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