+++ /dev/null
-/* -*-c-*-
- *
- * $Id$
- *
- * Efficient reduction modulo sparse binary polynomials
- *
- * (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/alloc.h>
-#include <mLib/darray.h>
-#include <mLib/macros.h>
-
-#include "gf.h"
-#include "gfreduce.h"
-#include "gfreduce-exp.h"
-#include "fibrand.h"
-#include "mprand.h"
-
-/*----- Data structures ---------------------------------------------------*/
-
-DA_DECL(instr_v, gfreduce_instr);
-
-/*----- Main code ---------------------------------------------------------*/
-
-/* --- What's going on here? --- *
- *
- * Let's face it, @gfx_div@ sucks. It works (I hope), but it's not in any
- * sense fast. Here, we do efficient reduction modulo sparse polynomials.
- *
- * Suppose we have a polynomial @X@ we're trying to reduce mod @P@. If we
- * take the topmost nonzero word of @X@, call it @w@, then we can eliminate
- * it by subtracting off @w P x^{k}@ for an appropriate value of @k@. The
- * trick is in observing that if @P@ is sparse we can do this multiplication
- * and subtraction efficiently, just by XORing appropriate shifts of @w@ into
- * @X@.
- *
- * The first tricky bit is in working out when to stop. I'll use eight-bit
- * words to demonstrate what I'm talking about.
- *
- * xxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx
- * 001ppppp pppppppp pppppppp pppppppp
- * |<rp>|
- * |<------------ bp ------------->|
- * |<------------ nw --------------->|
- *
- * The trick of taking whole words off of @X@ stops working when there are
- * only @nw@ words left. Then we have to mask off the bottom bits of @w@
- * before continuing.
- */
-
-/* --- @gfreduce_create@ --- *
- *
- * Arguments: @gfreduce *r@ = structure to fill in
- * @mp *x@ = a (hopefully sparse) polynomial
- *
- * Returns: ---
- *
- * Use: Initializes a context structure for reduction.
- */
-
-void gfreduce_create(gfreduce *r, mp *p)
-{
- instr_v iv = DA_INIT;
- unsigned long d;
- unsigned dw;
- mpscan sc;
- unsigned long i;
- gfreduce_instr *ip;
- unsigned f = 0;
- size_t w, ww, wi, wl, ll, bb;
-
- /* --- Sort out the easy stuff --- */
-
- d = mp_bits(p); assert(d); d--;
- r->lim = d/MPW_BITS;
- dw = d%MPW_BITS;
- if (!dw)
- r->mask = 0;
- else {
- r->mask = MPW(((mpw)-1) << dw);
- r->lim++;
- }
- r->p = mp_copy(p);
-
- /* --- Stash a new instruction --- */
-
-#define INSTR(op_, arg_) do { \
- DA_ENSURE(&iv, 1); \
- DA(&iv)[DA_LEN(&iv)].op = (op_); \
- DA(&iv)[DA_LEN(&iv)].arg = (arg_); \
- DA_EXTEND(&iv, 1); \
-} while (0)
-
-#define f_lsr 1u
-
- w = (d + MPW_BITS - 1)/MPW_BITS;
- INSTR(GFRI_LOAD, w);
- wi = DA_LEN(&iv);
- f = 0;
- ll = 0;
- bb = MPW_BITS - dw;
- for (i = 0, mp_scan(&sc, p); mp_step(&sc) && i < d; i++) {
- if (!mp_bit(&sc))
- continue;
- ww = (d - i + MPW_BITS - 1)/MPW_BITS;
- if (ww != w) {
- wl = DA_LEN(&iv);
- INSTR(GFRI_STORE, w);
- if (!ll)
- ll = DA_LEN(&iv);
- if (!(f & f_lsr))
- INSTR(GFRI_LOAD, ww);
- else {
- INSTR(GFRI_LOAD, w - 1);
- for (; wi < wl; wi++) {
- ip = &DA(&iv)[wi];
- assert(ip->op == GFRI_LSL);
- if (ip->arg)
- INSTR(GFRI_LSR, MPW_BITS - ip->arg);
- }
- if (w - 1 != ww) {
- INSTR(GFRI_STORE, w - 1);
- INSTR(GFRI_LOAD, ww);
- }
- f &= ~f_lsr;
- }
- w = ww;
- wi = DA_LEN(&iv);
- }
- INSTR(GFRI_LSL, (bb + i)%MPW_BITS);
- if ((bb + i)%MPW_BITS)
- f |= f_lsr;
- }
- wl = DA_LEN(&iv);
- INSTR(GFRI_STORE, w);
- if (!ll)
- ll = DA_LEN(&iv);
- if (f & f_lsr) {
- INSTR(GFRI_LOAD, w - 1);
- for (; wi < wl; wi++) {
- ip = &DA(&iv)[wi];
- assert(ip->op == GFRI_LSL);
- if (ip->arg)
- INSTR(GFRI_LSR, MPW_BITS - ip->arg);
- }
- INSTR(GFRI_STORE, w - 1);
- }
-
-#undef INSTR
-
- r->in = DA_LEN(&iv);
- r->iv = xmalloc(r->in * sizeof(gfreduce_instr));
- r->liv = r->iv + ll;
- memcpy(r->iv, DA(&iv), r->in * sizeof(gfreduce_instr));
- DA_DESTROY(&iv);
-}
-
-/* --- @gfreduce_destroy@ --- *
- *
- * Arguments: @gfreduce *r@ = structure to free
- *
- * Returns: ---
- *
- * Use: Reclaims the resources from a reduction context.
- */
-
-void gfreduce_destroy(gfreduce *r)
-{
- mp_drop(r->p);
- xfree(r->iv);
-}
-
-/* --- @gfreduce_dump@ --- *
- *
- * Arguments: @gfreduce *r@ = structure to dump
- * @FILE *fp@ = file to dump on
- *
- * Returns: ---
- *
- * Use: Dumps a reduction context.
- */
-
-void gfreduce_dump(gfreduce *r, FILE *fp)
-{
- size_t i;
-
- fprintf(fp, "poly = "); mp_writefile(r->p, fp, 16);
- fprintf(fp, "\n lim = %lu; mask = %lx\n",
- (unsigned long)r->lim, (unsigned long)r->mask);
- for (i = 0; i < r->in; i++) {
- static const char *opname[] = { "load", "lsl", "lsr", "store" };
- assert(r->iv[i].op < N(opname));
- fprintf(fp, " %s %lu\n",
- opname[r->iv[i].op],
- (unsigned long)r->iv[i].arg);
- }
-}
-
-/* --- @gfreduce_do@ --- *
- *
- * Arguments: @gfreduce *r@ = reduction context
- * @mp *d@ = destination
- * @mp *x@ = source
- *
- * Returns: Destination, @x@ reduced modulo the reduction poly.
- */
-
-static void run(const gfreduce_instr *i, const gfreduce_instr *il,
- mpw *v, mpw z)
-{
- mpw w = 0;
-
- for (; i < il; i++) {
- switch (i->op) {
- case GFRI_LOAD: w = *(v - i->arg); break;
- case GFRI_LSL: w ^= z << i->arg; break;
- case GFRI_LSR: w ^= z >> i->arg; break;
- case GFRI_STORE: *(v - i->arg) = MPW(w); break;
- default: abort();
- }
- }
-}
-
-mp *gfreduce_do(gfreduce *r, mp *d, mp *x)
-{
- mpw *v, *vl;
- const gfreduce_instr *il;
- mpw z;
-
- /* --- 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 --- */
-
- 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);
- }
- }
- if (r->mask) {
- while (*vl & r->mask) {
- z = *vl & r->mask;
- *vl &= ~r->mask;
- run(r->iv, il, vl, z);
- }
- }
- }
-
- /* --- Done --- */
-
- MP_SHRINK(x);
- return (x);
-}
-
-/* --- @gfreduce_sqrt@ --- *
- *
- * Arguments: @gfreduce *r@ = pointer to reduction context
- * @mp *d@ = destination
- * @mp *x@ = some polynomial
- *
- * Returns: The square root of @x@ modulo @r->p@, or null.
- */
-
-mp *gfreduce_sqrt(gfreduce *r, mp *d, mp *x)
-{
- mp *y = MP_COPY(x);
- mp *z, *spare = MP_NEW;
- unsigned long m = mp_bits(r->p) - 1;
- unsigned long i;
-
- for (i = 0; i < m - 1; i++) {
- mp *t = gf_sqr(spare, y);
- spare = y;
- y = gfreduce_do(r, t, t);
- }
- z = gf_sqr(spare, y);
- z = gfreduce_do(r, z, z);
- if (!MP_EQ(x, z)) {
- mp_drop(y);
- y = 0;
- }
- mp_drop(z);
- mp_drop(d);
- return (y);
-}
-
-/* --- @gfreduce_trace@ --- *
- *
- * Arguments: @gfreduce *r@ = pointer to reduction context
- * @mp *x@ = some polynomial
- *
- * Returns: The trace of @x@. (%$\Tr(x)=x + x^2 + \cdots + x^{2^{m-1}}$%
- * if %$x \in \gf{2^m}$%).
- */
-
-int gfreduce_trace(gfreduce *r, mp *x)
-{
- mp *y = MP_COPY(x);
- mp *spare = MP_NEW;
- unsigned long m = mp_bits(r->p) - 1;
- unsigned long i;
- int rc;
-
- for (i = 0; i < m - 1; i++) {
- mp *t = gf_sqr(spare, y);
- spare = y;
- y = gfreduce_do(r, t, t);
- y = gf_add(y, y, x);
- }
- rc = !MP_ZEROP(y);
- mp_drop(spare);
- mp_drop(y);
- return (rc);
-}
-
-/* --- @gfreduce_halftrace@ --- *
- *
- * Arguments: @gfreduce *r@ = pointer to reduction context
- * @mp *d@ = destination
- * @mp *x@ = some polynomial
- *
- * Returns: The half-trace of @x@.
- * (%$\HfTr(x)= x + x^{2^2} + \cdots + x^{2^{m-1}}$%
- * if %$x \in \gf{2^m}$% with %$m$% odd).
- */
-
-mp *gfreduce_halftrace(gfreduce *r, mp *d, mp *x)
-{
- mp *y = MP_COPY(x);
- mp *spare = MP_NEW;
- unsigned long m = mp_bits(r->p) - 1;
- unsigned long i;
-
- mp_drop(d);
- for (i = 0; i < m - 1; i += 2) {
- mp *t = gf_sqr(spare, y);
- spare = y;
- y = gfreduce_do(r, t, t);
- t = gf_sqr(spare, y);
- spare = y;
- y = gfreduce_do(r, t, t);
- y = gf_add(y, y, x);
- }
- mp_drop(spare);
- return (y);
-}
-
-/* --- @gfreduce_quadsolve@ --- *
- *
- * Arguments: @gfreduce *r@ = pointer to reduction context
- * @mp *d@ = destination
- * @mp *x@ = some polynomial
- *
- * Returns: A polynomial @y@ such that %$y^2 + y = x$%, or null.
- */
-
-mp *gfreduce_quadsolve(gfreduce *r, mp *d, mp *x)
-{
- unsigned long m = mp_bits(r->p) - 1;
- mp *t;
-
- MP_COPY(x);
- if (m & 1)
- d = gfreduce_halftrace(r, d, x);
- else {
- mp *z, *w, *rho = MP_NEW;
- mp *spare = MP_NEW;
- grand *fr = fibrand_create(0);
- unsigned long i;
-
- for (;;) {
- rho = mprand(rho, m, fr, 0);
- z = MP_ZERO;
- w = MP_COPY(rho);
- for (i = 0; i < m - 1; i++) {
- t = gf_sqr(spare, z); spare = z; z = gfreduce_do(r, t, t);
- t = gf_sqr(spare, w); spare = w; w = gfreduce_do(r, t, t);
- t = gf_mul(spare, w, x); t = gfreduce_do(r, t, t); spare = t;
- z = gf_add(z, z, t);
- w = gf_add(w, w, rho);
- }
- if (!MP_ZEROP(w))
- break;
- MP_DROP(z);
- MP_DROP(w);
- }
- if (d) MP_DROP(d);
- MP_DROP(w);
- MP_DROP(spare);
- MP_DROP(rho);
- fr->ops->destroy(fr);
- d = z;
- }
-
- t = gf_sqr(MP_NEW, d); t = gfreduce_do(r, t, t); t = gf_add(t, t, d);
- if (!MP_EQ(t, x)) {
- MP_DROP(d);
- d = 0;
- }
- MP_DROP(t);
- MP_DROP(x);
- if (d) d->v[0] &= ~(mpw)1;
- return (d);
-}
-
-/* --- @gfreduce_exp@ --- *
- *
- * Arguments: @gfreduce *gr@ = pointer to reduction context
- * @mp *d@ = fake destination
- * @mp *a@ = base
- * @mp *e@ = exponent
- *
- * Returns: Result, %$a^e \bmod m$%.
- */
-
-mp *gfreduce_exp(gfreduce *gr, 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 = gf_modinv(a, a, gr->p);
- if (MP_LEN(e) < EXP_THRESH)
- EXP_SIMPLE(x, a, e);
- else
- EXP_WINDOW(x, a, e);
- }
- mp_drop(d);
- mp_drop(a);
- 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;
- gfreduce rr;
-
- gfreduce_create(&rr, d);
- c = gfreduce_do(&rr, MP_NEW, n);
- if (!MP_EQ(c, r)) {
- fprintf(stderr, "\n*** reduction failed\n*** ");
- gfreduce_dump(&rr, stderr);
- fprintf(stderr, "\n*** n = "); mp_writefile(n, stderr, 16);
- fprintf(stderr, "\n*** r = "); mp_writefile(r, stderr, 16);
- fprintf(stderr, "\n*** c = "); mp_writefile(c, stderr, 16);
- fprintf(stderr, "\n");
- ok = 0;
- }
- gfreduce_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;
- gfreduce rr;
-
- gfreduce_create(&rr, p);
- c = gfreduce_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, 16);
- fprintf(stderr, "\n*** g = "); mp_writefile(g, stderr, 16);
- fprintf(stderr, "\n*** x = "); mp_writefile(x, stderr, 16);
- fprintf(stderr, "\n*** c = "); mp_writefile(c, stderr, 16);
- fprintf(stderr, "\n*** r = "); mp_writefile(r, stderr, 16);
- fprintf(stderr, "\n");
- ok = 0;
- }
- gfreduce_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 int vsqrt(dstr *v)
-{
- mp *p = *(mp **)v[0].buf;
- mp *x = *(mp **)v[1].buf;
- mp *r = *(mp **)v[2].buf;
- mp *c;
- int ok = 1;
- gfreduce rr;
-
- gfreduce_create(&rr, p);
- c = gfreduce_sqrt(&rr, MP_NEW, x);
- if (!MP_EQ(c, r)) {
- fprintf(stderr, "\n*** sqrt failed\n*** ");
- fprintf(stderr, "\n*** p = "); mp_writefile(p, stderr, 16);
- fprintf(stderr, "\n*** x = "); mp_writefile(x, stderr, 16);
- fprintf(stderr, "\n*** c = "); mp_writefile(c, stderr, 16);
- fprintf(stderr, "\n*** r = "); mp_writefile(r, stderr, 16);
- fprintf(stderr, "\n");
- ok = 0;
- }
- gfreduce_destroy(&rr);
- mp_drop(p); mp_drop(r); mp_drop(x); mp_drop(c);
- assert(mparena_count(MPARENA_GLOBAL) == 0);
- return (ok);
-}
-
-static int vtr(dstr *v)
-{
- mp *p = *(mp **)v[0].buf;
- mp *x = *(mp **)v[1].buf;
- int r = *(int *)v[2].buf, c;
- int ok = 1;
- gfreduce rr;
-
- gfreduce_create(&rr, p);
- c = gfreduce_trace(&rr, x);
- if (c != r) {
- fprintf(stderr, "\n*** trace failed\n*** ");
- fprintf(stderr, "\n*** p = "); mp_writefile(p, stderr, 16);
- fprintf(stderr, "\n*** x = "); mp_writefile(x, stderr, 16);
- fprintf(stderr, "\n*** c = %d", c);
- fprintf(stderr, "\n*** r = %d", r);
- fprintf(stderr, "\n");
- ok = 0;
- }
- gfreduce_destroy(&rr);
- mp_drop(p); mp_drop(x);
- assert(mparena_count(MPARENA_GLOBAL) == 0);
- return (ok);
-}
-
-static int vhftr(dstr *v)
-{
- mp *p = *(mp **)v[0].buf;
- mp *x = *(mp **)v[1].buf;
- mp *r = *(mp **)v[2].buf;
- mp *c;
- int ok = 1;
- gfreduce rr;
-
- gfreduce_create(&rr, p);
- c = gfreduce_halftrace(&rr, MP_NEW, x);
- if (!MP_EQ(c, r)) {
- fprintf(stderr, "\n*** halftrace failed\n*** ");
- fprintf(stderr, "\n*** p = "); mp_writefile(p, stderr, 16);
- fprintf(stderr, "\n*** x = "); mp_writefile(x, stderr, 16);
- fprintf(stderr, "\n*** c = "); mp_writefile(c, stderr, 16);
- fprintf(stderr, "\n*** r = "); mp_writefile(r, stderr, 16);
- fprintf(stderr, "\n");
- ok = 0;
- }
- gfreduce_destroy(&rr);
- mp_drop(p); mp_drop(r); mp_drop(x); mp_drop(c);
- assert(mparena_count(MPARENA_GLOBAL) == 0);
- return (ok);
-}
-
-static int vquad(dstr *v)
-{
- mp *p = *(mp **)v[0].buf;
- mp *x = *(mp **)v[1].buf;
- mp *r = *(mp **)v[2].buf;
- mp *c;
- int ok = 1;
- gfreduce rr;
-
- gfreduce_create(&rr, p);
- c = gfreduce_quadsolve(&rr, MP_NEW, x);
- if (!MP_EQ(c, r)) {
- fprintf(stderr, "\n*** quadsolve failed\n*** ");
- fprintf(stderr, "\n*** p = "); mp_writefile(p, stderr, 16);
- fprintf(stderr, "\n*** x = "); mp_writefile(x, stderr, 16);
- fprintf(stderr, "\n*** c = "); mp_writefile(c, stderr, 16);
- fprintf(stderr, "\n*** r = "); mp_writefile(r, stderr, 16);
- fprintf(stderr, "\n");
- ok = 0;
- }
- gfreduce_destroy(&rr);
- mp_drop(p); 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 } },
- { "sqrt", vsqrt, { &type_mp, &type_mp, &type_mp, 0 } },
- { "trace", vtr, { &type_mp, &type_mp, &type_int, 0 } },
- { "halftrace", vhftr, { &type_mp, &type_mp, &type_mp, 0 } },
- { "quadsolve", vquad, { &type_mp, &type_mp, &type_mp, 0 } },
- { 0, 0, { 0 } }
-};
-
-int main(int argc, char *argv[])
-{
- test_run(argc, argv, defs, SRCDIR"/tests/gfreduce");
- return (0);
-}
-
-#endif
-
-/*----- That's all, folks -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff