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