mdw@git.distorted.org.uk Git - catacomb/blob - math/mpmont.c

   1 /* -*-c-*-
   2  *
   3  * Montgomery reduction
   4  *
   5  * (c) 1999 Straylight/Edgeware
   6  */
   7
   8 /*----- Licensing notice --------------------------------------------------*
   9  *
  10  * This file is part of Catacomb.
  11  *
  12  * Catacomb is free software; you can redistribute it and/or modify
  13  * it under the terms of the GNU Library General Public License as
  14  * published by the Free Software Foundation; either version 2 of the
  15  * License, or (at your option) any later version.
  16  *
  17  * Catacomb is distributed in the hope that it will be useful,
  18  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  19  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  20  * GNU Library General Public License for more details.
  21  *
  22  * You should have received a copy of the GNU Library General Public
  23  * License along with Catacomb; if not, write to the Free
  24  * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
  25  * MA 02111-1307, USA.
  26  */
  27
  28 /*----- Header files ------------------------------------------------------*/
  29
  30 #include "config.h"
  31 #include "dispatch.h"
  32 #include "mp.h"
  33 #include "mpmont.h"
  34
  35 /*----- Tweakables --------------------------------------------------------*/
  36
  37 /* --- @MPMONT_DISABLE@ --- *
  38  *
  39  * Replace all the clever Montgomery reduction with good old-fashioned long
  40  * division.
  41  */
  42
  43 /* #define MPMONT_DISABLE */
  44
  45 #define MPMONT_KTHRESH (16*MPK_THRESH)
  46
  47 /*----- Low-level implementation ------------------------------------------*/
  48
  49 #ifndef MPMONT_DISABLE
  50
  51 /* --- @redccore@ --- *
  52  *
  53  * Arguments:   @mpw *dv, *dvl@ = base and limit of source/destination
  54  *              @const mpw *mv@ = base of modulus %$m$%
  55  *              @size_t n@ = length of modulus
  56  *              @const mpw *mi@ = base of REDC coefficient %$m'$%
  57  *
  58  * Returns:     ---
  59  *
  60  * Use:         Let %$a$% be the input operand.  Store in %$d$% the value
  61  *              %$a + (m' a \bmod R) m$%.  The destination has space for at
  62  *              least %$2 n + 1$% words of result.
  63  */
  64
  65 CPU_DISPATCH(static, (void), void, redccore,
  66              (mpw *dv, mpw *dvl, const mpw *mv, size_t n, const mpw *mi),
  67              (dv, dvl, mv, n, mi), pick_redccore, simple_redccore);
  68
  69 static void simple_redccore(mpw *dv, mpw *dvl, const mpw *mv,
  70                             size_t n, const mpw *mi)
  71 {
  72   mpw mi0 = *mi;
  73   size_t i;
  74
  75   for (i = 0; i < n; i++) {
  76     MPX_UMLAN(dv, dvl, mv, mv + n, MPW(*dv*mi0));
  77     dv++;
  78   }
  79 }
  80
  81 #define MAYBE_REDC4(impl)                                               \
  82   extern void mpxmont_redc4_##impl(mpw *dv, mpw *dvl, const mpw *mv,    \
  83                                    size_t n, const mpw *mi);            \
  84   static void maybe_redc4_##impl(mpw *dv, mpw *dvl, const mpw *mv,      \
  85                                  size_t n, const mpw *mi)               \
  86   {                                                                     \
  87     if (n%4) simple_redccore(dv, dvl, mv, n, mi);                       \
  88     else mpxmont_redc4_##impl(dv, dvl, mv, n, mi);                      \
  89   }
  90
  91 #if CPUFAM_X86
  92   MAYBE_REDC4(x86_sse2)
  93 #endif
  94
  95 static redccore__functype *pick_redccore(void)
  96 {
  97 #if CPUFAM_X86
  98   DISPATCH_PICK_COND(mpmont_reduce, maybe_redc4_x86_sse2,
  99                      cpu_feature_p(CPUFEAT_X86_SSE2));
 100 #endif
 101   DISPATCH_PICK_FALLBACK(mpmont_reduce, simple_redccore);
 102 }
 103
 104 /* --- @redccore@ --- *
 105  *
 106  * Arguments:   @mpw *dv, *dvl@ = base and limit of source/destination
 107  *              @const mpw *av, *avl@ = base and limit of first multiplicand
 108  *              @const mpw *bv, *bvl@ = base and limit of second multiplicand
 109  *              @const mpw *mv@ = base of modulus %$m$%
 110  *              @size_t n@ = length of modulus
 111  *              @const mpw *mi@ = base of REDC coefficient %$m'$%
 112  *
 113  * Returns:     ---
 114  *
 115  * Use:         Let %$a$% and %$b$% be the multiplicands.  Let %$w = a b$%.
 116  *              Store in %$d$% the value %$a b + (m' a b \bmod R) m$%.
 117  */
 118
 119 CPU_DISPATCH(static, (void), void, mulcore,
 120              (mpw *dv, mpw *dvl, const mpw *av, const mpw *avl,
 121               const mpw *bv, const mpw *bvl, const mpw *mv,
 122               size_t n, const mpw *mi),
 123              (dv, dvl, av, avl, bv, bvl, mv, n, mi),
 124              pick_mulcore, simple_mulcore);
 125
 126 static void simple_mulcore(mpw *dv, mpw *dvl,
 127                            const mpw *av, const mpw *avl,
 128                            const mpw *bv, const mpw *bvl,
 129                            const mpw *mv, size_t n, const mpw *mi)
 130 {
 131   mpw ai, b0, y, mi0 = *mi;
 132   const mpw *tv, *tvl;
 133   const mpw *mvl = mv + n;
 134   size_t i = 0;
 135
 136   /* --- Initial setup --- */
 137
 138   MPX_ZERO(dv, dvl);
 139   if (avl - av > bvl - bv) {
 140     tv = av; av = bv; bv = tv;
 141     tvl = avl; avl = bvl; bvl = tvl;
 142   }
 143   b0 = *bv;
 144
 145   /* --- Multiply, until we run out of multiplicand --- */
 146
 147   while (i < n && av < avl) {
 148     ai = *av++;
 149     y = MPW((*dv + ai*b0)*mi0);
 150     MPX_UMLAN(dv, dvl, bv, bvl, ai);
 151     MPX_UMLAN(dv, dvl, mv, mvl, y);
 152     dv++; i++;
 153   }
 154
 155   /* --- Continue reducing until we run out of modulus --- */
 156
 157   while (i < n) {
 158     y = MPW(*dv*mi0);
 159     MPX_UMLAN(dv, dvl, mv, mvl, y);
 160     dv++; i++;
 161   }
 162 }
 163
 164 #define MAYBE_MUL4(impl)                                                \
 165   extern void mpxmont_mul4_##impl(mpw *dv,                              \
 166                                   const mpw *av, const mpw *bv,         \
 167                                   const mpw *mv,                        \
 168                                   size_t n, const mpw *mi);             \
 169   static void maybe_mul4_##impl(mpw *dv, mpw *dvl,                      \
 170                            const mpw *av, const mpw *avl,               \
 171                            const mpw *bv, const mpw *bvl,               \
 172                            const mpw *mv, size_t n, const mpw *mi)      \
 173   {                                                                     \
 174     size_t an = avl - av, bn = bvl - bv;                                \
 175     if (n%4 || an != n || bn != n)                                      \
 176       simple_mulcore(dv, dvl, av, avl, bv, bvl, mv, n, mi);             \
 177     else {                                                              \
 178       mpxmont_mul4_##impl(dv, av, bv, mv, n, mi);                       \
 179       MPX_ZERO(dv + 2*n + 1, dvl);                                      \
 180     }                                                                   \
 181   }
 182
 183 #if CPUFAM_X86
 184   MAYBE_MUL4(x86_sse2)
 185 #endif
 186
 187 static mulcore__functype *pick_mulcore(void)
 188 {
 189 #if CPUFAM_X86
 190   DISPATCH_PICK_COND(mpmont_mul, maybe_mul4_x86_sse2,
 191                      cpu_feature_p(CPUFEAT_X86_SSE2));
 192 #endif
 193   DISPATCH_PICK_FALLBACK(mpmont_mul, simple_mulcore);
 194 }
 195
 196 /* --- @finish@ --- *
 197  *
 198  * Arguments:   @mpmont *mm@ = pointer to a Montgomery reduction context
 199  *              *mp *d@ = pointer to mostly-reduced operand
 200  *
 201  * Returns:     ---
 202  *
 203  * Use:         Applies the finishing touches to Montgomery reduction.  The
 204  *              operand @d@ is a multiple of %$R%$ at this point, so it needs
 205  *              to be shifted down; the result might need a further
 206  *              subtraction to get it into the right interval; and we may
 207  *              need to do an additional subtraction if %$d$% is negative.
 208  */
 209
 210 static void finish(mpmont *mm, mp *d)
 211 {
 212   mpw *dv = d->v, *dvl = d->vl;
 213   size_t n = mm->n;
 214
 215   memmove(dv, dv + n, MPWS(dvl - (dv + n)));
 216   dvl -= n;
 217
 218   if (MPX_UCMP(dv, dvl, >=, mm->m->v, mm->m->vl))
 219     mpx_usub(dv, dvl, dv, dvl, mm->m->v, mm->m->vl);
 220
 221   if (d->f & MP_NEG) {
 222     mpx_usub(dv, dvl, mm->m->v, mm->m->vl, dv, dvl);
 223     d->f &= ~MP_NEG;
 224   }
 225
 226   d->vl = dvl;
 227   MP_SHRINK(d);
 228 }
 229
 230 #endif
 231
 232 /*----- Reduction and multiplication --------------------------------------*/
 233
 234 /* --- @mpmont_create@ --- *
 235  *
 236  * Arguments:   @mpmont *mm@ = pointer to Montgomery reduction context
 237  *              @mp *m@ = modulus to use
 238  *
 239  * Returns:     Zero on success, nonzero on error.
 240  *
 241  * Use:         Initializes a Montgomery reduction context ready for use.
 242  *              The argument @m@ must be a positive odd integer.
 243  */
 244
 245 #ifdef MPMONT_DISABLE
 246
 247 int mpmont_create(mpmont *mm, mp *m)
 248 {
 249   mp_shrink(m);
 250   mm->m = MP_COPY(m);
 251   mm->r = MP_ONE;
 252   mm->r2 = MP_ONE;
 253   mm->mi = MP_ONE;
 254   return (0);
 255 }
 256
 257 #else
 258
 259 int mpmont_create(mpmont *mm, mp *m)
 260 {
 261   size_t n = MP_LEN(m);
 262   mp *r2 = mp_new(2 * n + 1, 0);
 263   mp r;
 264
 265   /* --- Take a copy of the modulus --- */
 266
 267  if (!MP_POSP(m) || !MP_ODDP(m))
 268    return (-1);
 269   mm->m = MP_COPY(m);
 270
 271   /* --- Determine %$R^2$% --- */
 272
 273   mm->n = n;
 274   MPX_ZERO(r2->v, r2->vl - 1);
 275   r2->vl[-1] = 1;
 276
 277   /* --- Find the magic value @mi@ --- */
 278
 279   mp_build(&r, r2->v + n, r2->vl);
 280   mm->mi = mp_modinv(MP_NEW, m, &r);
 281   mm->mi = mp_sub(mm->mi, &r, mm->mi);
 282   MP_ENSURE(mm->mi, n);
 283
 284   /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */
 285
 286   mm->r2 = MP_NEW;
 287   mp_div(0, &mm->r2, r2, m);
 288   mm->r = mpmont_reduce(mm, MP_NEW, mm->r2);
 289   MP_DROP(r2);
 290   return (0);
 291 }
 292
 293 #endif
 294
 295 /* --- @mpmont_destroy@ --- *
 296  *
 297  * Arguments:   @mpmont *mm@ = pointer to a Montgomery reduction context
 298  *
 299  * Returns:     ---
 300  *
 301  * Use:         Disposes of a context when it's no longer of any use to
 302  *              anyone.
 303  */
 304
 305 void mpmont_destroy(mpmont *mm)
 306 {
 307   MP_DROP(mm->m);
 308   MP_DROP(mm->r);
 309   MP_DROP(mm->r2);
 310   MP_DROP(mm->mi);
 311 }
 312
 313 /* --- @mpmont_reduce@ --- *
 314  *
 315  * Arguments:   @mpmont *mm@ = pointer to Montgomery reduction context
 316  *              @mp *d@ = destination
 317  *              @mp *a@ = source, assumed positive
 318  *
 319  * Returns:     Result, %$a R^{-1} \bmod m$%.
 320  */
 321
 322 #ifdef MPMONT_DISABLE
 323
 324 mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
 325 {
 326   mp_div(0, &d, a, mm->m);
 327   return (d);
 328 }
 329
 330 #else
 331
 332 mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
 333 {
 334   size_t n = mm->n;
 335
 336   /* --- Check for serious Karatsuba reduction --- */
 337
 338   if (n > MPMONT_KTHRESH) {
 339     mp al;
 340     mpw *vl;
 341     mp *u;
 342
 343     if (MP_LEN(a) >= n) vl = a->v + n;
 344     else vl = a->vl;
 345     mp_build(&al, a->v, vl);
 346     u = mp_mul(MP_NEW, &al, mm->mi);
 347     if (MP_LEN(u) > n) u->vl = u->v + n;
 348     u = mp_mul(u, u, mm->m);
 349     d = mp_add(d, a, u);
 350     MP_ENSURE(d, n);
 351     mp_drop(u);
 352   }
 353
 354   /* --- Otherwise do it the hard way --- */
 355
 356   else {
 357     a = MP_COPY(a);
 358     if (d) MP_DROP(d);
 359     d = a;
 360     MP_DEST(d, 2*mm->n + 1, a->f);
 361     redccore(d->v, d->vl, mm->m->v, mm->n, mm->mi->v);
 362   }
 363
 364   /* --- Wrap everything up --- */
 365
 366   finish(mm, d);
 367   return (d);
 368 }
 369
 370 #endif
 371
 372 /* --- @mpmont_mul@ --- *
 373  *
 374  * Arguments:   @mpmont *mm@ = pointer to Montgomery reduction context
 375  *              @mp *d@ = destination
 376  *              @mp *a, *b@ = sources, assumed positive
 377  *
 378  * Returns:     Result, %$a b R^{-1} \bmod m$%.
 379  */
 380
 381 #ifdef MPMONT_DISABLE
 382
 383 mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
 384 {
 385   d = mp_mul(d, a, b);
 386   mp_div(0, &d, d, mm->m);
 387   return (d);
 388 }
 389
 390 #else
 391
 392 mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
 393 {
 394   size_t n = mm->n;
 395
 396   if (n > MPMONT_KTHRESH) {
 397     d = mp_mul(d, a, b);
 398     d = mpmont_reduce(mm, d, d);
 399   } else {
 400     a = MP_COPY(a); b = MP_COPY(b);
 401     MP_DEST(d, 2*n + 1, a->f | b->f | MP_UNDEF);
 402     mulcore(d->v, d->vl, a->v, a->vl, b->v, b->vl,
 403             mm->m->v, mm->n, mm->mi->v);
 404     d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG);
 405     finish(mm, d);
 406     MP_DROP(a); MP_DROP(b);
 407   }
 408
 409   return (d);
 410 }
 411
 412 #endif
 413
 414 /*----- Test rig ----------------------------------------------------------*/
 415
 416 #ifdef TEST_RIG
 417
 418 static int tcreate(dstr *v)
 419 {
 420   mp *m = *(mp **)v[0].buf;
 421   mp *mi = *(mp **)v[1].buf;
 422   mp *r = *(mp **)v[2].buf;
 423   mp *r2 = *(mp **)v[3].buf;
 424
 425   mpmont mm;
 426   int ok = 1;
 427
 428   mpmont_create(&mm, m);
 429
 430   if (mm.mi->v[0] != mi->v[0]) {
 431     fprintf(stderr, "\n*** bad mi: found %lu, expected %lu",
 432             (unsigned long)mm.mi->v[0], (unsigned long)mi->v[0]);
 433     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 434     fputc('\n', stderr);
 435     ok = 0;
 436   }
 437
 438   if (!MP_EQ(mm.r, r)) {
 439     fputs("\n*** bad r", stderr);
 440     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 441     fputs("\nexpected ", stderr); mp_writefile(r, stderr, 10);
 442     fputs("\n   found ", stderr); mp_writefile(mm.r, stderr, 10);
 443     fputc('\n', stderr);
 444     ok = 0;
 445   }
 446
 447   if (!MP_EQ(mm.r2, r2)) {
 448     fputs("\n*** bad r2", stderr);
 449     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 450     fputs("\nexpected ", stderr); mp_writefile(r2, stderr, 10);
 451     fputs("\n   found ", stderr); mp_writefile(mm.r2, stderr, 10);
 452     fputc('\n', stderr);
 453     ok = 0;
 454   }
 455
 456   MP_DROP(m);
 457   MP_DROP(mi);
 458   MP_DROP(r);
 459   MP_DROP(r2);
 460   mpmont_destroy(&mm);
 461   assert(mparena_count(MPARENA_GLOBAL) == 0);
 462   return (ok);
 463 }
 464
 465 static int tmul(dstr *v)
 466 {
 467   mp *m = *(mp **)v[0].buf;
 468   mp *a = *(mp **)v[1].buf;
 469   mp *b = *(mp **)v[2].buf;
 470   mp *r = *(mp **)v[3].buf;
 471   int ok = 1;
 472
 473   mpmont mm;
 474   mpmont_create(&mm, m);
 475
 476   {
 477     mp *qr = mp_mul(MP_NEW, a, b);
 478     mp_div(0, &qr, qr, m);
 479
 480     if (!MP_EQ(qr, r)) {
 481       fputs("\n*** classical modmul failed", stderr);
 482       fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
 483       fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
 484       fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
 485       fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
 486       fputs("\nqr = ", stderr); mp_writefile(qr, stderr, 10);
 487       fputc('\n', stderr);
 488       ok = 0;
 489     }
 490
 491     mp_drop(qr);
 492   }
 493
 494   {
 495     mp *ar = mpmont_mul(&mm, MP_NEW, a, mm.r2);
 496     mp *br = mpmont_mul(&mm, MP_NEW, b, mm.r2);
 497     mp *mr = mpmont_mul(&mm, MP_NEW, ar, br);
 498     mr = mpmont_reduce(&mm, mr, mr);
 499     if (!MP_EQ(mr, r)) {
 500       fputs("\n*** montgomery modmul failed", stderr);
 501       fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
 502       fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
 503       fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
 504       fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
 505       fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10);
 506       fputc('\n', stderr);
 507       ok = 0;
 508     }
 509     MP_DROP(ar); MP_DROP(br);
 510     mp_drop(mr);
 511   }
 512
 513
 514   MP_DROP(m);
 515   MP_DROP(a);
 516   MP_DROP(b);
 517   MP_DROP(r);
 518   mpmont_destroy(&mm);
 519   assert(mparena_count(MPARENA_GLOBAL) == 0);
 520   return ok;
 521 }
 522
 523 static test_chunk tests[] = {
 524   { "create", tcreate, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 525   { "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 526   { 0, 0, { 0 } },
 527 };
 528
 529 int main(int argc, char *argv[])
 530 {
 531   sub_init();
 532   test_run(argc, argv, tests, SRCDIR "/t/mpmont");
 533   return (0);
 534 }
 535
 536 #endif
 537
 538 /*----- That's all, folks -------------------------------------------------*/