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   MAYBE_REDC4(x86_avx)
  94 #endif
  95
  96 #if CPUFAM_AMD64
  97   MAYBE_REDC4(amd64_sse2)
  98   MAYBE_REDC4(amd64_avx)
  99 #endif
 100
 101 #if CPUFAM_ARMEL
 102   MAYBE_REDC4(arm_neon)
 103 #endif
 104
 105 #if CPUFAM_ARM64
 106   MAYBE_REDC4(arm64_simd)
 107 #endif
 108
 109 static redccore__functype *pick_redccore(void)
 110 {
 111 #if CPUFAM_X86
 112   DISPATCH_PICK_COND(mpmont_reduce, maybe_redc4_x86_avx,
 113                      cpu_feature_p(CPUFEAT_X86_AVX));
 114   DISPATCH_PICK_COND(mpmont_reduce, maybe_redc4_x86_sse2,
 115                      cpu_feature_p(CPUFEAT_X86_SSE2));
 116 #endif
 117 #if CPUFAM_AMD64
 118   DISPATCH_PICK_COND(mpmont_reduce, maybe_redc4_amd64_avx,
 119                      cpu_feature_p(CPUFEAT_X86_AVX));
 120   DISPATCH_PICK_COND(mpmont_reduce, maybe_redc4_amd64_sse2,
 121                      cpu_feature_p(CPUFEAT_X86_SSE2));
 122 #endif
 123 #if CPUFAM_ARMEL
 124   DISPATCH_PICK_COND(mpmont_reduce, maybe_redc4_arm_neon,
 125                      cpu_feature_p(CPUFEAT_ARM_NEON));
 126 #endif
 127 #if CPUFAM_ARM64
 128   DISPATCH_PICK_COND(mpmont_reduce, maybe_redc4_arm64_simd, 1);
 129 #endif
 130   DISPATCH_PICK_FALLBACK(mpmont_reduce, simple_redccore);
 131 }
 132
 133 /* --- @mulcore@ --- *
 134  *
 135  * Arguments:   @mpw *dv, *dvl@ = base and limit of source/destination
 136  *              @const mpw *av, *avl@ = base and limit of first multiplicand
 137  *              @const mpw *bv, *bvl@ = base and limit of second multiplicand
 138  *              @const mpw *mv@ = base of modulus %$m$%
 139  *              @size_t n@ = length of modulus
 140  *              @const mpw *mi@ = base of REDC coefficient %$m'$%
 141  *
 142  * Returns:     ---
 143  *
 144  * Use:         Let %$a$% and %$b$% be the multiplicands.  Let %$w = a b$%.
 145  *              Store in %$d$% the value %$a b + (m' a b \bmod R) m$%.
 146  */
 147
 148 CPU_DISPATCH(static, (void), void, mulcore,
 149              (mpw *dv, mpw *dvl, const mpw *av, const mpw *avl,
 150               const mpw *bv, const mpw *bvl, const mpw *mv,
 151               size_t n, const mpw *mi),
 152              (dv, dvl, av, avl, bv, bvl, mv, n, mi),
 153              pick_mulcore, simple_mulcore);
 154
 155 static void simple_mulcore(mpw *dv, mpw *dvl,
 156                            const mpw *av, const mpw *avl,
 157                            const mpw *bv, const mpw *bvl,
 158                            const mpw *mv, size_t n, const mpw *mi)
 159 {
 160   mpw ai, b0, y, mi0 = *mi;
 161   const mpw *tv, *tvl;
 162   const mpw *mvl = mv + n;
 163   size_t i = 0;
 164
 165   /* --- Initial setup --- */
 166
 167   MPX_ZERO(dv, dvl);
 168   if (avl - av > bvl - bv) {
 169     tv = av; av = bv; bv = tv;
 170     tvl = avl; avl = bvl; bvl = tvl;
 171   }
 172   b0 = *bv;
 173
 174   /* --- Multiply, until we run out of multiplicand --- */
 175
 176   while (i < n && av < avl) {
 177     ai = *av++;
 178     y = MPW((*dv + ai*b0)*mi0);
 179     MPX_UMLAN(dv, dvl, bv, bvl, ai);
 180     MPX_UMLAN(dv, dvl, mv, mvl, y);
 181     dv++; i++;
 182   }
 183
 184   /* --- Continue reducing until we run out of modulus --- */
 185
 186   while (i < n) {
 187     y = MPW(*dv*mi0);
 188     MPX_UMLAN(dv, dvl, mv, mvl, y);
 189     dv++; i++;
 190   }
 191 }
 192
 193 #define MAYBE_MUL4(impl)                                                \
 194   extern void mpxmont_mul4_##impl(mpw *dv,                              \
 195                                   const mpw *av, const mpw *bv,         \
 196                                   const mpw *mv,                        \
 197                                   size_t n, const mpw *mi);             \
 198   static void maybe_mul4_##impl(mpw *dv, mpw *dvl,                      \
 199                            const mpw *av, const mpw *avl,               \
 200                            const mpw *bv, const mpw *bvl,               \
 201                            const mpw *mv, size_t n, const mpw *mi)      \
 202   {                                                                     \
 203     size_t an = avl - av, bn = bvl - bv;                                \
 204     if (n%4 || an != n || bn != n)                                      \
 205       simple_mulcore(dv, dvl, av, avl, bv, bvl, mv, n, mi);             \
 206     else {                                                              \
 207       mpxmont_mul4_##impl(dv, av, bv, mv, n, mi);                       \
 208       MPX_ZERO(dv + 2*n + 1, dvl);                                      \
 209     }                                                                   \
 210   }
 211
 212 #if CPUFAM_X86
 213   MAYBE_MUL4(x86_sse2)
 214   MAYBE_MUL4(x86_avx)
 215 #endif
 216
 217 #if CPUFAM_AMD64
 218   MAYBE_MUL4(amd64_sse2)
 219   MAYBE_MUL4(amd64_avx)
 220 #endif
 221
 222 #if CPUFAM_ARMEL
 223   MAYBE_MUL4(arm_neon)
 224 #endif
 225
 226 #if CPUFAM_ARM64
 227   MAYBE_MUL4(arm64_simd)
 228 #endif
 229
 230 static mulcore__functype *pick_mulcore(void)
 231 {
 232 #if CPUFAM_X86
 233   DISPATCH_PICK_COND(mpmont_mul, maybe_mul4_x86_avx,
 234                      cpu_feature_p(CPUFEAT_X86_AVX));
 235   DISPATCH_PICK_COND(mpmont_mul, maybe_mul4_x86_sse2,
 236                      cpu_feature_p(CPUFEAT_X86_SSE2));
 237 #endif
 238 #if CPUFAM_AMD64
 239   DISPATCH_PICK_COND(mpmont_mul, maybe_mul4_amd64_avx,
 240                      cpu_feature_p(CPUFEAT_X86_AVX));
 241   DISPATCH_PICK_COND(mpmont_mul, maybe_mul4_amd64_sse2,
 242                      cpu_feature_p(CPUFEAT_X86_SSE2));
 243 #endif
 244 #if CPUFAM_ARMEL
 245   DISPATCH_PICK_COND(mpmont_mul, maybe_mul4_arm_neon,
 246                      cpu_feature_p(CPUFEAT_ARM_NEON));
 247 #endif
 248 #if CPUFAM_ARM64
 249   DISPATCH_PICK_COND(mpmont_mul, maybe_mul4_arm64_simd, 1);
 250 #endif
 251   DISPATCH_PICK_FALLBACK(mpmont_mul, simple_mulcore);
 252 }
 253
 254 /* --- @finish@ --- *
 255  *
 256  * Arguments:   @const mpmont *mm@ = pointer to a Montgomery reduction
 257  *                      context
 258  *              *mp *d@ = pointer to mostly-reduced operand
 259  *
 260  * Returns:     ---
 261  *
 262  * Use:         Applies the finishing touches to Montgomery reduction.  The
 263  *              operand @d@ is a multiple of %$R%$ at this point, so it needs
 264  *              to be shifted down; the result might need a further
 265  *              subtraction to get it into the right interval; and we may
 266  *              need to do an additional subtraction if %$d$% is negative.
 267  */
 268
 269 static void finish(const mpmont *mm, mp *d)
 270 {
 271   mpw *dv = d->v, *dvl = d->vl;
 272   size_t n = mm->n;
 273
 274   memmove(dv, dv + n, MPWS(dvl - (dv + n)));
 275   dvl -= n;
 276
 277   if (MPX_UCMP(dv, dvl, >=, mm->m->v, mm->m->vl))
 278     mpx_usub(dv, dvl, dv, dvl, mm->m->v, mm->m->vl);
 279
 280   if (d->f & MP_NEG) {
 281     mpx_usub(dv, dvl, mm->m->v, mm->m->vl, dv, dvl);
 282     d->f &= ~MP_NEG;
 283   }
 284
 285   d->vl = dvl;
 286   MP_SHRINK(d);
 287 }
 288
 289 #endif
 290
 291 /*----- Reduction and multiplication --------------------------------------*/
 292
 293 /* --- @mpmont_create@ --- *
 294  *
 295  * Arguments:   @mpmont *mm@ = pointer to Montgomery reduction context
 296  *              @mp *m@ = modulus to use
 297  *
 298  * Returns:     Zero on success, nonzero on error.
 299  *
 300  * Use:         Initializes a Montgomery reduction context ready for use.
 301  *              The argument @m@ must be a positive odd integer.
 302  */
 303
 304 #ifdef MPMONT_DISABLE
 305
 306 int mpmont_create(mpmont *mm, mp *m)
 307 {
 308   mp_shrink(m);
 309   mm->m = MP_COPY(m);
 310   mm->r = MP_ONE;
 311   mm->r2 = MP_ONE;
 312   mm->mi = MP_ONE;
 313   return (0);
 314 }
 315
 316 #else
 317
 318 int mpmont_create(mpmont *mm, mp *m)
 319 {
 320   size_t n = MP_LEN(m);
 321   mp *r2 = mp_new(2 * n + 1, 0);
 322   mp r;
 323
 324   /* --- Take a copy of the modulus --- */
 325
 326  if (!MP_POSP(m) || !MP_ODDP(m))
 327    return (-1);
 328   mm->m = MP_COPY(m);
 329
 330   /* --- Determine %$R^2$% --- */
 331
 332   mm->n = n;
 333   MPX_ZERO(r2->v, r2->vl - 1);
 334   r2->vl[-1] = 1;
 335
 336   /* --- Find the magic value @mi@ --- */
 337
 338   mp_build(&r, r2->v + n, r2->vl);
 339   mm->mi = mp_modinv(MP_NEW, m, &r);
 340   mm->mi = mp_sub(mm->mi, &r, mm->mi);
 341   MP_ENSURE(mm->mi, n);
 342
 343   /* --- Discover the values %$R \bmod m$% and %$R^2 \bmod m$% --- */
 344
 345   mm->r2 = MP_NEW;
 346   mp_div(0, &mm->r2, r2, m);
 347   mm->r = mpmont_reduce(mm, MP_NEW, mm->r2);
 348   MP_DROP(r2);
 349   return (0);
 350 }
 351
 352 #endif
 353
 354 /* --- @mpmont_destroy@ --- *
 355  *
 356  * Arguments:   @mpmont *mm@ = pointer to a Montgomery reduction context
 357  *
 358  * Returns:     ---
 359  *
 360  * Use:         Disposes of a context when it's no longer of any use to
 361  *              anyone.
 362  */
 363
 364 void mpmont_destroy(mpmont *mm)
 365 {
 366   MP_DROP(mm->m);
 367   MP_DROP(mm->r);
 368   MP_DROP(mm->r2);
 369   MP_DROP(mm->mi);
 370 }
 371
 372 /* --- @mpmont_reduce@ --- *
 373  *
 374  * Arguments:   @const mpmont *mm@ = pointer to Montgomery reduction context
 375  *              @mp *d@ = destination
 376  *              @mp *a@ = source, assumed positive
 377  *
 378  * Returns:     Result, %$a R^{-1} \bmod m$%.
 379  */
 380
 381 #ifdef MPMONT_DISABLE
 382
 383 mp *mpmont_reduce(const mpmont *mm, mp *d, mp *a)
 384 {
 385   mp_div(0, &d, a, mm->m);
 386   return (d);
 387 }
 388
 389 #else
 390
 391 mp *mpmont_reduce(const mpmont *mm, mp *d, mp *a)
 392 {
 393   size_t n = mm->n;
 394
 395   /* --- Check for serious Karatsuba reduction --- */
 396
 397   if (n > MPMONT_KTHRESH) {
 398     mp al;
 399     mpw *vl;
 400     mp *u;
 401
 402     if (MP_LEN(a) >= n) vl = a->v + n;
 403     else vl = a->vl;
 404     mp_build(&al, a->v, vl);
 405     u = mp_mul(MP_NEW, &al, mm->mi);
 406     if (MP_LEN(u) > n) u->vl = u->v + n;
 407     u = mp_mul(u, u, mm->m);
 408     d = mp_add(d, a, u);
 409     MP_ENSURE(d, n);
 410     mp_drop(u);
 411   }
 412
 413   /* --- Otherwise do it the hard way --- */
 414
 415   else {
 416     a = MP_COPY(a);
 417     if (d) MP_DROP(d);
 418     d = a;
 419     MP_DEST(d, 2*mm->n + 1, a->f);
 420     redccore(d->v, d->vl, mm->m->v, mm->n, mm->mi->v);
 421   }
 422
 423   /* --- Wrap everything up --- */
 424
 425   finish(mm, d);
 426   return (d);
 427 }
 428
 429 #endif
 430
 431 /* --- @mpmont_mul@ --- *
 432  *
 433  * Arguments:   @const mpmont *mm@ = pointer to Montgomery reduction context
 434  *              @mp *d@ = destination
 435  *              @mp *a, *b@ = sources, assumed positive
 436  *
 437  * Returns:     Result, %$a b R^{-1} \bmod m$%.
 438  */
 439
 440 #ifdef MPMONT_DISABLE
 441
 442 mp *mpmont_mul(const mpmont *mm, mp *d, mp *a, mp *b)
 443 {
 444   d = mp_mul(d, a, b);
 445   mp_div(0, &d, d, mm->m);
 446   return (d);
 447 }
 448
 449 #else
 450
 451 mp *mpmont_mul(const mpmont *mm, mp *d, mp *a, mp *b)
 452 {
 453   size_t n = mm->n;
 454
 455   if (n > MPMONT_KTHRESH) {
 456     d = mp_mul(d, a, b);
 457     d = mpmont_reduce(mm, d, d);
 458   } else {
 459     a = MP_COPY(a); b = MP_COPY(b);
 460     MP_DEST(d, 2*n + 1, a->f | b->f | MP_UNDEF);
 461     mulcore(d->v, d->vl, a->v, a->vl, b->v, b->vl,
 462             mm->m->v, mm->n, mm->mi->v);
 463     d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG);
 464     finish(mm, d);
 465     MP_DROP(a); MP_DROP(b);
 466   }
 467
 468   return (d);
 469 }
 470
 471 #endif
 472
 473 /*----- Test rig ----------------------------------------------------------*/
 474
 475 #ifdef TEST_RIG
 476
 477 #ifdef ENABLE_ASM_DEBUG
 478 #  include "regdump.h"
 479 #endif
 480
 481 static int tcreate(dstr *v)
 482 {
 483   mp *m = *(mp **)v[0].buf;
 484   mp *mi = *(mp **)v[1].buf;
 485   mp *r = *(mp **)v[2].buf;
 486   mp *r2 = *(mp **)v[3].buf;
 487
 488   mpmont mm;
 489   int ok = 1;
 490
 491   mpmont_create(&mm, m);
 492
 493   if (mm.mi->v[0] != mi->v[0]) {
 494     fprintf(stderr, "\n*** bad mi: found %lu, expected %lu",
 495             (unsigned long)mm.mi->v[0], (unsigned long)mi->v[0]);
 496     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 497     fputc('\n', stderr);
 498     ok = 0;
 499   }
 500
 501   if (!MP_EQ(mm.r, r)) {
 502     fputs("\n*** bad r", stderr);
 503     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 504     fputs("\nexpected ", stderr); mp_writefile(r, stderr, 10);
 505     fputs("\n   found ", stderr); mp_writefile(mm.r, stderr, 10);
 506     fputc('\n', stderr);
 507     ok = 0;
 508   }
 509
 510   if (!MP_EQ(mm.r2, r2)) {
 511     fputs("\n*** bad r2", stderr);
 512     fputs("\nm = ", stderr); mp_writefile(m, stderr, 10);
 513     fputs("\nexpected ", stderr); mp_writefile(r2, stderr, 10);
 514     fputs("\n   found ", stderr); mp_writefile(mm.r2, stderr, 10);
 515     fputc('\n', stderr);
 516     ok = 0;
 517   }
 518
 519   MP_DROP(m);
 520   MP_DROP(mi);
 521   MP_DROP(r);
 522   MP_DROP(r2);
 523   mpmont_destroy(&mm);
 524   assert(mparena_count(MPARENA_GLOBAL) == 0);
 525   return (ok);
 526 }
 527
 528 static int tmul(dstr *v)
 529 {
 530   mp *m = *(mp **)v[0].buf;
 531   mp *a = *(mp **)v[1].buf;
 532   mp *b = *(mp **)v[2].buf;
 533   mp *r = *(mp **)v[3].buf;
 534   int ok = 1;
 535
 536   mpmont mm;
 537   mpmont_create(&mm, m);
 538
 539   {
 540     mp *qr = mp_mul(MP_NEW, a, b);
 541     mp_div(0, &qr, qr, m);
 542
 543     if (!MP_EQ(qr, r)) {
 544       fputs("\n*** classical modmul failed", stderr);
 545       fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
 546       fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
 547       fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
 548       fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
 549       fputs("\nqr = ", stderr); mp_writefile(qr, stderr, 10);
 550       fputc('\n', stderr);
 551       ok = 0;
 552     }
 553
 554     mp_drop(qr);
 555   }
 556
 557   {
 558     mp *ar = mpmont_mul(&mm, MP_NEW, a, mm.r2);
 559     mp *br = mpmont_mul(&mm, MP_NEW, b, mm.r2);
 560     mp *mr = mpmont_mul(&mm, MP_NEW, ar, br);
 561     mr = mpmont_reduce(&mm, mr, mr);
 562     if (!MP_EQ(mr, r)) {
 563       fputs("\n*** montgomery modmul failed", stderr);
 564       fputs("\n m = ", stderr); mp_writefile(m, stderr, 10);
 565       fputs("\n a = ", stderr); mp_writefile(a, stderr, 10);
 566       fputs("\n b = ", stderr); mp_writefile(b, stderr, 10);
 567       fputs("\n r = ", stderr); mp_writefile(r, stderr, 10);
 568       fputs("\nmr = ", stderr); mp_writefile(mr, stderr, 10);
 569       fputc('\n', stderr);
 570       ok = 0;
 571     }
 572     MP_DROP(ar); MP_DROP(br);
 573     mp_drop(mr);
 574   }
 575
 576   MP_DROP(m);
 577   MP_DROP(a);
 578   MP_DROP(b);
 579   MP_DROP(r);
 580   mpmont_destroy(&mm);
 581   assert(mparena_count(MPARENA_GLOBAL) == 0);
 582   return ok;
 583 }
 584
 585 static test_chunk tests[] = {
 586   { "create", tcreate, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 587   { "mul", tmul, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
 588   { 0, 0, { 0 } },
 589 };
 590
 591 int main(int argc, char *argv[])
 592 {
 593   sub_init();
 594 #ifdef ENABLE_ASM_DEBUG
 595   regdump_init();
 596 #endif
 597   test_run(argc, argv, tests, SRCDIR "/t/mpmont");
 598   return (0);
 599 }
 600
 601 #endif
 602
 603 /*----- That's all, folks -------------------------------------------------*/