertently free the mp\_int before it is truly not needed, because attempts
-to reference digits should fail immediately. The allocated digits are set to zero before being freed (line @24,memset@).
-This is ideal for cryptographic situations where the integer that the mp\_int represents might need to be kept a secret.
+The digits are deallocated off the heap via the XFREE macro. Similar to XMALLOC the XFREE macro actually evaluates to
+a standard C library function. In this case the free() function. Since free() only deallocates the memory the pointer
+still has to be reset to \textbf{NULL} manually (line @33,NULL@).
+
+Now that the digits have been cleared and deallocated the other members are set to their final values (lines @34,= 0@ and @35,ZPOS@).
\section{Maintenance Algorithms}
@@ -889,7 +912,7 @@ must be re-sized appropriately to accomodate the result. The mp\_grow algorithm
1. if $a.alloc \ge b$ then return(\textit{MP\_OKAY}) \\
2. $u \leftarrow b\mbox{ (mod }MP\_PREC\mbox{)}$ \\
3. $v \leftarrow b + 2 \cdot MP\_PREC - u$ \\
-4. Re-Allocate the array of digits $a$ to size $v$ \\
+4. Re-allocate the array of digits $a$ to size $v$ \\
5. If the allocation failed then return(\textit{MP\_MEM}). \\
6. for n from a.alloc to $v - 1$ do \\
\hspace{+3mm}6.1 $a_n \leftarrow 0$ \\
@@ -914,15 +937,19 @@ assumed to contain undefined values they are initially set to zero.
EXAM,bn_mp_grow.c
-The first step is to see if we actually need to perform a re-allocation at all (line @24,a->alloc < size@). If a reallocation
-must occur the digit count is padded upwards to help prevent many trivial reallocations (line @28,size@). Next the reallocation is performed
-and the return of realloc() is stored in a temporary pointer named $tmp$ (line @36,realloc@). The return is stored in a temporary
-instead of $a.dp$ to prevent the code from losing the original pointer in case the reallocation fails. Had the return been stored
-in $a.dp$ instead there would be no way to reclaim the heap originally used.
+A quick optimization is to first determine if a memory re-allocation is required at all. The if statement (line @23,if@) checks
+if the \textbf{alloc} member of the mp\_int is smaller than the requested digit count. If the count is not larger than \textbf{alloc}
+the function skips the re-allocation part thus saving time.
+
+When a re-allocation is performed it is turned into an optimal request to save time in the future. The requested digit count is
+padded upwards to 2nd multiple of \textbf{MP\_PREC} larger than \textbf{alloc} (line @25, size@). The XREALLOC function is used
+to re-allocate the memory. As per the other functions XREALLOC is actually a macro which evaluates to realloc by default. The realloc
+function leaves the base of the allocation intact which means the first \textbf{alloc} digits of the mp\_int are the same as before
+the re-allocation. All that is left is to clear the newly allocated digits and return.
-If the reallocation fails the function will return \textbf{MP\_MEM} (line @39,return@), otherwise, the value of $tmp$ is assigned
-to the pointer $a.dp$ and the function continues. A simple for loop from line @48,a->alloc@ to line @50,}@ will zero all digits
-that were above the old \textbf{alloc} limit to make sure the integer is in a known state.
+Note that the re-allocation result is actually stored in a temporary pointer $tmp$. This is to allow this function to return
+an error with a valid pointer. Earlier releases of the library stored the result of XREALLOC into the mp\_int $a$. That would
+result in a memory leak if XREALLOC ever failed.
\subsection{Initializing Variable Precision mp\_ints}
Occasionally the number of digits required will be known in advance of an initialization, based on, for example, the size
@@ -970,7 +997,7 @@ The number of digits $b$ requested is padded (line @22,MP_PREC@) by first augmen
mp\_int is placed in a default state representing the integer zero. Otherwise, the error code \textbf{MP\_MEM} will be
returned (line @27,return@).
-The digits are allocated and set to zero at the same time with the calloc() function (line @25,calloc@). The
+The digits are allocated and set to zero at the same time with the calloc() function (line @25,XCALLOC@). The
\textbf{used} count is set to zero, the \textbf{alloc} count set to the padded digit count and the \textbf{sign} flag set
to \textbf{MP\_ZPOS} to achieve a default valid mp\_int state (lines @29,used@, @30,alloc@ and @31,sign@). If the function
returns succesfully then it is correct to assume that the mp\_int structure is in a valid state for the remainder of the
diff --git a/tommath.tex b/tommath.tex
index 629edbad..d0ac9474 100644
--- a/tommath.tex
+++ b/tommath.tex
@@ -258,7 +258,7 @@ floating point is meant to be implemented in hardware the precision of the manti
a mantissa of much larger precision than hardware alone can efficiently support. This approach could be useful where
scientific applications must minimize the total output error over long calculations.
-Another use for large integers is within arithmetic on polynomials of large characteristic (i.e. $GF(p)[x]$ for large $p$).
+Yet another use for large integers is within arithmetic on polynomials of large characteristic (i.e. $GF(p)[x]$ for large $p$).
In fact the library discussed within this text has already been used to form a polynomial basis library\footnote{See \url{http://poly.libtomcrypt.org} for more details.}.
\subsection{Benefits of Multiple Precision Arithmetic}
@@ -316,7 +316,7 @@ the reader how the algorithms fit together as well as where to start on various
\section{Discussion and Notation}
\subsection{Notation}
-A multiple precision integer of $n$-digits shall be denoted as $x = (x_{n-1} ... x_1 x_0)_{ \beta }$ and represent
+A multiple precision integer of $n$-digits shall be denoted as $x = (x_{n-1}, \ldots, x_1, x_0)_{ \beta }$ and represent
the integer $x \equiv \sum_{i=0}^{n-1} x_i\beta^i$. The elements of the array $x$ are said to be the radix $\beta$ digits
of the integer. For example, $x = (1,2,3)_{10}$ would represent the integer
$1\cdot 10^2 + 2\cdot10^1 + 3\cdot10^0 = 123$.
@@ -339,12 +339,11 @@ algorithms will be used to establish the relevant theory which will subsequently
precision algorithm to solve the same problem.
\subsection{Precision Notation}
-For the purposes of this text a single precision variable must be able to represent integers in the range
-$0 \le x < q \beta$ while a double precision variable must be able to represent integers in the range
-$0 \le x < q \beta^2$. The variable $\beta$ represents the radix of a single digit of a multiple precision integer and
-must be of the form $q^p$ for $q, p \in \Z^+$. The extra radix-$q$ factor allows additions and subtractions to proceed
-without truncation of the carry. Since all modern computers are binary, it is assumed that $q$ is two, for all intents
-and purposes.
+The variable $\beta$ represents the radix of a single digit of a multiple precision integer and
+must be of the form $q^p$ for $q, p \in \Z^+$. A single precision variable must be able to represent integers in
+the range $0 \le x < q \beta$ while a double precision variable must be able to represent integers in the range
+$0 \le x < q \beta^2$. The extra radix-$q$ factor allows additions and subtractions to proceed without truncation of the
+carry. Since all modern computers are binary, it is assumed that $q$ is two.
\index{mp\_digit} \index{mp\_word}
Within the source code that will be presented for each algorithm, the data type \textbf{mp\_digit} will represent
@@ -376,7 +375,7 @@ the $/$ division symbol is used the intention is to perform an integer division
$5/2 = 2$ which will often be written as $\lfloor 5/2 \rfloor = 2$ for clarity. When an expression is written as a
fraction a real value division is implied, for example ${5 \over 2} = 2.5$.
-The norm of a multiple precision integer, for example, $\vert \vert x \vert \vert$ will be used to represent the number of digits in the representation
+The norm of a multiple precision integer, for example $\vert \vert x \vert \vert$, will be used to represent the number of digits in the representation
of the integer. For example, $\vert \vert 123 \vert \vert = 3$ and $\vert \vert 79452 \vert \vert = 5$.
\subsection{Work Effort}
@@ -569,7 +568,7 @@ By building outwards from a base foundation instead of using a parallel design m
highly modular. Being highly modular is a desirable property of any project as it often means the resulting product
has a small footprint and updates are easy to perform.
-Usually when I start a project I will begin with the header file. I define the data types I think I will need and
+Usually when I start a project I will begin with the header files. I define the data types I think I will need and
prototype the initial functions that are not dependent on other functions (within the library). After I
implement these base functions I prototype more dependent functions and implement them. The process repeats until
I implement all of the functions I require. For example, in the case of LibTomMath I implemented functions such as
@@ -625,14 +624,26 @@ any such data type but it does provide for making composite data types known as
used within LibTomMath.
\index{mp\_int}
-\begin{verbatim}
-typedef struct {
- int used, alloc, sign;
- mp_digit *dp;
-} mp_int;
-\end{verbatim}
+\begin{figure}[here]
+\begin{center}
+\begin{small}
+%\begin{verbatim}
+\begin{tabular}{|l|}
+\hline
+typedef struct \{ \\
+\hspace{3mm}int used, alloc, sign;\\
+\hspace{3mm}mp\_digit *dp;\\
+\} \textbf{mp\_int}; \\
+\hline
+\end{tabular}
+%\end{verbatim}
+\end{small}
+\caption{The mp\_int Structure}
+\label{fig:mpint}
+\end{center}
+\end{figure}
-The mp\_int structure can be broken down as follows.
+The mp\_int structure (fig. \ref{fig:mpint}) can be broken down as follows.
\begin{enumerate}
\item The \textbf{used} parameter denotes how many digits of the array \textbf{dp} contain the digits used to represent
@@ -707,9 +718,10 @@ fault by dereferencing memory not owned by the application.
In the case of LibTomMath the only errors that are checked for are related to inappropriate inputs (division by zero for
instance) and memory allocation errors. It will not check that the mp\_int passed to any function is valid nor
will it check pointers for validity. Any function that can cause a runtime error will return an error code as an
-\textbf{int} data type with one of the following values.
+\textbf{int} data type with one of the following values (fig \ref{fig:errcodes}).
\index{MP\_OKAY} \index{MP\_VAL} \index{MP\_MEM}
+\begin{figure}[here]
\begin{center}
\begin{tabular}{|l|l|}
\hline \textbf{Value} & \textbf{Meaning} \\
@@ -719,6 +731,9 @@ will it check pointers for validity. Any function that can cause a runtime erro
\hline
\end{tabular}
\end{center}
+\caption{LibTomMath Error Codes}
+\label{fig:errcodes}
+\end{figure}
When an error is detected within a function it should free any memory it allocated, often during the initialization of
temporary mp\_ints, and return as soon as possible. The goal is to leave the system in the same state it was when the
@@ -754,6 +769,7 @@ to zero. The \textbf{used} count set to zero and \textbf{sign} set to \textbf{M
An mp\_int is said to be initialized if it is set to a valid, preferably default, state such that all of the members of the
structure are set to valid values. The mp\_init algorithm will perform such an action.
+\index{mp\_init}
\begin{figure}[here]
\begin{center}
\begin{tabular}{l}
@@ -776,17 +792,23 @@ structure are set to valid values. The mp\_init algorithm will perform such an
\end{figure}
\textbf{Algorithm mp\_init.}
-The \textbf{MP\_PREC} name represents a constant\footnote{Defined in the ``tommath.h'' header file within LibTomMath.}
-used to dictate the minimum precision of allocated mp\_int integers. Ideally, it is at least equal to $32$ since for most
-purposes that will be more than enough.
+The purpose of this function is to initialize an mp\_int structure so that the rest of the library can properly
+manipulte it. It is assumed that the input may not have had any of its members previously initialized which is certainly
+a valid assumption if the input resides on the stack.
+
+Before any of the members such as \textbf{sign}, \textbf{used} or \textbf{alloc} are initialized the memory for
+the digits is allocated. If this fails the function returns before setting any of the other members. The \textbf{MP\_PREC}
+name represents a constant\footnote{Defined in the ``tommath.h'' header file within LibTomMath.}
+used to dictate the minimum precision of newly initialized mp\_int integers. Ideally, it is at least equal to the smallest
+precision number you'll be working with.
-Memory for the default number of digits is allocated first. If the allocation fails the algorithm returns immediately
-with the \textbf{MP\_MEM} error code. If the allocation succeeds the remaining members of the mp\_int structure
-must be initialized to reflect the default initial state.
+Allocating a block of digits at first instead of a single digit has the benefit of lowering the number of usually slow
+heap operations later functions will have to perform in the future. If \textbf{MP\_PREC} is set correctly the slack
+memory and the number of heap operations will be trivial.
-The allocated digits are all set to zero (step three) to ensure they are in a known state. The \textbf{sign}, \textbf{used}
-and \textbf{alloc} are subsequently initialized to represent the zero integer. By step seven the algorithm returns a success
-code and the mp\_int $a$ has been successfully initialized to a valid state representing the integer zero.
+Once the allocation has been made the digits have to be set to zero as well as the \textbf{used}, \textbf{sign} and
+\textbf{alloc} members initialized. This ensures that the mp\_int will always represent the default state of zero regardless
+of the original condition of the input.
\textbf{Remark.}
This function introduces the idiosyncrasy that all iterative loops, commonly initiated with the ``for'' keyword, iterate incrementally
@@ -801,23 +823,31 @@ decrementally.
\vspace{-3mm}
\begin{alltt}
016
-017 /* init a new bigint */
+017 /* init a new mp_int */
018 int mp_init (mp_int * a)
019 \{
-020 /* allocate memory required and clear it */
-021 a->dp = OPT_CAST(mp_digit) XCALLOC (sizeof (mp_digit), MP_PREC);
-022 if (a->dp == NULL) \{
-023 return MP_MEM;
-024 \}
-025
-026 /* set the used to zero, allocated digits to the default precision
-027 * and sign to positive */
-028 a->used = 0;
-029 a->alloc = MP_PREC;
-030 a->sign = MP_ZPOS;
-031
-032 return MP_OKAY;
-033 \}
+020 int i;
+021
+022 /* allocate memory required and clear it */
+023 a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC);
+024 if (a->dp == NULL) \{
+025 return MP_MEM;
+026 \}
+027
+028 /* set the digits to zero */
+029 for (i = 0; i < MP_PREC; i++) \{
+030 a->dp[i] = 0;
+031 \}
+032
+033 /* set the used to zero, allocated digits to the default precision
+034 * and sign to positive */
+035 a->used = 0;
+036 a->alloc = MP_PREC;
+037 a->sign = MP_ZPOS;
+038
+039 return MP_OKAY;
+040 \}
+041 #endif
\end{alltt}
\end{small}
@@ -825,19 +855,21 @@ One immediate observation of this initializtion function is that it does not ret
is assumed that the caller has already allocated memory for the mp\_int structure, typically on the application stack. The
call to mp\_init() is used only to initialize the members of the structure to a known default state.
-Before any of the other members of the structure are initialized memory from the application heap is allocated with
-the calloc() function (line @22,calloc@). The size of the allocated memory is large enough to hold \textbf{MP\_PREC}
-mp\_digit variables. The calloc() function is used instead\footnote{calloc() will allocate memory in the same
-manner as malloc() except that it also sets the contents to zero upon successfully allocating the memory.} of malloc()
-since digits have to be set to zero for the function to finish correctly. The \textbf{OPT\_CAST} token is a macro
-definition which will turn into a cast from void * to mp\_digit * for C++ compilers. It is not required for C compilers.
+Here we see (line 23) the memory allocation is performed first. This allows us to exit cleanly and quickly
+if there is an error. If the allocation fails the routine will return \textbf{MP\_MEM} to the caller to indicate there
+was a memory error. The function XMALLOC is what actually allocates the memory. Technically XMALLOC is not a function
+but a macro defined in ``tommath.h``. By default, XMALLOC will evaluate to malloc() which is the C library's built--in
+memory allocation routine.
-After the memory has been successfully allocated the remainder of the members are initialized
-(lines 28 through 30) to their respective default states. At this point the algorithm has succeeded and
-a success code is returned to the calling function.
+In order to assure the mp\_int is in a known state the digits must be set to zero. On most platforms this could have been
+accomplished by using calloc() instead of malloc(). However, to correctly initialize a integer type to a given value in a
+portable fashion you have to actually assign the value. The for loop (line 29) performs this required
+operation.
-If this function returns \textbf{MP\_OKAY} it is safe to assume the mp\_int structure has been properly initialized and
-is safe to use with other functions within the library.
+After the memory has been successfully initialized the remainder of the members are initialized
+(lines 33 through 34) to their respective default states. At this point the algorithm has succeeded and
+a success code is returned to the calling function. If this function returns \textbf{MP\_OKAY} it is safe to assume the
+mp\_int structure has been properly initialized and is safe to use with other functions within the library.
\subsection{Clearing an mp\_int}
When an mp\_int is no longer required by the application, the memory that has been allocated for its digits must be
@@ -848,7 +880,7 @@ returned to the application's memory pool with the mp\_clear algorithm.
\begin{tabular}{l}
\hline Algorithm \textbf{mp\_clear}. \\
\textbf{Input}. An mp\_int $a$ \\
-\textbf{Output}. The memory for $a$ is freed for reuse. \\
+\textbf{Output}. The memory for $a$ shall be deallocated. \\
\hline \\
1. If $a$ has been previously freed then return(\textit{MP\_OKAY}). \\
2. for $n$ from 0 to $a.used - 1$ do \\
@@ -865,20 +897,15 @@ returned to the application's memory pool with the mp\_clear algorithm.
\end{figure}
\textbf{Algorithm mp\_clear.}
-This algorithm releases the memory allocated for an mp\_int back into the memory pool for reuse. It is designed
-such that a given mp\_int structure can be cleared multiple times between initializations without attempting to
-free the memory twice\footnote{In ISO C for example, calling free() twice on the same memory block causes undefinied
-behaviour.}.
-
-The first step determines if the mp\_int structure has been marked as free already. If it has, the algorithm returns
-success immediately as no further actions are required. Otherwise, the algorithm will proceed to put the structure
-in a known empty and otherwise invalid state. First the digits of the mp\_int are set to zero. The memory that has been allocated for the
-digits is then freed. The \textbf{used} and \textbf{alloc} counts are both set to zero and the \textbf{sign} set to
-\textbf{MP\_ZPOS}. This known fixed state for cleared mp\_int structures will make debuging easier for the end
-developer. That is, if they spot (via their debugger) an mp\_int they are using that is in this state it will be
-obvious that they erroneously and prematurely cleared the mp\_int structure.
-
-Note that once an mp\_int has been cleared the mp\_int structure is no longer in a valid state for any other algorithm
+This algorithm accomplishes two goals. First, it clears the digits and the other mp\_int members. This ensures that
+if a developer accidentally re-uses a cleared structure it is less likely to cause problems. The second goal
+is to free the allocated memory.
+
+The logic behind the algorithm is extended by marking cleared mp\_int structures so that subsequent calls to this
+algorithm will not try to free the memory multiple times. Cleared mp\_ints are detectable by having a pre-defined invalid
+digit pointer \textbf{dp} setting.
+
+Once an mp\_int has been cleared the mp\_int structure is no longer in a valid state for any other algorithm
with the exception of algorithms mp\_init, mp\_init\_copy, mp\_init\_size and mp\_clear.
\vspace{+3mm}\begin{small}
@@ -890,31 +917,40 @@ with the exception of algorithms mp\_init, mp\_init\_copy, mp\_init\_size and mp
018 void
019 mp_clear (mp_int * a)
020 \{
-021 /* only do anything if a hasn't been freed previously */
-022 if (a->dp != NULL) \{
-023 /* first zero the digits */
-024 memset (a->dp, 0, sizeof (mp_digit) * a->used);
-025
-026 /* free ram */
-027 XFREE(a->dp);
-028
-029 /* reset members to make debugging easier */
-030 a->dp = NULL;
-031 a->alloc = a->used = 0;
-032 a->sign = MP_ZPOS;
-033 \}
-034 \}
+021 int i;
+022
+023 /* only do anything if a hasn't been freed previously */
+024 if (a->dp != NULL) \{
+025 /* first zero the digits */
+026 for (i = 0; i < a->used; i++) \{
+027 a->dp[i] = 0;
+028 \}
+029
+030 /* free ram */
+031 XFREE(a->dp);
+032
+033 /* reset members to make debugging easier */
+034 a->dp = NULL;
+035 a->alloc = a->used = 0;
+036 a->sign = MP_ZPOS;
+037 \}
+038 \}
+039 #endif
\end{alltt}
\end{small}
-The ``if'' statement (line 22) prevents the heap from being corrupted if a user double-frees an
-mp\_int. This is because once the memory is freed the pointer is set to \textbf{NULL} (line 30).
+The algorithm only operates on the mp\_int if it hasn't been previously cleared. The if statement (line 24)
+checks to see if the \textbf{dp} member is not \textbf{NULL}. If the mp\_int is a valid mp\_int then \textbf{dp} cannot be
+\textbf{NULL} in which case the if statement will evaluate to true.
-Without the check, code that accidentally calls mp\_clear twice for a given mp\_int structure would try to free the memory
-allocated for the digits twice. This may cause some C libraries to signal a fault. By setting the pointer to
-\textbf{NULL} it helps debug code that may inadvertently free the mp\_int before it is truly not needed, because attempts
-to reference digits should fail immediately. The allocated digits are set to zero before being freed (line 24).
-This is ideal for cryptographic situations where the integer that the mp\_int represents might need to be kept a secret.
+The digits of the mp\_int are cleared by the for loop (line 26) which assigns a zero to every digit. Similar to mp\_init()
+the digits are assigned zero instead of using block memory operations (such as memset()) since this is more portable.
+
+The digits are deallocated off the heap via the XFREE macro. Similar to XMALLOC the XFREE macro actually evaluates to
+a standard C library function. In this case the free() function. Since free() only deallocates the memory the pointer
+still has to be reset to \textbf{NULL} manually (line 34).
+
+Now that the digits have been cleared and deallocated the other members are set to their final values (lines 35 and 36).
\section{Maintenance Algorithms}
@@ -942,7 +978,7 @@ must be re-sized appropriately to accomodate the result. The mp\_grow algorithm
1. if $a.alloc \ge b$ then return(\textit{MP\_OKAY}) \\
2. $u \leftarrow b\mbox{ (mod }MP\_PREC\mbox{)}$ \\
3. $v \leftarrow b + 2 \cdot MP\_PREC - u$ \\
-4. Re-Allocate the array of digits $a$ to size $v$ \\
+4. Re-allocate the array of digits $a$ to size $v$ \\
5. If the allocation failed then return(\textit{MP\_MEM}). \\
6. for n from a.alloc to $v - 1$ do \\
\hspace{+3mm}6.1 $a_n \leftarrow 0$ \\
@@ -1005,18 +1041,23 @@ assumed to contain undefined values they are initially set to zero.
049 \}
050 return MP_OKAY;
051 \}
+052 #endif
\end{alltt}
\end{small}
-The first step is to see if we actually need to perform a re-allocation at all (line 24). If a reallocation
-must occur the digit count is padded upwards to help prevent many trivial reallocations (line 26). Next the reallocation is performed
-and the return of realloc() is stored in a temporary pointer named $tmp$ (line 36). The return is stored in a temporary
-instead of $a.dp$ to prevent the code from losing the original pointer in case the reallocation fails. Had the return been stored
-in $a.dp$ instead there would be no way to reclaim the heap originally used.
+A quick optimization is to first determine if a memory re-allocation is required at all. The if statement (line 23) checks
+if the \textbf{alloc} member of the mp\_int is smaller than the requested digit count. If the count is not larger than \textbf{alloc}
+the function skips the re-allocation part thus saving time.
+
+When a re-allocation is performed it is turned into an optimal request to save time in the future. The requested digit count is
+padded upwards to 2nd multiple of \textbf{MP\_PREC} larger than \textbf{alloc} (line 26). The XREALLOC function is used
+to re-allocate the memory. As per the other functions XREALLOC is actually a macro which evaluates to realloc by default. The realloc
+function leaves the base of the allocation intact which means the first \textbf{alloc} digits of the mp\_int are the same as before
+the re-allocation. All that is left is to clear the newly allocated digits and return.
-If the reallocation fails the function will return \textbf{MP\_MEM} (line 37), otherwise, the value of $tmp$ is assigned
-to the pointer $a.dp$ and the function continues. A simple for loop from line 46 to line 51 will zero all digits
-that were above the old \textbf{alloc} limit to make sure the integer is in a known state.
+Note that the re-allocation result is actually stored in a temporary pointer $tmp$. This is to allow this function to return
+an error with a valid pointer. Earlier releases of the library stored the result of XREALLOC into the mp\_int $a$. That would
+result in a memory leak if XREALLOC ever failed.
\subsection{Initializing Variable Precision mp\_ints}
Occasionally the number of digits required will be known in advance of an initialization, based on, for example, the size
@@ -1065,31 +1106,41 @@ correct no further memory re-allocations are required to work with the mp\_int.
017 /* init an mp_init for a given size */
018 int mp_init_size (mp_int * a, int size)
019 \{
-020 /* pad size so there are always extra digits */
-021 size += (MP_PREC * 2) - (size % MP_PREC);
-022
-023 /* alloc mem */
-024 a->dp = OPT_CAST(mp_digit) XCALLOC (sizeof (mp_digit), size);
-025 if (a->dp == NULL) \{
-026 return MP_MEM;
-027 \}
-028 a->used = 0;
-029 a->alloc = size;
-030 a->sign = MP_ZPOS;
-031
-032 return MP_OKAY;
-033 \}
+020 int x;
+021
+022 /* pad size so there are always extra digits */
+023 size += (MP_PREC * 2) - (size % MP_PREC);
+024
+025 /* alloc mem */
+026 a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
+027 if (a->dp == NULL) \{
+028 return MP_MEM;
+029 \}
+030
+031 /* set the members */
+032 a->used = 0;
+033 a->alloc = size;
+034 a->sign = MP_ZPOS;
+035
+036 /* zero the digits */
+037 for (x = 0; x < size; x++) \{
+038 a->dp[x] = 0;
+039 \}
+040
+041 return MP_OKAY;
+042 \}
+043 #endif
\end{alltt}
\end{small}
-The number of digits $b$ requested is padded (line 21) by first augmenting it to the next multiple of
+The number of digits $b$ requested is padded (line 23) by first augmenting it to the next multiple of
\textbf{MP\_PREC} and then adding \textbf{MP\_PREC} to the result. If the memory can be successfully allocated the
mp\_int is placed in a default state representing the integer zero. Otherwise, the error code \textbf{MP\_MEM} will be
-returned (line 26).
+returned (line 28).
-The digits are allocated and set to zero at the same time with the calloc() function (line @25,calloc@). The
+The digits are allocated and set to zero at the same time with the calloc() function (line @25,XCALLOC@). The
\textbf{used} count is set to zero, the \textbf{alloc} count set to the padded digit count and the \textbf{sign} flag set
-to \textbf{MP\_ZPOS} to achieve a default valid mp\_int state (lines 28, 29 and 30). If the function
+to \textbf{MP\_ZPOS} to achieve a default valid mp\_int state (lines 32, 33 and 34). If the function
returns succesfully then it is correct to assume that the mp\_int structure is in a valid state for the remainder of the
functions to work with.
@@ -1165,6 +1216,7 @@ initialization which allows for quick recovery from runtime errors.
051 return res; /* Assumed ok, if error flagged above. */
052 \}
053
+054 #endif
\end{alltt}
\end{small}
@@ -1249,6 +1301,7 @@ when all of the digits are zero to ensure that the mp\_int is valid at all times
036 a->sign = MP_ZPOS;
037 \}
038 \}
+039 #endif
\end{alltt}
\end{small}
@@ -1385,6 +1438,7 @@ implement the pseudo-code.
060 b->sign = a->sign;
061 return MP_OKAY;
062 \}
+063 #endif
\end{alltt}
\end{small}
@@ -1498,6 +1552,7 @@ such this algorithm will perform two operations in one step.
024 \}
025 return mp_copy (b, a);
026 \}
+027 #endif
\end{alltt}
\end{small}
@@ -1542,6 +1597,7 @@ This algorithm simply resets a mp\_int to the default state.
022 a->used = 0;
023 memset (a->dp, 0, sizeof (mp_digit) * a->alloc);
024 \}
+025 #endif
\end{alltt}
\end{small}
@@ -1602,6 +1658,7 @@ logic to handle it.
035
036 return MP_OKAY;
037 \}
+038 #endif
\end{alltt}
\end{small}
@@ -1653,6 +1710,7 @@ zero as negative.
026 \}
027 return MP_OKAY;
028 \}
+029 #endif
\end{alltt}
\end{small}
@@ -1695,6 +1753,7 @@ single digit is set (\textit{modulo $\beta$}) and the \textbf{used} count is adj
021 a->dp[0] = b & MP_MASK;
022 a->used = (a->dp[0] != 0) ? 1 : 0;
023 \}
+024 #endif
\end{alltt}
\end{small}
@@ -1771,6 +1830,7 @@ Excess zero digits are trimmed in steps 2.1 and 3 by using higher level algorith
040 mp_clamp (a);
041 return MP_OKAY;
042 \}
+043 #endif
\end{alltt}
\end{small}
@@ -1872,6 +1932,7 @@ the zero'th digit. If after all of the digits have been compared, no difference
047 \}
048 return MP_EQ;
049 \}
+050 #endif
\end{alltt}
\end{small}
@@ -1935,6 +1996,7 @@ $\vert a \vert < \vert b \vert$. Step number four will compare the two when the
035 return mp_cmp_mag(a, b);
036 \}
037 \}
+038 #endif
\end{alltt}
\end{small}
@@ -2152,6 +2214,7 @@ The final carry is stored in $c_{max}$ and digits above $max$ upto $oldused$ are
101 mp_clamp (c);
102 return MP_OKAY;
103 \}
+104 #endif
\end{alltt}
\end{small}
@@ -2320,6 +2383,7 @@ If $b$ has a smaller magnitude than $a$ then step 9 will force the carry and cop
081 return MP_OKAY;
082 \}
083
+084 #endif
\end{alltt}
\end{small}
@@ -2451,6 +2515,7 @@ within algorithm s\_mp\_add will force $-0$ to become $0$.
045 return res;
046 \}
047
+048 #endif
\end{alltt}
\end{small}
@@ -2562,6 +2627,7 @@ algorithm from producing $-a - -a = -0$ as a result.
051 return res;
052 \}
053
+054 #endif
\end{alltt}
\end{small}
@@ -2695,6 +2761,7 @@ Step 8 clears any leading digits of $b$ in case it originally had a larger magni
074 b->sign = a->sign;
075 return MP_OKAY;
076 \}
+077 #endif
\end{alltt}
\end{small}
@@ -2794,6 +2861,7 @@ least significant bit not the most significant bit.
060 mp_clamp (b);
061 return MP_OKAY;
062 \}
+063 #endif
\end{alltt}
\end{small}
@@ -2913,6 +2981,7 @@ step 8 sets the lower $b$ digits to zero.
059 \}
060 return MP_OKAY;
061 \}
+062 #endif
\end{alltt}
\end{small}
@@ -3022,6 +3091,7 @@ Once the window copy is complete the upper digits must be zeroed and the \textbf
064 /* remove excess digits */
065 a->used -= b;
066 \}
+067 #endif
\end{alltt}
\end{small}
@@ -3154,6 +3224,7 @@ complete. It is possible to optimize this algorithm down to a $O(n)$ algorithm
077 mp_clamp (c);
078 return MP_OKAY;
079 \}
+080 #endif
\end{alltt}
\end{small}
@@ -3281,6 +3352,7 @@ by using algorithm mp\_mod\_2d.
089 mp_clear (&t);
090 return MP_OKAY;
091 \}
+092 #endif
\end{alltt}
\end{small}
@@ -3370,6 +3442,7 @@ is copied to $b$, leading digits are removed and the remaining leading digit is
047 mp_clamp (c);
048 return MP_OKAY;
049 \}
+050 #endif
\end{alltt}
\end{small}
@@ -3603,6 +3676,7 @@ exceed the precision requested.
083 mp_clear (&t);
084 return MP_OKAY;
085 \}
+086 #endif
\end{alltt}
\end{small}
@@ -3806,109 +3880,82 @@ and addition operations in the nested loop in parallel.
033 int
034 fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
035 \{
-036 int olduse, res, pa, ix;
-037 mp_word W[MP_WARRAY];
-038
-039 /* grow the destination as required */
-040 if (c->alloc < digs) \{
-041 if ((res = mp_grow (c, digs)) != MP_OKAY) \{
-042 return res;
-043 \}
-044 \}
-045
-046 /* clear temp buf (the columns) */
-047 memset (W, 0, sizeof (mp_word) * digs);
-048
-049 /* calculate the columns */
-050 pa = a->used;
-051 for (ix = 0; ix < pa; ix++) \{
-052 /* this multiplier has been modified to allow you to
-053 * control how many digits of output are produced.
-054 * So at most we want to make upto "digs" digits of output.
-055 *
-056 * this adds products to distinct columns (at ix+iy) of W
-057 * note that each step through the loop is not dependent on
-058 * the previous which means the compiler can easily unroll
-059 * the loop without scheduling problems
-060 */
-061 \{
-062 register mp_digit tmpx, *tmpy;
-063 register mp_word *_W;
-064 register int iy, pb;
-065
-066 /* alias for the the word on the left e.g. A[ix] * A[iy] */
-067 tmpx = a->dp[ix];
-068
-069 /* alias for the right side */
-070 tmpy = b->dp;
-071
-072 /* alias for the columns, each step through the loop adds a new
-073 term to each column
-074 */
-075 _W = W + ix;
-076
-077 /* the number of digits is limited by their placement. E.g.
-078 we avoid multiplying digits that will end up above the # of
-079 digits of precision requested
-080 */
-081 pb = MIN (b->used, digs - ix);
-082
-083 for (iy = 0; iy < pb; iy++) \{
-084 *_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++);
-085 \}
-086 \}
-087
-088 \}
-089
-090 /* setup dest */
-091 olduse = c->used;
-092 c->used = digs;
+036 int olduse, res, pa, ix, iz;
+037 mp_digit W[MP_WARRAY];
+038 register mp_word _W;
+039
+040 /* grow the destination as required */
+041 if (c->alloc < digs) \{
+042 if ((res = mp_grow (c, digs)) != MP_OKAY) \{
+043 return res;
+044 \}
+045 \}
+046
+047 /* number of output digits to produce */
+048 pa = MIN(digs, a->used + b->used);
+049
+050 /* clear the carry */
+051 _W = 0;
+052 for (ix = 0; ix <= pa; ix++) \{
+053 int tx, ty;
+054 int iy;
+055 mp_digit *tmpx, *tmpy;
+056
+057 /* get offsets into the two bignums */
+058 ty = MIN(b->used-1, ix);
+059 tx = ix - ty;
+060
+061 /* setup temp aliases */
+062 tmpx = a->dp + tx;
+063 tmpy = b->dp + ty;
+064
+065 /* this is the number of times the loop will iterrate, essentially its
+
+066 while (tx++ < a->used && ty-- >= 0) \{ ... \}
+067 */
+068 iy = MIN(a->used-tx, ty+1);
+069
+070 /* execute loop */
+071 for (iz = 0; iz < iy; ++iz) \{
+072 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
+073 \}
+074
+075 /* store term */
+076 W[ix] = ((mp_digit)_W) & MP_MASK;
+077
+078 /* make next carry */
+079 _W = _W >> ((mp_word)DIGIT_BIT);
+080 \}
+081
+082 /* setup dest */
+083 olduse = c->used;
+084 c->used = digs;
+085
+086 \{
+087 register mp_digit *tmpc;
+088 tmpc = c->dp;
+089 for (ix = 0; ix < digs; ix++) \{
+090 /* now extract the previous digit [below the carry] */
+091 *tmpc++ = W[ix];
+092 \}
093
-094 \{
-095 register mp_digit *tmpc;
-096
-097 /* At this point W[] contains the sums of each column. To get the
-098 * correct result we must take the extra bits from each column and
-099 * carry them down
-100 *
-101 * Note that while this adds extra code to the multiplier it
-102 * saves time since the carry propagation is removed from the
-103 * above nested loop.This has the effect of reducing the work
-104 * from N*(N+N*c)==N**2 + c*N**2 to N**2 + N*c where c is the
-105 * cost of the shifting. On very small numbers this is slower
-106 * but on most cryptographic size numbers it is faster.
-107 *
-108 * In this particular implementation we feed the carries from
-109 * behind which means when the loop terminates we still have one
-110 * last digit to copy
-111 */
-112 tmpc = c->dp;
-113 for (ix = 1; ix < digs; ix++) \{
-114 /* forward the carry from the previous temp */
-115 W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
-116
-117 /* now extract the previous digit [below the carry] */
-118 *tmpc++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
-119 \}
-120 /* fetch the last digit */
-121 *tmpc++ = (mp_digit) (W[digs - 1] & ((mp_word) MP_MASK));
-122
-123 /* clear unused digits [that existed in the old copy of c] */
-124 for (; ix < olduse; ix++) \{
-125 *tmpc++ = 0;
-126 \}
-127 \}
-128 mp_clamp (c);
-129 return MP_OKAY;
-130 \}
+094 /* clear unused digits [that existed in the old copy of c] */
+095 for (; ix < olduse; ix++) \{
+096 *tmpc++ = 0;
+097 \}
+098 \}
+099 mp_clamp (c);
+100 return MP_OKAY;
+101 \}
+102 #endif
\end{alltt}
\end{small}
-The memset on line 47 clears the initial $\hat W$ array to zero in a single step. Like the slower baseline multiplication
-implementation a series of aliases (\textit{lines 67, 70 and 75}) are used to simplify the inner $O(n^2)$ loop.
+The memset on line @47,memset@ clears the initial $\hat W$ array to zero in a single step. Like the slower baseline multiplication
+implementation a series of aliases (\textit{lines 62, 63 and 76}) are used to simplify the inner $O(n^2)$ loop.
In this case a new alias $\_\hat W$ has been added which refers to the double precision columns offset by $ix$ in each pass.
-The inner loop on lines 83, 84 and 85 is where the algorithm will spend the majority of the time, which is why it has been
+The inner loop on lines 89, 79 and 80 is where the algorithm will spend the majority of the time, which is why it has been
stripped to the bones of any extra baggage\footnote{Hence the pointer aliases.}. On x86 processors the multiplication and additions amount to at the
very least five instructions (\textit{two loads, two additions, one multiply}) while on the ARMv4 processors they amount to only three
(\textit{one load, one store, one multiply-add}). For both of the x86 and ARMv4 processors the GCC compiler performs a good job at unrolling the loop
@@ -4168,92 +4215,90 @@ The remaining steps 13 through 18 compute the Karatsuba polynomial through a var
076 goto X0Y0;
077
078 /* now shift the digits */
-079 x0.sign = x1.sign = a->sign;
-080 y0.sign = y1.sign = b->sign;
-081
-082 x0.used = y0.used = B;
-083 x1.used = a->used - B;
-084 y1.used = b->used - B;
-085
-086 \{
-087 register int x;
-088 register mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
-089
-090 /* we copy the digits directly instead of using higher level functions
-091 * since we also need to shift the digits
-092 */
-093 tmpa = a->dp;
-094 tmpb = b->dp;
-095
-096 tmpx = x0.dp;
-097 tmpy = y0.dp;
-098 for (x = 0; x < B; x++) \{
-099 *tmpx++ = *tmpa++;
-100 *tmpy++ = *tmpb++;
-101 \}
-102
-103 tmpx = x1.dp;
-104 for (x = B; x < a->used; x++) \{
-105 *tmpx++ = *tmpa++;
-106 \}
-107
-108 tmpy = y1.dp;
-109 for (x = B; x < b->used; x++) \{
-110 *tmpy++ = *tmpb++;
-111 \}
-112 \}
-113
-114 /* only need to clamp the lower words since by definition the
-115 * upper words x1/y1 must have a known number of digits
-116 */
-117 mp_clamp (&x0);
-118 mp_clamp (&y0);
-119
-120 /* now calc the products x0y0 and x1y1 */
-121 /* after this x0 is no longer required, free temp [x0==t2]! */
-122 if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY)
-123 goto X1Y1; /* x0y0 = x0*y0 */
-124 if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY)
-125 goto X1Y1; /* x1y1 = x1*y1 */
-126
-127 /* now calc x1-x0 and y1-y0 */
-128 if (mp_sub (&x1, &x0, &t1) != MP_OKAY)
-129 goto X1Y1; /* t1 = x1 - x0 */
-130 if (mp_sub (&y1, &y0, &x0) != MP_OKAY)
-131 goto X1Y1; /* t2 = y1 - y0 */
-132 if (mp_mul (&t1, &x0, &t1) != MP_OKAY)
-133 goto X1Y1; /* t1 = (x1 - x0) * (y1 - y0) */
-134
-135 /* add x0y0 */
-136 if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY)
-137 goto X1Y1; /* t2 = x0y0 + x1y1 */
-138 if (mp_sub (&x0, &t1, &t1) != MP_OKAY)
-139 goto X1Y1; /* t1 = x0y0 + x1y1 - (x1-x0)*(y1-y0) */
-140
-141 /* shift by B */
-142 if (mp_lshd (&t1, B) != MP_OKAY)
-143 goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
-144 if (mp_lshd (&x1y1, B * 2) != MP_OKAY)
-145 goto X1Y1; /* x1y1 = x1y1 << 2*B */
-146
-147 if (mp_add (&x0y0, &t1, &t1) != MP_OKAY)
-148 goto X1Y1; /* t1 = x0y0 + t1 */
-149 if (mp_add (&t1, &x1y1, c) != MP_OKAY)
-150 goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */
+079 x0.used = y0.used = B;
+080 x1.used = a->used - B;
+081 y1.used = b->used - B;
+082
+083 \{
+084 register int x;
+085 register mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
+086
+087 /* we copy the digits directly instead of using higher level functions
+088 * since we also need to shift the digits
+089 */
+090 tmpa = a->dp;
+091 tmpb = b->dp;
+092
+093 tmpx = x0.dp;
+094 tmpy = y0.dp;
+095 for (x = 0; x < B; x++) \{
+096 *tmpx++ = *tmpa++;
+097 *tmpy++ = *tmpb++;
+098 \}
+099
+100 tmpx = x1.dp;
+101 for (x = B; x < a->used; x++) \{
+102 *tmpx++ = *tmpa++;
+103 \}
+104
+105 tmpy = y1.dp;
+106 for (x = B; x < b->used; x++) \{
+107 *tmpy++ = *tmpb++;
+108 \}
+109 \}
+110
+111 /* only need to clamp the lower words since by definition the
+112 * upper words x1/y1 must have a known number of digits
+113 */
+114 mp_clamp (&x0);
+115 mp_clamp (&y0);
+116
+117 /* now calc the products x0y0 and x1y1 */
+118 /* after this x0 is no longer required, free temp [x0==t2]! */
+119 if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY)
+120 goto X1Y1; /* x0y0 = x0*y0 */
+121 if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY)
+122 goto X1Y1; /* x1y1 = x1*y1 */
+123
+124 /* now calc x1-x0 and y1-y0 */
+125 if (mp_sub (&x1, &x0, &t1) != MP_OKAY)
+126 goto X1Y1; /* t1 = x1 - x0 */
+127 if (mp_sub (&y1, &y0, &x0) != MP_OKAY)
+128 goto X1Y1; /* t2 = y1 - y0 */
+129 if (mp_mul (&t1, &x0, &t1) != MP_OKAY)
+130 goto X1Y1; /* t1 = (x1 - x0) * (y1 - y0) */
+131
+132 /* add x0y0 */
+133 if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY)
+134 goto X1Y1; /* t2 = x0y0 + x1y1 */
+135 if (mp_sub (&x0, &t1, &t1) != MP_OKAY)
+136 goto X1Y1; /* t1 = x0y0 + x1y1 - (x1-x0)*(y1-y0) */
+137
+138 /* shift by B */
+139 if (mp_lshd (&t1, B) != MP_OKAY)
+140 goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
+141 if (mp_lshd (&x1y1, B * 2) != MP_OKAY)
+142 goto X1Y1; /* x1y1 = x1y1 << 2*B */
+143
+144 if (mp_add (&x0y0, &t1, &t1) != MP_OKAY)
+145 goto X1Y1; /* t1 = x0y0 + t1 */
+146 if (mp_add (&t1, &x1y1, c) != MP_OKAY)
+147 goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */
+148
+149 /* Algorithm succeeded set the return code to MP_OKAY */
+150 err = MP_OKAY;
151
-152 /* Algorithm succeeded set the return code to MP_OKAY */
-153 err = MP_OKAY;
-154
-155 X1Y1:mp_clear (&x1y1);
-156 X0Y0:mp_clear (&x0y0);
-157 T1:mp_clear (&t1);
-158 Y1:mp_clear (&y1);
-159 Y0:mp_clear (&y0);
-160 X1:mp_clear (&x1);
-161 X0:mp_clear (&x0);
-162 ERR:
-163 return err;
-164 \}
+152 X1Y1:mp_clear (&x1y1);
+153 X0Y0:mp_clear (&x0y0);
+154 T1:mp_clear (&t1);
+155 Y1:mp_clear (&y1);
+156 Y0:mp_clear (&y0);
+157 X1:mp_clear (&x1);
+158 X0:mp_clear (&x0);
+159 ERR:
+160 return err;
+161 \}
+162 #endif
\end{alltt}
\end{small}
@@ -4269,13 +4314,13 @@ number of digits for the next section of code.
The first algebraic portion of the algorithm is to split the two inputs into their halves. However, instead of using mp\_mod\_2d and mp\_rshd
to extract the halves, the respective code has been placed inline within the body of the function. To initialize the halves, the \textbf{used} and
-\textbf{sign} members are copied first. The first for loop on line 98 copies the lower halves. Since they are both the same magnitude it
-is simpler to calculate both lower halves in a single loop. The for loop on lines 104 and 109 calculate the upper halves $x1$ and
+\textbf{sign} members are copied first. The first for loop on line 101 copies the lower halves. Since they are both the same magnitude it
+is simpler to calculate both lower halves in a single loop. The for loop on lines 106 and 106 calculate the upper halves $x1$ and
$y1$ respectively.
By inlining the calculation of the halves, the Karatsuba multiplier has a slightly lower overhead and can be used for smaller magnitude inputs.
-When line 153 is reached, the algorithm has completed succesfully. The ``error status'' variable $err$ is set to \textbf{MP\_OKAY} so that
+When line 150 is reached, the algorithm has completed succesfully. The ``error status'' variable $err$ is set to \textbf{MP\_OKAY} so that
the same code that handles errors can be used to clear the temporary variables and return.
\subsection{Toom-Cook $3$-Way Multiplication}
@@ -4394,262 +4439,269 @@ result $a \cdot b$ is produced.
\vspace{-3mm}
\begin{alltt}
016
-017 /* multiplication using the Toom-Cook 3-way algorithm */
-018 int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
-019 \{
-020 mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
-021 int res, B;
-022
-023 /* init temps */
-024 if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
-025 &a0, &a1, &a2, &b0, &b1,
-026 &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) \{
-027 return res;
-028 \}
-029
-030 /* B */
-031 B = MIN(a->used, b->used) / 3;
-032
-033 /* a = a2 * B**2 + a1 * B + a0 */
-034 if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) \{
-035 goto ERR;
-036 \}
-037
-038 if ((res = mp_copy(a, &a1)) != MP_OKAY) \{
-039 goto ERR;
-040 \}
-041 mp_rshd(&a1, B);
-042 mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
-043
-044 if ((res = mp_copy(a, &a2)) != MP_OKAY) \{
-045 goto ERR;
-046 \}
-047 mp_rshd(&a2, B*2);
-048
-049 /* b = b2 * B**2 + b1 * B + b0 */
-050 if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) \{
-051 goto ERR;
-052 \}
-053
-054 if ((res = mp_copy(b, &b1)) != MP_OKAY) \{
-055 goto ERR;
-056 \}
-057 mp_rshd(&b1, B);
-058 mp_mod_2d(&b1, DIGIT_BIT * B, &b1);
-059
-060 if ((res = mp_copy(b, &b2)) != MP_OKAY) \{
-061 goto ERR;
-062 \}
-063 mp_rshd(&b2, B*2);
-064
-065 /* w0 = a0*b0 */
-066 if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) \{
-067 goto ERR;
-068 \}
+017 /* multiplication using the Toom-Cook 3-way algorithm
+018 *
+019 * Much more complicated than Karatsuba but has a lower asymptotic running t
+ ime of
+020 * O(N**1.464). This algorithm is only particularly useful on VERY large
+021 * inputs (we're talking 1000s of digits here...).
+022 */
+023 int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
+024 \{
+025 mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
+026 int res, B;
+027
+028 /* init temps */
+029 if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4,
+030 &a0, &a1, &a2, &b0, &b1,
+031 &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) \{
+032 return res;
+033 \}
+034
+035 /* B */
+036 B = MIN(a->used, b->used) / 3;
+037
+038 /* a = a2 * B**2 + a1 * B + a0 */
+039 if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) \{
+040 goto ERR;
+041 \}
+042
+043 if ((res = mp_copy(a, &a1)) != MP_OKAY) \{
+044 goto ERR;
+045 \}
+046 mp_rshd(&a1, B);
+047 mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
+048
+049 if ((res = mp_copy(a, &a2)) != MP_OKAY) \{
+050 goto ERR;
+051 \}
+052 mp_rshd(&a2, B*2);
+053
+054 /* b = b2 * B**2 + b1 * B + b0 */
+055 if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) \{
+056 goto ERR;
+057 \}
+058
+059 if ((res = mp_copy(b, &b1)) != MP_OKAY) \{
+060 goto ERR;
+061 \}
+062 mp_rshd(&b1, B);
+063 mp_mod_2d(&b1, DIGIT_BIT * B, &b1);
+064
+065 if ((res = mp_copy(b, &b2)) != MP_OKAY) \{
+066 goto ERR;
+067 \}
+068 mp_rshd(&b2, B*2);
069
-070 /* w4 = a2 * b2 */
-071 if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) \{
+070 /* w0 = a0*b0 */
+071 if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) \{
072 goto ERR;
073 \}
074
-075 /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
-076 if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) \{
+075 /* w4 = a2 * b2 */
+076 if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) \{
077 goto ERR;
078 \}
-079 if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) \{
-080 goto ERR;
-081 \}
-082 if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) \{
-083 goto ERR;
-084 \}
-085 if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) \{
-086 goto ERR;
-087 \}
-088
-089 if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) \{
-090 goto ERR;
-091 \}
-092 if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) \{
-093 goto ERR;
-094 \}
-095 if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) \{
-096 goto ERR;
-097 \}
-098 if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) \{
-099 goto ERR;
-100 \}
-101
-102 if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) \{
-103 goto ERR;
-104 \}
-105
-106 /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
-107 if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) \{
+079
+080 /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
+081 if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) \{
+082 goto ERR;
+083 \}
+084 if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) \{
+085 goto ERR;
+086 \}
+087 if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) \{
+088 goto ERR;
+089 \}
+090 if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) \{
+091 goto ERR;
+092 \}
+093
+094 if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) \{
+095 goto ERR;
+096 \}
+097 if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) \{
+098 goto ERR;
+099 \}
+100 if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) \{
+101 goto ERR;
+102 \}
+103 if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) \{
+104 goto ERR;
+105 \}
+106
+107 if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) \{
108 goto ERR;
109 \}
-110 if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) \{
-111 goto ERR;
-112 \}
-113 if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) \{
-114 goto ERR;
-115 \}
-116 if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) \{
-117 goto ERR;
-118 \}
-119
-120 if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) \{
-121 goto ERR;
-122 \}
-123 if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) \{
-124 goto ERR;
-125 \}
-126 if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) \{
-127 goto ERR;
-128 \}
-129 if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) \{
-130 goto ERR;
-131 \}
-132
-133 if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) \{
-134 goto ERR;
-135 \}
-136
-137
-138 /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
-139 if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) \{
-140 goto ERR;
-141 \}
-142 if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) \{
-143 goto ERR;
-144 \}
-145 if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) \{
-146 goto ERR;
-147 \}
-148 if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) \{
-149 goto ERR;
-150 \}
-151 if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) \{
-152 goto ERR;
-153 \}
-154
-155 /* now solve the matrix
-156
-157 0 0 0 0 1
-158 1 2 4 8 16
-159 1 1 1 1 1
-160 16 8 4 2 1
-161 1 0 0 0 0
-162
-163 using 12 subtractions, 4 shifts,
-164 2 small divisions and 1 small multiplication
-165 */
-166
-167 /* r1 - r4 */
-168 if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) \{
-169 goto ERR;
-170 \}
-171 /* r3 - r0 */
-172 if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) \{
-173 goto ERR;
-174 \}
-175 /* r1/2 */
-176 if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) \{
-177 goto ERR;
-178 \}
-179 /* r3/2 */
-180 if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) \{
-181 goto ERR;
-182 \}
-183 /* r2 - r0 - r4 */
-184 if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) \{
-185 goto ERR;
-186 \}
-187 if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) \{
-188 goto ERR;
-189 \}
-190 /* r1 - r2 */
-191 if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) \{
-192 goto ERR;
-193 \}
-194 /* r3 - r2 */
-195 if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) \{
-196 goto ERR;
-197 \}
-198 /* r1 - 8r0 */
-199 if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) \{
-200 goto ERR;
-201 \}
-202 if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) \{
-203 goto ERR;
-204 \}
-205 /* r3 - 8r4 */
-206 if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) \{
-207 goto ERR;
-208 \}
-209 if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) \{
-210 goto ERR;
-211 \}
-212 /* 3r2 - r1 - r3 */
-213 if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) \{
-214 goto ERR;
-215 \}
-216 if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) \{
-217 goto ERR;
-218 \}
-219 if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) \{
-220 goto ERR;
-221 \}
-222 /* r1 - r2 */
-223 if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) \{
-224 goto ERR;
-225 \}
-226 /* r3 - r2 */
-227 if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) \{
-228 goto ERR;
-229 \}
-230 /* r1/3 */
-231 if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) \{
-232 goto ERR;
-233 \}
-234 /* r3/3 */
-235 if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) \{
-236 goto ERR;
-237 \}
-238
-239 /* at this point shift W[n] by B*n */
-240 if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) \{
+110
+111 /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
+112 if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) \{
+113 goto ERR;
+114 \}
+115 if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) \{
+116 goto ERR;
+117 \}
+118 if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) \{
+119 goto ERR;
+120 \}
+121 if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) \{
+122 goto ERR;
+123 \}
+124
+125 if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) \{
+126 goto ERR;
+127 \}
+128 if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) \{
+129 goto ERR;
+130 \}
+131 if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) \{
+132 goto ERR;
+133 \}
+134 if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) \{
+135 goto ERR;
+136 \}
+137
+138 if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) \{
+139 goto ERR;
+140 \}
+141
+142
+143 /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
+144 if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) \{
+145 goto ERR;
+146 \}
+147 if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) \{
+148 goto ERR;
+149 \}
+150 if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) \{
+151 goto ERR;
+152 \}
+153 if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) \{
+154 goto ERR;
+155 \}
+156 if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) \{
+157 goto ERR;
+158 \}
+159
+160 /* now solve the matrix
+161
+162 0 0 0 0 1
+163 1 2 4 8 16
+164 1 1 1 1 1
+165 16 8 4 2 1
+166 1 0 0 0 0
+167
+168 using 12 subtractions, 4 shifts,
+169 2 small divisions and 1 small multiplication
+170 */
+171
+172 /* r1 - r4 */
+173 if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) \{
+174 goto ERR;
+175 \}
+176 /* r3 - r0 */
+177 if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) \{
+178 goto ERR;
+179 \}
+180 /* r1/2 */
+181 if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) \{
+182 goto ERR;
+183 \}
+184 /* r3/2 */
+185 if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) \{
+186 goto ERR;
+187 \}
+188 /* r2 - r0 - r4 */
+189 if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) \{
+190 goto ERR;
+191 \}
+192 if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) \{
+193 goto ERR;
+194 \}
+195 /* r1 - r2 */
+196 if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) \{
+197 goto ERR;
+198 \}
+199 /* r3 - r2 */
+200 if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) \{
+201 goto ERR;
+202 \}
+203 /* r1 - 8r0 */
+204 if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) \{
+205 goto ERR;
+206 \}
+207 if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) \{
+208 goto ERR;
+209 \}
+210 /* r3 - 8r4 */
+211 if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) \{
+212 goto ERR;
+213 \}
+214 if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) \{
+215 goto ERR;
+216 \}
+217 /* 3r2 - r1 - r3 */
+218 if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) \{
+219 goto ERR;
+220 \}
+221 if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) \{
+222 goto ERR;
+223 \}
+224 if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) \{
+225 goto ERR;
+226 \}
+227 /* r1 - r2 */
+228 if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) \{
+229 goto ERR;
+230 \}
+231 /* r3 - r2 */
+232 if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) \{
+233 goto ERR;
+234 \}
+235 /* r1/3 */
+236 if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) \{
+237 goto ERR;
+238 \}
+239 /* r3/3 */
+240 if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) \{
241 goto ERR;
242 \}
-243 if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) \{
-244 goto ERR;
-245 \}
-246 if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) \{
-247 goto ERR;
-248 \}
-249 if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) \{
-250 goto ERR;
-251 \}
-252
-253 if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) \{
-254 goto ERR;
-255 \}
-256 if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) \{
-257 goto ERR;
-258 \}
-259 if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) \{
-260 goto ERR;
-261 \}
-262 if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) \{
-263 goto ERR;
-264 \}
-265
-266 ERR:
-267 mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
-268 &a0, &a1, &a2, &b0, &b1,
-269 &b2, &tmp1, &tmp2, NULL);
-270 return res;
-271 \}
-272
+243
+244 /* at this point shift W[n] by B*n */
+245 if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) \{
+246 goto ERR;
+247 \}
+248 if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) \{
+249 goto ERR;
+250 \}
+251 if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) \{
+252 goto ERR;
+253 \}
+254 if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) \{
+255 goto ERR;
+256 \}
+257
+258 if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) \{
+259 goto ERR;
+260 \}
+261 if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) \{
+262 goto ERR;
+263 \}
+264 if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) \{
+265 goto ERR;
+266 \}
+267 if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) \{
+268 goto ERR;
+269 \}
+270
+271 ERR:
+272 mp_clear_multi(&w0, &w1, &w2, &w3, &w4,
+273 &a0, &a1, &a2, &b0, &b1,
+274 &b2, &tmp1, &tmp2, NULL);
+275 return res;
+276 \}
+277
+278 #endif
\end{alltt}
\end{small}
@@ -4707,36 +4759,49 @@ s\_mp\_mul\_digs will clear it.
021 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
022
023 /* use Toom-Cook? */
-024 if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) \{
-025 res = mp_toom_mul(a, b, c);
-026 /* use Karatsuba? */
-027 \} else if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) \{
-028 res = mp_karatsuba_mul (a, b, c);
-029 \} else \{
-030 /* can we use the fast multiplier?
-031 *
-032 * The fast multiplier can be used if the output will
-033 * have less than MP_WARRAY digits and the number of
-034 * digits won't affect carry propagation
-035 */
-036 int digs = a->used + b->used + 1;
-037
-038 if ((digs < MP_WARRAY) &&
-039 MIN(a->used, b->used) <=
-040 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) \{
-041 res = fast_s_mp_mul_digs (a, b, c, digs);
-042 \} else \{
-043 res = s_mp_mul (a, b, c);
-044 \}
-045 \}
-046 c->sign = neg;
-047 return res;
-048 \}
+024 #ifdef BN_MP_TOOM_MUL_C
+025 if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) \{
+026 res = mp_toom_mul(a, b, c);
+027 \} else
+028 #endif
+029 #ifdef BN_MP_KARATSUBA_MUL_C
+030 /* use Karatsuba? */
+031 if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) \{
+032 res = mp_karatsuba_mul (a, b, c);
+033 \} else
+034 #endif
+035 \{
+036 /* can we use the fast multiplier?
+037 *
+038 * The fast multiplier can be used if the output will
+039 * have less than MP_WARRAY digits and the number of
+040 * digits won't affect carry propagation
+041 */
+042 int digs = a->used + b->used + 1;
+043
+044 #ifdef BN_FAST_S_MP_MUL_DIGS_C
+045 if ((digs < MP_WARRAY) &&
+046 MIN(a->used, b->used) <=
+047 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) \{
+048 res = fast_s_mp_mul_digs (a, b, c, digs);
+049 \} else
+050 #endif
+051 #ifdef BN_S_MP_MUL_DIGS_C
+052 res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
+053 #else
+054 res = MP_VAL;
+055 #endif
+056
+057 \}
+058 c->sign = (c->used > 0) ? neg : MP_ZPOS;
+059 return res;
+060 \}
+061 #endif
\end{alltt}
\end{small}
The implementation is rather simplistic and is not particularly noteworthy. Line 23 computes the sign of the result using the ``?''
-operator from the C programming language. Line 40 computes $\delta$ using the fact that $1 << k$ is equal to $2^k$.
+operator from the C programming language. Line 47 computes $\delta$ using the fact that $1 << k$ is equal to $2^k$.
\section{Squaring}
\label{sec:basesquare}
@@ -4901,6 +4966,7 @@ results calculated so far. This involves expensive carry propagation which will
077 mp_clear (&t);
078 return MP_OKAY;
079 \}
+080 #endif
\end{alltt}
\end{small}
@@ -5003,112 +5069,105 @@ squares in place.
031 * Based on Algorithm 14.16 on pp.597 of HAC.
032 *
033 */
-034 int fast_s_mp_sqr (mp_int * a, mp_int * b)
-035 \{
-036 int olduse, newused, res, ix, pa;
-037 mp_word W2[MP_WARRAY], W[MP_WARRAY];
-038
-039 /* calculate size of product and allocate as required */
-040 pa = a->used;
-041 newused = pa + pa + 1;
-042 if (b->alloc < newused) \{
-043 if ((res = mp_grow (b, newused)) != MP_OKAY) \{
-044 return res;
-045 \}
-046 \}
-047
-048 /* zero temp buffer (columns)
-049 * Note that there are two buffers. Since squaring requires
-050 * a outer and inner product and the inner product requires
-051 * computing a product and doubling it (a relatively expensive
-052 * op to perform n**2 times if you don't have to) the inner and
-053 * outer products are computed in different buffers. This way
-054 * the inner product can be doubled using n doublings instead of
-055 * n**2
-056 */
-057 memset (W, 0, newused * sizeof (mp_word));
-058 memset (W2, 0, newused * sizeof (mp_word));
+034 /* the jist of squaring...
+035
+036 you do like mult except the offset of the tmpx [one that starts closer to ze
+ ro]
+037 can't equal the offset of tmpy. So basically you set up iy like before then
+ you min it with
+038 (ty-tx) so that it never happens. You double all those you add in the inner
+ loop
+039
+040 After that loop you do the squares and add them in.
+041
+042 Remove W2 and don't memset W
+043
+044 */
+045
+046 int fast_s_mp_sqr (mp_int * a, mp_int * b)
+047 \{
+048 int olduse, res, pa, ix, iz;
+049 mp_digit W[MP_WARRAY], *tmpx;
+050 mp_word W1;
+051
+052 /* grow the destination as required */
+053 pa = a->used + a->used;
+054 if (b->alloc < pa) \{
+055 if ((res = mp_grow (b, pa)) != MP_OKAY) \{
+056 return res;
+057 \}
+058 \}
059
-060 /* This computes the inner product. To simplify the inner N**2 loop
-061 * the multiplication by two is done afterwards in the N loop.
-062 */
-063 for (ix = 0; ix < pa; ix++) \{
-064 /* compute the outer product
-065 *
-066 * Note that every outer product is computed
-067 * for a particular column only once which means that
-068 * there is no need todo a double precision addition
-069 * into the W2[] array.
-070 */
-071 W2[ix + ix] = ((mp_word)a->dp[ix]) * ((mp_word)a->dp[ix]);
-072
-073 \{
-074 register mp_digit tmpx, *tmpy;
-075 register mp_word *_W;
-076 register int iy;
+060 /* number of output digits to produce */
+061 W1 = 0;
+062 for (ix = 0; ix <= pa; ix++) \{
+063 int tx, ty, iy;
+064 mp_word _W;
+065 mp_digit *tmpy;
+066
+067 /* clear counter */
+068 _W = 0;
+069
+070 /* get offsets into the two bignums */
+071 ty = MIN(a->used-1, ix);
+072 tx = ix - ty;
+073
+074 /* setup temp aliases */
+075 tmpx = a->dp + tx;
+076 tmpy = a->dp + ty;
077
-078 /* copy of left side */
-079 tmpx = a->dp[ix];
-080
-081 /* alias for right side */
-082 tmpy = a->dp + (ix + 1);
-083
-084 /* the column to store the result in */
-085 _W = W + (ix + ix + 1);
-086
-087 /* inner products */
-088 for (iy = ix + 1; iy < pa; iy++) \{
-089 *_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++);
-090 \}
-091 \}
-092 \}
+078 /* this is the number of times the loop will iterrate, essentially its
+
+079 while (tx++ < a->used && ty-- >= 0) \{ ... \}
+080 */
+081 iy = MIN(a->used-tx, ty+1);
+082
+083 /* now for squaring tx can never equal ty
+084 * we halve the distance since they approach at a rate of 2x
+085 * and we have to round because odd cases need to be executed
+086 */
+087 iy = MIN(iy, (ty-tx+1)>>1);
+088
+089 /* execute loop */
+090 for (iz = 0; iz < iy; iz++) \{
+091 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
+092 \}
093
-094 /* setup dest */
-095 olduse = b->used;
-096 b->used = newused;
-097
-098 /* now compute digits
-099 *
-100 * We have to double the inner product sums, add in the
-101 * outer product sums, propagate carries and convert
-102 * to single precision.
-103 */
-104 \{
-105 register mp_digit *tmpb;
-106
-107 /* double first value, since the inner products are
-108 * half of what they should be
-109 */
-110 W[0] += W[0] + W2[0];
-111
-112 tmpb = b->dp;
-113 for (ix = 1; ix < newused; ix++) \{
-114 /* double/add next digit */
-115 W[ix] += W[ix] + W2[ix];
-116
-117 /* propagate carry forwards [from the previous digit] */
-118 W[ix] = W[ix] + (W[ix - 1] >> ((mp_word) DIGIT_BIT));
+094 /* double the inner product and add carry */
+095 _W = _W + _W + W1;
+096
+097 /* even columns have the square term in them */
+098 if ((ix&1) == 0) \{
+099 _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
+100 \}
+101
+102 /* store it */
+103 W[ix] = _W;
+104
+105 /* make next carry */
+106 W1 = _W >> ((mp_word)DIGIT_BIT);
+107 \}
+108
+109 /* setup dest */
+110 olduse = b->used;
+111 b->used = a->used+a->used;
+112
+113 \{
+114 mp_digit *tmpb;
+115 tmpb = b->dp;
+116 for (ix = 0; ix < pa; ix++) \{
+117 *tmpb++ = W[ix] & MP_MASK;
+118 \}
119
-120 /* store the current digit now that the carry isn't
-121 * needed
-122 */
-123 *tmpb++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
-124 \}
-125 /* set the last value. Note even if the carry is zero
-126 * this is required since the next step will not zero
-127 * it if b originally had a value at b->dp[2*a.used]
-128 */
-129 *tmpb++ = (mp_digit) (W[(newused) - 1] & ((mp_word) MP_MASK));
-130
-131 /* clear high digits of b if there were any originally */
-132 for (; ix < olduse; ix++) \{
-133 *tmpb++ = 0;
-134 \}
-135 \}
-136
-137 mp_clamp (b);
-138 return MP_OKAY;
-139 \}
+120 /* clear unused digits [that existed in the old copy of c] */
+121 for (; ix < olduse; ix++) \{
+122 *tmpb++ = 0;
+123 \}
+124 \}
+125 mp_clamp (b);
+126 return MP_OKAY;
+127 \}
+128 #endif
\end{alltt}
\end{small}
@@ -5221,7 +5280,7 @@ ratio of 1:7. } than simpler operations such as addition.
017 /* Karatsuba squaring, computes b = a*a using three
018 * half size squarings
019 *
-020 * See comments of mp_karatsuba_mul for details. It
+020 * See comments of karatsuba_mul for details. It
021 * is essentially the same algorithm but merely
022 * tuned to perform recursive squarings.
023 */
@@ -5317,6 +5376,7 @@ ratio of 1:7. } than simpler operations such as addition.
113 ERR:
114 return err;
115 \}
+116 #endif
\end{alltt}
\end{small}
@@ -5383,25 +5443,37 @@ neither of the polynomial basis algorithms should be used then either the Comba
020 \{
021 int res;
022
-023 /* use Toom-Cook? */
-024 if (a->used >= TOOM_SQR_CUTOFF) \{
-025 res = mp_toom_sqr(a, b);
-026 /* Karatsuba? */
-027 \} else if (a->used >= KARATSUBA_SQR_CUTOFF) \{
-028 res = mp_karatsuba_sqr (a, b);
-029 \} else \{
-030 /* can we use the fast comba multiplier? */
-031 if ((a->used * 2 + 1) < MP_WARRAY &&
-032 a->used <
-033 (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) \{
-034 res = fast_s_mp_sqr (a, b);
-035 \} else \{
-036 res = s_mp_sqr (a, b);
-037 \}
-038 \}
-039 b->sign = MP_ZPOS;
-040 return res;
-041 \}
+023 #ifdef BN_MP_TOOM_SQR_C
+024 /* use Toom-Cook? */
+025 if (a->used >= TOOM_SQR_CUTOFF) \{
+026 res = mp_toom_sqr(a, b);
+027 /* Karatsuba? */
+028 \} else
+029 #endif
+030 #ifdef BN_MP_KARATSUBA_SQR_C
+031 if (a->used >= KARATSUBA_SQR_CUTOFF) \{
+032 res = mp_karatsuba_sqr (a, b);
+033 \} else
+034 #endif
+035 \{
+036 #ifdef BN_FAST_S_MP_SQR_C
+037 /* can we use the fast comba multiplier? */
+038 if ((a->used * 2 + 1) < MP_WARRAY &&
+039 a->used <
+040 (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) \{
+041 res = fast_s_mp_sqr (a, b);
+042 \} else
+043 #endif
+044 #ifdef BN_S_MP_SQR_C
+045 res = s_mp_sqr (a, b);
+046 #else
+047 res = MP_VAL;
+048 #endif
+049 \}
+050 b->sign = MP_ZPOS;
+051 return res;
+052 \}
+053 #endif
\end{alltt}
\end{small}
@@ -5675,50 +5747,62 @@ performed at most twice, and on average once. However, if $a \ge b^2$ than it wi
038 goto CLEANUP;
039 \}
040 \} else \{
-041 if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) \{
-042 goto CLEANUP;
-043 \}
-044 \}
-045
-046 /* q3 = q2 / b**(k+1) */
-047 mp_rshd (&q, um + 1);
-048
-049 /* x = x mod b**(k+1), quick (no division) */
-050 if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) \{
-051 goto CLEANUP;
-052 \}
-053
-054 /* q = q * m mod b**(k+1), quick (no division) */
-055 if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) \{
-056 goto CLEANUP;
-057 \}
-058
-059 /* x = x - q */
-060 if ((res = mp_sub (x, &q, x)) != MP_OKAY) \{
-061 goto CLEANUP;
-062 \}
-063
-064 /* If x < 0, add b**(k+1) to it */
-065 if (mp_cmp_d (x, 0) == MP_LT) \{
-066 mp_set (&q, 1);
-067 if ((res = mp_lshd (&q, um + 1)) != MP_OKAY)
-068 goto CLEANUP;
-069 if ((res = mp_add (x, &q, x)) != MP_OKAY)
-070 goto CLEANUP;
-071 \}
-072
-073 /* Back off if it's too big */
-074 while (mp_cmp (x, m) != MP_LT) \{
-075 if ((res = s_mp_sub (x, m, x)) != MP_OKAY) \{
-076 goto CLEANUP;
-077 \}
-078 \}
-079
-080 CLEANUP:
-081 mp_clear (&q);
-082
-083 return res;
-084 \}
+041 #ifdef BN_S_MP_MUL_HIGH_DIGS_C
+042 if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) \{
+043 goto CLEANUP;
+044 \}
+045 #elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
+046 if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) \{
+047 goto CLEANUP;
+048 \}
+049 #else
+050 \{
+051 res = MP_VAL;
+052 goto CLEANUP;
+053 \}
+054 #endif
+055 \}
+056
+057 /* q3 = q2 / b**(k+1) */
+058 mp_rshd (&q, um + 1);
+059
+060 /* x = x mod b**(k+1), quick (no division) */
+061 if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) \{
+062 goto CLEANUP;
+063 \}
+064
+065 /* q = q * m mod b**(k+1), quick (no division) */
+066 if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) \{
+067 goto CLEANUP;
+068 \}
+069
+070 /* x = x - q */
+071 if ((res = mp_sub (x, &q, x)) != MP_OKAY) \{
+072 goto CLEANUP;
+073 \}
+074
+075 /* If x < 0, add b**(k+1) to it */
+076 if (mp_cmp_d (x, 0) == MP_LT) \{
+077 mp_set (&q, 1);
+078 if ((res = mp_lshd (&q, um + 1)) != MP_OKAY)
+079 goto CLEANUP;
+080 if ((res = mp_add (x, &q, x)) != MP_OKAY)
+081 goto CLEANUP;
+082 \}
+083
+084 /* Back off if it's too big */
+085 while (mp_cmp (x, m) != MP_LT) \{
+086 if ((res = s_mp_sub (x, m, x)) != MP_OKAY) \{
+087 goto CLEANUP;
+088 \}
+089 \}
+090
+091 CLEANUP:
+092 mp_clear (&q);
+093
+094 return res;
+095 \}
+096 #endif
\end{alltt}
\end{small}
@@ -5761,16 +5845,16 @@ is equivalent and much faster. The final value is computed by taking the intege
017 /* pre-calculate the value required for Barrett reduction
018 * For a given modulus "b" it calulates the value required in "a"
019 */
-020 int
-021 mp_reduce_setup (mp_int * a, mp_int * b)
-022 \{
-023 int res;
-024
-025 if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) \{
-026 return res;
-027 \}
-028 return mp_div (a, b, a, NULL);
-029 \}
+020 int mp_reduce_setup (mp_int * a, mp_int * b)
+021 \{
+022 int res;
+023
+024 if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) \{
+025 return res;
+026 \}
+027 return mp_div (a, b, a, NULL);
+028 \}
+029 #endif
\end{alltt}
\end{small}
@@ -6038,7 +6122,7 @@ multiplications.
023
024 /* can the fast reduction [comba] method be used?
025 *
-026 * Note that unlike in mp_mul you're safely allowed *less*
+026 * Note that unlike in mul you're safely allowed *less*
027 * than the available columns [255 per default] since carries
028 * are fixed up in the inner loop.
029 */
@@ -6061,7 +6145,7 @@ multiplications.
046 /* mu = ai * rho mod b
047 *
048 * The value of rho must be precalculated via
-049 * bn_mp_montgomery_setup() such that
+049 * montgomery_setup() such that
050 * it equals -1/n0 mod b this allows the
051 * following inner loop to reduce the
052 * input one digit at a time
@@ -6125,6 +6209,7 @@ multiplications.
110
111 return MP_OKAY;
112 \}
+113 #endif
\end{alltt}
\end{small}
@@ -6220,7 +6305,7 @@ stored in the destination $x$.
016
017 /* computes xR**-1 == x (mod N) via Montgomery Reduction
018 *
-019 * This is an optimized implementation of mp_montgomery_reduce
+019 * This is an optimized implementation of montgomery_reduce
020 * which uses the comba method to quickly calculate the columns of the
021 * reduction.
022 *
@@ -6369,6 +6454,7 @@ stored in the destination $x$.
165 \}
166 return MP_OKAY;
167 \}
+168 #endif
\end{alltt}
\end{small}
@@ -6450,10 +6536,11 @@ to calculate $1/n_0$ when $\beta$ is a power of two.
047 #endif
048
049 /* rho = -1/m mod b */
-050 *rho = (((mp_digit) 1 << ((mp_digit) DIGIT_BIT)) - x) & MP_MASK;
+050 *rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
051
052 return MP_OKAY;
053 \}
+054 #endif
\end{alltt}
\end{small}
@@ -6719,6 +6806,7 @@ at step 3.
086 \}
087 return MP_OKAY;
088 \}
+089 #endif
\end{alltt}
\end{small}
@@ -6773,6 +6861,7 @@ completeness.
024 ((mp_word)a->dp[0]));
025 \}
026
+027 #endif
\end{alltt}
\end{small}
@@ -6830,6 +6919,7 @@ step 3 then $n$ must be of Diminished Radix form.
035 return 1;
036 \}
037
+038 #endif
\end{alltt}
\end{small}
@@ -6914,6 +7004,7 @@ shift which makes the algorithm fairly inexpensive to use.
054 return res;
055 \}
056
+057 #endif
\end{alltt}
\end{small}
@@ -6983,6 +7074,7 @@ is sufficient to solve for $k$. Alternatively if $n$ has more than one digit th
040 mp_clear(&tmp);
041 return MP_OKAY;
042 \}
+043 #endif
\end{alltt}
\end{small}
@@ -7031,32 +7123,34 @@ This algorithm quickly determines if a modulus is of the form required for algor
017 /* determines if mp_reduce_2k can be used */
018 int mp_reduce_is_2k(mp_int *a)
019 \{
-020 int ix, iy, iz, iw;
-021
-022 if (a->used == 0) \{
-023 return 0;
-024 \} else if (a->used == 1) \{
-025 return 1;
-026 \} else if (a->used > 1) \{
-027 iy = mp_count_bits(a);
-028 iz = 1;
-029 iw = 1;
-030
-031 /* Test every bit from the second digit up, must be 1 */
-032 for (ix = DIGIT_BIT; ix < iy; ix++) \{
-033 if ((a->dp[iw] & iz) == 0) \{
-034 return 0;
-035 \}
-036 iz <<= 1;
-037 if (iz > (int)MP_MASK) \{
-038 ++iw;
-039 iz = 1;
-040 \}
-041 \}
-042 \}
-043 return 1;
-044 \}
-045
+020 int ix, iy, iw;
+021 mp_digit iz;
+022
+023 if (a->used == 0) \{
+024 return 0;
+025 \} else if (a->used == 1) \{
+026 return 1;
+027 \} else if (a->used > 1) \{
+028 iy = mp_count_bits(a);
+029 iz = 1;
+030 iw = 1;
+031
+032 /* Test every bit from the second digit up, must be 1 */
+033 for (ix = DIGIT_BIT; ix < iy; ix++) \{
+034 if ((a->dp[iw] & iz) == 0) \{
+035 return 0;
+036 \}
+037 iz <<= 1;
+038 if (iz > (mp_digit)MP_MASK) \{
+039 ++iw;
+040 iz = 1;
+041 \}
+042 \}
+043 \}
+044 return 1;
+045 \}
+046
+047 #endif
\end{alltt}
\end{small}
@@ -7265,6 +7359,7 @@ iteration of the loop moves the bits of the exponent $b$ upwards to the most sig
049 mp_clear (&g);
050 return MP_OKAY;
051 \}
+052 #endif
\end{alltt}
\end{small}
@@ -7470,51 +7565,72 @@ algorithm since their arguments are essentially the same (\textit{two mp\_ints a
031
032 /* if exponent X is negative we have to recurse */
033 if (X->sign == MP_NEG) \{
-034 mp_int tmpG, tmpX;
-035 int err;
-036
-037 /* first compute 1/G mod P */
-038 if ((err = mp_init(&tmpG)) != MP_OKAY) \{
-039 return err;
-040 \}
-041 if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) \{
-042 mp_clear(&tmpG);
-043 return err;
-044 \}
-045
-046 /* now get |X| */
-047 if ((err = mp_init(&tmpX)) != MP_OKAY) \{
-048 mp_clear(&tmpG);
-049 return err;
-050 \}
-051 if ((err = mp_abs(X, &tmpX)) != MP_OKAY) \{
-052 mp_clear_multi(&tmpG, &tmpX, NULL);
-053 return err;
-054 \}
-055
-056 /* and now compute (1/G)**|X| instead of G**X [X < 0] */
-057 err = mp_exptmod(&tmpG, &tmpX, P, Y);
-058 mp_clear_multi(&tmpG, &tmpX, NULL);
-059 return err;
-060 \}
-061
-062 /* is it a DR modulus? */
-063 dr = mp_dr_is_modulus(P);
-064
-065 /* if not, is it a uDR modulus? */
-066 if (dr == 0) \{
-067 dr = mp_reduce_is_2k(P) << 1;
-068 \}
-069
-070 /* if the modulus is odd or dr != 0 use the fast method */
-071 if (mp_isodd (P) == 1 || dr != 0) \{
-072 return mp_exptmod_fast (G, X, P, Y, dr);
-073 \} else \{
-074 /* otherwise use the generic Barrett reduction technique */
-075 return s_mp_exptmod (G, X, P, Y);
-076 \}
-077 \}
-078
+034 #ifdef BN_MP_INVMOD_C
+035 mp_int tmpG, tmpX;
+036 int err;
+037
+038 /* first compute 1/G mod P */
+039 if ((err = mp_init(&tmpG)) != MP_OKAY) \{
+040 return err;
+041 \}
+042 if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) \{
+043 mp_clear(&tmpG);
+044 return err;
+045 \}
+046
+047 /* now get |X| */
+048 if ((err = mp_init(&tmpX)) != MP_OKAY) \{
+049 mp_clear(&tmpG);
+050 return err;
+051 \}
+052 if ((err = mp_abs(X, &tmpX)) != MP_OKAY) \{
+053 mp_clear_multi(&tmpG, &tmpX, NULL);
+054 return err;
+055 \}
+056
+057 /* and now compute (1/G)**|X| instead of G**X [X < 0] */
+058 err = mp_exptmod(&tmpG, &tmpX, P, Y);
+059 mp_clear_multi(&tmpG, &tmpX, NULL);
+060 return err;
+061 #else
+062 /* no invmod */
+063 return MP_VAL
+064 #endif
+065 \}
+066
+067 #ifdef BN_MP_DR_IS_MODULUS_C
+068 /* is it a DR modulus? */
+069 dr = mp_dr_is_modulus(P);
+070 #else
+071 dr = 0;
+072 #endif
+073
+074 #ifdef BN_MP_REDUCE_IS_2K_C
+075 /* if not, is it a uDR modulus? */
+076 if (dr == 0) \{
+077 dr = mp_reduce_is_2k(P) << 1;
+078 \}
+079 #endif
+080
+081 /* if the modulus is odd or dr != 0 use the fast method */
+082 #ifdef BN_MP_EXPTMOD_FAST_C
+083 if (mp_isodd (P) == 1 || dr != 0) \{
+084 return mp_exptmod_fast (G, X, P, Y, dr);
+085 \} else \{
+086 #endif
+087 #ifdef BN_S_MP_EXPTMOD_C
+088 /* otherwise use the generic Barrett reduction technique */
+089 return s_mp_exptmod (G, X, P, Y);
+090 #else
+091 /* no exptmod for evens */
+092 return MP_VAL;
+093 #endif
+094 #ifdef BN_MP_EXPTMOD_FAST_C
+095 \}
+096 #endif
+097 \}
+098
+099 #endif
\end{alltt}
\end{small}
@@ -7523,8 +7639,8 @@ negative the algorithm tries to perform a modular exponentiation with the modula
the modular inverse of $G$ and $tmpX$ is assigned the absolute value of $X$. The algorithm will recuse with these new values with a positive
exponent.
-If the exponent is positive the algorithm resumes the exponentiation. Line 63 determines if the modulus is of the restricted Diminished Radix
-form. If it is not line 67 attempts to determine if it is of a unrestricted Diminished Radix form. The integer $dr$ will take on one
+If the exponent is positive the algorithm resumes the exponentiation. Line 69 determines if the modulus is of the restricted Diminished Radix
+form. If it is not line 77 attempts to determine if it is of a unrestricted Diminished Radix form. The integer $dr$ will take on one
of three values.
\begin{enumerate}
@@ -7533,7 +7649,7 @@ of three values.
\item $dr = 2$ means that the modulus is of unrestricted Diminished Radix form.
\end{enumerate}
-Line 70 determines if the fast modular exponentiation algorithm can be used. It is allowed if $dr \ne 0$ or if the modulus is odd. Otherwise,
+Line 67 determines if the fast modular exponentiation algorithm can be used. It is allowed if $dr \ne 0$ or if the modulus is odd. Otherwise,
the slower s\_mp\_exptmod algorithm is used which uses Barrett reduction.
\subsection{Barrett Modular Exponentiation}
@@ -7913,6 +8029,7 @@ a Left-to-Right algorithm is used to process the remaining few bits.
232 \}
233 return err;
234 \}
+235 #endif
\end{alltt}
\end{small}
@@ -7981,10 +8098,11 @@ equivalent to $m \cdot 2^k$. By this logic when $m = 1$ a quick power of two ca
036 a->used = b / DIGIT_BIT + 1;
037
038 /* put the single bit in its place */
-039 a->dp[b / DIGIT_BIT] = 1 << (b % DIGIT_BIT);
+039 a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
040
041 return MP_OKAY;
042 \}
+043 #endif
\end{alltt}
\end{small}
@@ -8234,201 +8352,277 @@ respectively be replaced with a zero.
\vspace{-3mm}
\begin{alltt}
016
-017 /* integer signed division.
-018 * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
-019 * HAC pp.598 Algorithm 14.20
-020 *
-021 * Note that the description in HAC is horribly
-022 * incomplete. For example, it doesn't consider
-023 * the case where digits are removed from 'x' in
-024 * the inner loop. It also doesn't consider the
-025 * case that y has fewer than three digits, etc..
-026 *
-027 * The overall algorithm is as described as
-028 * 14.20 from HAC but fixed to treat these cases.
-029 */
-030 int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
-031 \{
-032 mp_int q, x, y, t1, t2;
-033 int res, n, t, i, norm, neg;
-034
-035 /* is divisor zero ? */
-036 if (mp_iszero (b) == 1) \{
-037 return MP_VAL;
-038 \}
-039
-040 /* if a < b then q=0, r = a */
-041 if (mp_cmp_mag (a, b) == MP_LT) \{
-042 if (d != NULL) \{
-043 res = mp_copy (a, d);
-044 \} else \{
-045 res = MP_OKAY;
-046 \}
-047 if (c != NULL) \{
-048 mp_zero (c);
-049 \}
-050 return res;
-051 \}
-052
-053 if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) \{
-054 return res;
-055 \}
-056 q.used = a->used + 2;
+017 #ifdef BN_MP_DIV_SMALL
+018
+019 /* slower bit-bang division... also smaller */
+020 int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+021 \{
+022 mp_int ta, tb, tq, q;
+023 int res, n, n2;
+024
+025 /* is divisor zero ? */
+026 if (mp_iszero (b) == 1) \{
+027 return MP_VAL;
+028 \}
+029
+030 /* if a < b then q=0, r = a */
+031 if (mp_cmp_mag (a, b) == MP_LT) \{
+032 if (d != NULL) \{
+033 res = mp_copy (a, d);
+034 \} else \{
+035 res = MP_OKAY;
+036 \}
+037 if (c != NULL) \{
+038 mp_zero (c);
+039 \}
+040 return res;
+041 \}
+042
+043 /* init our temps */
+044 if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) \{
+045 return res;
+046 \}
+047
+048
+049 mp_set(&tq, 1);
+050 n = mp_count_bits(a) - mp_count_bits(b);
+051 if (((res = mp_copy(a, &ta)) != MP_OKAY) ||
+052 ((res = mp_copy(b, &tb)) != MP_OKAY) ||
+053 ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
+054 ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) \{
+055 goto __ERR;
+056 \}
057
-058 if ((res = mp_init (&t1)) != MP_OKAY) \{
-059 goto __Q;
-060 \}
-061
-062 if ((res = mp_init (&t2)) != MP_OKAY) \{
-063 goto __T1;
-064 \}
-065
-066 if ((res = mp_init_copy (&x, a)) != MP_OKAY) \{
-067 goto __T2;
-068 \}
-069
-070 if ((res = mp_init_copy (&y, b)) != MP_OKAY) \{
-071 goto __X;
-072 \}
-073
-074 /* fix the sign */
-075 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
-076 x.sign = y.sign = MP_ZPOS;
-077
-078 /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
-079 norm = mp_count_bits(&y) % DIGIT_BIT;
-080 if (norm < (int)(DIGIT_BIT-1)) \{
-081 norm = (DIGIT_BIT-1) - norm;
-082 if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) \{
-083 goto __Y;
-084 \}
-085 if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) \{
-086 goto __Y;
-087 \}
-088 \} else \{
-089 norm = 0;
-090 \}
-091
-092 /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
-093 n = x.used - 1;
-094 t = y.used - 1;
-095
-096 /* while (x >= y*b**n-t) do \{ q[n-t] += 1; x -= y*b**\{n-t\} \} */
-097 if ((res = mp_lshd (&y, n - t)) != MP_OKAY) \{ /* y = y*b**\{n-t\} */
-098 goto __Y;
-099 \}
-100
-101 while (mp_cmp (&x, &y) != MP_LT) \{
-102 ++(q.dp[n - t]);
-103 if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) \{
-104 goto __Y;
-105 \}
-106 \}
-107
-108 /* reset y by shifting it back down */
-109 mp_rshd (&y, n - t);
-110
-111 /* step 3. for i from n down to (t + 1) */
-112 for (i = n; i >= (t + 1); i--) \{
-113 if (i > x.used) \{
-114 continue;
-115 \}
-116
-117 /* step 3.1 if xi == yt then set q\{i-t-1\} to b-1,
-118 * otherwise set q\{i-t-1\} to (xi*b + x\{i-1\})/yt */
-119 if (x.dp[i] == y.dp[t]) \{
-120 q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
-121 \} else \{
-122 mp_word tmp;
-123 tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
-124 tmp |= ((mp_word) x.dp[i - 1]);
-125 tmp /= ((mp_word) y.dp[t]);
-126 if (tmp > (mp_word) MP_MASK)
-127 tmp = MP_MASK;
-128 q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
-129 \}
-130
-131 /* while (q\{i-t-1\} * (yt * b + y\{t-1\})) >
-132 xi * b**2 + xi-1 * b + xi-2
-133
-134 do q\{i-t-1\} -= 1;
-135 */
-136 q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;
-137 do \{
-138 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;
-139
-140 /* find left hand */
-141 mp_zero (&t1);
-142 t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
-143 t1.dp[1] = y.dp[t];
-144 t1.used = 2;
-145 if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) \{
-146 goto __Y;
-147 \}
-148
-149 /* find right hand */
-150 t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
-151 t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
-152 t2.dp[2] = x.dp[i];
-153 t2.used = 3;
-154 \} while (mp_cmp_mag(&t1, &t2) == MP_GT);
-155
-156 /* step 3.3 x = x - q\{i-t-1\} * y * b**\{i-t-1\} */
-157 if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) \{
-158 goto __Y;
-159 \}
-160
-161 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) \{
-162 goto __Y;
-163 \}
-164
-165 if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) \{
-166 goto __Y;
-167 \}
-168
-169 /* if x < 0 then \{ x = x + y*b**\{i-t-1\}; q\{i-t-1\} -= 1; \} */
-170 if (x.sign == MP_NEG) \{
-171 if ((res = mp_copy (&y, &t1)) != MP_OKAY) \{
-172 goto __Y;
-173 \}
-174 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) \{
-175 goto __Y;
-176 \}
-177 if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) \{
-178 goto __Y;
-179 \}
-180
-181 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
-182 \}
-183 \}
-184
-185 /* now q is the quotient and x is the remainder
-186 * [which we have to normalize]
-187 */
-188
-189 /* get sign before writing to c */
-190 x.sign = a->sign;
-191
-192 if (c != NULL) \{
-193 mp_clamp (&q);
-194 mp_exch (&q, c);
-195 c->sign = neg;
-196 \}
-197
-198 if (d != NULL) \{
-199 mp_div_2d (&x, norm, &x, NULL);
-200 mp_exch (&x, d);
-201 \}
+058 while (n-- >= 0) \{
+059 if (mp_cmp(&tb, &ta) != MP_GT) \{
+060 if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
+061 ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) \{
+062 goto __ERR;
+063 \}
+064 \}
+065 if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
+066 ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) \{
+067 goto __ERR;
+068 \}
+069 \}
+070
+071 /* now q == quotient and ta == remainder */
+072 n = a->sign;
+073 n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
+074 if (c != NULL) \{
+075 mp_exch(c, &q);
+076 c->sign = n2;
+077 \}
+078 if (d != NULL) \{
+079 mp_exch(d, &ta);
+080 d->sign = n;
+081 \}
+082 __ERR:
+083 mp_clear_multi(&ta, &tb, &tq, &q, NULL);
+084 return res;
+085 \}
+086
+087 #else
+088
+089 /* integer signed division.
+090 * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
+091 * HAC pp.598 Algorithm 14.20
+092 *
+093 * Note that the description in HAC is horribly
+094 * incomplete. For example, it doesn't consider
+095 * the case where digits are removed from 'x' in
+096 * the inner loop. It also doesn't consider the
+097 * case that y has fewer than three digits, etc..
+098 *
+099 * The overall algorithm is as described as
+100 * 14.20 from HAC but fixed to treat these cases.
+101 */
+102 int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+103 \{
+104 mp_int q, x, y, t1, t2;
+105 int res, n, t, i, norm, neg;
+106
+107 /* is divisor zero ? */
+108 if (mp_iszero (b) == 1) \{
+109 return MP_VAL;
+110 \}
+111
+112 /* if a < b then q=0, r = a */
+113 if (mp_cmp_mag (a, b) == MP_LT) \{
+114 if (d != NULL) \{
+115 res = mp_copy (a, d);
+116 \} else \{
+117 res = MP_OKAY;
+118 \}
+119 if (c != NULL) \{
+120 mp_zero (c);
+121 \}
+122 return res;
+123 \}
+124
+125 if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) \{
+126 return res;
+127 \}
+128 q.used = a->used + 2;
+129
+130 if ((res = mp_init (&t1)) != MP_OKAY) \{
+131 goto __Q;
+132 \}
+133
+134 if ((res = mp_init (&t2)) != MP_OKAY) \{
+135 goto __T1;
+136 \}
+137
+138 if ((res = mp_init_copy (&x, a)) != MP_OKAY) \{
+139 goto __T2;
+140 \}
+141
+142 if ((res = mp_init_copy (&y, b)) != MP_OKAY) \{
+143 goto __X;
+144 \}
+145
+146 /* fix the sign */
+147 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
+148 x.sign = y.sign = MP_ZPOS;
+149
+150 /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
+151 norm = mp_count_bits(&y) % DIGIT_BIT;
+152 if (norm < (int)(DIGIT_BIT-1)) \{
+153 norm = (DIGIT_BIT-1) - norm;
+154 if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) \{
+155 goto __Y;
+156 \}
+157 if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) \{
+158 goto __Y;
+159 \}
+160 \} else \{
+161 norm = 0;
+162 \}
+163
+164 /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
+165 n = x.used - 1;
+166 t = y.used - 1;
+167
+168 /* while (x >= y*b**n-t) do \{ q[n-t] += 1; x -= y*b**\{n-t\} \} */
+169 if ((res = mp_lshd (&y, n - t)) != MP_OKAY) \{ /* y = y*b**\{n-t\} */
+170 goto __Y;
+171 \}
+172
+173 while (mp_cmp (&x, &y) != MP_LT) \{
+174 ++(q.dp[n - t]);
+175 if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) \{
+176 goto __Y;
+177 \}
+178 \}
+179
+180 /* reset y by shifting it back down */
+181 mp_rshd (&y, n - t);
+182
+183 /* step 3. for i from n down to (t + 1) */
+184 for (i = n; i >= (t + 1); i--) \{
+185 if (i > x.used) \{
+186 continue;
+187 \}
+188
+189 /* step 3.1 if xi == yt then set q\{i-t-1\} to b-1,
+190 * otherwise set q\{i-t-1\} to (xi*b + x\{i-1\})/yt */
+191 if (x.dp[i] == y.dp[t]) \{
+192 q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
+193 \} else \{
+194 mp_word tmp;
+195 tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
+196 tmp |= ((mp_word) x.dp[i - 1]);
+197 tmp /= ((mp_word) y.dp[t]);
+198 if (tmp > (mp_word) MP_MASK)
+199 tmp = MP_MASK;
+200 q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
+201 \}
202
-203 res = MP_OKAY;
-204
-205 __Y:mp_clear (&y);
-206 __X:mp_clear (&x);
-207 __T2:mp_clear (&t2);
-208 __T1:mp_clear (&t1);
-209 __Q:mp_clear (&q);
-210 return res;
-211 \}
+203 /* while (q\{i-t-1\} * (yt * b + y\{t-1\})) >
+204 xi * b**2 + xi-1 * b + xi-2
+205
+206 do q\{i-t-1\} -= 1;
+207 */
+208 q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;
+209 do \{
+210 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;
+211
+212 /* find left hand */
+213 mp_zero (&t1);
+214 t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
+215 t1.dp[1] = y.dp[t];
+216 t1.used = 2;
+217 if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) \{
+218 goto __Y;
+219 \}
+220
+221 /* find right hand */
+222 t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
+223 t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
+224 t2.dp[2] = x.dp[i];
+225 t2.used = 3;
+226 \} while (mp_cmp_mag(&t1, &t2) == MP_GT);
+227
+228 /* step 3.3 x = x - q\{i-t-1\} * y * b**\{i-t-1\} */
+229 if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) \{
+230 goto __Y;
+231 \}
+232
+233 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) \{
+234 goto __Y;
+235 \}
+236
+237 if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) \{
+238 goto __Y;
+239 \}
+240
+241 /* if x < 0 then \{ x = x + y*b**\{i-t-1\}; q\{i-t-1\} -= 1; \} */
+242 if (x.sign == MP_NEG) \{
+243 if ((res = mp_copy (&y, &t1)) != MP_OKAY) \{
+244 goto __Y;
+245 \}
+246 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) \{
+247 goto __Y;
+248 \}
+249 if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) \{
+250 goto __Y;
+251 \}
+252
+253 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
+254 \}
+255 \}
+256
+257 /* now q is the quotient and x is the remainder
+258 * [which we have to normalize]
+259 */
+260
+261 /* get sign before writing to c */
+262 x.sign = x.used == 0 ? MP_ZPOS : a->sign;
+263
+264 if (c != NULL) \{
+265 mp_clamp (&q);
+266 mp_exch (&q, c);
+267 c->sign = neg;
+268 \}
+269
+270 if (d != NULL) \{
+271 mp_div_2d (&x, norm, &x, NULL);
+272 mp_exch (&x, d);
+273 \}
+274
+275 res = MP_OKAY;
+276
+277 __Y:mp_clear (&y);
+278 __X:mp_clear (&x);
+279 __T2:mp_clear (&t2);
+280 __T1:mp_clear (&t1);
+281 __Q:mp_clear (&q);
+282 return res;
+283 \}
+284
+285 #endif
+286
+287 #endif
\end{alltt}
\end{small}
@@ -8440,23 +8634,23 @@ algorithm with only the quotient is
mp_div(&a, &b, &c, NULL); /* c = [a/b] */
\end{verbatim}
-Lines 36 and 42 handle the two trivial cases of inputs which are division by zero and dividend smaller than the divisor
-respectively. After the two trivial cases all of the temporary variables are initialized. Line 75 determines the sign of
+Lines 37 and 44 handle the two trivial cases of inputs which are division by zero and dividend smaller than the divisor
+respectively. After the two trivial cases all of the temporary variables are initialized. Line 105 determines the sign of
the quotient and line 76 ensures that both $x$ and $y$ are positive.
-The number of bits in the leading digit is calculated on line 80. Implictly an mp\_int with $r$ digits will require $lg(\beta)(r-1) + k$ bits
+The number of bits in the leading digit is calculated on line 105. Implictly an mp\_int with $r$ digits will require $lg(\beta)(r-1) + k$ bits
of precision which when reduced modulo $lg(\beta)$ produces the value of $k$. In this case $k$ is the number of bits in the leading digit which is
exactly what is required. For the algorithm to operate $k$ must equal $lg(\beta) - 1$ and when it does not the inputs must be normalized by shifting
them to the left by $lg(\beta) - 1 - k$ bits.
Throughout the variables $n$ and $t$ will represent the highest digit of $x$ and $y$ respectively. These are first used to produce the
-leading digit of the quotient. The loop beginning on line 112 will produce the remainder of the quotient digits.
+leading digit of the quotient. The loop beginning on line 183 will produce the remainder of the quotient digits.
-The conditional ``continue'' on line 113 is used to prevent the algorithm from reading past the leading edge of $x$ which can occur when the
+The conditional ``continue'' on line 114 is used to prevent the algorithm from reading past the leading edge of $x$ which can occur when the
algorithm eliminates multiple non-zero digits in a single iteration. This ensures that $x_i$ is always non-zero since by definition the digits
above the $i$'th position $x$ must be zero in order for the quotient to be precise\footnote{Precise as far as integer division is concerned.}.
-Lines 142, 143 and 150 through 152 manually construct the high accuracy estimations by setting the digits of the two mp\_int
+Lines 130, 130 and 134 through 134 manually construct the high accuracy estimations by setting the digits of the two mp\_int
variables directly.
\section{Single Digit Helpers}
@@ -8582,6 +8776,7 @@ This algorithm initiates a temporary mp\_int with the value of the single digit
101 return MP_OKAY;
102 \}
103
+104 #endif
\end{alltt}
\end{small}
@@ -8689,6 +8884,7 @@ Unlike the full multiplication algorithms this algorithm does not require any si
070
071 return MP_OKAY;
072 \}
+073 #endif
\end{alltt}
\end{small}
@@ -8785,7 +8981,7 @@ from chapter seven.
054 /* power of two ? */
055 if (s_is_power_of_two(b, &ix) == 1) \{
056 if (d != NULL) \{
-057 *d = a->dp[0] & ((1<<ix) - 1);
+057 *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
058 \}
059 if (c != NULL) \{
060 return mp_div_2d(a, ix, c, NULL);
@@ -8793,44 +8989,47 @@ from chapter seven.
062 return MP_OKAY;
063 \}
064
-065 /* three? */
-066 if (b == 3) \{
-067 return mp_div_3(a, c, d);
-068 \}
-069
-070 /* no easy answer [c'est la vie]. Just division */
-071 if ((res = mp_init_size(&q, a->used)) != MP_OKAY) \{
-072 return res;
-073 \}
-074
-075 q.used = a->used;
-076 q.sign = a->sign;
-077 w = 0;
-078 for (ix = a->used - 1; ix >= 0; ix--) \{
-079 w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
-080
-081 if (w >= b) \{
-082 t = (mp_digit)(w / b);
-083 w -= ((mp_word)t) * ((mp_word)b);
-084 \} else \{
-085 t = 0;
-086 \}
-087 q.dp[ix] = (mp_digit)t;
-088 \}
-089
-090 if (d != NULL) \{
-091 *d = (mp_digit)w;
-092 \}
-093
-094 if (c != NULL) \{
-095 mp_clamp(&q);
-096 mp_exch(&q, c);
-097 \}
-098 mp_clear(&q);
-099
-100 return res;
-101 \}
-102
+065 #ifdef BN_MP_DIV_3_C
+066 /* three? */
+067 if (b == 3) \{
+068 return mp_div_3(a, c, d);
+069 \}
+070 #endif
+071
+072 /* no easy answer [c'est la vie]. Just division */
+073 if ((res = mp_init_size(&q, a->used)) != MP_OKAY) \{
+074 return res;
+075 \}
+076
+077 q.used = a->used;
+078 q.sign = a->sign;
+079 w = 0;
+080 for (ix = a->used - 1; ix >= 0; ix--) \{
+081 w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
+082
+083 if (w >= b) \{
+084 t = (mp_digit)(w / b);
+085 w -= ((mp_word)t) * ((mp_word)b);
+086 \} else \{
+087 t = 0;
+088 \}
+089 q.dp[ix] = (mp_digit)t;
+090 \}
+091
+092 if (d != NULL) \{
+093 *d = (mp_digit)w;
+094 \}
+095
+096 if (c != NULL) \{
+097 mp_clamp(&q);
+098 mp_exch(&q, c);
+099 \}
+100 mp_clear(&q);
+101
+102 return res;
+103 \}
+104
+105 #endif
\end{alltt}
\end{small}
@@ -9016,6 +9215,7 @@ root. Ideally this algorithm is meant to find the $n$'th root of an input where
124 __T1:mp_clear (&t1);
125 return res;
126 \}
+127 #endif
\end{alltt}
\end{small}
@@ -9091,6 +9291,7 @@ the integers from $0$ to $\beta - 1$.
047
048 return MP_OKAY;
049 \}
+050 #endif
\end{alltt}
\end{small}
@@ -9234,6 +9435,7 @@ as part of larger input without any significant problem.
074 \}
075 return MP_OKAY;
076 \}
+077 #endif
\end{alltt}
\end{small}
@@ -9352,6 +9554,7 @@ are required instead of a series of $n \times k$ divisions. One design flaw of
067 return MP_OKAY;
068 \}
069
+070 #endif
\end{alltt}
\end{small}
@@ -9631,6 +9834,7 @@ must be adjusted by multiplying by the common factors of two ($2^k$) removed ear
105 __U:mp_clear (&v);
106 return res;
107 \}
+108 #endif
\end{alltt}
\end{small}
@@ -9725,6 +9929,7 @@ dividing the product of the two inputs by their greatest common divisor.
052 mp_clear_multi (&t1, &t2, NULL);
053 return res;
054 \}
+055 #endif
\end{alltt}
\end{small}
@@ -9966,6 +10171,7 @@ $\left ( {p' \over a'} \right )$ which is multiplied against the current Jacobi
097 __A1:mp_clear (&a1);
098 return res;
099 \}
+100 #endif
\end{alltt}
\end{small}
@@ -10095,161 +10301,25 @@ then only a couple of additions or subtractions will be required to adjust the i
017 /* hac 14.61, pp608 */
018 int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
019 \{
-020 mp_int x, y, u, v, A, B, C, D;
-021 int res;
-022
-023 /* b cannot be negative */
-024 if (b->sign == MP_NEG || mp_iszero(b) == 1) \{
-025 return MP_VAL;
-026 \}
-027
-028 /* if the modulus is odd we can use a faster routine instead */
-029 if (mp_isodd (b) == 1) \{
-030 return fast_mp_invmod (a, b, c);
-031 \}
-032
-033 /* init temps */
-034 if ((res = mp_init_multi(&x, &y, &u, &v,
-035 &A, &B, &C, &D, NULL)) != MP_OKAY) \{
-036 return res;
-037 \}
-038
-039 /* x = a, y = b */
-040 if ((res = mp_copy (a, &x)) != MP_OKAY) \{
-041 goto __ERR;
-042 \}
-043 if ((res = mp_copy (b, &y)) != MP_OKAY) \{
-044 goto __ERR;
-045 \}
-046
-047 /* 2. [modified] if x,y are both even then return an error! */
-048 if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) \{
-049 res = MP_VAL;
-050 goto __ERR;
-051 \}
-052
-053 /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
-054 if ((res = mp_copy (&x, &u)) != MP_OKAY) \{
-055 goto __ERR;
-056 \}
-057 if ((res = mp_copy (&y, &v)) != MP_OKAY) \{
-058 goto __ERR;
-059 \}
-060 mp_set (&A, 1);
-061 mp_set (&D, 1);
-062
-063 top:
-064 /* 4. while u is even do */
-065 while (mp_iseven (&u) == 1) \{
-066 /* 4.1 u = u/2 */
-067 if ((res = mp_div_2 (&u, &u)) != MP_OKAY) \{
-068 goto __ERR;
-069 \}
-070 /* 4.2 if A or B is odd then */
-071 if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) \{
-072 /* A = (A+y)/2, B = (B-x)/2 */
-073 if ((res = mp_add (&A, &y, &A)) != MP_OKAY) \{
-074 goto __ERR;
-075 \}
-076 if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) \{
-077 goto __ERR;
-078 \}
-079 \}
-080 /* A = A/2, B = B/2 */
-081 if ((res = mp_div_2 (&A, &A)) != MP_OKAY) \{
-082 goto __ERR;
-083 \}
-084 if ((res = mp_div_2 (&B, &B)) != MP_OKAY) \{
-085 goto __ERR;
-086 \}
-087 \}
-088
-089 /* 5. while v is even do */
-090 while (mp_iseven (&v) == 1) \{
-091 /* 5.1 v = v/2 */
-092 if ((res = mp_div_2 (&v, &v)) != MP_OKAY) \{
-093 goto __ERR;
-094 \}
-095 /* 5.2 if C or D is odd then */
-096 if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) \{
-097 /* C = (C+y)/2, D = (D-x)/2 */
-098 if ((res = mp_add (&C, &y, &C)) != MP_OKAY) \{
-099 goto __ERR;
-100 \}
-101 if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) \{
-102 goto __ERR;
-103 \}
-104 \}
-105 /* C = C/2, D = D/2 */
-106 if ((res = mp_div_2 (&C, &C)) != MP_OKAY) \{
-107 goto __ERR;
-108 \}
-109 if ((res = mp_div_2 (&D, &D)) != MP_OKAY) \{
-110 goto __ERR;
-111 \}
-112 \}
-113
-114 /* 6. if u >= v then */
-115 if (mp_cmp (&u, &v) != MP_LT) \{
-116 /* u = u - v, A = A - C, B = B - D */
-117 if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) \{
-118 goto __ERR;
-119 \}
-120
-121 if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) \{
-122 goto __ERR;
-123 \}
-124
-125 if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) \{
-126 goto __ERR;
-127 \}
-128 \} else \{
-129 /* v - v - u, C = C - A, D = D - B */
-130 if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) \{
-131 goto __ERR;
-132 \}
-133
-134 if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) \{
-135 goto __ERR;
-136 \}
-137
-138 if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) \{
-139 goto __ERR;
-140 \}
-141 \}
-142
-143 /* if not zero goto step 4 */
-144 if (mp_iszero (&u) == 0)
-145 goto top;
-146
-147 /* now a = C, b = D, gcd == g*v */
-148
-149 /* if v != 1 then there is no inverse */
-150 if (mp_cmp_d (&v, 1) != MP_EQ) \{
-151 res = MP_VAL;
-152 goto __ERR;
-153 \}
-154
-155 /* if its too low */
-156 while (mp_cmp_d(&C, 0) == MP_LT) \{
-157 if ((res = mp_add(&C, b, &C)) != MP_OKAY) \{
-158 goto __ERR;
-159 \}
-160 \}
-161
-162 /* too big */
-163 while (mp_cmp_mag(&C, b) != MP_LT) \{
-164 if ((res = mp_sub(&C, b, &C)) != MP_OKAY) \{
-165 goto __ERR;
-166 \}
-167 \}
-168
-169 /* C is now the inverse */
-170 mp_exch (&C, c);
-171 res = MP_OKAY;
-172 __ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
-173 return res;
-174 \}
+020 /* b cannot be negative */
+021 if (b->sign == MP_NEG || mp_iszero(b) == 1) \{
+022 return MP_VAL;
+023 \}
+024
+025 #ifdef BN_FAST_MP_INVMOD_C
+026 /* if the modulus is odd we can use a faster routine instead */
+027 if (mp_isodd (b) == 1) \{
+028 return fast_mp_invmod (a, b, c);
+029 \}
+030 #endif
+031
+032 #ifdef BN_MP_INVMOD_SLOW_C
+033 return mp_invmod_slow(a, b, c);
+034 #endif
+035
+036 return MP_VAL;
+037 \}
+038 #endif
\end{alltt}
\end{small}
@@ -10350,6 +10420,7 @@ This algorithm attempts to determine if a candidate integer $n$ is composite by
042
043 return MP_OKAY;
044 \}
+045 #endif
\end{alltt}
\end{small}
@@ -10400,6 +10471,7 @@ mp\_digit. The table \_\_prime\_tab is defined in the following file.
053 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
054 #endif
055 \};
+056 #endif
\end{alltt}
\end{small}
@@ -10487,6 +10559,7 @@ determine the result.
054 __T:mp_clear (&t);
055 return err;
056 \}
+057 #endif
\end{alltt}
\end{small}
@@ -10621,6 +10694,7 @@ composite then it is \textit{probably} prime.
095 __N1:mp_clear (&n1);
096 return err;
097 \}
+098 #endif
\end{alltt}
\end{small}
diff --git a/tommath_class.h b/tommath_class.h
new file mode 100644
index 00000000..2a17d430
--- /dev/null
+++ b/tommath_class.h
@@ -0,0 +1,951 @@
+#if !(defined(LTM1) && defined(LTM2) && defined(LTM3))
+#if defined(LTM2)
+#define LTM3
+#endif
+#if defined(LTM1)
+#define LTM2
+#endif
+#define LTM1
+
+#if defined(LTM_ALL)
+#define BN_ERROR_C
+#define BN_FAST_MP_INVMOD_C
+#define BN_FAST_MP_MONTGOMERY_REDUCE_C
+#define BN_FAST_S_MP_MUL_DIGS_C
+#define BN_FAST_S_MP_MUL_HIGH_DIGS_C
+#define BN_FAST_S_MP_SQR_C
+#define BN_MP_2EXPT_C
+#define BN_MP_ABS_C
+#define BN_MP_ADD_C
+#define BN_MP_ADD_D_C
+#define BN_MP_ADDMOD_C
+#define BN_MP_AND_C
+#define BN_MP_CLAMP_C
+#define BN_MP_CLEAR_C
+#define BN_MP_CLEAR_MULTI_C
+#define BN_MP_CMP_C
+#define BN_MP_CMP_D_C
+#define BN_MP_CMP_MAG_C
+#define BN_MP_CNT_LSB_C
+#define BN_MP_COPY_C
+#define BN_MP_COUNT_BITS_C
+#define BN_MP_DIV_C
+#define BN_MP_DIV_2_C
+#define BN_MP_DIV_2D_C
+#define BN_MP_DIV_3_C
+#define BN_MP_DIV_D_C
+#define BN_MP_DR_IS_MODULUS_C
+#define BN_MP_DR_REDUCE_C
+#define BN_MP_DR_SETUP_C
+#define BN_MP_EXCH_C
+#define BN_MP_EXPT_D_C
+#define BN_MP_EXPTMOD_C
+#define BN_MP_EXPTMOD_FAST_C
+#define BN_MP_EXTEUCLID_C
+#define BN_MP_FREAD_C
+#define BN_MP_FWRITE_C
+#define BN_MP_GCD_C
+#define BN_MP_GET_INT_C
+#define BN_MP_GROW_C
+#define BN_MP_INIT_C
+#define BN_MP_INIT_COPY_C
+#define BN_MP_INIT_MULTI_C
+#define BN_MP_INIT_SET_C
+#define BN_MP_INIT_SET_INT_C
+#define BN_MP_INIT_SIZE_C
+#define BN_MP_INVMOD_C
+#define BN_MP_INVMOD_SLOW_C
+#define BN_MP_IS_SQUARE_C
+#define BN_MP_JACOBI_C
+#define BN_MP_KARATSUBA_MUL_C
+#define BN_MP_KARATSUBA_SQR_C
+#define BN_MP_LCM_C
+#define BN_MP_LSHD_C
+#define BN_MP_MOD_C
+#define BN_MP_MOD_2D_C
+#define BN_MP_MOD_D_C
+#define BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+#define BN_MP_MONTGOMERY_REDUCE_C
+#define BN_MP_MONTGOMERY_SETUP_C
+#define BN_MP_MUL_C
+#define BN_MP_MUL_2_C
+#define BN_MP_MUL_2D_C
+#define BN_MP_MUL_D_C
+#define BN_MP_MULMOD_C
+#define BN_MP_N_ROOT_C
+#define BN_MP_NEG_C
+#define BN_MP_OR_C
+#define BN_MP_PRIME_FERMAT_C
+#define BN_MP_PRIME_IS_DIVISIBLE_C
+#define BN_MP_PRIME_IS_PRIME_C
+#define BN_MP_PRIME_MILLER_RABIN_C
+#define BN_MP_PRIME_NEXT_PRIME_C
+#define BN_MP_PRIME_RABIN_MILLER_TRIALS_C
+#define BN_MP_PRIME_RANDOM_EX_C
+#define BN_MP_RADIX_SIZE_C
+#define BN_MP_RADIX_SMAP_C
+#define BN_MP_RAND_C
+#define BN_MP_READ_RADIX_C
+#define BN_MP_READ_SIGNED_BIN_C
+#define BN_MP_READ_UNSIGNED_BIN_C
+#define BN_MP_REDUCE_C
+#define BN_MP_REDUCE_2K_C
+#define BN_MP_REDUCE_2K_SETUP_C
+#define BN_MP_REDUCE_IS_2K_C
+#define BN_MP_REDUCE_SETUP_C
+#define BN_MP_RSHD_C
+#define BN_MP_SET_C
+#define BN_MP_SET_INT_C
+#define BN_MP_SHRINK_C
+#define BN_MP_SIGNED_BIN_SIZE_C
+#define BN_MP_SQR_C
+#define BN_MP_SQRMOD_C
+#define BN_MP_SQRT_C
+#define BN_MP_SUB_C
+#define BN_MP_SUB_D_C
+#define BN_MP_SUBMOD_C
+#define BN_MP_TO_SIGNED_BIN_C
+#define BN_MP_TO_UNSIGNED_BIN_C
+#define BN_MP_TOOM_MUL_C
+#define BN_MP_TOOM_SQR_C
+#define BN_MP_TORADIX_C
+#define BN_MP_TORADIX_N_C
+#define BN_MP_UNSIGNED_BIN_SIZE_C
+#define BN_MP_XOR_C
+#define BN_MP_ZERO_C
+#define BN_PRIME_TAB_C
+#define BN_REVERSE_C
+#define BN_S_MP_ADD_C
+#define BN_S_MP_EXPTMOD_C
+#define BN_S_MP_MUL_DIGS_C
+#define BN_S_MP_MUL_HIGH_DIGS_C
+#define BN_S_MP_SQR_C
+#define BN_S_MP_SUB_C
+#define BNCORE_C
+#endif
+
+#if defined(BN_ERROR_C)
+ #define BN_MP_ERROR_TO_STRING_C
+#endif
+
+#if defined(BN_FAST_MP_INVMOD_C)
+ #define BN_MP_ISEVEN_C
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_COPY_C
+ #define BN_MP_ABS_C
+ #define BN_MP_SET_C
+ #define BN_MP_DIV_2_C
+ #define BN_MP_ISODD_C
+ #define BN_MP_SUB_C
+ #define BN_MP_CMP_C
+ #define BN_MP_ISZERO_C
+ #define BN_MP_CMP_D_C
+ #define BN_MP_ADD_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_MULTI_C
+#endif
+
+#if defined(BN_FAST_MP_MONTGOMERY_REDUCE_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_S_MP_SUB_C
+#endif
+
+#if defined(BN_FAST_S_MP_MUL_DIGS_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_FAST_S_MP_SQR_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_2EXPT_C)
+ #define BN_MP_ZERO_C
+ #define BN_MP_GROW_C
+#endif
+
+#if defined(BN_MP_ABS_C)
+ #define BN_MP_COPY_C
+#endif
+
+#if defined(BN_MP_ADD_C)
+ #define BN_S_MP_ADD_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_S_MP_SUB_C
+#endif
+
+#if defined(BN_MP_ADD_D_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_SUB_D_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_ADDMOD_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_ADD_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_MOD_C
+#endif
+
+#if defined(BN_MP_AND_C)
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_CLAMP_C)
+#endif
+
+#if defined(BN_MP_CLEAR_C)
+#endif
+
+#if defined(BN_MP_CLEAR_MULTI_C)
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_CMP_C)
+ #define BN_MP_CMP_MAG_C
+#endif
+
+#if defined(BN_MP_CMP_D_C)
+#endif
+
+#if defined(BN_MP_CMP_MAG_C)
+#endif
+
+#if defined(BN_MP_CNT_LSB_C)
+ #define BN_MP_ISZERO_C
+#endif
+
+#if defined(BN_MP_COPY_C)
+ #define BN_MP_GROW_C
+#endif
+
+#if defined(BN_MP_COUNT_BITS_C)
+#endif
+
+#if defined(BN_MP_DIV_C)
+ #define BN_MP_ISZERO_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_MP_COPY_C
+ #define BN_MP_ZERO_C
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_SET_C
+ #define BN_MP_COUNT_BITS_C
+ #define BN_MP_MUL_2D_C
+ #define BN_MP_CMP_C
+ #define BN_MP_SUB_C
+ #define BN_MP_ADD_C
+ #define BN_MP_DIV_2D_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_MULTI_C
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_INIT_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_LSHD_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_MUL_D_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_DIV_2_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_DIV_2D_C)
+ #define BN_MP_COPY_C
+ #define BN_MP_ZERO_C
+ #define BN_MP_INIT_C
+ #define BN_MP_MOD_2D_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+#endif
+
+#if defined(BN_MP_DIV_3_C)
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_DIV_D_C)
+ #define BN_MP_ISZERO_C
+ #define BN_MP_COPY_C
+ #define BN_MP_DIV_2D_C
+ #define BN_MP_DIV_3_C
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_DR_IS_MODULUS_C)
+#endif
+
+#if defined(BN_MP_DR_REDUCE_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_S_MP_SUB_C
+#endif
+
+#if defined(BN_MP_DR_SETUP_C)
+#endif
+
+#if defined(BN_MP_EXCH_C)
+#endif
+
+#if defined(BN_MP_EXPT_D_C)
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_SET_C
+ #define BN_MP_SQR_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_MUL_C
+#endif
+
+#if defined(BN_MP_EXPTMOD_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_INVMOD_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_ABS_C
+ #define BN_MP_CLEAR_MULTI_C
+ #define BN_MP_DR_IS_MODULUS_C
+ #define BN_MP_REDUCE_IS_2K_C
+ #define BN_MP_ISODD_C
+ #define BN_MP_EXPTMOD_FAST_C
+ #define BN_S_MP_EXPTMOD_C
+#endif
+
+#if defined(BN_MP_EXPTMOD_FAST_C)
+ #define BN_MP_COUNT_BITS_C
+ #define BN_MP_INIT_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_MONTGOMERY_SETUP_C
+ #define BN_FAST_MP_MONTGOMERY_REDUCE_C
+ #define BN_MP_MONTGOMERY_REDUCE_C
+ #define BN_MP_DR_SETUP_C
+ #define BN_MP_DR_REDUCE_C
+ #define BN_MP_REDUCE_2K_SETUP_C
+ #define BN_MP_REDUCE_2K_C
+ #define BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
+ #define BN_MP_MULMOD_C
+ #define BN_MP_SET_C
+ #define BN_MP_MOD_C
+ #define BN_MP_COPY_C
+ #define BN_MP_SQR_C
+ #define BN_MP_MUL_C
+ #define BN_MP_EXCH_C
+#endif
+
+#if defined(BN_MP_EXTEUCLID_C)
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_SET_C
+ #define BN_MP_COPY_C
+ #define BN_MP_ISZERO_C
+ #define BN_MP_DIV_C
+ #define BN_MP_MUL_C
+ #define BN_MP_SUB_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_MULTI_C
+#endif
+
+#if defined(BN_MP_FREAD_C)
+ #define BN_MP_ZERO_C
+ #define BN_MP_S_RMAP_C
+ #define BN_MP_MUL_D_C
+ #define BN_MP_ADD_D_C
+ #define BN_MP_CMP_D_C
+#endif
+
+#if defined(BN_MP_FWRITE_C)
+ #define BN_MP_RADIX_SIZE_C
+ #define BN_MP_TORADIX_C
+#endif
+
+#if defined(BN_MP_GCD_C)
+ #define BN_MP_ISZERO_C
+ #define BN_MP_ABS_C
+ #define BN_MP_ZERO_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_CNT_LSB_C
+ #define BN_MP_DIV_2D_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_MP_EXCH_C
+ #define BN_S_MP_SUB_C
+ #define BN_MP_MUL_2D_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_GET_INT_C)
+#endif
+
+#if defined(BN_MP_GROW_C)
+#endif
+
+#if defined(BN_MP_INIT_C)
+#endif
+
+#if defined(BN_MP_INIT_COPY_C)
+ #define BN_MP_COPY_C
+#endif
+
+#if defined(BN_MP_INIT_MULTI_C)
+ #define BN_MP_ERR_C
+ #define BN_MP_INIT_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_INIT_SET_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_SET_C
+#endif
+
+#if defined(BN_MP_INIT_SET_INT_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_SET_INT_C
+#endif
+
+#if defined(BN_MP_INIT_SIZE_C)
+ #define BN_MP_INIT_C
+#endif
+
+#if defined(BN_MP_INVMOD_C)
+ #define BN_MP_ISZERO_C
+ #define BN_MP_ISODD_C
+ #define BN_FAST_MP_INVMOD_C
+ #define BN_MP_INVMOD_SLOW_C
+#endif
+
+#if defined(BN_MP_INVMOD_SLOW_C)
+ #define BN_MP_ISZERO_C
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_COPY_C
+ #define BN_MP_ISEVEN_C
+ #define BN_MP_SET_C
+ #define BN_MP_DIV_2_C
+ #define BN_MP_ISODD_C
+ #define BN_MP_ADD_C
+ #define BN_MP_SUB_C
+ #define BN_MP_CMP_C
+ #define BN_MP_CMP_D_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_MULTI_C
+#endif
+
+#if defined(BN_MP_IS_SQUARE_C)
+ #define BN_MP_MOD_D_C
+ #define BN_MP_INIT_SET_INT_C
+ #define BN_MP_MOD_C
+ #define BN_MP_GET_INT_C
+ #define BN_MP_SQRT_C
+ #define BN_MP_SQR_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_JACOBI_C)
+ #define BN_MP_CMP_D_C
+ #define BN_MP_ISZERO_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_CNT_LSB_C
+ #define BN_MP_DIV_2D_C
+ #define BN_MP_MOD_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_KARATSUBA_MUL_C)
+ #define BN_MP_MUL_C
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_SUB_C
+ #define BN_MP_ADD_C
+ #define BN_MP_LSHD_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_KARATSUBA_SQR_C)
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_SQR_C
+ #define BN_MP_SUB_C
+ #define BN_S_MP_ADD_C
+ #define BN_MP_LSHD_C
+ #define BN_MP_ADD_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_LCM_C)
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_GCD_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_MP_DIV_C
+ #define BN_MP_MUL_C
+ #define BN_MP_CLEAR_MULTI_C
+#endif
+
+#if defined(BN_MP_LSHD_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_RSHD_C
+#endif
+
+#if defined(BN_MP_MOD_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_DIV_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_ADD_C
+ #define BN_MP_EXCH_C
+#endif
+
+#if defined(BN_MP_MOD_2D_C)
+ #define BN_MP_ZERO_C
+ #define BN_MP_COPY_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_MOD_D_C)
+ #define BN_MP_DIV_D_C
+#endif
+
+#if defined(BN_MP_MONTGOMERY_CALC_NORMALIZATION_C)
+ #define BN_MP_COUNT_BITS_C
+ #define BN_MP_2EXPT_C
+ #define BN_MP_SET_C
+ #define BN_MP_MUL_2_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_S_MP_SUB_C
+#endif
+
+#if defined(BN_MP_MONTGOMERY_REDUCE_C)
+ #define BN_FAST_MP_MONTGOMERY_REDUCE_C
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_S_MP_SUB_C
+#endif
+
+#if defined(BN_MP_MONTGOMERY_SETUP_C)
+#endif
+
+#if defined(BN_MP_MUL_C)
+ #define BN_MP_TOOM_MUL_C
+ #define BN_MP_KARATSUBA_MUL_C
+ #define BN_FAST_S_MP_MUL_DIGS_C
+ #define BN_S_MP_MUL_C
+ #define BN_S_MP_MUL_DIGS_C
+#endif
+
+#if defined(BN_MP_MUL_2_C)
+ #define BN_MP_GROW_C
+#endif
+
+#if defined(BN_MP_MUL_2D_C)
+ #define BN_MP_COPY_C
+ #define BN_MP_GROW_C
+ #define BN_MP_LSHD_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_MUL_D_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_MULMOD_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_MUL_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_MOD_C
+#endif
+
+#if defined(BN_MP_N_ROOT_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_SET_C
+ #define BN_MP_COPY_C
+ #define BN_MP_EXPT_D_C
+ #define BN_MP_MUL_C
+ #define BN_MP_SUB_C
+ #define BN_MP_MUL_D_C
+ #define BN_MP_DIV_C
+ #define BN_MP_CMP_C
+ #define BN_MP_SUB_D_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_NEG_C)
+ #define BN_MP_COPY_C
+ #define BN_MP_ISZERO_C
+#endif
+
+#if defined(BN_MP_OR_C)
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_PRIME_FERMAT_C)
+ #define BN_MP_CMP_D_C
+ #define BN_MP_INIT_C
+ #define BN_MP_EXPTMOD_C
+ #define BN_MP_CMP_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_PRIME_IS_DIVISIBLE_C)
+ #define BN_MP_MOD_D_C
+#endif
+
+#if defined(BN_MP_PRIME_IS_PRIME_C)
+ #define BN_MP_CMP_D_C
+ #define BN_MP_PRIME_IS_DIVISIBLE_C
+ #define BN_MP_INIT_C
+ #define BN_MP_SET_C
+ #define BN_MP_PRIME_MILLER_RABIN_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_PRIME_MILLER_RABIN_C)
+ #define BN_MP_CMP_D_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_SUB_D_C
+ #define BN_MP_CNT_LSB_C
+ #define BN_MP_DIV_2D_C
+ #define BN_MP_EXPTMOD_C
+ #define BN_MP_CMP_C
+ #define BN_MP_SQRMOD_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_PRIME_NEXT_PRIME_C)
+ #define BN_MP_CMP_D_C
+ #define BN_MP_SET_C
+ #define BN_MP_SUB_D_C
+ #define BN_MP_ISEVEN_C
+ #define BN_MP_MOD_D_C
+ #define BN_MP_INIT_C
+ #define BN_MP_ADD_D_C
+ #define BN_MP_PRIME_MILLER_RABIN_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_PRIME_RABIN_MILLER_TRIALS_C)
+#endif
+
+#if defined(BN_MP_PRIME_RANDOM_EX_C)
+ #define BN_MP_READ_UNSIGNED_BIN_C
+ #define BN_MP_PRIME_IS_PRIME_C
+ #define BN_MP_SUB_D_C
+ #define BN_MP_DIV_2_C
+ #define BN_MP_MUL_2_C
+ #define BN_MP_ADD_D_C
+#endif
+
+#if defined(BN_MP_RADIX_SIZE_C)
+ #define BN_MP_COUNT_BITS_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_ISZERO_C
+ #define BN_MP_DIV_D_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_RADIX_SMAP_C)
+ #define BN_MP_S_RMAP_C
+#endif
+
+#if defined(BN_MP_RAND_C)
+ #define BN_MP_ZERO_C
+ #define BN_MP_ADD_D_C
+ #define BN_MP_LSHD_C
+#endif
+
+#if defined(BN_MP_READ_RADIX_C)
+ #define BN_MP_ZERO_C
+ #define BN_MP_S_RMAP_C
+ #define BN_MP_MUL_D_C
+ #define BN_MP_ADD_D_C
+ #define BN_MP_ISZERO_C
+#endif
+
+#if defined(BN_MP_READ_SIGNED_BIN_C)
+ #define BN_MP_READ_UNSIGNED_BIN_C
+#endif
+
+#if defined(BN_MP_READ_UNSIGNED_BIN_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_ZERO_C
+ #define BN_MP_MUL_2D_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_REDUCE_C)
+ #define BN_MP_REDUCE_SETUP_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_MUL_C
+ #define BN_S_MP_MUL_HIGH_DIGS_C
+ #define BN_FAST_S_MP_MUL_HIGH_DIGS_C
+ #define BN_MP_MOD_2D_C
+ #define BN_S_MP_MUL_DIGS_C
+ #define BN_MP_SUB_C
+ #define BN_MP_CMP_D_C
+ #define BN_MP_SET_C
+ #define BN_MP_LSHD_C
+ #define BN_MP_ADD_C
+ #define BN_MP_CMP_C
+ #define BN_S_MP_SUB_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_REDUCE_2K_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_COUNT_BITS_C
+ #define BN_MP_DIV_2D_C
+ #define BN_MP_MUL_D_C
+ #define BN_S_MP_ADD_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_S_MP_SUB_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_REDUCE_2K_SETUP_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_COUNT_BITS_C
+ #define BN_MP_2EXPT_C
+ #define BN_MP_CLEAR_C
+ #define BN_S_MP_SUB_C
+#endif
+
+#if defined(BN_MP_REDUCE_IS_2K_C)
+ #define BN_MP_REDUCE_2K_C
+ #define BN_MP_COUNT_BITS_C
+#endif
+
+#if defined(BN_MP_REDUCE_SETUP_C)
+ #define BN_MP_2EXPT_C
+ #define BN_MP_DIV_C
+#endif
+
+#if defined(BN_MP_RSHD_C)
+ #define BN_MP_ZERO_C
+#endif
+
+#if defined(BN_MP_SET_C)
+ #define BN_MP_ZERO_C
+#endif
+
+#if defined(BN_MP_SET_INT_C)
+ #define BN_MP_ZERO_C
+ #define BN_MP_MUL_2D_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_SHRINK_C)
+#endif
+
+#if defined(BN_MP_SIGNED_BIN_SIZE_C)
+ #define BN_MP_UNSIGNED_BIN_SIZE_C
+#endif
+
+#if defined(BN_MP_SQR_C)
+ #define BN_MP_TOOM_SQR_C
+ #define BN_MP_KARATSUBA_SQR_C
+ #define BN_FAST_S_MP_SQR_C
+ #define BN_S_MP_SQR_C
+#endif
+
+#if defined(BN_MP_SQRMOD_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_SQR_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_MOD_C
+#endif
+
+#if defined(BN_MP_SQRT_C)
+ #define BN_MP_N_ROOT_C
+ #define BN_MP_ISZERO_C
+ #define BN_MP_ZERO_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_DIV_C
+ #define BN_MP_ADD_C
+ #define BN_MP_DIV_2_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_SUB_C)
+ #define BN_S_MP_ADD_C
+ #define BN_MP_CMP_MAG_C
+ #define BN_S_MP_SUB_C
+#endif
+
+#if defined(BN_MP_SUB_D_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_ADD_D_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_MP_SUBMOD_C)
+ #define BN_MP_INIT_C
+ #define BN_MP_SUB_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_MOD_C
+#endif
+
+#if defined(BN_MP_TO_SIGNED_BIN_C)
+ #define BN_MP_TO_UNSIGNED_BIN_C
+#endif
+
+#if defined(BN_MP_TO_UNSIGNED_BIN_C)
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_ISZERO_C
+ #define BN_MP_DIV_2D_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_TOOM_MUL_C)
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_MOD_2D_C
+ #define BN_MP_COPY_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_MUL_C
+ #define BN_MP_MUL_2_C
+ #define BN_MP_ADD_C
+ #define BN_MP_SUB_C
+ #define BN_MP_DIV_2_C
+ #define BN_MP_MUL_2D_C
+ #define BN_MP_MUL_D_C
+ #define BN_MP_DIV_3_C
+ #define BN_MP_LSHD_C
+ #define BN_MP_CLEAR_MULTI_C
+#endif
+
+#if defined(BN_MP_TOOM_SQR_C)
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_MOD_2D_C
+ #define BN_MP_COPY_C
+ #define BN_MP_RSHD_C
+ #define BN_MP_SQR_C
+ #define BN_MP_MUL_2_C
+ #define BN_MP_ADD_C
+ #define BN_MP_SUB_C
+ #define BN_MP_DIV_2_C
+ #define BN_MP_MUL_2D_C
+ #define BN_MP_MUL_D_C
+ #define BN_MP_DIV_3_C
+ #define BN_MP_LSHD_C
+ #define BN_MP_CLEAR_MULTI_C
+#endif
+
+#if defined(BN_MP_TORADIX_C)
+ #define BN_MP_ISZERO_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_DIV_D_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_S_RMAP_C
+#endif
+
+#if defined(BN_MP_TORADIX_N_C)
+ #define BN_MP_ISZERO_C
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_DIV_D_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_S_RMAP_C
+#endif
+
+#if defined(BN_MP_UNSIGNED_BIN_SIZE_C)
+ #define BN_MP_COUNT_BITS_C
+#endif
+
+#if defined(BN_MP_XOR_C)
+ #define BN_MP_INIT_COPY_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_MP_ZERO_C)
+#endif
+
+#if defined(BN_PRIME_TAB_C)
+#endif
+
+#if defined(BN_REVERSE_C)
+#endif
+
+#if defined(BN_S_MP_ADD_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BN_S_MP_EXPTMOD_C)
+ #define BN_MP_COUNT_BITS_C
+ #define BN_MP_INIT_C
+ #define BN_MP_CLEAR_C
+ #define BN_MP_REDUCE_SETUP_C
+ #define BN_MP_MOD_C
+ #define BN_MP_COPY_C
+ #define BN_MP_SQR_C
+ #define BN_MP_REDUCE_C
+ #define BN_MP_MUL_C
+ #define BN_MP_SET_C
+ #define BN_MP_EXCH_C
+#endif
+
+#if defined(BN_S_MP_MUL_DIGS_C)
+ #define BN_FAST_S_MP_MUL_DIGS_C
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_S_MP_MUL_HIGH_DIGS_C)
+ #define BN_FAST_S_MP_MUL_HIGH_DIGS_C
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_S_MP_SQR_C)
+ #define BN_MP_INIT_SIZE_C
+ #define BN_MP_CLAMP_C
+ #define BN_MP_EXCH_C
+ #define BN_MP_CLEAR_C
+#endif
+
+#if defined(BN_S_MP_SUB_C)
+ #define BN_MP_GROW_C
+ #define BN_MP_CLAMP_C
+#endif
+
+#if defined(BNCORE_C)
+#endif
+
+#ifdef LTM3
+#define LTM_LAST
+#endif
+#include <tommath_superclass.h>
+#include <tommath_class.h>
+#else
+#define LTM_LAST
+#endif
diff --git a/tommath_superclass.h b/tommath_superclass.h
new file mode 100644
index 00000000..b50ecb09
--- /dev/null
+++ b/tommath_superclass.h
@@ -0,0 +1,72 @@
+/* super class file for PK algos */
+
+/* default ... include all MPI */
+#define LTM_ALL
+
+/* RSA only (does not support DH/DSA/ECC) */
+// #define SC_RSA_1
+
+/* For reference.... On an Athlon64 optimizing for speed...
+
+ LTM's mpi.o with all functions [striped] is 142KiB in size.
+
+*/
+
+/* Works for RSA only, mpi.o is 68KiB */
+#ifdef SC_RSA_1
+ #define BN_MP_SHRINK_C
+ #define BN_MP_LCM_C
+ #define BN_MP_PRIME_RANDOM_EX_C
+ #define BN_MP_INVMOD_C
+ #define BN_MP_GCD_C
+ #define BN_MP_MOD_C
+ #define BN_MP_MULMOD_C
+ #define BN_MP_ADDMOD_C
+ #define BN_MP_EXPTMOD_C
+ #define BN_MP_SET_INT_C
+ #define BN_MP_INIT_MULTI_C
+ #define BN_MP_CLEAR_MULTI_C
+ #define BN_MP_UNSIGNED_BIN_SIZE_C
+ #define BN_MP_TO_UNSIGNED_BIN_C
+ #define BN_MP_MOD_D_C
+ #define BN_MP_PRIME_RABIN_MILLER_TRIALS_C
+ #define BN_REVERSE_C
+ #define BN_PRIME_TAB_C
+
+ /* other modifiers */
+ #define BN_MP_DIV_SMALL /* Slower division, not critical */
+
+ /* here we are on the last pass so we turn things off. The functions classes are still there
+ * but we remove them specifically from the build. This also invokes tweaks in functions
+ * like removing support for even moduli, etc...
+ */
+#ifdef LTM_LAST
+ #undef BN_MP_TOOM_MUL_C
+ #undef BN_MP_TOOM_SQR_C
+ #undef BN_MP_KARATSUBA_MUL_C
+ #undef BN_MP_KARATSUBA_SQR_C
+ #undef BN_MP_REDUCE_C
+ #undef BN_MP_REDUCE_SETUP_C
+ #undef BN_MP_DR_IS_MODULUS_C
+ #undef BN_MP_DR_SETUP_C
+ #undef BN_MP_DR_REDUCE_C
+ #undef BN_MP_REDUCE_IS_2K_C
+ #undef BN_MP_REDUCE_2K_SETUP_C
+ #undef BN_MP_REDUCE_2K_C
+ #undef BN_S_MP_EXPTMOD_C
+ #undef BN_MP_DIV_3_C
+ #undef BN_S_MP_MUL_HIGH_DIGS_C
+ #undef BN_FAST_S_MP_MUL_HIGH_DIGS_C
+ #undef BN_FAST_MP_INVMOD_C
+
+ /* To safely undefine these you have to make sure your RSA key won't exceed the Comba threshold
+ * which is roughly 255 digits [7140 bits for 32-bit machines, 15300 bits for 64-bit machines]
+ * which means roughly speaking you can handle upto 2536-bit RSA keys with these defined without
+ * trouble.
+ */
+ #undef BN_S_MP_MUL_DIGS_C
+ #undef BN_S_MP_SQR_C
+ #undef BN_MP_MONTGOMERY_REDUCE_C
+#endif
+
+#endif
--
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