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added tomsfastmath-0.06

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Tom St Denis 2005-10-31 15:32:05 +00:00 committed by Steffen Jaeckel
parent a6c4c5a261
commit 091b337fe8
20 changed files with 161 additions and 73 deletions
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6
changes.txt
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@ -1,3 +1,9 @@
October 31st, 2005
0.06 -- fixed fp_mul() and fp_sqr() to trim digits when overflows would occur. Produces numerically inprecise results
(e.g. the lower FP_SIZE digits) but shouldn't segfault at least ;-)
-- Updated the combas so you can turn on and off specific unrolled loops at build time
-- Michael Heyman reported a bug in s_fp_sub() that was pretty substantial and a bug in fp_montgomery_calc_normalization(). Fixed.
August 1st, 2005
0.05 -- Quick fix to the fp_invmod.c code to let it handle even moduli [required for LTC]
-- Added makefile.shared to make shared objects [required for LTC]

6
demo/test.c
View File

@ -283,7 +283,8 @@ sqrtime:
//#else
monttime:
printf("Montgomery:\n");
for (t = 2; t <= (FP_SIZE/2)-2; t += 2) {
for (t = 2; t <= (FP_SIZE/2)-4; t += 2) {
// printf("%5lu-bit: %9llu\n", t * DIGIT_BIT, t2);
fp_zero(&a);
for (ix = 0; ix < t; ix++) {
a.dp[ix] = ix | 1;
@ -343,6 +344,9 @@ expttime:
return;
testing:
fp_zero(&b); fp_zero(&c); fp_zero(&d); fp_zero(&e); fp_zero(&f); fp_zero(&a);
div2_n = mul2_n = inv_n = expt_n = lcm_n = gcd_n = add_n =
sub_n = mul_n = div_n = sqr_n = mul2d_n = div2d_n = cnt = add_d_n = sub_d_n= mul_d_n = 0;

BIN
doc/tfm.pdf
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Binary file not shown.

1
fp_montgomery_calc_normalization.c
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@ -18,6 +18,7 @@ void fp_montgomery_calc_normalization(fp_int *a, fp_int *b)
/* how many bits of last digit does b use */
bits = fp_count_bits (b) % DIGIT_BIT;
if (!bits) bits = DIGIT_BIT;
/* compute A = B^(n-1) * 2^(bits-1) */
if (b->used > 1) {

11
fp_montgomery_reduce.c
View File

@ -64,6 +64,8 @@ asm( \
:"0"(_c[LO]), "1"(cy), "r"(mu), "r"(*tmpm++) \
: "%rax", "%rdx", "%cc")
#ifdef TFM_HUGE
#define INNERMUL8 \
asm( \
"movq 0(%5),%%rax \n\t" \
@ -157,6 +159,8 @@ asm( \
: "0"(_c), "1"(cy), "g"(mu), "r"(tmpm)\
: "%rax", "%rdx", "%r10", "%r11", "%cc")
#endif
#define PROPCARRY \
asm( \
@ -306,6 +310,11 @@ void fp_montgomery_reduce(fp_int *a, fp_int *m, fp_digit mp)
fp_digit c[FP_SIZE], *_c, *tmpm, mu;
int oldused, x, y, pa;
/* bail if too large */
if (m->used > (FP_SIZE/2)) {
return;
}
#if defined(USE_MEMSET)
/* now zero the buff */
memset(c, 0, sizeof c);
@ -331,7 +340,7 @@ void fp_montgomery_reduce(fp_int *a, fp_int *m, fp_digit mp)
_c = c + x;
tmpm = m->dp;
y = 0;
#if defined(TFM_X86_64)
#if defined(TFM_X86_64) && defined(TFM_HUGE)
for (; y < (pa & ~7); y += 8) {
INNERMUL8;
_c += 8;

12
fp_mul.c
View File

@ -15,6 +15,12 @@ void fp_mul(fp_int *A, fp_int *B, fp_int *C)
int r, y, yy, s;
fp_int ac, bd, comp, amb, cmd, t1, t2;
/* call generic if we're out of range */
if (A->used + B->used > FP_SIZE) {
fp_mul_comba(A, B, C);
return ;
}
y = MAX(A->used, B->used);
yy = MIN(A->used, B->used);
if (yy <= 8 || y <= 64) {
@ -31,11 +37,15 @@ void fp_mul(fp_int *A, fp_int *B, fp_int *C)
#elif defined(TFM_HUGE)
if (0) { 1;
#endif
#if defined(TFM_HUGE)
#if defined(TFM_MUL32)
} else if (y <= 32) {
fp_mul_comba32(A,B,C);
#endif
#if defined(TFM_MUL48)
} else if (y <= 48) {
fp_mul_comba48(A,B,C);
#endif
#if defined(TFM_MUL64)
} else if (y <= 64) {
fp_mul_comba64(A,B,C);
#endif

11
fp_mul_comba.c
View File

@ -266,8 +266,8 @@ void fp_mul_comba(fp_int *A, fp_int *B, fp_int *C)
COMBA_FINI;
dst->used = pa;
dst->sign = A->sign ^ B->sign;
fp_clamp(dst);
dst->sign = dst->used ? A->sign ^ B->sign : FP_ZPOS;
fp_copy(dst, C);
}
@ -1497,8 +1497,7 @@ void fp_mul_comba_small(fp_int *A, fp_int *B, fp_int *C)
#endif
#ifdef TFM_HUGE
#ifdef TFM_MUL32
void fp_mul_comba32(fp_int *A, fp_int *B, fp_int *C)
{
fp_digit c0, c1, c2, at[64];
@ -1765,7 +1764,9 @@ void fp_mul_comba32(fp_int *A, fp_int *B, fp_int *C)
fp_clamp(C);
COMBA_FINI;
}
#endif
#ifdef TFM_MUL64
void fp_mul_comba64(fp_int *A, fp_int *B, fp_int *C)
{
fp_digit c0, c1, c2, at[128];
@ -2288,7 +2289,9 @@ void fp_mul_comba64(fp_int *A, fp_int *B, fp_int *C)
fp_clamp(C);
COMBA_FINI;
}
#endif
#ifdef TFM_MUL48
void fp_mul_comba48(fp_int *A, fp_int *B, fp_int *C)
{
fp_digit c0, c1, c2, at[96];
@ -2683,8 +2686,6 @@ void fp_mul_comba48(fp_int *A, fp_int *B, fp_int *C)
fp_clamp(C);
COMBA_FINI;
}
#endif

2
fp_set.c
View File

@ -13,7 +13,7 @@ void fp_set(fp_int *a, fp_digit b)
{
fp_zero(a);
a->dp[0] = b;
a->used = b ? 1 : 0;
a->used = a->dp[0] ? 1 : 0;
}
/* $Source$ */

12
fp_sqr.c
View File

@ -15,6 +15,12 @@ void fp_sqr(fp_int *A, fp_int *B)
int r, y, s;
fp_int aa, bb, comp, amb, t1;
/* call generic if we're out of range */
if (A->used + A->used > FP_SIZE) {
fp_sqr_comba(A, B);
return ;
}
y = A->used;
if (y <= 64) {
@ -24,11 +30,15 @@ void fp_sqr(fp_int *A, fp_int *B)
#elif defined(TFM_HUGE)
if (0) { 1;
#endif
#if defined(TFM_HUGE)
#if defined(TFM_SQR32)
} else if (y <= 32) {
fp_sqr_comba32(A,B);
#endif
#if defined(TFM_SQR48)
} else if (y <= 48) {
fp_sqr_comba48(A,B);
#endif
#if defined(TFM_SQR64)
} else if (y <= 64) {
fp_sqr_comba64(A,B);
#endif

12
fp_sqr_comba.c
View File

@ -1945,7 +1945,7 @@ void fp_sqr_comba_small(fp_int *A, fp_int *B)
#endif /* TFM_SMALL_SET */
#ifdef TFM_HUGE
#ifdef TFM_SQR32
void fp_sqr_comba32(fp_int *A, fp_int *B)
{
fp_digit *a, b[64], c0, c1, c2, sc0, sc1, sc2;
@ -2272,16 +2272,14 @@ void fp_sqr_comba32(fp_int *A, fp_int *B)
COMBA_STORE2(b[63]);
COMBA_FINI;
memcpy(B->dp, b, 64 * sizeof(fp_digit));
B->used = 64;
B->sign = FP_ZPOS;
memcpy(B->dp, b, 64 * sizeof(fp_digit));
fp_clamp(B);
}
#endif
#ifdef TFM_HUGE
#ifdef TFM_SQR64
void fp_sqr_comba64(fp_int *A, fp_int *B)
{
fp_digit *a, b[128], c0, c1, c2, sc0, sc1, sc2;
@ -2933,7 +2931,9 @@ void fp_sqr_comba64(fp_int *A, fp_int *B)
memcpy(B->dp, b, 128 * sizeof(fp_digit));
fp_clamp(B);
}
#endif
#ifdef TFM_SQR48
void fp_sqr_comba48(fp_int *A, fp_int *B)
{
fp_digit *a, b[96], c0, c1, c2, sc0, sc1, sc2;
@ -3420,9 +3420,9 @@ void fp_sqr_comba48(fp_int *A, fp_int *B)
COMBA_STORE2(b[95]);
COMBA_FINI;
memcpy(B->dp, b, 96 * sizeof(fp_digit));
B->used = 96;
B->sign = FP_ZPOS;
memcpy(B->dp, b, 96 * sizeof(fp_digit));
fp_clamp(B);
}

8
makefile
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@ -1,7 +1,7 @@
#makefile for TomsFastMath
#
#
VERSION=0.05
VERSION=0.06
CFLAGS += -Wall -W -Wshadow -I./
@ -85,7 +85,7 @@ install: $(LIBNAME)
install -g $(GROUP) -o $(USER) $(HEADERS) $(DESTDIR)$(INCPATH)
mtest/mtest: mtest/mtest.c
cd mtest ; make mtest
cd mtest ; CFLAGS="$(CFLAGS) -I../" make mtest
test: $(LIBNAME) demo/test.o mtest/mtest
$(CC) $(CFLAGS) demo/test.o $(LIBNAME) $(PROF) -o test
@ -143,5 +143,5 @@ zipup: no_oops docs clean
zip -9r tfm-$(VERSION).zip tomsfastmath-$(VERSION)/*
# $Source: /cvs/libtom/tomsfastmath/makefile,v $
# $Revision: 1.17 $
# $Date: 2005/07/30 04:23:55 $
# $Revision: 1.19 $
# $Date: 2005/08/25 23:53:40 $

12
makefile.shared
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@ -1,6 +1,7 @@
#makefile for TomsFastMath
#
#
VERSION=0:6
CC=libtool --mode=compile gcc
@ -19,7 +20,6 @@ CFLAGS += -fomit-frame-pointer
endif
VERSION=0:5
OBJECTS = \
fp_set.o \
@ -81,12 +81,12 @@ endif
default: $(LIBNAME)
objs: $(OBJECTS)
$(LIBNAME): $(OBJECTS)
libtool --silent --mode=link gcc $(CFLAGS) `find . -type f | grep "[.]lo" | xargs` -o $(LIBNAME) -rpath $(LIBPATH) -version-info $(VERSION)
install: $(LIBNAME)
libtool --silent --mode=link gcc $(CFLAGS) `find . -type f | grep "[.]lo" | xargs` -o $(LIBNAME) -rpath $(LIBPATH) -version-info $(VERSION)
libtool --silent --mode=link gcc $(CFLAGS) `find . -type f | grep "[.]o" | xargs` -o $(LIBNAME_S)
ranlib $(LIBNAME_S)
libtool --silent --mode=install install -c $(LIBNAME) $(LIBPATH)/$(LIBNAME)
install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(INCPATH)
install -g $(GROUP) -o $(USER) $(HEADERS) $(DESTDIR)$(INCPATH)
@ -104,6 +104,6 @@ stest: $(LIBNAME) demo/stest.o
$(CC) $(CFLAGS) demo/stest.o $(LIBNAME_S) -o stest
# $Source: /cvs/libtom/tomsfastmath/makefile.shared,v $
# $Revision: 1.4 $
# $Date: 2005/07/28 03:08:35 $
# $Revision: 1.7 $
# $Date: 2005/10/06 23:31:17 $

7
mtest/mtest.c
View File

@ -38,6 +38,8 @@ mulmod
#include <stdlib.h>
#include <time.h>
#include <tommath.h>
#define CRYPT
#include "../tfm.h"
FILE *rng;
@ -47,7 +49,7 @@ void rand_num(mp_int *a)
int n, size;
unsigned char buf[2048];
size = 1 + ((fgetc(rng)<<8) + fgetc(rng)) % 256;
size = 1 + ((fgetc(rng)<<8) + fgetc(rng)) % (FP_MAX_SIZE/16 - DIGIT_BIT/2);
buf[0] = (fgetc(rng)&1)?1:0;
fread(buf+1, 1, size, rng);
while (buf[1] == 0) buf[1] = fgetc(rng);
@ -60,7 +62,7 @@ void rand_num2(mp_int *a)
int n, size;
unsigned char buf[2048];
size = 1 + ((fgetc(rng)<<8) + fgetc(rng)) % 256;
size = 1 + ((fgetc(rng)<<8) + fgetc(rng)) % (FP_MAX_SIZE/16 - DIGIT_BIT/2);
buf[0] = (fgetc(rng)&1)?1:0;
fread(buf+1, 1, size, rng);
while (buf[1] == 0) buf[1] = fgetc(rng);
@ -118,7 +120,6 @@ int main(void)
}
#endif
n = fgetc(rng) % 16;
if (n == 0) {
/* add tests */
rand_num(&a);

78
pre_gen/mpi.c
View File

@ -1663,6 +1663,7 @@ void fp_montgomery_calc_normalization(fp_int *a, fp_int *b)
/* how many bits of last digit does b use */
bits = fp_count_bits (b) % DIGIT_BIT;
if (!bits) bits = DIGIT_BIT;
/* compute A = B^(n-1) * 2^(bits-1) */
if (b->used > 1) {
@ -1755,6 +1756,8 @@ asm( \
:"0"(_c[LO]), "1"(cy), "r"(mu), "r"(*tmpm++) \
: "%rax", "%rdx", "%cc")
#ifdef TFM_HUGE
#define INNERMUL8 \
asm( \
"movq 0(%5),%%rax \n\t" \
@ -1848,6 +1851,8 @@ asm( \
: "0"(_c), "1"(cy), "g"(mu), "r"(tmpm)\
: "%rax", "%rdx", "%r10", "%r11", "%cc")
#endif
#define PROPCARRY \
asm( \
@ -1997,6 +2002,11 @@ void fp_montgomery_reduce(fp_int *a, fp_int *m, fp_digit mp)
fp_digit c[FP_SIZE], *_c, *tmpm, mu;
int oldused, x, y, pa;
/* bail if too large */
if (m->used > (FP_SIZE/2)) {
return;
}
#if defined(USE_MEMSET)
/* now zero the buff */
memset(c, 0, sizeof c);
@ -2022,7 +2032,7 @@ void fp_montgomery_reduce(fp_int *a, fp_int *m, fp_digit mp)
_c = c + x;
tmpm = m->dp;
y = 0;
#if defined(TFM_X86_64)
#if defined(TFM_X86_64) && defined(TFM_HUGE)
for (; y < (pa & ~7); y += 8) {
INNERMUL8;
_c += 8;
@ -2140,6 +2150,12 @@ void fp_mul(fp_int *A, fp_int *B, fp_int *C)
int r, y, yy, s;
fp_int ac, bd, comp, amb, cmd, t1, t2;
/* call generic if we're out of range */
if (A->used + B->used > FP_SIZE) {
fp_mul_comba(A, B, C);
return ;
}
y = MAX(A->used, B->used);
yy = MIN(A->used, B->used);
if (yy <= 8 || y <= 64) {
@ -2156,11 +2172,15 @@ void fp_mul(fp_int *A, fp_int *B, fp_int *C)
#elif defined(TFM_HUGE)
if (0) { 1;
#endif
#if defined(TFM_HUGE)
#if defined(TFM_MUL32)
} else if (y <= 32) {
fp_mul_comba32(A,B,C);
#endif
#if defined(TFM_MUL48)
} else if (y <= 48) {
fp_mul_comba48(A,B,C);
#endif
#if defined(TFM_MUL64)
} else if (y <= 64) {
fp_mul_comba64(A,B,C);
#endif
@ -2663,8 +2683,8 @@ void fp_mul_comba(fp_int *A, fp_int *B, fp_int *C)
COMBA_FINI;
dst->used = pa;
dst->sign = A->sign ^ B->sign;
fp_clamp(dst);
dst->sign = dst->used ? A->sign ^ B->sign : FP_ZPOS;
fp_copy(dst, C);
}
@ -3894,8 +3914,7 @@ void fp_mul_comba_small(fp_int *A, fp_int *B, fp_int *C)
#endif
#ifdef TFM_HUGE
#ifdef TFM_MUL32
void fp_mul_comba32(fp_int *A, fp_int *B, fp_int *C)
{
fp_digit c0, c1, c2, at[64];
@ -4162,7 +4181,9 @@ void fp_mul_comba32(fp_int *A, fp_int *B, fp_int *C)
fp_clamp(C);
COMBA_FINI;
}
#endif
#ifdef TFM_MUL64
void fp_mul_comba64(fp_int *A, fp_int *B, fp_int *C)
{
fp_digit c0, c1, c2, at[128];
@ -4685,7 +4706,9 @@ void fp_mul_comba64(fp_int *A, fp_int *B, fp_int *C)
fp_clamp(C);
COMBA_FINI;
}
#endif
#ifdef TFM_MUL48
void fp_mul_comba48(fp_int *A, fp_int *B, fp_int *C)
{
fp_digit c0, c1, c2, at[96];
@ -5080,8 +5103,6 @@ void fp_mul_comba48(fp_int *A, fp_int *B, fp_int *C)
fp_clamp(C);
COMBA_FINI;
}
#endif
@ -5657,7 +5678,7 @@ void fp_set(fp_int *a, fp_digit b)
{
fp_zero(a);
a->dp[0] = b;
a->used = b ? 1 : 0;
a->used = a->dp[0] ? 1 : 0;
}
/* $Source$ */
@ -5707,6 +5728,12 @@ void fp_sqr(fp_int *A, fp_int *B)
int r, y, s;
fp_int aa, bb, comp, amb, t1;
/* call generic if we're out of range */
if (A->used + A->used > FP_SIZE) {
fp_sqr_comba(A, B);
return ;
}
y = A->used;
if (y <= 64) {
@ -5716,11 +5743,15 @@ void fp_sqr(fp_int *A, fp_int *B)
#elif defined(TFM_HUGE)
if (0) { 1;
#endif
#if defined(TFM_HUGE)
#if defined(TFM_SQR32)
} else if (y <= 32) {
fp_sqr_comba32(A,B);
#endif
#if defined(TFM_SQR48)
} else if (y <= 48) {
fp_sqr_comba48(A,B);
#endif
#if defined(TFM_SQR64)
} else if (y <= 64) {
fp_sqr_comba64(A,B);
#endif
@ -7761,7 +7792,7 @@ void fp_sqr_comba_small(fp_int *A, fp_int *B)
#endif /* TFM_SMALL_SET */
#ifdef TFM_HUGE
#ifdef TFM_SQR32
void fp_sqr_comba32(fp_int *A, fp_int *B)
{
fp_digit *a, b[64], c0, c1, c2, sc0, sc1, sc2;
@ -8088,16 +8119,14 @@ void fp_sqr_comba32(fp_int *A, fp_int *B)
COMBA_STORE2(b[63]);
COMBA_FINI;
memcpy(B->dp, b, 64 * sizeof(fp_digit));
B->used = 64;
B->sign = FP_ZPOS;
memcpy(B->dp, b, 64 * sizeof(fp_digit));
fp_clamp(B);
}
#endif
#ifdef TFM_HUGE
#ifdef TFM_SQR64
void fp_sqr_comba64(fp_int *A, fp_int *B)
{
fp_digit *a, b[128], c0, c1, c2, sc0, sc1, sc2;
@ -8749,7 +8778,9 @@ void fp_sqr_comba64(fp_int *A, fp_int *B)
memcpy(B->dp, b, 128 * sizeof(fp_digit));
fp_clamp(B);
}
#endif
#ifdef TFM_SQR48
void fp_sqr_comba48(fp_int *A, fp_int *B)
{
fp_digit *a, b[96], c0, c1, c2, sc0, sc1, sc2;
@ -9236,9 +9267,9 @@ void fp_sqr_comba48(fp_int *A, fp_int *B)
COMBA_STORE2(b[95]);
COMBA_FINI;
memcpy(B->dp, b, 96 * sizeof(fp_digit));
B->used = 96;
B->sign = FP_ZPOS;
memcpy(B->dp, b, 96 * sizeof(fp_digit));
fp_clamp(B);
}
@ -9652,11 +9683,11 @@ void s_fp_add(fp_int *a, fp_int *b, fp_int *c)
c->dp[x] = (fp_digit)t;
t >>= DIGIT_BIT;
}
if (t != 0 && x != FP_SIZE) {
if (t != 0 && x < FP_SIZE) {
c->dp[c->used++] = (fp_digit)t;
++x;
}
c->used = x;
for (; x < oldused; x++) {
c->dp[x] = 0;
}
@ -9684,18 +9715,23 @@ void s_fp_add(fp_int *a, fp_int *b, fp_int *c)
/* unsigned subtraction ||a|| >= ||b|| ALWAYS! */
void s_fp_sub(fp_int *a, fp_int *b, fp_int *c)
{
int x, oldused;
int x, oldbused, oldused;
fp_word t;
oldused = c->used;
oldbused = b->used;
c->used = a->used;
t = 0;
for (x = 0; x < a->used; x++) {
for (x = 0; x < oldbused; x++) {
t = ((fp_word)a->dp[x]) - (((fp_word)b->dp[x]) + t);
c->dp[x] = (fp_digit)t;
t = (t >> DIGIT_BIT) & 1;
t = (t >> DIGIT_BIT)&1;
}
for (; x < a->used; x++) {
t = ((fp_word)a->dp[x]) - t;
c->dp[x] = (fp_digit)t;
t = (t >> DIGIT_BIT);
}
for (; x < oldused; x++) {
c->dp[x] = 0;
}

4
s_fp_add.c
View File

@ -25,11 +25,11 @@ void s_fp_add(fp_int *a, fp_int *b, fp_int *c)
c->dp[x] = (fp_digit)t;
t >>= DIGIT_BIT;
}
if (t != 0 && x != FP_SIZE) {
if (t != 0 && x < FP_SIZE) {
c->dp[c->used++] = (fp_digit)t;
++x;
}
c->used = x;
for (; x < oldused; x++) {
c->dp[x] = 0;
}

13
s_fp_sub.c
View File

@ -12,18 +12,23 @@
/* unsigned subtraction ||a|| >= ||b|| ALWAYS! */
void s_fp_sub(fp_int *a, fp_int *b, fp_int *c)
{
int x, oldused;
int x, oldbused, oldused;
fp_word t;
oldused = c->used;
oldbused = b->used;
c->used = a->used;
t = 0;
for (x = 0; x < a->used; x++) {
for (x = 0; x < oldbused; x++) {
t = ((fp_word)a->dp[x]) - (((fp_word)b->dp[x]) + t);
c->dp[x] = (fp_digit)t;
t = (t >> DIGIT_BIT) & 1;
t = (t >> DIGIT_BIT)&1;
}
for (; x < a->used; x++) {
t = ((fp_word)a->dp[x]) - t;
c->dp[x] = (fp_digit)t;
t = (t >> DIGIT_BIT);
}
for (; x < oldused; x++) {
c->dp[x] = 0;
}

BIN
tfm.dvi
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Binary file not shown.

9
tfm.h
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@ -37,7 +37,12 @@
Enable these if you are doing 32, 48 or 64 digit multiplications (useful for RSA)
Less important on 64-bit machines as 32 digits == 2048 bits
*/
#define TFM_HUGE
#define TFM_MUL32
#define TFM_MUL48
#define TFM_MUL64
#define TFM_SQR32
#define TFM_SQR48
#define TFM_SQR64
/* do we want some overflow checks
Not required if you make sure your numbers are within range (e.g. by default a modulus for fp_exptmod() can only be upto 2048 bits long)
@ -61,7 +66,7 @@
* You can externally define this or it defaults to 4096-bits [allowing multiplications upto 2048x2048 bits ]
*/
#ifndef FP_MAX_SIZE
#define FP_MAX_SIZE (4096+(4*DIGIT_BIT))
#define FP_MAX_SIZE (4096+(8*DIGIT_BIT))
#endif
/* will this lib work? */

4
tfm.log
View File

@ -1,4 +1,4 @@
This is pdfeTeX, Version 3.141592-1.21a-2.2 (Web2C 7.5.4) (format=latex 2005.4.10) 1 AUG 2005 13:34
This is pdfeTeX, Version 3.141592-1.21a-2.2 (Web2C 7.5.4) (format=latex 2005.9.20) 31 OCT 2005 11:30
entering extended mode
**tfm
(./tfm.tex
@ -329,4 +329,4 @@ Here is how much of TeX's memory you used:
580 hyphenation exceptions out of 1000
25i,9n,25p,195b,321s stack positions out of 1500i,500n,1500p,200000b,5000s
Output written on tfm.dvi (25 pages, 51612 bytes).
Output written on tfm.dvi (25 pages, 51616 bytes).

2
tfm.tex
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@ -49,7 +49,7 @@
\begin{document}
\frontmatter
\pagestyle{empty}
\title{TomsFastMath User Manual \\ v0.05}
\title{TomsFastMath User Manual \\ v0.06}
\author{Tom St Denis \\ tomstdenis@gmail.com}
\maketitle
This text and library are all hereby placed in the public domain. This book has been formatted for B5