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added libtommath-0.21

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1 parent 0fe7a2d commit 49bef068787763b3fe70a9e417f64824e9554939 Tom St Denis committed with sjaeckel Jun 19, 2003
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BIN bn.pdf
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2 bn.tex
@@ -1,7 +1,7 @@
\documentclass[]{article}
\begin{document}
-\title{LibTomMath v0.20 \\ A Free Multiple Precision Integer Library \\ http://math.libtomcrypt.org }
+\title{LibTomMath v0.21 \\ A Free Multiple Precision Integer Library \\ http://math.libtomcrypt.org }
\author{Tom St Denis \\ tomstdenis@iahu.ca}
\maketitle
\newpage
@@ -124,7 +124,7 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
_W = W + n->used;
for (ix = 0; ix < n->used + 1; ix++) {
- *tmpx++ = *_W++ & ((mp_word) MP_MASK);
+ *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
}
/* zero oldused digits, if the input a was larger than
View
@@ -14,22 +14,25 @@
*/
#include <tommath.h>
-/* integer signed division. c*b + d == a [e.g. a/b, c=quotient, d=remainder]
+/* integer signed division.
+ * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
* HAC pp.598 Algorithm 14.20
*
- * Note that the description in HAC is horribly incomplete. For example,
- * it doesn't consider the case where digits are removed from 'x' in the inner
- * loop. It also doesn't consider the case that y has fewer than three digits, etc..
+ * Note that the description in HAC is horribly
+ * incomplete. For example, it doesn't consider
+ * the case where digits are removed from 'x' in
+ * the inner loop. It also doesn't consider the
+ * case that y has fewer than three digits, etc..
*
- * The overall algorithm is as described as 14.20 from HAC but fixed to treat these cases.
+ * The overall algorithm is as described as
+ * 14.20 from HAC but fixed to treat these cases.
*/
int
mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
{
mp_int q, x, y, t1, t2;
int res, n, t, i, norm, neg;
-
/* is divisor zero ? */
if (mp_iszero (b) == 1) {
return MP_VAL;
@@ -73,7 +76,7 @@ mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
x.sign = y.sign = MP_ZPOS;
- /* normalize both x and y, ensure that y >= b/2, [b == 2^DIGIT_BIT] */
+ /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
norm = mp_count_bits(&y) % DIGIT_BIT;
if (norm < (int)(DIGIT_BIT-1)) {
norm = (DIGIT_BIT-1) - norm;
@@ -91,8 +94,8 @@ mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
n = x.used - 1;
t = y.used - 1;
- /* step 2. while (x >= y*b^n-t) do { q[n-t] += 1; x -= y*b^{n-t} } */
- if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b^{n-t} */
+ /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
+ if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
goto __Y;
}
@@ -111,7 +114,8 @@ mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
if (i > x.used)
continue;
- /* step 3.1 if xi == yt then set q{i-t-1} to b-1, otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
+ /* step 3.1 if xi == yt then set q{i-t-1} to b-1,
+ * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
if (x.dp[i] == y.dp[t]) {
q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
} else {
@@ -124,7 +128,11 @@ mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
}
- /* step 3.2 while (q{i-t-1} * (yt * b + y{t-1})) > xi * b^2 + xi-1 * b + xi-2 do q{i-t-1} -= 1; */
+ /* while (q{i-t-1} * (yt * b + y{t-1})) >
+ xi * b**2 + xi-1 * b + xi-2
+
+ do q{i-t-1} -= 1;
+ */
q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;
do {
q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;
@@ -145,7 +153,7 @@ mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
t2.used = 3;
} while (mp_cmp_mag(&t1, &t2) == MP_GT);
- /* step 3.3 x = x - q{i-t-1} * y * b^{i-t-1} */
+ /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
goto __Y;
}
@@ -158,7 +166,7 @@ mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
goto __Y;
}
- /* step 3.4 if x < 0 then { x = x + y*b^{i-t-1}; q{i-t-1} -= 1; } */
+ /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
if (x.sign == MP_NEG) {
if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
goto __Y;
@@ -174,7 +182,10 @@ mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
}
}
- /* now q is the quotient and x is the remainder [which we have to normalize] */
+ /* now q is the quotient and x is the remainder
+ * [which we have to normalize]
+ */
+
/* get sign before writing to c */
x.sign = a->sign;
View
@@ -46,11 +46,11 @@ mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
} else {
t = 0;
}
- q.dp[ix] = t;
+ q.dp[ix] = (mp_digit)t;
}
if (d != NULL) {
- *d = w;
+ *d = (mp_digit)w;
}
if (c != NULL) {
View
@@ -19,7 +19,8 @@ int
mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
{
mp_int q;
- mp_word w, t;
+ mp_word w;
+ mp_digit t;
int res, ix;
if (b == 0) {
@@ -41,16 +42,16 @@ mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
if (w >= b) {
- t = w / b;
+ t = (mp_digit)(w / b);
w = w % b;
} else {
t = 0;
}
- q.dp[ix] = t;
+ q.dp[ix] = (mp_digit)t;
}
if (d != NULL) {
- *d = w;
+ *d = (mp_digit)w;
}
if (c != NULL) {
View
@@ -60,8 +60,8 @@ mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k)
/* compute (x mod B**m) + mp * [x/B**m] inline and inplace */
for (i = 0; i < m; i++) {
r = ((mp_word)*tmpx2++) * ((mp_word)k) + *tmpx1 + mu;
- *tmpx1++ = r & MP_MASK;
- mu = r >> ((mp_word)DIGIT_BIT);
+ *tmpx1++ = (mp_digit)(r & MP_MASK);
+ mu = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
}
/* set final carry */
@@ -61,10 +61,10 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
/* Multiply and add in place */
for (iy = 0; iy < n->used; iy++) {
- r = ((mp_word) mu) * ((mp_word) * tmpn++) +
- ((mp_word) u) + ((mp_word) * tmpx);
- u = (r >> ((mp_word) DIGIT_BIT));
- *tmpx++ = (r & ((mp_word) MP_MASK));
+ r = ((mp_word) mu) * ((mp_word) * tmpn++) +
+ ((mp_word) u) + ((mp_word) * tmpx);
+ u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+ *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
}
/* propagate carries */
while (u) {
View
@@ -33,6 +33,7 @@ mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
/* set the new temporary used count */
c->used = pa + 1;
+ c->sign = a->sign;
{
register mp_digit u, *tmpa, *tmpc;
View
@@ -16,11 +16,13 @@
/* find the n'th root of an integer
*
- * Result found such that (c)^b <= a and (c+1)^b > a
+ * Result found such that (c)**b <= a and (c+1)**b > a
*
- * This algorithm uses Newton's approximation x[i+1] = x[i] - f(x[i])/f'(x[i])
- * which will find the root in log(N) time where each step involves a fair bit. This
- * is not meant to find huge roots [square and cube at most].
+ * This algorithm uses Newton's approximation
+ * x[i+1] = x[i] - f(x[i])/f'(x[i])
+ * which will find the root in log(N) time where
+ * each step involves a fair bit. This is not meant to
+ * find huge roots [square and cube, etc].
*/
int
mp_n_root (mp_int * a, mp_digit b, mp_int * c)
@@ -58,33 +60,39 @@ mp_n_root (mp_int * a, mp_digit b, mp_int * c)
goto __T3;
}
- /* t2 = t1 - ((t1^b - a) / (b * t1^(b-1))) */
- if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) { /* t3 = t1^(b-1) */
+ /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
+
+ /* t3 = t1**(b-1) */
+ if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) {
goto __T3;
}
/* numerator */
- if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) { /* t2 = t1^b */
+ /* t2 = t1**b */
+ if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {
goto __T3;
}
- if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) { /* t2 = t1^b - a */
+ /* t2 = t1**b - a */
+ if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {
goto __T3;
}
- if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) { /* t3 = t1^(b-1) * b */
+ /* denominator */
+ /* t3 = t1**(b-1) * b */
+ if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {
goto __T3;
}
- if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) { /* t3 = (t1^b - a)/(b * t1^(b-1)) */
+ /* t3 = (t1**b - a)/(b * t1**(b-1)) */
+ if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {
goto __T3;
}
if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
goto __T3;
}
- }
- while (mp_cmp (&t1, &t2) != MP_EQ);
+ } while (mp_cmp (&t1, &t2) != MP_EQ);
/* result can be off by a few so check */
for (;;) {
@@ -94,7 +102,7 @@ mp_n_root (mp_int * a, mp_digit b, mp_int * c)
if (mp_cmp (&t2, a) == MP_GT) {
if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
- goto __T3;
+ goto __T3;
}
} else {
break;
View
@@ -32,8 +32,8 @@ mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
/* q1 = x / b**(k-1) */
mp_rshd (&q, um - 1);
- /* according to HAC this is optimization is ok */
- if (((unsigned long) m->used) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
+ /* according to HAC this optimization is ok */
+ if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
goto CLEANUP;
}
@@ -73,7 +73,7 @@ mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
/* Back off if it's too big */
while (mp_cmp (x, m) != MP_LT) {
if ((res = s_mp_sub (x, m, x)) != MP_OKAY) {
- break;
+ goto CLEANUP;
}
}
View
@@ -56,7 +56,9 @@ mp_read_radix (mp_int * a, char *str, int radix)
}
++str;
}
- a->sign = neg;
+ if (mp_iszero(a) != 1) {
+ a->sign = neg;
+ }
return MP_OKAY;
}
View
@@ -39,7 +39,7 @@ s_mp_sqr (mp_int * a, mp_int * b)
t.dp[2*ix] = (mp_digit) (r & ((mp_word) MP_MASK));
/* get the carry */
- u = (r >> ((mp_word) DIGIT_BIT));
+ u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
/* left hand side of A[ix] * A[iy] */
tmpx = a->dp[ix];
@@ -60,13 +60,13 @@ s_mp_sqr (mp_int * a, mp_int * b)
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
/* get carry */
- u = (r >> ((mp_word) DIGIT_BIT));
+ u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
}
/* propagate upwards */
while (u != ((mp_digit) 0)) {
r = ((mp_word) * tmpt) + ((mp_word) u);
*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
- u = (r >> ((mp_word) DIGIT_BIT));
+ u = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
}
}
View
@@ -1,3 +1,7 @@
+June 19th, 2003
+v0.21 -- Fixed bug in mp_mul_d which would not handle sign correctly [would not always forward it]
+ -- Removed the #line lines from gen.pl [was in violation of ISO C]
+
June 8th, 2003
v0.20 -- Removed the book from the package. Added the TDCAL license document.
-- This release is officially pure-bred TDCAL again [last officially TDCAL based release was v0.16]
View
@@ -162,6 +162,8 @@ int main(void)
fprintf(log, "%d %9llu\n", cnt*DIGIT_BIT, (((unsigned long long)rr)*CLOCKS_PER_SEC)/tt);
}
fclose(log);
+
+ return 0;
log = fopen("logs/sub.log", "w");
for (cnt = 8; cnt <= 128; cnt += 8) {
View
@@ -1 +1,2 @@
-259-bits (k = 17745) = 926336713898529563388567880069503262826159877325124512315660672063305037101743
+256-bits (k = 36113) = 115792089237316195423570985008687907853269984665640564039457584007913129603823
+512-bits (k = 38117) = 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006045979
View
@@ -2,7 +2,7 @@
#
#Tom St Denis
-CFLAGS = /I../ /Ogityb2 /Gs /DWIN32 /W3
+CFLAGS = /I../ /Ox /DWIN32 /W3
pprime: pprime.obj
cl pprime.obj ../tommath.lib
View
1 gen.pl
@@ -9,7 +9,6 @@
foreach my $filename (glob "bn*.c") {
open( SRC, "<$filename" ) or die "Couldn't open $filename for reading: $!";
print OUT "/* Start: $filename */\n";
- print OUT qq[#line 0 "$filename"\n];
print OUT while <SRC>;
print OUT "\n/* End: $filename */\n\n";
close SRC or die "Error closing $filename after reading: $!";
View
@@ -1,16 +0,0 @@
-224 11069160
-448 9156136
-672 8089755
-896 7399424
-1120 6389352
-1344 5818648
-1568 5257112
-1792 4982160
-2016 4527856
-2240 4325312
-2464 4051760
-2688 3767640
-2912 3612520
-3136 3415208
-3360 3258656
-3584 3113360
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