+++ /dev/null
-/* -*-c-*-
- *
- * $Id$
- *
- * Efficient reduction modulo nice primes
- *
- * (c) 2004 Straylight/Edgeware
- */
-
-/*----- Licensing notice --------------------------------------------------*
- *
- * This file is part of Catacomb.
- *
- * Catacomb is free software; you can redistribute it and/or modify
- * it under the terms of the GNU Library General Public License as
- * published by the Free Software Foundation; either version 2 of the
- * License, or (at your option) any later version.
- *
- * Catacomb is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU Library General Public License for more details.
- *
- * You should have received a copy of the GNU Library General Public
- * License along with Catacomb; if not, write to the Free
- * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- */
-
-/*----- Header files ------------------------------------------------------*/
-
-#include <mLib/darray.h>
-#include <mLib/macros.h>
-
-#include "mp.h"
-#include "mpreduce.h"
-#include "mpreduce-exp.h"
-
-/*----- Data structures ---------------------------------------------------*/
-
-DA_DECL(instr_v, mpreduce_instr);
-
-/*----- Main code ---------------------------------------------------------*/
-
-/* --- @mpreduce_create@ --- *
- *
- * Arguments: @gfreduce *r@ = structure to fill in
- * @mp *x@ = an integer
- *
- * Returns: Zero if successful; nonzero on failure.
- *
- * Use: Initializes a context structure for reduction.
- */
-
-int mpreduce_create(mpreduce *r, mp *p)
-{
- mpscan sc;
- enum { Z = 0, Z1 = 2, X = 4, X0 = 6 };
- unsigned st = Z;
- instr_v iv = DA_INIT;
- unsigned long d, i;
- unsigned op;
- size_t w, b, bb;
-
- /* --- Fill in the easy stuff --- */
-
- if (!MP_POSP(p))
- return (-1);
- d = mp_bits(p);
- r->lim = d/MPW_BITS;
- r->s = d%MPW_BITS;
- if (r->s)
- r->lim++;
- r->p = mp_copy(p);
-
- /* --- Stash a new instruction --- */
-
-#define INSTR(op_, argx_, argy_) do { \
- DA_ENSURE(&iv, 1); \
- DA(&iv)[DA_LEN(&iv)].op = (op_); \
- DA(&iv)[DA_LEN(&iv)].argx = (argx_); \
- DA(&iv)[DA_LEN(&iv)].argy = (argy_); \
- DA_EXTEND(&iv, 1); \
-} while (0)
-
- /* --- Main loop --- *
- *
- * A simple state machine decomposes @p@ conveniently into positive and
- * negative powers of 2. The pure form of the state machine is left below
- * for reference (and in case I need inspiration for a NAF exponentiator).
- */
-
-#ifdef DEBUG
- for (i = 0, mp_scan(&sc, p); mp_step(&sc); i++) {
- switch (st | mp_bit(&sc)) {
- case Z | 1: st = Z1; break;
- case Z1 | 0: st = Z; printf("+ %lu\n", i - 1); break;
- case Z1 | 1: st = X; printf("- %lu\n", i - 1); break;
- case X | 0: st = X0; break;
- case X0 | 1: st = X; printf("- %lu\n", i - 1); break;
- case X0 | 0: st = Z; printf("+ %lu\n", i - 1); break;
- }
- }
- if (st >= X) printf("+ %lu\n", i - 1);
- st = Z;
-#endif
-
- bb = MPW_BITS - (d + 1)%MPW_BITS;
- for (i = 0, mp_scan(&sc, p); i < d && mp_step(&sc); i++) {
- switch (st | mp_bit(&sc)) {
- case Z | 1: st = Z1; break;
- case Z1 | 0: st = Z; op = MPRI_SUB; goto instr;
- case Z1 | 1: st = X; op = MPRI_ADD; goto instr;
- case X | 0: st = X0; break;
- case X0 | 1: st = X; op = MPRI_ADD; goto instr;
- case X0 | 0: st = Z; op = MPRI_SUB; goto instr;
- instr:
- w = (d - i)/MPW_BITS + 1;
- b = (bb + i)%MPW_BITS;
- INSTR(op | !!b, w, b);
- }
- }
- if (DA_LEN(&iv) && (DA(&iv)[DA_LEN(&iv) - 1].op & ~1u) == MPRI_SUB) {
- mp_drop(r->p);
- DA_DESTROY(&iv);
- return (-1);
- }
-
-#undef INSTR
-
- /* --- Wrap up --- */
-
- r->in = DA_LEN(&iv);
- if (!r->in)
- r->iv = 0;
- else if (!r->s) {
- r->iv = xmalloc(r->in * sizeof(mpreduce_instr));
- memcpy(r->iv, DA(&iv), r->in * sizeof(mpreduce_instr));
- } else {
- r->iv = xmalloc(r->in * 2 * sizeof(mpreduce_instr));
- for (i = 0; i < r->in; i++) {
- r->iv[i] = DA(&iv)[i];
- op = r->iv[i].op & ~1u;
- w = r->iv[i].argx;
- b = r->iv[i].argy;
- b += r->s;
- if (b >= MPW_BITS) {
- b -= MPW_BITS;
- w--;
- }
- if (b) op |= 1;
- r->iv[i + r->in].op = op;
- r->iv[i + r->in].argx = w;
- r->iv[i + r->in].argy = b;
- }
- }
- DA_DESTROY(&iv);
-
-#ifdef DEBUG
- mpreduce_dump(r, stdout);
-#endif
- return (0);
-}
-
-/* --- @mpreduce_destroy@ --- *
- *
- * Arguments: @mpreduce *r@ = structure to free
- *
- * Returns: ---
- *
- * Use: Reclaims the resources from a reduction context.
- */
-
-void mpreduce_destroy(mpreduce *r)
-{
- mp_drop(r->p);
- if (r->iv) xfree(r->iv);
-}
-
-/* --- @mpreduce_dump@ --- *
- *
- * Arguments: @mpreduce *r@ = structure to dump
- * @FILE *fp@ = file to dump on
- *
- * Returns: ---
- *
- * Use: Dumps a reduction context.
- */
-
-void mpreduce_dump(mpreduce *r, FILE *fp)
-{
- size_t i;
- static const char *opname[] = { "add", "addshift", "sub", "subshift" };
-
- fprintf(fp, "mod = "); mp_writefile(r->p, fp, 16);
- fprintf(fp, "\n lim = %lu; s = %d\n", (unsigned long)r->lim, r->s);
- for (i = 0; i < r->in; i++) {
- assert(r->iv[i].op < N(opname));
- fprintf(fp, " %s %lu %lu\n",
- opname[r->iv[i].op],
- (unsigned long)r->iv[i].argx,
- (unsigned long)r->iv[i].argy);
- }
- if (r->s) {
- fprintf(fp, "tail end charlie\n");
- for (i = r->in; i < 2 * r->in; i++) {
- assert(r->iv[i].op < N(opname));
- fprintf(fp, " %s %lu %lu\n",
- opname[r->iv[i].op],
- (unsigned long)r->iv[i].argx,
- (unsigned long)r->iv[i].argy);
- }
- }
-}
-
-/* --- @mpreduce_do@ --- *
- *
- * Arguments: @mpreduce *r@ = reduction context
- * @mp *d@ = destination
- * @mp *x@ = source
- *
- * Returns: Destination, @x@ reduced modulo the reduction poly.
- */
-
-static void run(const mpreduce_instr *i, const mpreduce_instr *il,
- mpw *v, mpw z)
-{
- for (; i < il; i++) {
-#ifdef DEBUG
- mp vv;
- mp_build(&vv, v - i->argx, v + 1);
- printf(" 0x"); mp_writefile(&vv, stdout, 16);
- printf(" %c (0x%lx << %u) == 0x",
- (i->op & ~1u) == MPRI_ADD ? '+' : '-',
- (unsigned long)z,
- i->argy);
-#endif
- switch (i->op) {
- case MPRI_ADD: MPX_UADDN(v - i->argx, v + 1, z); break;
- case MPRI_ADDLSL: mpx_uaddnlsl(v - i->argx, v + 1, z, i->argy); break;
- case MPRI_SUB: MPX_USUBN(v - i->argx, v + 1, z); break;
- case MPRI_SUBLSL: mpx_usubnlsl(v - i->argx, v + 1, z, i->argy); break;
- default:
- abort();
- }
-#ifdef DEBUG
- mp_build(&vv, v - i->argx, v + 1);
- mp_writefile(&vv, stdout, 16);
- printf("\n");
-#endif
- }
-}
-
-mp *mpreduce_do(mpreduce *r, mp *d, mp *x)
-{
- mpw *v, *vl;
- const mpreduce_instr *il;
- mpw z;
-
-#ifdef DEBUG
- mp *_r = 0, *_rr = 0;
-#endif
-
- /* --- If source is negative, divide --- */
-
- if (MP_NEGP(x)) {
- mp_div(0, &d, x, r->p);
- return (d);
- }
-
- /* --- Try to reuse the source's space --- */
-
- MP_COPY(x);
- if (d) MP_DROP(d);
- MP_DEST(x, MP_LEN(x), x->f);
-
- /* --- Do the reduction --- */
-
-#ifdef DEBUG
- _r = MP_NEW;
- mp_div(0, &_r, x, r->p);
- MP_PRINTX("x", x);
- _rr = 0;
-#endif
-
- il = r->iv + r->in;
- if (MP_LEN(x) >= r->lim) {
- v = x->v + r->lim;
- vl = x->vl;
- while (vl-- > v) {
- while (*vl) {
- z = *vl;
- *vl = 0;
- run(r->iv, il, vl, z);
-#ifdef DEBUG
- MP_PRINTX("x", x);
- mp_div(0, &_rr, x, r->p);
- assert(MP_EQ(_r, _rr));
-#endif
- }
- }
- if (r->s) {
- while (*vl >> r->s) {
- z = *vl >> r->s;
- *vl &= ((1 << r->s) - 1);
- run(r->iv + r->in, il + r->in, vl, z);
-#ifdef DEBUG
- MP_PRINTX("x", x);
- mp_div(0, &_rr, x, r->p);
- assert(MP_EQ(_r, _rr));
-#endif
- }
- }
- }
-
- /* --- Finishing touches --- */
-
- MP_SHRINK(x);
- if (MP_CMP(x, >=, r->p))
- x = mp_sub(x, x, r->p);
-
- /* --- Done --- */
-
-#ifdef DEBUG
- assert(MP_EQ(_r, x));
- mp_drop(_r);
- mp_drop(_rr);
-#endif
- return (x);
-}
-
-/* --- @mpreduce_exp@ --- *
- *
- * Arguments: @mpreduce *mr@ = pointer to reduction context
- * @mp *d@ = fake destination
- * @mp *a@ = base
- * @mp *e@ = exponent
- *
- * Returns: Result, %$a^e \bmod m$%.
- */
-
-mp *mpreduce_exp(mpreduce *mr, mp *d, mp *a, mp *e)
-{
- mp *x = MP_ONE;
- mp *spare = (e->f & MP_BURN) ? MP_NEWSEC : MP_NEW;
-
- MP_SHRINK(e);
- MP_COPY(a);
- if (MP_ZEROP(e))
- ;
- else {
- if (MP_NEGP(e))
- a = mp_modinv(a, a, mr->p);
- if (MP_LEN(e) < EXP_THRESH)
- EXP_SIMPLE(x, a, e);
- else
- EXP_WINDOW(x, a, e);
- }
- mp_drop(a);
- mp_drop(d);
- mp_drop(spare);
- return (x);
-}
-
-/*----- Test rig ----------------------------------------------------------*/
-
-
-#ifdef TEST_RIG
-
-#define MP(x) mp_readstring(MP_NEW, #x, 0, 0)
-
-static int vreduce(dstr *v)
-{
- mp *d = *(mp **)v[0].buf;
- mp *n = *(mp **)v[1].buf;
- mp *r = *(mp **)v[2].buf;
- mp *c;
- int ok = 1;
- mpreduce rr;
-
- mpreduce_create(&rr, d);
- c = mpreduce_do(&rr, MP_NEW, n);
- if (!MP_EQ(c, r)) {
- fprintf(stderr, "\n*** reduction failed\n*** ");
- mpreduce_dump(&rr, stderr);
- fprintf(stderr, "\n*** n = "); mp_writefile(n, stderr, 10);
- fprintf(stderr, "\n*** r = "); mp_writefile(r, stderr, 10);
- fprintf(stderr, "\n*** c = "); mp_writefile(c, stderr, 10);
- fprintf(stderr, "\n");
- ok = 0;
- }
- mpreduce_destroy(&rr);
- mp_drop(n); mp_drop(d); mp_drop(r); mp_drop(c);
- assert(mparena_count(MPARENA_GLOBAL) == 0);
- return (ok);
-}
-
-static int vmodexp(dstr *v)
-{
- mp *p = *(mp **)v[0].buf;
- mp *g = *(mp **)v[1].buf;
- mp *x = *(mp **)v[2].buf;
- mp *r = *(mp **)v[3].buf;
- mp *c;
- int ok = 1;
- mpreduce rr;
-
- mpreduce_create(&rr, p);
- c = mpreduce_exp(&rr, MP_NEW, g, x);
- if (!MP_EQ(c, r)) {
- fprintf(stderr, "\n*** modexp failed\n*** ");
- fprintf(stderr, "\n*** p = "); mp_writefile(p, stderr, 10);
- fprintf(stderr, "\n*** g = "); mp_writefile(g, stderr, 10);
- fprintf(stderr, "\n*** x = "); mp_writefile(x, stderr, 10);
- fprintf(stderr, "\n*** c = "); mp_writefile(c, stderr, 10);
- fprintf(stderr, "\n*** r = "); mp_writefile(r, stderr, 10);
- fprintf(stderr, "\n");
- ok = 0;
- }
- mpreduce_destroy(&rr);
- mp_drop(p); mp_drop(g); mp_drop(r); mp_drop(x); mp_drop(c);
- assert(mparena_count(MPARENA_GLOBAL) == 0);
- return (ok);
-}
-
-static test_chunk defs[] = {
- { "reduce", vreduce, { &type_mp, &type_mp, &type_mp, 0 } },
- { "modexp", vmodexp, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
- { 0, 0, { 0 } }
-};
-
-int main(int argc, char *argv[])
-{
- test_run(argc, argv, defs, SRCDIR"/tests/mpreduce");
- return (0);
-}
-
-#endif
-
-/*----- That's all, folks -------------------------------------------------*/