added tomsfastmath-0.05
This commit is contained in:
Tom St Denis
Steffen Jaeckel
parent
f91cf2d1cf
commit
a6c4c5a261
@ -1,3 +1,10 @@
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August 1st, 2005
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0.05 -- Quick fix to the fp_invmod.c code to let it handle even moduli [required for LTC]
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-- Added makefile.shared to make shared objects [required for LTC]
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-- Improved makefiles to make them way more configurable
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-- Added timing resistant fp_exptmod() enabled with TFM_TIMING_RESISTANT
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July 23rd, 2005
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0.04 -- Fixed bugs in the SSE2 squaring code
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-- Rewrote the multipliers to be optimized for small inputs
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-- Nelson Bolyard of the NSS crew submitted [among other things] new faster Montgomery reduction
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139
comba_mont_gen.c
139
comba_mont_gen.c
@ -1,59 +1,112 @@
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/* generate montgomery reductions for m->used = 1...16 */
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#include <stdio.h>
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int main(void)
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{
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int N;
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for (N = 1; N <= 16; N++) {
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printf("void fp_montgomery_reduce_%d(fp_int *a, fp_int *m, fp_digit mp)\n", N);
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int x, y, z;
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printf(
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#if 0
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"#ifdef TFM_SMALL_SET\n"
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"/* computes x/R == x (mod N) via Montgomery Reduction */\n"
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"void fp_montgomery_reduce_small(fp_int *a, fp_int *m, fp_digit mp)\n"
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"{\n"
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" fp_digit c[3*FP_SIZE], *_c, *tmpm, mu;\n"
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" int oldused, x, y;\n"
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" fp_digit c[FP_SIZE], *_c, *tmpm, mu, cy;\n"
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" int oldused, x, y, pa;\n"
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"\n"
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"#if defined(USE_MEMSET)\n"
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" /* now zero the buff */\n"
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" memset(c, 0, sizeof(c));\n"
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" memset(c, 0, sizeof c);\n"
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"#endif\n"
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" pa = m->used;\n"
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"\n"
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" /* copy the input */\n"
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" oldused = a->used;\n"
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" for (x = 0; x < oldused; x++) {\n"
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" c[x] = a->dp[x];\n"
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" }\n"
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"\n"
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"#if !defined(USE_MEMSET)\n"
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" for (; x < 2*pa+3; x++) {\n"
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" c[x] = 0;\n"
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" }\n"
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"#endif\n"
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" MONT_START;\n"
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#endif
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"\n"
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" /* now let's get bizz-sy! */\n"
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" for (x = 0; x < %d; x++) {\n"
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" /* get Mu for this round */\n"
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" LOOP_START;\n"
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"\n"
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" /* our friendly neighbourhood alias */\n"
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" _c = c + x;\n"
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" tmpm = m->dp;\n"
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"\n"
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" for (y = 0; y < %d; y++) {\n"
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" INNERMUL;\n"
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" ++_c;\n"
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" }\n"
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" /* send carry up man... */\n"
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" _c = c + x;\n"
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" PROPCARRY;\n"
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" } \n"
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"\n"
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" /* fix the rest of the carries */\n"
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" _c = c + %d;\n"
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" for (x = %d; x < %d * 2 + 2; x++) {\n"
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" PROPCARRY;\n"
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" ++_c;\n"
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" switch (pa) {\n");
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for (x = 1; x <= 64; x++) {
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if (x > 16 && (x != 32 && x != 48 && x != 64)) continue;
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if (x > 16) printf("#ifdef TFM_HUGE\n");
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printf(" case %d:\n", x);
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for (y = 0; y < x; y++) {
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printf(" x = %d; cy = 0;\n"
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" LOOP_START;\n"
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" _c = c + %d;\n"
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" tmpm = m->dp;\n", y, y);
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printf("#ifdef INNERMUL8\n");
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for (z = 0; z+8 <= x; z += 8) {
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printf(" INNERMUL8; _c += 8; tmpm += 8;\n");
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}
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for (; z < x; z++) {
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printf(" INNERMUL; ++_c;\n");
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}
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printf("#else\n");
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for (z = 0; z < x; z++) {
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printf(" INNERMUL; ++_c;\n");
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}
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printf("#endif\n");
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printf(" LOOP_END;\n"
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" while (cy) {\n"
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" PROPCARRY;\n"
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" ++_c;\n"
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" }\n");
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}
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//printf(" }\n");
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printf(" break;\n");
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#define LOOP_MACRO(stride) \
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for (x = 0; x < stride; x++) { \
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fp_digit cy = 0; \
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/* get Mu for this round */ \
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LOOP_START; \
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_c = c + x; \
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tmpm = m->dp; \
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for (y = 0; y < stride; y++) { \
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INNERMUL; \
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++_c; \
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} \
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LOOP_END; \
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while (cy) { \
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PROPCARRY; \
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++_c; \
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} \
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}
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if (x > 16) printf("#endif /* TFM_HUGE */\n");
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}
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#if 0
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printf(
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" }\n"
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"\n"
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" /* now copy out */\n"
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" _c = c + %d;\n"
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" _c = c + pa;\n"
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" tmpm = a->dp;\n"
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" for (x = 0; x < %d+1; x++) {\n"
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" for (x = 0; x < pa+1; x++) {\n"
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" *tmpm++ = *_c++;\n"
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" }\n"
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"\n"
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@ -63,19 +116,17 @@ printf(
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"\n"
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" MONT_FINI;\n"
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"\n"
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" a->used = %d+1;\n"
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" a->used = pa+1;\n"
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" fp_clamp(a);\n"
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"\n"
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" /* if A >= m then A = A - m */\n"
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" if (fp_cmp_mag (a, m) != FP_LT) {\n"
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" s_fp_sub (a, m, a);\n"
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" }\n"
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"}\n", N,N,N,N,N,N,N,N);
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}
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"}\n\n#endif\n");
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#endif
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return 0;
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}
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@ -213,7 +213,7 @@ t1 = TIMFUNC();
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sleep(1);
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printf("Ticks per second: %llu\n", TIMFUNC() - t1);
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goto expttime;
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goto multtime;
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/* do some timings... */
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printf("Addition:\n");
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for (t = 2; t <= FP_SIZE/2; t += 2) {
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BIN
doc/tfm.pdf
BIN
doc/tfm.pdf
Binary file not shown.
71
fp_exptmod.c
71
fp_exptmod.c
@ -9,6 +9,75 @@
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*/
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#include <tfm.h>
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#ifdef TFM_TIMING_RESISTANT
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/* timing resistant montgomery ladder based exptmod
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Based on work by Marc Joye, Sung-Ming Yen, "The Montgomery Powering Ladder", Cryptographic Hardware and Embedded Systems, CHES 2002
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*/
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static int _fp_exptmod(fp_int * G, fp_int * X, fp_int * P, fp_int * Y)
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{
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fp_int R[2];
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fp_digit buf, mp;
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int err, bitcnt, digidx, y;
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/* now setup montgomery */
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if ((err = fp_montgomery_setup (P, &mp)) != FP_OKAY) {
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return err;
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}
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fp_init(&R[0]);
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fp_init(&R[1]);
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/* now we need R mod m */
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fp_montgomery_calc_normalization (&R[0], P);
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/* now set R[0][1] to G * R mod m */
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if (fp_cmp_mag(P, G) != FP_GT) {
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/* G > P so we reduce it first */
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fp_mod(G, P, &R[1]);
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} else {
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fp_copy(G, &R[1]);
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}
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fp_mulmod (&R[1], &R[0], P, &R[1]);
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/* for j = t-1 downto 0 do
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r_!k = R0*R1; r_k = r_k^2
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*/
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/* set initial mode and bit cnt */
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bitcnt = 1;
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buf = 0;
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digidx = X->used - 1;
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for (;;) {
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/* grab next digit as required */
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if (--bitcnt == 0) {
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/* if digidx == -1 we are out of digits so break */
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if (digidx == -1) {
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break;
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}
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/* read next digit and reset bitcnt */
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buf = X->dp[digidx--];
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bitcnt = (int)DIGIT_BIT;
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}
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/* grab the next msb from the exponent */
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y = (fp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
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buf <<= (fp_digit)1;
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/* do ops */
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fp_mul(&R[0], &R[1], &R[y^1]); fp_montgomery_reduce(&R[y^1], P, mp);
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fp_sqr(&R[y], &R[y]); fp_montgomery_reduce(&R[y], P, mp);
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}
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fp_montgomery_reduce(&R[0], P, mp);
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fp_copy(&R[0], Y);
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return FP_OKAY;
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}
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#else
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/* y = g**x (mod b)
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* Some restrictions... x must be positive and < b
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*/
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@ -168,6 +237,8 @@ static int _fp_exptmod(fp_int * G, fp_int * X, fp_int * P, fp_int * Y)
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return FP_OKAY;
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}
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#endif
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int fp_exptmod(fp_int * G, fp_int * X, fp_int * P, fp_int * Y)
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{
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107
fp_invmod.c
107
fp_invmod.c
@ -9,6 +9,111 @@
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*/
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#include <tfm.h>
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static int fp_invmod_slow (fp_int * a, fp_int * b, fp_int * c)
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{
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fp_int x, y, u, v, A, B, C, D;
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int res;
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/* b cannot be negative */
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if (b->sign == FP_NEG || fp_iszero(b) == 1) {
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return FP_VAL;
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}
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/* init temps */
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fp_init(&x); fp_init(&y);
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fp_init(&u); fp_init(&v);
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fp_init(&A); fp_init(&B);
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fp_init(&C); fp_init(&D);
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/* x = a, y = b */
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if ((res = fp_mod(a, b, &x)) != FP_OKAY) {
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return res;
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}
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fp_copy(b, &y);
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/* 2. [modified] if x,y are both even then return an error! */
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if (fp_iseven (&x) == 1 && fp_iseven (&y) == 1) {
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return FP_VAL;
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}
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/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
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fp_copy (&x, &u);
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fp_copy (&y, &v);
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fp_set (&A, 1);
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fp_set (&D, 1);
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top:
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/* 4. while u is even do */
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while (fp_iseven (&u) == 1) {
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/* 4.1 u = u/2 */
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fp_div_2 (&u, &u);
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/* 4.2 if A or B is odd then */
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if (fp_isodd (&A) == 1 || fp_isodd (&B) == 1) {
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/* A = (A+y)/2, B = (B-x)/2 */
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fp_add (&A, &y, &A);
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fp_sub (&B, &x, &B);
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}
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/* A = A/2, B = B/2 */
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fp_div_2 (&A, &A);
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fp_div_2 (&B, &B);
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}
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/* 5. while v is even do */
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while (fp_iseven (&v) == 1) {
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/* 5.1 v = v/2 */
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fp_div_2 (&v, &v);
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/* 5.2 if C or D is odd then */
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if (fp_isodd (&C) == 1 || fp_isodd (&D) == 1) {
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/* C = (C+y)/2, D = (D-x)/2 */
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fp_add (&C, &y, &C);
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fp_sub (&D, &x, &D);
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}
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/* C = C/2, D = D/2 */
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fp_div_2 (&C, &C);
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fp_div_2 (&D, &D);
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}
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/* 6. if u >= v then */
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if (fp_cmp (&u, &v) != FP_LT) {
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/* u = u - v, A = A - C, B = B - D */
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fp_sub (&u, &v, &u);
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fp_sub (&A, &C, &A);
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fp_sub (&B, &D, &B);
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} else {
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/* v - v - u, C = C - A, D = D - B */
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fp_sub (&v, &u, &v);
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fp_sub (&C, &A, &C);
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fp_sub (&D, &B, &D);
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}
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/* if not zero goto step 4 */
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if (fp_iszero (&u) == 0)
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goto top;
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/* now a = C, b = D, gcd == g*v */
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/* if v != 1 then there is no inverse */
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if (fp_cmp_d (&v, 1) != FP_EQ) {
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return FP_VAL;
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}
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/* if its too low */
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while (fp_cmp_d(&C, 0) == FP_LT) {
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fp_add(&C, b, &C);
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}
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/* too big */
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while (fp_cmp_mag(&C, b) != FP_LT) {
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fp_sub(&C, b, &C);
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}
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/* C is now the inverse */
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fp_copy(&C, c);
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return FP_OKAY;
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}
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/* c = 1/a (mod b) for odd b only */
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int fp_invmod(fp_int *a, fp_int *b, fp_int *c)
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{
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@ -17,7 +122,7 @@ int fp_invmod(fp_int *a, fp_int *b, fp_int *c)
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/* 2. [modified] b must be odd */
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if (fp_iseven (b) == FP_YES) {
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return FP_VAL;
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return fp_invmod_slow(a,b,c);
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}
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/* init all our temps */
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@ -299,8 +299,6 @@ asm( \
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#define LO 0
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#define HI 1
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#define CY 2
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/* computes x/R == x (mod N) via Montgomery Reduction */
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void fp_montgomery_reduce(fp_int *a, fp_int *m, fp_digit mp)
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@ -347,7 +345,7 @@ void fp_montgomery_reduce(fp_int *a, fp_int *m, fp_digit mp)
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}
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LOOP_END;
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while (cy) {
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PROPCARRY; // cy = cy > (*_c += cy);
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PROPCARRY;
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++_c;
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}
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}
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@ -374,7 +372,7 @@ void fp_montgomery_reduce(fp_int *a, fp_int *m, fp_digit mp)
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}
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}
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/* $Source$ */
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/* $Revision$ */
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/* $Date$ */
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@ -47,7 +47,7 @@
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/* this should multiply i and j */
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#define MULADD(i, j) \
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asm ( \
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asm( \
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"movl %6,%%eax \n\t" \
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"mull %7 \n\t" \
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"addl %%eax,%0 \n\t" \
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@ -118,7 +118,7 @@ asm ( \
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/* this should multiply i and j */
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#define MULADD(i, j) \
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asm volatile ( \
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asm( \
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"movd %6,%%mm0 \n\t" \
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"movd %7,%%mm1 \n\t" \
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"pmuludq %%mm1,%%mm0\n\t" \
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@ -36,7 +36,7 @@
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#define COMBA_FINI
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#define SQRADD(i, j) \
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asm volatile ( \
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asm( \
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"movl %6,%%eax \n\t" \
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"mull %%eax \n\t" \
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"addl %%eax,%0 \n\t" \
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@ -45,7 +45,7 @@ asm volatile ( \
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:"=r"(c0), "=r"(c1), "=r"(c2): "0"(c0), "1"(c1), "2"(c2), "m"(i) :"%eax","%edx","%cc");
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#define SQRADD2(i, j) \
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asm volatile ( \
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asm( \
|
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"movl %6,%%eax \n\t" \
|
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"mull %7 \n\t" \
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"addl %%eax,%0 \n\t" \
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@ -57,7 +57,7 @@ asm volatile ( \
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:"=r"(c0), "=r"(c1), "=r"(c2): "0"(c0), "1"(c1), "2"(c2), "m"(i), "m"(j) :"%eax","%edx","%cc");
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|
||||
#define SQRADDSC(i, j) \
|
||||
asm ( \
|
||||
asm( \
|
||||
"movl %6,%%eax \n\t" \
|
||||
"mull %7 \n\t" \
|
||||
"movl %%eax,%0 \n\t" \
|
||||
@ -66,7 +66,7 @@ asm ( \
|
||||
:"=r"(sc0), "=r"(sc1), "=r"(sc2): "0"(sc0), "1"(sc1), "2"(sc2), "g"(i), "g"(j) :"%eax","%edx","%cc");
|
||||
|
||||
#define SQRADDAC(i, j) \
|
||||
asm ( \
|
||||
asm( \
|
||||
"movl %6,%%eax \n\t" \
|
||||
"mull %7 \n\t" \
|
||||
"addl %%eax,%0 \n\t" \
|
||||
@ -75,7 +75,7 @@ asm ( \
|
||||
:"=r"(sc0), "=r"(sc1), "=r"(sc2): "0"(sc0), "1"(sc1), "2"(sc2), "g"(i), "g"(j) :"%eax","%edx","%cc");
|
||||
|
||||
#define SQRADDDB \
|
||||
asm ( \
|
||||
asm( \
|
||||
"addl %6,%0 \n\t" \
|
||||
"adcl %7,%1 \n\t" \
|
||||
"adcl %8,%2 \n\t" \
|
||||
@ -104,7 +104,7 @@ asm ( \
|
||||
#define COMBA_FINI
|
||||
|
||||
#define SQRADD(i, j) \
|
||||
asm ( \
|
||||
asm( \
|
||||
"movq %6,%%rax \n\t" \
|
||||
"mulq %%rax \n\t" \
|
||||
"addq %%rax,%0 \n\t" \
|
||||
@ -113,7 +113,7 @@ asm ( \
|
||||
:"=r"(c0), "=r"(c1), "=r"(c2): "0"(c0), "1"(c1), "2"(c2), "g"(i) :"%rax","%rdx","%cc");
|
||||
|
||||
#define SQRADD2(i, j) \
|
||||
asm ( \
|
||||
asm( \
|
||||
"movq %6,%%rax \n\t" \
|
||||
"mulq %7 \n\t" \
|
||||
"addq %%rax,%0 \n\t" \
|
||||
@ -125,7 +125,7 @@ asm ( \
|
||||
:"=r"(c0), "=r"(c1), "=r"(c2): "0"(c0), "1"(c1), "2"(c2), "g"(i), "g"(j) :"%rax","%rdx","%cc");
|
||||
|
||||
#define SQRADDSC(i, j) \
|
||||
asm ( \
|
||||
asm( \
|
||||
"movq %6,%%rax \n\t" \
|
||||
"mulq %7 \n\t" \
|
||||
"movq %%rax,%0 \n\t" \
|
||||
@ -134,7 +134,7 @@ asm ( \
|
||||
:"=r"(sc0), "=r"(sc1), "=r"(sc2): "0"(sc0), "1"(sc1), "2"(sc2), "g"(i), "g"(j) :"%rax","%rdx","%cc");
|
||||
|
||||
#define SQRADDAC(i, j) \
|
||||
asm ( \
|
||||
asm( \
|
||||
"movq %6,%%rax \n\t" \
|
||||
"mulq %7 \n\t" \
|
||||
"addq %%rax,%0 \n\t" \
|
||||
@ -143,7 +143,7 @@ asm ( \
|
||||
:"=r"(sc0), "=r"(sc1), "=r"(sc2): "0"(sc0), "1"(sc1), "2"(sc2), "g"(i), "g"(j) :"%rax","%rdx","%cc");
|
||||
|
||||
#define SQRADDDB \
|
||||
asm ( \
|
||||
asm( \
|
||||
"addq %6,%0 \n\t" \
|
||||
"adcq %7,%1 \n\t" \
|
||||
"adcq %8,%2 \n\t" \
|
||||
@ -173,7 +173,7 @@ asm ( \
|
||||
asm("emms");
|
||||
|
||||
#define SQRADD(i, j) \
|
||||
asm volatile ( \
|
||||
asm( \
|
||||
"movd %6,%%mm0 \n\t" \
|
||||
"pmuludq %%mm0,%%mm0\n\t" \
|
||||
"movd %%mm0,%%eax \n\t" \
|
||||
@ -185,7 +185,7 @@ asm volatile ( \
|
||||
:"=r"(c0), "=r"(c1), "=r"(c2): "0"(c0), "1"(c1), "2"(c2), "m"(i) :"%eax","%cc");
|
||||
|
||||
#define SQRADD2(i, j) \
|
||||
asm volatile ( \
|
||||
asm( \
|
||||
"movd %6,%%mm0 \n\t" \
|
||||
"movd %7,%%mm1 \n\t" \
|
||||
"pmuludq %%mm1,%%mm0\n\t" \
|
||||
@ -201,7 +201,7 @@ asm volatile ( \
|
||||
:"=r"(c0), "=r"(c1), "=r"(c2): "0"(c0), "1"(c1), "2"(c2), "m"(i), "m"(j) :"%eax","%edx","%cc");
|
||||
|
||||
#define SQRADDSC(i, j) \
|
||||
asm volatile ( \
|
||||
asm( \
|
||||
"movd %6,%%mm0 \n\t" \
|
||||
"movd %7,%%mm1 \n\t" \
|
||||
"pmuludq %%mm1,%%mm0\n\t" \
|
||||
@ -212,7 +212,7 @@ asm volatile ( \
|
||||
:"=r"(sc0), "=r"(sc1), "=r"(sc2): "0"(sc0), "1"(sc1), "2"(sc2), "m"(i), "m"(j));
|
||||
|
||||
#define SQRADDAC(i, j) \
|
||||
asm volatile ( \
|
||||
asm( \
|
||||
"movd %6,%%mm0 \n\t" \
|
||||
"movd %7,%%mm1 \n\t" \
|
||||
"pmuludq %%mm1,%%mm0\n\t" \
|
||||
@ -225,7 +225,7 @@ asm volatile ( \
|
||||
:"=r"(sc0), "=r"(sc1), "=r"(sc2): "0"(sc0), "1"(sc1), "2"(sc2), "m"(i), "m"(j) :"%eax","%edx","%cc");
|
||||
|
||||
#define SQRADDDB \
|
||||
asm ( \
|
||||
asm( \
|
||||
"addl %6,%0 \n\t" \
|
||||
"adcl %7,%1 \n\t" \
|
||||
"adcl %8,%2 \n\t" \
|
||||
|
||||
67
makefile
67
makefile
@ -1,7 +1,13 @@
|
||||
#makefile for TomsFastMath
|
||||
#
|
||||
#
|
||||
CFLAGS += -Wall -W -Wshadow -I./ -O3 -funroll-all-loops
|
||||
VERSION=0.05
|
||||
|
||||
CFLAGS += -Wall -W -Wshadow -I./
|
||||
|
||||
ifndef IGNORE_SPEED
|
||||
|
||||
CFLAGS += -O3 -funroll-all-loops
|
||||
|
||||
#profiling
|
||||
#PROF=-pg -g
|
||||
@ -10,9 +16,7 @@ CFLAGS += -Wall -W -Wshadow -I./ -O3 -funroll-all-loops
|
||||
#speed
|
||||
CFLAGS += -fomit-frame-pointer
|
||||
|
||||
VERSION=0.04
|
||||
|
||||
default: libtfm.a
|
||||
endif
|
||||
|
||||
OBJECTS = \
|
||||
fp_set.o \
|
||||
@ -52,23 +56,29 @@ ifndef INCPATH
|
||||
INCPATH=/usr/include
|
||||
endif
|
||||
|
||||
ifndef TFM_GROUP
|
||||
ifndef INSTALL_GROUP
|
||||
GROUP=wheel
|
||||
else
|
||||
GROUP=$(INSTALL_GROUP)
|
||||
endif
|
||||
|
||||
ifndef TFM_USER
|
||||
ifndef INSTALL_USER
|
||||
USER=root
|
||||
else
|
||||
USER=$(INSTALL_USER)
|
||||
endif
|
||||
|
||||
ifndef LIBNAME
|
||||
LIBNAME=libtfm.a
|
||||
endif
|
||||
|
||||
$(LIBNAME): $(OBJECTS)
|
||||
$(AR) $(ARFLAGS) $(LIBNAME) $(OBJECTS)
|
||||
ranlib $(LIBNAME)
|
||||
default: $(LIBNAME)
|
||||
|
||||
install: libtfm.a
|
||||
$(LIBNAME): $(OBJECTS)
|
||||
$(AR) $(ARFLAGS) $@ $(OBJECTS)
|
||||
ranlib $@
|
||||
|
||||
install: $(LIBNAME)
|
||||
install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(LIBPATH)
|
||||
install -d -g $(GROUP) -o $(USER) $(DESTDIR)$(INCPATH)
|
||||
install -g $(GROUP) -o $(USER) $(LIBNAME) $(DESTDIR)$(LIBPATH)
|
||||
@ -77,17 +87,17 @@ install: libtfm.a
|
||||
mtest/mtest: mtest/mtest.c
|
||||
cd mtest ; make mtest
|
||||
|
||||
test: libtfm.a demo/test.o mtest/mtest
|
||||
$(CC) $(CFLAGS) demo/test.o libtfm.a $(PROF) -o test
|
||||
test: $(LIBNAME) demo/test.o mtest/mtest
|
||||
$(CC) $(CFLAGS) demo/test.o $(LIBNAME) $(PROF) -o test
|
||||
|
||||
timing: libtfm.a demo/test.o
|
||||
$(CC) $(CFLAGS) demo/test.o libtfm.a $(PROF) -o test
|
||||
timing: $(LIBNAME) demo/test.o
|
||||
$(CC) $(CFLAGS) demo/test.o $(LIBNAME) $(PROF) -o test
|
||||
|
||||
stest: libtfm.a demo/stest.o
|
||||
$(CC) $(CFLAGS) demo/stest.o libtfm.a -o stest
|
||||
stest: $(LIBNAME) demo/stest.o
|
||||
$(CC) $(CFLAGS) demo/stest.o $(LIBNAME) -o stest
|
||||
|
||||
rsatest: libtfm.a demo/rsa.o
|
||||
$(CC) $(CFLAGS) demo/rsa.o libtfm.a -o rsatest
|
||||
rsatest: $(LIBNAME) demo/rsa.o
|
||||
$(CC) $(CFLAGS) demo/rsa.o $(LIBNAME) -o rsatest
|
||||
|
||||
docdvi: tfm.tex
|
||||
touch tfm.ind
|
||||
@ -101,8 +111,23 @@ docs: docdvi
|
||||
dvipdf tfm
|
||||
mv -f tfm.pdf doc
|
||||
|
||||
#This rule cleans the source tree of all compiled code, not including the pdf
|
||||
#documentation.
|
||||
clean:
|
||||
rm -f $(OBJECTS) *.a demo/*.o test tfm.aux tfm.dvi tfm.idx tfm.ilg tfm.ind tfm.lof tfm.log tfm.toc stest *~ rsatest *.gcda *.gcno demo/*.gcda demo/*.gcno mtest/*.gcno mtest/*.gcda
|
||||
rm -f `find . -type f | grep "[.]o" | xargs`
|
||||
rm -f `find . -type f | grep "[.]lo" | xargs`
|
||||
rm -f `find . -type f | grep "[.]a" | xargs`
|
||||
rm -f `find . -type f | grep "[.]la" | xargs`
|
||||
rm -f `find . -type f | grep "[.]obj" | xargs`
|
||||
rm -f `find . -type f | grep "[.]lib" | xargs`
|
||||
rm -f `find . -type f | grep "[.]exe" | xargs`
|
||||
rm -f `find . -type f | grep "[.]gcda" | xargs`
|
||||
rm -f `find . -type f | grep "[.]gcno" | xargs`
|
||||
rm -f `find . -type f | grep "[.]il" | xargs`
|
||||
rm -f `find . -type f | grep "[.]dyn" | xargs`
|
||||
rm -f `find . -type f | grep "[.]dpi" | xargs`
|
||||
rm -rf `find . -type d | grep "[.]libs" | xargs`
|
||||
rm -f tfm.aux tfm.dvi tfm.idx tfm.ilg tfm.ind tfm.lof tfm.log tfm.toc
|
||||
cd mtest ; make clean
|
||||
|
||||
no_oops: clean
|
||||
@ -116,3 +141,7 @@ zipup: no_oops docs clean
|
||||
cp -R ./tomsfastmath/* ./tomsfastmath-$(VERSION)/ ; \
|
||||
tar -c tomsfastmath-$(VERSION)/* | bzip2 -9vvc > tfm-$(VERSION).tar.bz2 ; \
|
||||
zip -9r tfm-$(VERSION).zip tomsfastmath-$(VERSION)/*
|
||||
|
||||
# $Source: /cvs/libtom/tomsfastmath/makefile,v $
|
||||
# $Revision: 1.17 $
|
||||
# $Date: 2005/07/30 04:23:55 $
|
||||
|
||||
55
makefile.gba
55
makefile.gba
@ -1,55 +0,0 @@
|
||||
#makefile for TomsFastMath
|
||||
#
|
||||
#For the GameboyAdance... er.... ARMv4
|
||||
SFLAGS = $(CFLAGS) -Wall -W -Wshadow -I./ -O3 -funroll-all-loops -mthumb -mthumb-interwork -I../devkitadv/mylib/lib
|
||||
CFLAGS += -Wall -W -Wshadow -I./ -O3 -funroll-all-loops -marm -mthumb-interwork -I../devkitadv/mylib/lib
|
||||
|
||||
#profiling
|
||||
#PROF=-pg -g
|
||||
#CFLAGS += $(PROF)
|
||||
|
||||
#speed
|
||||
CFLAGS += -fomit-frame-pointer
|
||||
|
||||
VERSION=0.01
|
||||
|
||||
default: libtfm.a
|
||||
|
||||
OBJECTS = \
|
||||
fp_set.o \
|
||||
\
|
||||
fp_rshd.o fp_lshd.o fp_div_2d.o fp_mod_2d.o fp_mul_2d.o fp_2expt.o \
|
||||
fp_mul_2.o fp_div_2.o \
|
||||
\
|
||||
fp_cnt_lsb.o \
|
||||
\
|
||||
fp_add.o fp_sub.o fp_mul.o fp_sqr.o fp_div.o fp_mod.o \
|
||||
s_fp_add.o s_fp_sub.o \
|
||||
\
|
||||
fp_cmp_d.o fp_add_d.o fp_sub_d.o fp_mul_d.o fp_div_d.o fp_mod_d.o \
|
||||
fp_addmod.o fp_submod.o fp_mulmod.o fp_sqrmod.o fp_invmod.o \
|
||||
fp_gcd.o fp_lcm.o fp_prime_miller_rabin.o fp_isprime.o \
|
||||
fp_prime_random_ex.o fp_mul_comba.o fp_sqr_comba.o \
|
||||
\
|
||||
fp_montgomery_setup.o fp_montgomery_calc_normalization.o fp_montgomery_reduce.o \
|
||||
\
|
||||
fp_exptmod.o \
|
||||
\
|
||||
fp_cmp.o fp_cmp_mag.o \
|
||||
\
|
||||
fp_unsigned_bin_size.o fp_read_unsigned_bin.o fp_to_unsigned_bin.o \
|
||||
fp_signed_bin_size.o fp_read_signed_bin.o fp_to_signed_bin.o \
|
||||
fp_read_radix.o fp_toradix.o fp_count_bits.o fp_reverse.o fp_s_rmap.o \
|
||||
\
|
||||
|
||||
libtfm.a: $(OBJECTS)
|
||||
$(AR) $(ARFLAGS) libtfm.a $(OBJECTS)
|
||||
ranlib libtfm.a
|
||||
|
||||
demo/stest.o: demo/stest.c
|
||||
$(CC) $(SFLAGS) -DGBA_MODE demo/stest.c -c -o demo/stest.o
|
||||
|
||||
stest: libtfm.a demo/stest.o
|
||||
$(CC) -mthumb -mthumb-interwork demo/stest.o libtfm.a ../devkitadv/mylib/lib/gba.a -o stest.elf
|
||||
objcopy -O binary stest.elf stest.bin
|
||||
|
||||
109
makefile.shared
Normal file
109
makefile.shared
Normal file
@ -0,0 +1,109 @@
|
||||
#makefile for TomsFastMath
|
||||
#
|
||||
#
|
||||
|
||||
CC=libtool --mode=compile gcc
|
||||
|
||||
CFLAGS += -Wall -W -Wshadow -I./
|
||||
|
||||
ifndef IGNORE_SPEED
|
||||
|
||||
CFLAGS += -O3 -funroll-all-loops
|
||||
|
||||
#profiling
|
||||
#PROF=-pg -g
|
||||
#CFLAGS += $(PROF)
|
||||
|
||||
#speed
|
||||
CFLAGS += -fomit-frame-pointer
|
||||
|
||||
endif
|
||||
|
||||
VERSION=0:5
|
||||
|
||||
OBJECTS = \
|
||||
fp_set.o \
|
||||
\
|
||||
fp_rshd.o fp_lshd.o fp_div_2d.o fp_mod_2d.o fp_mul_2d.o fp_2expt.o \
|
||||
fp_mul_2.o fp_div_2.o \
|
||||
\
|
||||
fp_cnt_lsb.o \
|
||||
\
|
||||
fp_add.o fp_sub.o fp_mul.o fp_sqr.o fp_div.o fp_mod.o \
|
||||
s_fp_add.o s_fp_sub.o \
|
||||
\
|
||||
fp_cmp_d.o fp_add_d.o fp_sub_d.o fp_mul_d.o fp_div_d.o fp_mod_d.o \
|
||||
fp_addmod.o fp_submod.o fp_mulmod.o fp_sqrmod.o fp_invmod.o \
|
||||
fp_gcd.o fp_lcm.o fp_prime_miller_rabin.o fp_isprime.o \
|
||||
fp_prime_random_ex.o fp_mul_comba.o fp_sqr_comba.o \
|
||||
\
|
||||
fp_montgomery_setup.o fp_montgomery_calc_normalization.o fp_montgomery_reduce.o \
|
||||
\
|
||||
fp_exptmod.o \
|
||||
\
|
||||
fp_cmp.o fp_cmp_mag.o \
|
||||
\
|
||||
fp_unsigned_bin_size.o fp_read_unsigned_bin.o fp_to_unsigned_bin.o \
|
||||
fp_signed_bin_size.o fp_read_signed_bin.o fp_to_signed_bin.o \
|
||||
fp_read_radix.o fp_toradix.o fp_radix_size.o fp_count_bits.o fp_reverse.o fp_s_rmap.o \
|
||||
\
|
||||
fp_ident.o
|
||||
|
||||
HEADERS=tfm.h
|
||||
|
||||
ifndef LIBPATH
|
||||
LIBPATH=/usr/lib
|
||||
endif
|
||||
|
||||
ifndef INCPATH
|
||||
INCPATH=/usr/include
|
||||
endif
|
||||
|
||||
ifndef INSTALL_GROUP
|
||||
GROUP=wheel
|
||||
else
|
||||
GROUP=$(INSTALL_GROUP)
|
||||
endif
|
||||
|
||||
ifndef INSTALL_USER
|
||||
USER=root
|
||||
else
|
||||
USER=$(INSTALL_USER)
|
||||
endif
|
||||
|
||||
ifndef LIBNAME
|
||||
LIBNAME=libtfm.la
|
||||
endif
|
||||
|
||||
ifndef LIBNAME_S
|
||||
LIBNAME_S=libtfm.a
|
||||
endif
|
||||
|
||||
default: $(LIBNAME)
|
||||
|
||||
$(LIBNAME): $(OBJECTS)
|
||||
|
||||
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)
|
||||
|
||||
mtest/mtest: mtest/mtest.c
|
||||
cd mtest ; make mtest
|
||||
|
||||
test: $(LIBNAME) demo/test.o mtest/mtest
|
||||
$(CC) $(CFLAGS) demo/test.o $(LIBNAME_S) $(PROF) -o test
|
||||
|
||||
timing: $(LIBNAME) demo/test.o
|
||||
$(CC) $(CFLAGS) demo/test.o $(LIBNAME_S) $(PROF) -o test
|
||||
|
||||
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 $
|
||||
|
||||
218
pre_gen/mpi.c
218
pre_gen/mpi.c
@ -757,6 +757,75 @@ int fp_div_d(fp_int *a, fp_digit b, fp_int *c, fp_digit *d)
|
||||
*/
|
||||
#include <tfm.h>
|
||||
|
||||
#ifdef TFM_TIMING_RESISTANT
|
||||
|
||||
/* timing resistant montgomery ladder based exptmod
|
||||
|
||||
Based on work by Marc Joye, Sung-Ming Yen, "The Montgomery Powering Ladder", Cryptographic Hardware and Embedded Systems, CHES 2002
|
||||
*/
|
||||
static int _fp_exptmod(fp_int * G, fp_int * X, fp_int * P, fp_int * Y)
|
||||
{
|
||||
fp_int R[2];
|
||||
fp_digit buf, mp;
|
||||
int err, bitcnt, digidx, y;
|
||||
|
||||
/* now setup montgomery */
|
||||
if ((err = fp_montgomery_setup (P, &mp)) != FP_OKAY) {
|
||||
return err;
|
||||
}
|
||||
|
||||
fp_init(&R[0]);
|
||||
fp_init(&R[1]);
|
||||
|
||||
/* now we need R mod m */
|
||||
fp_montgomery_calc_normalization (&R[0], P);
|
||||
|
||||
/* now set R[0][1] to G * R mod m */
|
||||
if (fp_cmp_mag(P, G) != FP_GT) {
|
||||
/* G > P so we reduce it first */
|
||||
fp_mod(G, P, &R[1]);
|
||||
} else {
|
||||
fp_copy(G, &R[1]);
|
||||
}
|
||||
fp_mulmod (&R[1], &R[0], P, &R[1]);
|
||||
|
||||
/* for j = t-1 downto 0 do
|
||||
r_!k = R0*R1; r_k = r_k^2
|
||||
*/
|
||||
|
||||
/* set initial mode and bit cnt */
|
||||
bitcnt = 1;
|
||||
buf = 0;
|
||||
digidx = X->used - 1;
|
||||
|
||||
for (;;) {
|
||||
/* grab next digit as required */
|
||||
if (--bitcnt == 0) {
|
||||
/* if digidx == -1 we are out of digits so break */
|
||||
if (digidx == -1) {
|
||||
break;
|
||||
}
|
||||
/* read next digit and reset bitcnt */
|
||||
buf = X->dp[digidx--];
|
||||
bitcnt = (int)DIGIT_BIT;
|
||||
}
|
||||
|
||||
/* grab the next msb from the exponent */
|
||||
y = (fp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
|
||||
buf <<= (fp_digit)1;
|
||||
|
||||
/* do ops */
|
||||
fp_mul(&R[0], &R[1], &R[y^1]); fp_montgomery_reduce(&R[y^1], P, mp);
|
||||
fp_sqr(&R[y], &R[y]); fp_montgomery_reduce(&R[y], P, mp);
|
||||
}
|
||||
|
||||
fp_montgomery_reduce(&R[0], P, mp);
|
||||
fp_copy(&R[0], Y);
|
||||
return FP_OKAY;
|
||||
}
|
||||
|
||||
#else
|
||||
|
||||
/* y = g**x (mod b)
|
||||
* Some restrictions... x must be positive and < b
|
||||
*/
|
||||
@ -916,6 +985,8 @@ static int _fp_exptmod(fp_int * G, fp_int * X, fp_int * P, fp_int * Y)
|
||||
return FP_OKAY;
|
||||
}
|
||||
|
||||
#endif
|
||||
|
||||
|
||||
int fp_exptmod(fp_int * G, fp_int * X, fp_int * P, fp_int * Y)
|
||||
{
|
||||
@ -1105,6 +1176,111 @@ int main(void)
|
||||
*/
|
||||
#include <tfm.h>
|
||||
|
||||
static int fp_invmod_slow (fp_int * a, fp_int * b, fp_int * c)
|
||||
{
|
||||
fp_int x, y, u, v, A, B, C, D;
|
||||
int res;
|
||||
|
||||
/* b cannot be negative */
|
||||
if (b->sign == FP_NEG || fp_iszero(b) == 1) {
|
||||
return FP_VAL;
|
||||
}
|
||||
|
||||
/* init temps */
|
||||
fp_init(&x); fp_init(&y);
|
||||
fp_init(&u); fp_init(&v);
|
||||
fp_init(&A); fp_init(&B);
|
||||
fp_init(&C); fp_init(&D);
|
||||
|
||||
/* x = a, y = b */
|
||||
if ((res = fp_mod(a, b, &x)) != FP_OKAY) {
|
||||
return res;
|
||||
}
|
||||
fp_copy(b, &y);
|
||||
|
||||
/* 2. [modified] if x,y are both even then return an error! */
|
||||
if (fp_iseven (&x) == 1 && fp_iseven (&y) == 1) {
|
||||
return FP_VAL;
|
||||
}
|
||||
|
||||
/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
|
||||
fp_copy (&x, &u);
|
||||
fp_copy (&y, &v);
|
||||
fp_set (&A, 1);
|
||||
fp_set (&D, 1);
|
||||
|
||||
top:
|
||||
/* 4. while u is even do */
|
||||
while (fp_iseven (&u) == 1) {
|
||||
/* 4.1 u = u/2 */
|
||||
fp_div_2 (&u, &u);
|
||||
|
||||
/* 4.2 if A or B is odd then */
|
||||
if (fp_isodd (&A) == 1 || fp_isodd (&B) == 1) {
|
||||
/* A = (A+y)/2, B = (B-x)/2 */
|
||||
fp_add (&A, &y, &A);
|
||||
fp_sub (&B, &x, &B);
|
||||
}
|
||||
/* A = A/2, B = B/2 */
|
||||
fp_div_2 (&A, &A);
|
||||
fp_div_2 (&B, &B);
|
||||
}
|
||||
|
||||
/* 5. while v is even do */
|
||||
while (fp_iseven (&v) == 1) {
|
||||
/* 5.1 v = v/2 */
|
||||
fp_div_2 (&v, &v);
|
||||
|
||||
/* 5.2 if C or D is odd then */
|
||||
if (fp_isodd (&C) == 1 || fp_isodd (&D) == 1) {
|
||||
/* C = (C+y)/2, D = (D-x)/2 */
|
||||
fp_add (&C, &y, &C);
|
||||
fp_sub (&D, &x, &D);
|
||||
}
|
||||
/* C = C/2, D = D/2 */
|
||||
fp_div_2 (&C, &C);
|
||||
fp_div_2 (&D, &D);
|
||||
}
|
||||
|
||||
/* 6. if u >= v then */
|
||||
if (fp_cmp (&u, &v) != FP_LT) {
|
||||
/* u = u - v, A = A - C, B = B - D */
|
||||
fp_sub (&u, &v, &u);
|
||||
fp_sub (&A, &C, &A);
|
||||
fp_sub (&B, &D, &B);
|
||||
} else {
|
||||
/* v - v - u, C = C - A, D = D - B */
|
||||
fp_sub (&v, &u, &v);
|
||||
fp_sub (&C, &A, &C);
|
||||
fp_sub (&D, &B, &D);
|
||||
}
|
||||
|
||||
/* if not zero goto step 4 */
|
||||
if (fp_iszero (&u) == 0)
|
||||
goto top;
|
||||
|
||||
/* now a = C, b = D, gcd == g*v */
|
||||
|
||||
/* if v != 1 then there is no inverse */
|
||||
if (fp_cmp_d (&v, 1) != FP_EQ) {
|
||||
return FP_VAL;
|
||||
}
|
||||
|
||||
/* if its too low */
|
||||
while (fp_cmp_d(&C, 0) == FP_LT) {
|
||||
fp_add(&C, b, &C);
|
||||
}
|
||||
|
||||
/* too big */
|
||||
while (fp_cmp_mag(&C, b) != FP_LT) {
|
||||
fp_sub(&C, b, &C);
|
||||
}
|
||||
|
||||
/* C is now the inverse */
|
||||
fp_copy(&C, c);
|
||||
return FP_OKAY;
|
||||
}
|
||||
|
||||
/* c = 1/a (mod b) for odd b only */
|
||||
int fp_invmod(fp_int *a, fp_int *b, fp_int *c)
|
||||
{
|
||||
@ -1113,7 +1289,7 @@ int fp_invmod(fp_int *a, fp_int *b, fp_int *c)
|
||||
|
||||
/* 2. [modified] b must be odd */
|
||||
if (fp_iseven (b) == FP_YES) {
|
||||
return FP_VAL;
|
||||
return fp_invmod_slow(a,b,c);
|
||||
}
|
||||
|
||||
/* init all our temps */
|
||||
@ -1814,8 +1990,6 @@ asm( \
|
||||
|
||||
|
||||
#define LO 0
|
||||
#define HI 1
|
||||
#define CY 2
|
||||
|
||||
/* computes x/R == x (mod N) via Montgomery Reduction */
|
||||
void fp_montgomery_reduce(fp_int *a, fp_int *m, fp_digit mp)
|
||||
@ -1862,7 +2036,7 @@ void fp_montgomery_reduce(fp_int *a, fp_int *m, fp_digit mp)
|
||||
}
|
||||
LOOP_END;
|
||||
while (cy) {
|
||||
PROPCARRY; // cy = cy > (*_c += cy);
|
||||
PROPCARRY;
|
||||
++_c;
|
||||
}
|
||||
}
|
||||
@ -1889,10 +2063,10 @@ void fp_montgomery_reduce(fp_int *a, fp_int *m, fp_digit mp)
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
/* $Source$ */
|
||||
/* $Revision$ */
|
||||
/* $Date$ */
|
||||
|
||||
|
||||
/* End: fp_montgomery_reduce.c */
|
||||
|
||||
@ -2270,7 +2444,7 @@ void fp_mul_2d(fp_int *a, int b, fp_int *c)
|
||||
|
||||
/* this should multiply i and j */
|
||||
#define MULADD(i, j) \
|
||||
asm ( \
|
||||
asm( \
|
||||
"movl %6,%%eax \n\t" \
|
||||
"mull %7 \n\t" \
|
||||
"addl %%eax,%0 \n\t" \
|
||||
@ -2341,7 +2515,7 @@ asm ( \
|
||||
|
||||
/* this should multiply i and j */
|
||||
#define MULADD(i, j) \
|
||||
asm volatile ( \
|
||||
asm( \
|
||||
"movd %6,%%mm0 \n\t" \
|
||||
"movd %7,%%mm1 \n\t" \
|
||||
"pmuludq %%mm1,%%mm0\n\t" \
|
||||
@ -5678,7 +5852,7 @@ Obvious points of optimization
|
||||
#define COMBA_FINI
|
||||
|
||||
#define SQRADD(i, j) \
|
||||
asm volatile ( \
|
||||
asm( \
|
||||
"movl %6,%%eax \n\t" \
|
||||
"mull %%eax \n\t" \
|
||||
"addl %%eax,%0 \n\t" \
|
||||
@ -5687,7 +5861,7 @@ asm volatile ( \
|
||||
:"=r"(c0), "=r"(c1), "=r"(c2): "0"(c0), "1"(c1), "2"(c2), "m"(i) :"%eax","%edx","%cc");
|
||||
|
||||
#define SQRADD2(i, j) \
|
||||
asm volatile ( \
|
||||
asm( \
|
||||
"movl %6,%%eax \n\t" \
|
||||
"mull %7 \n\t" \
|
||||
"addl %%eax,%0 \n\t" \
|
||||
@ -5699,7 +5873,7 @@ asm volatile ( \
|
||||
:"=r"(c0), "=r"(c1), "=r"(c2): "0"(c0), "1"(c1), "2"(c2), "m"(i), "m"(j) :"%eax","%edx","%cc");
|
||||
|
||||
#define SQRADDSC(i, j) \
|
||||
asm ( \
|
||||
asm( \
|
||||
"movl %6,%%eax \n\t" \
|
||||
"mull %7 \n\t" \
|
||||
"movl %%eax,%0 \n\t" \
|
||||
@ -5708,7 +5882,7 @@ asm ( \
|
||||
:"=r"(sc0), "=r"(sc1), "=r"(sc2): "0"(sc0), "1"(sc1), "2"(sc2), "g"(i), "g"(j) :"%eax","%edx","%cc");
|
||||
|
||||
#define SQRADDAC(i, j) \
|
||||
asm ( \
|
||||
asm( \
|
||||
"movl %6,%%eax \n\t" \
|
||||
"mull %7 \n\t" \
|
||||
"addl %%eax,%0 \n\t" \
|
||||
@ -5717,7 +5891,7 @@ asm ( \
|
||||
:"=r"(sc0), "=r"(sc1), "=r"(sc2): "0"(sc0), "1"(sc1), "2"(sc2), "g"(i), "g"(j) :"%eax","%edx","%cc");
|
||||
|
||||
#define SQRADDDB \
|
||||
asm ( \
|
||||
asm( \
|
||||
"addl %6,%0 \n\t" \
|
||||
"adcl %7,%1 \n\t" \
|
||||
"adcl %8,%2 \n\t" \
|
||||
@ -5746,7 +5920,7 @@ asm ( \
|
||||
#define COMBA_FINI
|
||||
|
||||
#define SQRADD(i, j) \
|
||||
asm ( \
|
||||
asm( \
|
||||
"movq %6,%%rax \n\t" \
|
||||
"mulq %%rax \n\t" \
|
||||
"addq %%rax,%0 \n\t" \
|
||||
@ -5755,7 +5929,7 @@ asm ( \
|
||||
:"=r"(c0), "=r"(c1), "=r"(c2): "0"(c0), "1"(c1), "2"(c2), "g"(i) :"%rax","%rdx","%cc");
|
||||
|
||||
#define SQRADD2(i, j) \
|
||||
asm ( \
|
||||
asm( \
|
||||
"movq %6,%%rax \n\t" \
|
||||
"mulq %7 \n\t" \
|
||||
"addq %%rax,%0 \n\t" \
|
||||
@ -5767,7 +5941,7 @@ asm ( \
|
||||
:"=r"(c0), "=r"(c1), "=r"(c2): "0"(c0), "1"(c1), "2"(c2), "g"(i), "g"(j) :"%rax","%rdx","%cc");
|
||||
|
||||
#define SQRADDSC(i, j) \
|
||||
asm ( \
|
||||
asm( \
|
||||
"movq %6,%%rax \n\t" \
|
||||
"mulq %7 \n\t" \
|
||||
"movq %%rax,%0 \n\t" \
|
||||
@ -5776,7 +5950,7 @@ asm ( \
|
||||
:"=r"(sc0), "=r"(sc1), "=r"(sc2): "0"(sc0), "1"(sc1), "2"(sc2), "g"(i), "g"(j) :"%rax","%rdx","%cc");
|
||||
|
||||
#define SQRADDAC(i, j) \
|
||||
asm ( \
|
||||
asm( \
|
||||
"movq %6,%%rax \n\t" \
|
||||
"mulq %7 \n\t" \
|
||||
"addq %%rax,%0 \n\t" \
|
||||
@ -5785,7 +5959,7 @@ asm ( \
|
||||
:"=r"(sc0), "=r"(sc1), "=r"(sc2): "0"(sc0), "1"(sc1), "2"(sc2), "g"(i), "g"(j) :"%rax","%rdx","%cc");
|
||||
|
||||
#define SQRADDDB \
|
||||
asm ( \
|
||||
asm( \
|
||||
"addq %6,%0 \n\t" \
|
||||
"adcq %7,%1 \n\t" \
|
||||
"adcq %8,%2 \n\t" \
|
||||
@ -5815,7 +5989,7 @@ asm ( \
|
||||
asm("emms");
|
||||
|
||||
#define SQRADD(i, j) \
|
||||
asm volatile ( \
|
||||
asm( \
|
||||
"movd %6,%%mm0 \n\t" \
|
||||
"pmuludq %%mm0,%%mm0\n\t" \
|
||||
"movd %%mm0,%%eax \n\t" \
|
||||
@ -5827,7 +6001,7 @@ asm volatile ( \
|
||||
:"=r"(c0), "=r"(c1), "=r"(c2): "0"(c0), "1"(c1), "2"(c2), "m"(i) :"%eax","%cc");
|
||||
|
||||
#define SQRADD2(i, j) \
|
||||
asm volatile ( \
|
||||
asm( \
|
||||
"movd %6,%%mm0 \n\t" \
|
||||
"movd %7,%%mm1 \n\t" \
|
||||
"pmuludq %%mm1,%%mm0\n\t" \
|
||||
@ -5843,7 +6017,7 @@ asm volatile ( \
|
||||
:"=r"(c0), "=r"(c1), "=r"(c2): "0"(c0), "1"(c1), "2"(c2), "m"(i), "m"(j) :"%eax","%edx","%cc");
|
||||
|
||||
#define SQRADDSC(i, j) \
|
||||
asm volatile ( \
|
||||
asm( \
|
||||
"movd %6,%%mm0 \n\t" \
|
||||
"movd %7,%%mm1 \n\t" \
|
||||
"pmuludq %%mm1,%%mm0\n\t" \
|
||||
@ -5854,7 +6028,7 @@ asm volatile ( \
|
||||
:"=r"(sc0), "=r"(sc1), "=r"(sc2): "0"(sc0), "1"(sc1), "2"(sc2), "m"(i), "m"(j));
|
||||
|
||||
#define SQRADDAC(i, j) \
|
||||
asm volatile ( \
|
||||
asm( \
|
||||
"movd %6,%%mm0 \n\t" \
|
||||
"movd %7,%%mm1 \n\t" \
|
||||
"pmuludq %%mm1,%%mm0\n\t" \
|
||||
@ -5867,7 +6041,7 @@ asm volatile ( \
|
||||
:"=r"(sc0), "=r"(sc1), "=r"(sc2): "0"(sc0), "1"(sc1), "2"(sc2), "m"(i), "m"(j) :"%eax","%edx","%cc");
|
||||
|
||||
#define SQRADDDB \
|
||||
asm ( \
|
||||
asm( \
|
||||
"addl %6,%0 \n\t" \
|
||||
"adcl %7,%1 \n\t" \
|
||||
"adcl %8,%2 \n\t" \
|
||||
|
||||
56
tfm.aux
56
tfm.aux
@ -17,40 +17,42 @@
|
||||
\@writefile{toc}{\contentsline {section}{\numberline {1.1}What is TomsFastMath?}{1}{section.1.1}}
|
||||
\@writefile{toc}{\contentsline {section}{\numberline {1.2}License}{2}{section.1.2}}
|
||||
\@writefile{toc}{\contentsline {section}{\numberline {1.3}Building}{2}{section.1.3}}
|
||||
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3.1}Build Limitations}{2}{subsection.1.3.1}}
|
||||
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3.2}Optimization Configuration}{2}{subsection.1.3.2}}
|
||||
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3.1}Intel CC}{2}{subsection.1.3.1}}
|
||||
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3.2}MSVC}{2}{subsection.1.3.2}}
|
||||
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3.3}Build Limitations}{3}{subsection.1.3.3}}
|
||||
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3.4}Optimization Configuration}{3}{subsection.1.3.4}}
|
||||
\@writefile{toc}{\contentsline {subsubsection}{x86--32}{3}{section*.3}}
|
||||
\@writefile{toc}{\contentsline {subsubsection}{SSE2}{3}{section*.4}}
|
||||
\@writefile{toc}{\contentsline {subsubsection}{x86--64}{3}{section*.5}}
|
||||
\@writefile{toc}{\contentsline {subsubsection}{ARM}{3}{section*.6}}
|
||||
\@writefile{toc}{\contentsline {subsubsection}{PPC32}{3}{section*.7}}
|
||||
\@writefile{toc}{\contentsline {subsubsection}{x86--64}{4}{section*.5}}
|
||||
\@writefile{toc}{\contentsline {subsubsection}{ARM}{4}{section*.6}}
|
||||
\@writefile{toc}{\contentsline {subsubsection}{PPC32}{4}{section*.7}}
|
||||
\@writefile{toc}{\contentsline {subsubsection}{Future Releases}{4}{section*.8}}
|
||||
\@writefile{lof}{\contentsline {figure}{\numberline {1.1}{\ignorespaces Recommended Build Modes}}{4}{figure.1.1}}
|
||||
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3.3}Precision Configuration}{4}{subsection.1.3.3}}
|
||||
\@writefile{toc}{\contentsline {chapter}{\numberline {2}Getting Started}{5}{chapter.2}}
|
||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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||||
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|
||||
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|
||||
|
||||
17
tfm.h
17
tfm.h
@ -48,6 +48,11 @@
|
||||
*/
|
||||
/* #define TFM_PRESCOTT */
|
||||
|
||||
/* Do we want timing resistant fp_exptmod() ?
|
||||
* This makes it slower but also timing invariant with respect to the exponent
|
||||
*/
|
||||
/* #define TFM_TIMING_RESISTANT */
|
||||
|
||||
#endif
|
||||
|
||||
/* Max size of any number in bits. Basically the largest size you will be multiplying
|
||||
@ -355,15 +360,25 @@ int fp_toradix_n(fp_int * a, char *str, int radix, int maxlen);
|
||||
void s_fp_add(fp_int *a, fp_int *b, fp_int *c);
|
||||
void s_fp_sub(fp_int *a, fp_int *b, fp_int *c);
|
||||
void bn_reverse(unsigned char *s, int len);
|
||||
|
||||
void fp_mul_comba(fp_int *A, fp_int *B, fp_int *C);
|
||||
|
||||
#ifdef TFM_SMALL_SET
|
||||
void fp_mul_comba_small(fp_int *A, fp_int *B, fp_int *C);
|
||||
#endif
|
||||
|
||||
#ifdef TFM_HUGE
|
||||
void fp_mul_comba32(fp_int *A, fp_int *B, fp_int *C);
|
||||
void fp_mul_comba48(fp_int *A, fp_int *B, fp_int *C);
|
||||
void fp_mul_comba64(fp_int *A, fp_int *B, fp_int *C);
|
||||
#endif
|
||||
void fp_mul_comba_small(fp_int *A, fp_int *B, fp_int *C);
|
||||
|
||||
void fp_sqr_comba(fp_int *A, fp_int *B);
|
||||
|
||||
#ifdef TFM_SMALL_SET
|
||||
void fp_sqr_comba_small(fp_int *A, fp_int *B);
|
||||
#endif
|
||||
|
||||
#ifdef TFM_HUGE
|
||||
void fp_sqr_comba32(fp_int *A, fp_int *B);
|
||||
void fp_sqr_comba48(fp_int *A, fp_int *B);
|
||||
|
||||
58
tfm.idx
58
tfm.idx
@ -1,29 +1,29 @@
|
||||
\indexentry{fp\_init|hyperpage}{6}
|
||||
\indexentry{fp\_set|hyperpage}{6}
|
||||
\indexentry{fp\_init\_copy|hyperpage}{6}
|
||||
\indexentry{fp\_iszero|hyperpage}{7}
|
||||
\indexentry{fp\_iseven|hyperpage}{7}
|
||||
\indexentry{fp\_isodd|hyperpage}{7}
|
||||
\indexentry{fp\_neg|hyperpage}{7}
|
||||
\indexentry{fp\_abs|hyperpage}{7}
|
||||
\indexentry{fp\_cmp|hyperpage}{8}
|
||||
\indexentry{fp\_cmp\_mag|hyperpage}{8}
|
||||
\indexentry{fp\_lshd|hyperpage}{8}
|
||||
\indexentry{fp\_rshd|hyperpage}{8}
|
||||
\indexentry{fp\_div\_2d|hyperpage}{8}
|
||||
\indexentry{fp\_mod\_2d|hyperpage}{8}
|
||||
\indexentry{fp\_mul\_2d|hyperpage}{8}
|
||||
\indexentry{fp\_div\_2|hyperpage}{8}
|
||||
\indexentry{fp\_mul\_2|hyperpage}{8}
|
||||
\indexentry{fp\_cnt\_lsb|hyperpage}{8}
|
||||
\indexentry{fp\_add|hyperpage}{9}
|
||||
\indexentry{fp\_sub|hyperpage}{9}
|
||||
\indexentry{fp\_mul|hyperpage}{9}
|
||||
\indexentry{fp\_sqr|hyperpage}{9}
|
||||
\indexentry{fp\_div|hyperpage}{9}
|
||||
\indexentry{fp\_mod|hyperpage}{9}
|
||||
\indexentry{fp\_exptmod|hyperpage}{9}
|
||||
\indexentry{fp\_invmod|hyperpage}{9}
|
||||
\indexentry{fp\_gcd|hyperpage}{9}
|
||||
\indexentry{fp\_lcm|hyperpage}{9}
|
||||
\indexentry{fp\_isprime|hyperpage}{10}
|
||||
\indexentry{fp\_init|hyperpage}{8}
|
||||
\indexentry{fp\_set|hyperpage}{8}
|
||||
\indexentry{fp\_init\_copy|hyperpage}{8}
|
||||
\indexentry{fp\_iszero|hyperpage}{9}
|
||||
\indexentry{fp\_iseven|hyperpage}{9}
|
||||
\indexentry{fp\_isodd|hyperpage}{9}
|
||||
\indexentry{fp\_neg|hyperpage}{9}
|
||||
\indexentry{fp\_abs|hyperpage}{9}
|
||||
\indexentry{fp\_cmp|hyperpage}{10}
|
||||
\indexentry{fp\_cmp\_mag|hyperpage}{10}
|
||||
\indexentry{fp\_lshd|hyperpage}{10}
|
||||
\indexentry{fp\_rshd|hyperpage}{10}
|
||||
\indexentry{fp\_div\_2d|hyperpage}{10}
|
||||
\indexentry{fp\_mod\_2d|hyperpage}{10}
|
||||
\indexentry{fp\_mul\_2d|hyperpage}{10}
|
||||
\indexentry{fp\_div\_2|hyperpage}{10}
|
||||
\indexentry{fp\_mul\_2|hyperpage}{10}
|
||||
\indexentry{fp\_cnt\_lsb|hyperpage}{10}
|
||||
\indexentry{fp\_add|hyperpage}{11}
|
||||
\indexentry{fp\_sub|hyperpage}{11}
|
||||
\indexentry{fp\_mul|hyperpage}{11}
|
||||
\indexentry{fp\_sqr|hyperpage}{11}
|
||||
\indexentry{fp\_div|hyperpage}{11}
|
||||
\indexentry{fp\_mod|hyperpage}{11}
|
||||
\indexentry{fp\_exptmod|hyperpage}{11}
|
||||
\indexentry{fp\_invmod|hyperpage}{11}
|
||||
\indexentry{fp\_gcd|hyperpage}{11}
|
||||
\indexentry{fp\_lcm|hyperpage}{11}
|
||||
\indexentry{fp\_isprime|hyperpage}{12}
|
||||
|
||||
58
tfm.ind
58
tfm.ind
@ -1,33 +1,33 @@
|
||||
\begin{theindex}
|
||||
|
||||
\item fp\_abs, \hyperpage{7}
|
||||
\item fp\_add, \hyperpage{9}
|
||||
\item fp\_cmp, \hyperpage{8}
|
||||
\item fp\_cmp\_mag, \hyperpage{8}
|
||||
\item fp\_cnt\_lsb, \hyperpage{8}
|
||||
\item fp\_div, \hyperpage{9}
|
||||
\item fp\_div\_2, \hyperpage{8}
|
||||
\item fp\_div\_2d, \hyperpage{8}
|
||||
\item fp\_exptmod, \hyperpage{9}
|
||||
\item fp\_gcd, \hyperpage{9}
|
||||
\item fp\_init, \hyperpage{6}
|
||||
\item fp\_init\_copy, \hyperpage{6}
|
||||
\item fp\_invmod, \hyperpage{9}
|
||||
\item fp\_iseven, \hyperpage{7}
|
||||
\item fp\_isodd, \hyperpage{7}
|
||||
\item fp\_isprime, \hyperpage{10}
|
||||
\item fp\_iszero, \hyperpage{7}
|
||||
\item fp\_lcm, \hyperpage{9}
|
||||
\item fp\_lshd, \hyperpage{8}
|
||||
\item fp\_mod, \hyperpage{9}
|
||||
\item fp\_mod\_2d, \hyperpage{8}
|
||||
\item fp\_mul, \hyperpage{9}
|
||||
\item fp\_mul\_2, \hyperpage{8}
|
||||
\item fp\_mul\_2d, \hyperpage{8}
|
||||
\item fp\_neg, \hyperpage{7}
|
||||
\item fp\_rshd, \hyperpage{8}
|
||||
\item fp\_set, \hyperpage{6}
|
||||
\item fp\_sqr, \hyperpage{9}
|
||||
\item fp\_sub, \hyperpage{9}
|
||||
\item fp\_abs, \hyperpage{9}
|
||||
\item fp\_add, \hyperpage{11}
|
||||
\item fp\_cmp, \hyperpage{10}
|
||||
\item fp\_cmp\_mag, \hyperpage{10}
|
||||
\item fp\_cnt\_lsb, \hyperpage{10}
|
||||
\item fp\_div, \hyperpage{11}
|
||||
\item fp\_div\_2, \hyperpage{10}
|
||||
\item fp\_div\_2d, \hyperpage{10}
|
||||
\item fp\_exptmod, \hyperpage{11}
|
||||
\item fp\_gcd, \hyperpage{11}
|
||||
\item fp\_init, \hyperpage{8}
|
||||
\item fp\_init\_copy, \hyperpage{8}
|
||||
\item fp\_invmod, \hyperpage{11}
|
||||
\item fp\_iseven, \hyperpage{9}
|
||||
\item fp\_isodd, \hyperpage{9}
|
||||
\item fp\_isprime, \hyperpage{12}
|
||||
\item fp\_iszero, \hyperpage{9}
|
||||
\item fp\_lcm, \hyperpage{11}
|
||||
\item fp\_lshd, \hyperpage{10}
|
||||
\item fp\_mod, \hyperpage{11}
|
||||
\item fp\_mod\_2d, \hyperpage{10}
|
||||
\item fp\_mul, \hyperpage{11}
|
||||
\item fp\_mul\_2, \hyperpage{10}
|
||||
\item fp\_mul\_2d, \hyperpage{10}
|
||||
\item fp\_neg, \hyperpage{9}
|
||||
\item fp\_rshd, \hyperpage{10}
|
||||
\item fp\_set, \hyperpage{8}
|
||||
\item fp\_sqr, \hyperpage{11}
|
||||
\item fp\_sub, \hyperpage{11}
|
||||
|
||||
\end{theindex}
|
||||
|
||||
52
tfm.log
52
tfm.log
@ -1,4 +1,4 @@
|
||||
This is pdfeTeX, Version 3.141592-1.21a-2.2 (Web2C 7.5.4) (format=latex 2005.4.10) 23 JUL 2005 07:42
|
||||
This is pdfeTeX, Version 3.141592-1.21a-2.2 (Web2C 7.5.4) (format=latex 2005.4.10) 1 AUG 2005 13:34
|
||||
entering extended mode
|
||||
**tfm
|
||||
(./tfm.tex
|
||||
@ -216,107 +216,107 @@ File: umsb.fd 2002/01/19 v2.2g AMS font definitions
|
||||
Chapter 1.
|
||||
[1
|
||||
|
||||
] [2] [3] [4]
|
||||
] [2] [3] [4] [5] [6
|
||||
|
||||
]
|
||||
Chapter 2.
|
||||
|
||||
Underfull \vbox (badness 7649) has occurred while \output is active []
|
||||
|
||||
[5
|
||||
|
||||
]
|
||||
[6]
|
||||
[7]
|
||||
[8]
|
||||
Chapter 3.
|
||||
[7
|
||||
[9
|
||||
|
||||
] [8] [9] [10]
|
||||
] [10] [11] [12]
|
||||
Chapter 4.
|
||||
[11
|
||||
[13
|
||||
|
||||
] [12] [13]
|
||||
Overfull \hbox (74.99634pt too wide) in paragraph at lines 547--547
|
||||
] [14] [15]
|
||||
Overfull \hbox (74.99634pt too wide) in paragraph at lines 559--559
|
||||
[]\OT1/cmtt/m/n/10 #define SQRADDSC(i, j)
|
||||
\[]
|
||||
[]
|
||||
|
||||
|
||||
Overfull \hbox (74.99634pt too wide) in paragraph at lines 547--547
|
||||
Overfull \hbox (74.99634pt too wide) in paragraph at lines 559--559
|
||||
[] \OT1/cmtt/m/n/10 do { fp_word t;
|
||||
\[]
|
||||
[]
|
||||
|
||||
|
||||
Overfull \hbox (74.99634pt too wide) in paragraph at lines 547--547
|
||||
Overfull \hbox (74.99634pt too wide) in paragraph at lines 559--559
|
||||
[] \OT1/cmtt/m/n/10 t = ((fp_word)i) * ((fp_word)j);
|
||||
\[]
|
||||
[]
|
||||
|
||||
|
||||
Overfull \hbox (74.99634pt too wide) in paragraph at lines 547--547
|
||||
Overfull \hbox (74.99634pt too wide) in paragraph at lines 559--559
|
||||
[] \OT1/cmtt/m/n/10 sc0 = (fp_digit)t; sc1 = (t >> DIGIT_BIT); sc2 = 0;
|
||||
\[]
|
||||
[]
|
||||
|
||||
|
||||
Overfull \hbox (25.129pt too wide) in paragraph at lines 548--549
|
||||
Overfull \hbox (25.129pt too wide) in paragraph at lines 560--561
|
||||
\OT1/cmr/m/n/10 This com-putes a prod-uct and stores it in the ``sec-ondary'' c
|
||||
arry reg-is-ters $[]$.
|
||||
[]
|
||||
|
||||
|
||||
Overfull \hbox (74.99634pt too wide) in paragraph at lines 556--556
|
||||
Overfull \hbox (74.99634pt too wide) in paragraph at lines 568--568
|
||||
[]\OT1/cmtt/m/n/10 #define SQRADDAC(i, j)
|
||||
\[]
|
||||
[]
|
||||
|
||||
|
||||
Overfull \hbox (74.99634pt too wide) in paragraph at lines 556--556
|
||||
Overfull \hbox (74.99634pt too wide) in paragraph at lines 568--568
|
||||
[] \OT1/cmtt/m/n/10 do { fp_word t;
|
||||
\[]
|
||||
[]
|
||||
|
||||
|
||||
Overfull \hbox (74.99634pt too wide) in paragraph at lines 556--556
|
||||
Overfull \hbox (74.99634pt too wide) in paragraph at lines 568--568
|
||||
[] \OT1/cmtt/m/n/10 t = sc0 + ((fp_word)i) * ((fp_word)j); sc0 = t;
|
||||
\[]
|
||||
[]
|
||||
|
||||
|
||||
Overfull \hbox (74.99634pt too wide) in paragraph at lines 556--556
|
||||
Overfull \hbox (74.99634pt too wide) in paragraph at lines 568--568
|
||||
[] \OT1/cmtt/m/n/10 t = sc1 + (t >> DIGIT_BIT); sc1 = t; sc2 += t
|
||||
>> DIGIT_BIT; \[]
|
||||
[]
|
||||
|
||||
|
||||
Overfull \hbox (74.99634pt too wide) in paragraph at lines 566--566
|
||||
Overfull \hbox (74.99634pt too wide) in paragraph at lines 578--578
|
||||
[]\OT1/cmtt/m/n/10 #define SQRADDDB
|
||||
\[]
|
||||
[]
|
||||
|
||||
|
||||
Overfull \hbox (74.99634pt too wide) in paragraph at lines 566--566
|
||||
Overfull \hbox (74.99634pt too wide) in paragraph at lines 578--578
|
||||
[] \OT1/cmtt/m/n/10 do { fp_word t;
|
||||
\[]
|
||||
[]
|
||||
|
||||
|
||||
Overfull \hbox (190.49533pt too wide) in paragraph at lines 566--566
|
||||
Overfull \hbox (190.49533pt too wide) in paragraph at lines 578--578
|
||||
[] \OT1/cmtt/m/n/10 t = ((fp_word)sc0) + ((fp_word)sc0) + c0; c0 = t;
|
||||
\[]
|
||||
[]
|
||||
|
||||
|
||||
Overfull \hbox (190.49533pt too wide) in paragraph at lines 566--566
|
||||
Overfull \hbox (190.49533pt too wide) in paragraph at lines 578--578
|
||||
[] \OT1/cmtt/m/n/10 t = ((fp_word)sc1) + ((fp_word)sc1) + c1 + (t >> DIGIT_BI
|
||||
T); c1 = t; \[]
|
||||
[]
|
||||
|
||||
|
||||
Overfull \hbox (190.49533pt too wide) in paragraph at lines 566--566
|
||||
Overfull \hbox (190.49533pt too wide) in paragraph at lines 578--578
|
||||
[] \OT1/cmtt/m/n/10 c2 = c2 + ((fp_word)sc2) + ((fp_word)sc2) + (t >> DIGIT_B
|
||||
IT); \[]
|
||||
[]
|
||||
|
||||
[14] [15] (./tfm.ind [16] [17
|
||||
[16] [17] (./tfm.ind [18] [19
|
||||
|
||||
|
||||
]) (./tfm.aux) )
|
||||
@ -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 (23 pages, 49708 bytes).
|
||||
Output written on tfm.dvi (25 pages, 51612 bytes).
|
||||
|
||||
30
tfm.tex
30
tfm.tex
@ -49,8 +49,8 @@
|
||||
\begin{document}
|
||||
\frontmatter
|
||||
\pagestyle{empty}
|
||||
\title{TomsFastMath User Manual \\ v0.04}
|
||||
\author{Tom St Denis \\ tomstdenis@iahu.ca}
|
||||
\title{TomsFastMath User Manual \\ v0.05}
|
||||
\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
|
||||
[176x250] paper using the \LaTeX{} {\em book} macro package.
|
||||
@ -101,14 +101,26 @@ fast multiplication and squaring and has the side effect of speeding up ECC oper
|
||||
TomsFastMath is public domain.
|
||||
|
||||
\section{Building}
|
||||
Currently only a GCC makefile has been provided. To build the library simply type
|
||||
``make''. The library is a bit too new to put into production so no install
|
||||
scripts exist yet. You can build the test program with ``make test''.
|
||||
To build the library simply type ``make''. Or to install in typical *unix like directories use
|
||||
``make install''. Similarly a shared library can be built with ``make -f makefile.shared install''.
|
||||
|
||||
To perform simple static testing (useful to test out new assembly ports) use the stest
|
||||
program. Type ``make stest'' and run it on your target. The program will perform three
|
||||
multiplications, squarings and montgomery reductions. Likely if your assembly
|
||||
code is invalid this code will exhibit the bug.
|
||||
You can build the test program with ``make test''. To perform simple static testing (useful to
|
||||
test out new assembly ports) use the stest program. Type ``make stest'' and run it on your
|
||||
target. The program will perform three multiplications, squarings and montgomery reductions.
|
||||
Likely if your assembly code is invalid this code will exhibit the bug.
|
||||
|
||||
\subsection{Intel CC}
|
||||
In theory you should be able to build the library with
|
||||
|
||||
\begin{verbatim}
|
||||
CFLAGS="-O3 -ip" CC=icc make IGNORE_SPEED=1
|
||||
\end{verbatim}
|
||||
|
||||
However, Intels inline assembler is way less advanced than GCCs. As a result it doesn't compile.
|
||||
Fortunately it doesn't really matter.
|
||||
|
||||
\subsection{MSVC}
|
||||
The library doesn't build with MSVC. Imagine that.
|
||||
|
||||
\subsection{Build Limitations}
|
||||
TomsFastMath has the following build requirements which are non--portable but under most
|
||||
|
||||
54
tfm.toc
54
tfm.toc
@ -2,32 +2,34 @@
|
||||
\contentsline {section}{\numberline {1.1}What is TomsFastMath?}{1}{section.1.1}
|
||||
\contentsline {section}{\numberline {1.2}License}{2}{section.1.2}
|
||||
\contentsline {section}{\numberline {1.3}Building}{2}{section.1.3}
|
||||
\contentsline {subsection}{\numberline {1.3.1}Build Limitations}{2}{subsection.1.3.1}
|
||||
\contentsline {subsection}{\numberline {1.3.2}Optimization Configuration}{2}{subsection.1.3.2}
|
||||
\contentsline {subsection}{\numberline {1.3.1}Intel CC}{2}{subsection.1.3.1}
|
||||
\contentsline {subsection}{\numberline {1.3.2}MSVC}{2}{subsection.1.3.2}
|
||||
\contentsline {subsection}{\numberline {1.3.3}Build Limitations}{3}{subsection.1.3.3}
|
||||
\contentsline {subsection}{\numberline {1.3.4}Optimization Configuration}{3}{subsection.1.3.4}
|
||||
\contentsline {subsubsection}{x86--32}{3}{section*.3}
|
||||
\contentsline {subsubsection}{SSE2}{3}{section*.4}
|
||||
\contentsline {subsubsection}{x86--64}{3}{section*.5}
|
||||
\contentsline {subsubsection}{ARM}{3}{section*.6}
|
||||
\contentsline {subsubsection}{PPC32}{3}{section*.7}
|
||||
\contentsline {subsubsection}{x86--64}{4}{section*.5}
|
||||
\contentsline {subsubsection}{ARM}{4}{section*.6}
|
||||
\contentsline {subsubsection}{PPC32}{4}{section*.7}
|
||||
\contentsline {subsubsection}{Future Releases}{4}{section*.8}
|
||||
\contentsline {subsection}{\numberline {1.3.3}Precision Configuration}{4}{subsection.1.3.3}
|
||||
\contentsline {chapter}{\numberline {2}Getting Started}{5}{chapter.2}
|
||||
\contentsline {section}{\numberline {2.1}Data Types}{5}{section.2.1}
|
||||
\contentsline {section}{\numberline {2.2}Initialization}{6}{section.2.2}
|
||||
\contentsline {subsection}{\numberline {2.2.1}Simple Initialization}{6}{subsection.2.2.1}
|
||||
\contentsline {subsection}{\numberline {2.2.2}Initialize Small Constants}{6}{subsection.2.2.2}
|
||||
\contentsline {subsection}{\numberline {2.2.3}Initialize Copy}{6}{subsection.2.2.3}
|
||||
\contentsline {chapter}{\numberline {3}Arithmetic Operations}{7}{chapter.3}
|
||||
\contentsline {section}{\numberline {3.1}Odds and Evens}{7}{section.3.1}
|
||||
\contentsline {section}{\numberline {3.2}Sign Manipulation}{7}{section.3.2}
|
||||
\contentsline {section}{\numberline {3.3}Comparisons}{8}{section.3.3}
|
||||
\contentsline {section}{\numberline {3.4}Shifting}{8}{section.3.4}
|
||||
\contentsline {section}{\numberline {3.5}Basic Algebra}{9}{section.3.5}
|
||||
\contentsline {section}{\numberline {3.6}Modular Exponentiation}{9}{section.3.6}
|
||||
\contentsline {section}{\numberline {3.7}Number Theoretic}{9}{section.3.7}
|
||||
\contentsline {section}{\numberline {3.8}Prime Numbers}{10}{section.3.8}
|
||||
\contentsline {chapter}{\numberline {4}Porting TomsFastMath}{11}{chapter.4}
|
||||
\contentsline {section}{\numberline {4.1}Getting Started}{11}{section.4.1}
|
||||
\contentsline {section}{\numberline {4.2}Multiply with Comba}{11}{section.4.2}
|
||||
\contentsline {section}{\numberline {4.3}Squaring with Comba}{13}{section.4.3}
|
||||
\contentsline {section}{\numberline {4.4}Montgomery with Comba}{15}{section.4.4}
|
||||
\contentsline {subsection}{\numberline {1.3.5}Precision Configuration}{5}{subsection.1.3.5}
|
||||
\contentsline {chapter}{\numberline {2}Getting Started}{7}{chapter.2}
|
||||
\contentsline {section}{\numberline {2.1}Data Types}{7}{section.2.1}
|
||||
\contentsline {section}{\numberline {2.2}Initialization}{8}{section.2.2}
|
||||
\contentsline {subsection}{\numberline {2.2.1}Simple Initialization}{8}{subsection.2.2.1}
|
||||
\contentsline {subsection}{\numberline {2.2.2}Initialize Small Constants}{8}{subsection.2.2.2}
|
||||
\contentsline {subsection}{\numberline {2.2.3}Initialize Copy}{8}{subsection.2.2.3}
|
||||
\contentsline {chapter}{\numberline {3}Arithmetic Operations}{9}{chapter.3}
|
||||
\contentsline {section}{\numberline {3.1}Odds and Evens}{9}{section.3.1}
|
||||
\contentsline {section}{\numberline {3.2}Sign Manipulation}{9}{section.3.2}
|
||||
\contentsline {section}{\numberline {3.3}Comparisons}{10}{section.3.3}
|
||||
\contentsline {section}{\numberline {3.4}Shifting}{10}{section.3.4}
|
||||
\contentsline {section}{\numberline {3.5}Basic Algebra}{11}{section.3.5}
|
||||
\contentsline {section}{\numberline {3.6}Modular Exponentiation}{11}{section.3.6}
|
||||
\contentsline {section}{\numberline {3.7}Number Theoretic}{11}{section.3.7}
|
||||
\contentsline {section}{\numberline {3.8}Prime Numbers}{12}{section.3.8}
|
||||
\contentsline {chapter}{\numberline {4}Porting TomsFastMath}{13}{chapter.4}
|
||||
\contentsline {section}{\numberline {4.1}Getting Started}{13}{section.4.1}
|
||||
\contentsline {section}{\numberline {4.2}Multiply with Comba}{13}{section.4.2}
|
||||
\contentsline {section}{\numberline {4.3}Squaring with Comba}{15}{section.4.3}
|
||||
\contentsline {section}{\numberline {4.4}Montgomery with Comba}{17}{section.4.4}
|
||||
|
||||
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Reference in New Issue
Block a user