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 #if CPUFAM_AMD64
  96   MAYBE_REDC4(amd64_sse2)
  97 #endif
  98
  99 static redccore__functype *pick_redccore(void)
 100 {
 101 #if CPUFAM_X86
 102   DISPATCH_PICK_COND(mpmont_reduce, maybe_redc4_x86_sse2,
 103                      cpu_feature_p(CPUFEAT_X86_SSE2));
 104 #endif
 105 #if CPUFAM_AMD64
 106   DISPATCH_PICK_COND(mpmont_reduce, maybe_redc4_amd64_sse2,
 107                      cpu_feature_p(CPUFEAT_X86_SSE2));
 108 #endif
 109   DISPATCH_PICK_FALLBACK(mpmont_reduce, simple_redccore);
 110 }
 111
 112 /* --- @redccore@ --- *
 113  *
 114  * Arguments:   @mpw *dv, *dvl@ = base and limit of source/destination
 115  *              @const mpw *av, *avl@ = base and limit of first multiplicand
 116  *              @const mpw *bv, *bvl@ = base and limit of second multiplicand
 117  *              @const mpw *mv@ = base of modulus %$m$%
 118  *              @size_t n@ = length of modulus
 119  *              @const mpw *mi@ = base of REDC coefficient %$m'$%
 120  *
 121  * Returns:     ---
 122  *
 123  * Use:         Let %$a$% and %$b$% be the multiplicands.  Let %$w = a b$%.
 124  *              Store in %$d$% the value %$a b + (m' a b \bmod R) m$%.
 125  */
 126
 127 CPU_DISPATCH(static, (void), void, mulcore,
 128              (mpw *dv, mpw *dvl, const mpw *av, const mpw *avl,
 129               const mpw *bv, const mpw *bvl, const mpw *mv,
 130               size_t n, const mpw *mi),
 131              (dv, dvl, av, avl, bv, bvl, mv, n, mi),
 132              pick_mulcore, simple_mulcore);
 133
 134 static void simple_mulcore(mpw *dv, mpw *dvl,
 135                            const mpw *av, const mpw *avl,
 136                            const mpw *bv, const mpw *bvl,
 137                            const mpw *mv, size_t n, const mpw *mi)
 138 {
 139   mpw ai, b0, y, mi0 = *mi;
 140   const mpw *tv, *tvl;
 141   const mpw *mvl = mv + n;
 142   size_t i = 0;
 143
 144   /* --- Initial setup --- */
 145
 146   MPX_ZERO(dv, dvl);
 147   if (avl - av > bvl - bv) {
 148     tv = av; av = bv; bv = tv;
 149     tvl = avl; avl = bvl; bvl = tvl;
 150   }
 151   b0 = *bv;
 152
 153   /* --- Multiply, until we run out of multiplicand --- */
 154
 155   while (i < n && av < avl) {
 156     ai = *av++;
 157     y = MPW((*dv + ai*b0)*mi0);
 158     MPX_UMLAN(dv, dvl, bv, bvl, ai);
 159     MPX_UMLAN(dv, dvl, mv, mvl, y);
 160     dv++; i++;
 161   }
 162
 163   /* --- Continue reducing until we run out of modulus --- */
 164
 165   while (i < n) {
 166     y = MPW(*dv*mi0);
 167     MPX_UMLAN(dv, dvl, mv, mvl, y);
 168     dv++; i++;
 169   }
 170 }
 171
 172 #define MAYBE_MUL4(impl)                                                \
 173   extern void mpxmont_mul4_##impl(mpw *dv,                              \
 174                                   const mpw *av, const mpw *bv,         \
 175                                   const mpw *mv,                        \
 176                                   size_t n, const mpw *mi);             \
 177   static void maybe_mul4_##impl(mpw *dv, mpw *dvl,                      \
 178                            const mpw *av, const mpw *avl,               \
 179                            const mpw *bv, const mpw *bvl,               \
 180                            const mpw *mv, size_t n, const mpw *mi)      \
 181   {                                                                     \
 182     size_t an = avl - av, bn = bvl - bv;                                \
 183     if (n%4 || an != n || bn != n)                                      \
 184       simple_mulcore(dv, dvl, av, avl, bv, bvl, mv, n, mi);             \
 185     else {                                                              \
 186       mpxmont_mul4_##impl(dv, av, bv, mv, n, mi);                       \
 187       MPX_ZERO(dv + 2*n + 1, dvl);                                      \
 188     }                                                                   \
 189   }
 190
 191 #if CPUFAM_X86
 192   MAYBE_MUL4(x86_sse2)
 193 #endif
 194
 195 #if CPUFAM_AMD64
 196   MAYBE_MUL4(amd64_sse2)
 197 #endif
 198
 199 static mulcore__functype *pick_mulcore(void)
 200 {
 201 #if CPUFAM_X86
 202   DISPATCH_PICK_COND(mpmont_mul, maybe_mul4_x86_sse2,
 203                      cpu_feature_p(CPUFEAT_X86_SSE2));
 204 #endif
 205 #if CPUFAM_AMD64
 206   DISPATCH_PICK_COND(mpmont_mul, maybe_mul4_amd64_sse2,
 207                      cpu_feature_p(CPUFEAT_X86_SSE2));
 208 #endif
 209   DISPATCH_PICK_FALLBACK(mpmont_mul, simple_mulcore);
 210 }
 211
 212 /* --- @finish@ --- *
 213  *
 214  * Arguments:   @mpmont *mm@ = pointer to a Montgomery reduction context
 215  *              *mp *d@ = pointer to mostly-reduced operand
 216  *
 217  * Returns:     ---
 218  *
 219  * Use:         Applies the finishing touches to Montgomery reduction.  The
 220  *              operand @d@ is a multiple of %$R%$ at this point, so it needs
 221  *              to be shifted down; the result might need a further
 222  *              subtraction to get it into the right interval; and we may
 223  *              need to do an additional subtraction if %$d$% is negative.
 224  */
 225
 226 static void finish(mpmont *mm, mp *d)
 227 {
 228   mpw *dv = d->v, *dvl = d->vl;
 229   size_t n = mm->n;
 230
 231   memmove(dv, dv + n, MPWS(dvl - (dv + n)));
 232   dvl -= n;
 233
 234   if (MPX_UCMP(dv, dvl, >=, mm->m->v, mm->m->vl))
 235     mpx_usub(dv, dvl, dv, dvl, mm->m->v, mm->m->vl);
 236
 237   if (d->f & MP_NEG) {
 238     mpx_usub(dv, dvl, mm->m->v, mm->m->vl, dv, dvl);
 239     d->f &= ~MP_NEG;
 240   }
 241
 242   d->vl = dvl;
 243   MP_SHRINK(d);
 244 }
 245
 246 #endif
 247
 248 /*----- Reduction and multiplication --------------------------------------*/
 249
 250 /* --- @mpmont_create@ --- *
 251  *
 252  * Arguments:   @mpmont *mm@ = pointer to Montgomery reduction context
 253  *              @mp *m@ = modulus to use
 254  *
 255  * Returns:     Zero on success, nonzero on error.
 256  *
 257  * Use:         Initializes a Montgomery reduction context ready for use.
 258  *              The argument @m@ must be a positive odd integer.
 259  */
 260
 261 #ifdef MPMONT_DISABLE
 262
 263 int mpmont_create(mpmont *mm, mp *m)
 264 {
 265   mp_shrink(m);
 266   mm->m = MP_COPY(m);
 267   mm->r = MP_ONE;
 268   mm->r2 = MP_ONE;
 269   mm->mi = MP_ONE;
 270   return (0);
 271 }
 272
 273 #else
 274
 275 int mpmont_create(mpmont *mm, mp *m)
 276 {
 277   size_t n = MP_LEN(m);
 278   mp *r2 = mp_new(2 * n + 1, 0);
 279   mp r;
 280
 281   /* --- Take a copy of the modulus --- */
 282
 283  if (!MP_POSP(m) || !MP_ODDP(m))
 284    return (-1);
 285   mm->m = MP_COPY(m);
 286
 287   /* --- Determine %$R^2$% --- */
 288
 289   mm->n = n;
 290   MPX_ZERO(r2->v, r2->vl - 1);
 291   r2->vl[-1] = 1;
 292
 293   /* --- Find the magic value @mi@ --- */
 294
 295   mp_build(&r, r2->v + n, r2->vl);
 296   mm->mi = mp_modinv(MP_NEW, m, &r);
 297   mm->mi = mp_sub(mm->mi, &r, mm->mi);
 298   MP_ENSURE(mm->mi, n);
 299
 300   /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */
 301
 302   mm->r2 = MP_NEW;
 303   mp_div(0, &mm->r2, r2, m);
 304   mm->r = mpmont_reduce(mm, MP_NEW, mm->r2);
 305   MP_DROP(r2);
 306   return (0);
 307 }
 308
 309 #endif
 310
 311 /* --- @mpmont_destroy@ --- *
 312  *
 313  * Arguments:   @mpmont *mm@ = pointer to a Montgomery reduction context
 314  *
 315  * Returns:     ---
 316  *
 317  * Use:         Disposes of a context when it's no longer of any use to
 318  *              anyone.
 319  */
 320
 321 void mpmont_destroy(mpmont *mm)
 322 {
 323   MP_DROP(mm->m);
 324   MP_DROP(mm->r);
 325   MP_DROP(mm->r2);
 326   MP_DROP(mm->mi);
 327 }
 328
 329 /* --- @mpmont_reduce@ --- *
 330  *
 331  * Arguments:   @mpmont *mm@ = pointer to Montgomery reduction context
 332  *              @mp *d@ = destination
 333  *              @mp *a@ = source, assumed positive
 334  *
 335  * Returns:     Result, %$a R^{-1} \bmod m$%.
 336  */
 337
 338 #ifdef MPMONT_DISABLE
 339
 340 mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
 341 {
 342   mp_div(0, &d, a, mm->m);
 343   return (d);
 344 }
 345
 346 #else
 347
 348 mp *mpmont_reduce(mpmont *mm, mp *d, mp *a)
 349 {
 350   size_t n = mm->n;
 351
 352   /* --- Check for serious Karatsuba reduction --- */
 353
 354   if (n > MPMONT_KTHRESH) {
 355     mp al;
 356     mpw *vl;
 357     mp *u;
 358
 359     if (MP_LEN(a) >= n) vl = a->v + n;
 360     else vl = a->vl;
 361     mp_build(&al, a->v, vl);
 362     u = mp_mul(MP_NEW, &al, mm->mi);
 363     if (MP_LEN(u) > n) u->vl = u->v + n;
 364     u = mp_mul(u, u, mm->m);
 365     d = mp_add(d, a, u);
 366     MP_ENSURE(d, n);
 367     mp_drop(u);
 368   }
 369
 370   /* --- Otherwise do it the hard way --- */
 371
 372   else {
 373     a = MP_COPY(a);
 374     if (d) MP_DROP(d);
 375     d = a;
 376     MP_DEST(d, 2*mm->n + 1, a->f);
 377     redccore(d->v, d->vl, mm->m->v, mm->n, mm->mi->v);
 378   }
 379
 380   /* --- Wrap everything up --- */
 381
 382   finish(mm, d);
 383   return (d);
 384 }
 385
 386 #endif
 387
 388 /* --- @mpmont_mul@ --- *
 389  *
 390  * Arguments:   @mpmont *mm@ = pointer to Montgomery reduction context
 391  *              @mp *d@ = destination
 392  *              @mp *a, *b@ = sources, assumed positive
 393  *
 394  * Returns:     Result, %$a b R^{-1} \bmod m$%.
 395  */
 396
 397 #ifdef MPMONT_DISABLE
 398
 399 mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
 400 {
 401   d = mp_mul(d, a, b);
 402   mp_div(0, &d, d, mm->m);
 403   return (d);
 404 }
 405
 406 #else
 407
 408 mp *mpmont_mul(mpmont *mm, mp *d, mp *a, mp *b)
 409 {
 410   size_t n = mm->n;
 411
 412   if (n > MPMONT_KTHRESH) {
 413     d = mp_mul(d, a, b);
 414     d = mpmont_reduce(mm, d, d);
 415   } else {
 416     a = MP_COPY(a); b = MP_COPY(b);
 417     MP_DEST(d, 2*n + 1, a->f | b->f | MP_UNDEF);
 418     mulcore(d->v, d->vl, a->v, a->vl, b->v, b->vl,
 419             mm->m->v, mm->n, mm->mi->v);
 420     d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG);
 421     finish(mm, d);
 422     MP_DROP(a); MP_DROP(b);
 423   }
 424
 425   return (d);
 426 }
 427
 428 #endif
 429
 430 /*----- Test rig ----------------------------------------------------------*/
 431
 432 #ifdef TEST_RIG
 433
 434 static int tcreate(dstr *v)
 435 {
 436   mp *m = *(mp **)v[0].buf;
 437   mp *mi = *(mp **)v[1].buf;
 438   mp *r = *(mp **)v[2].buf;
 439   mp *r2 = *(mp **)v[3].buf;
 440
 441   mpmont mm;
 442   int ok = 1;
 443
 444   mpmont_create(&mm, m);
 445
 446   if (mm.mi->v[0] != mi->v[0]) {
 447     fprintf(stderr, "\n*** bad mi: found %lu, expected %lu",
 448             (unsigned long)mm.mi->v[0], (unsigned long)mi->v[0]);
 449     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 450     fputc('\n', stderr);
 451     ok = 0;
 452   }
 453
 454   if (!MP_EQ(mm.r, r)) {
 455     fputs("\n*** bad r", stderr);
 456     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 457     fputs("\nexpected ", stderr); mp_writefile(r, stderr, 10);
 458     fputs("\n   found ", stderr); mp_writefile(mm.r, stderr, 10);
 459     fputc('\n', stderr);
 460     ok = 0;
 461   }
 462
 463   if (!MP_EQ(mm.r2, r2)) {
 464     fputs("\n*** bad r2", stderr);
 465     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 466     fputs("\nexpected ", stderr); mp_writefile(r2, stderr, 10);
 467     fputs("\n   found ", stderr); mp_writefile(mm.r2, stderr, 10);
 468     fputc('\n', stderr);
 469     ok = 0;
 470   }
 471
 472   MP_DROP(m);
 473   MP_DROP(mi);
 474   MP_DROP(r);
 475   MP_DROP(r2);
 476   mpmont_destroy(&mm);
 477   assert(mparena_count(MPARENA_GLOBAL) == 0);
 478   return (ok);
 479 }
 480
 481 static int tmul(dstr *v)
 482 {
 483   mp *m = *(mp **)v[0].buf;
 484   mp *a = *(mp **)v[1].buf;
 485   mp *b = *(mp **)v[2].buf;
 486   mp *r = *(mp **)v[3].buf;
 487   int ok = 1;
 488
 489   mpmont mm;
 490   mpmont_create(&mm, m);
 491
 492   {
 493     mp *qr = mp_mul(MP_NEW, a, b);
 494     mp_div(0, &qr, qr, m);
 495
 496     if (!MP_EQ(qr, r)) {
 497       fputs("\n*** classical modmul failed", stderr);
 498       fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
 499       fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
 500       fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
 501       fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
 502       fputs("\nqr = ", stderr); mp_writefile(qr, stderr, 10);
 503       fputc('\n', stderr);
 504       ok = 0;
 505     }
 506
 507     mp_drop(qr);
 508   }
 509
 510   {
 511     mp *ar = mpmont_mul(&mm, MP_NEW, a, mm.r2);
 512     mp *br = mpmont_mul(&mm, MP_NEW, b, mm.r2);
 513     mp *mr = mpmont_mul(&mm, MP_NEW, ar, br);
 514     mr = mpmont_reduce(&mm, mr, mr);
 515     if (!MP_EQ(mr, r)) {
 516       fputs("\n*** montgomery modmul failed", stderr);
 517       fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
 518       fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
 519       fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
 520       fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
 521       fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10);
 522       fputc('\n', stderr);
 523       ok = 0;
 524     }
 525     MP_DROP(ar); MP_DROP(br);
 526     mp_drop(mr);
 527   }
 528
 529
 530   MP_DROP(m);
 531   MP_DROP(a);
 532   MP_DROP(b);
 533   MP_DROP(r);
 534   mpmont_destroy(&mm);
 535   assert(mparena_count(MPARENA_GLOBAL) == 0);
 536   return ok;
 537 }
 538
 539 static test_chunk tests[] = {
 540   { "create", tcreate, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 541   { "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 542   { 0, 0, { 0 } },
 543 };
 544
 545 int main(int argc, char *argv[])
 546 {
 547   sub_init();
 548   test_run(argc, argv, tests, SRCDIR "/t/mpmont");
 549   return (0);
 550 }
 551
 552 #endif
 553
 554 /*----- That's all, folks -------------------------------------------------*/