crypto/openssl-0.9/crypto/bn/bn_mul.c

   1 /* crypto/bn/bn_mul.c */
   2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
   3  * All rights reserved.
   4  *
   5  * This package is an SSL implementation written
   6  * by Eric Young (eay@cryptsoft.com).
   7  * The implementation was written so as to conform with Netscapes SSL.
   8  *
   9  * This library is free for commercial and non-commercial use as long as
  10  * the following conditions are aheared to.  The following conditions
  11  * apply to all code found in this distribution, be it the RC4, RSA,
  12  * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
  13  * included with this distribution is covered by the same copyright terms
  14  * except that the holder is Tim Hudson (tjh@cryptsoft.com).
  15  *
  16  * Copyright remains Eric Young's, and as such any Copyright notices in
  17  * the code are not to be removed.
  18  * If this package is used in a product, Eric Young should be given attribution
  19  * as the author of the parts of the library used.
  20  * This can be in the form of a textual message at program startup or
  21  * in documentation (online or textual) provided with the package.
  22  *
  23  * Redistribution and use in source and binary forms, with or without
  24  * modification, are permitted provided that the following conditions
  25  * are met:
  26  * 1. Redistributions of source code must retain the copyright
  27  *    notice, this list of conditions and the following disclaimer.
  28  * 2. Redistributions in binary form must reproduce the above copyright
  29  *    notice, this list of conditions and the following disclaimer in the
  30  *    documentation and/or other materials provided with the distribution.
  31  * 3. All advertising materials mentioning features or use of this software
  32  *    must display the following acknowledgement:
  33  *    "This product includes cryptographic software written by
  34  *     Eric Young (eay@cryptsoft.com)"
  35  *    The word 'cryptographic' can be left out if the rouines from the library
  36  *    being used are not cryptographic related :-).
  37  * 4. If you include any Windows specific code (or a derivative thereof) from
  38  *    the apps directory (application code) you must include an acknowledgement:
  39  *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
  40  *
  41  * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
  42  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  43  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  44  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
  45  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  46  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  47  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  48  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  49  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  50  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  51  * SUCH DAMAGE.
  52  *
  53  * The licence and distribution terms for any publically available version or
  54  * derivative of this code cannot be changed.  i.e. this code cannot simply be
  55  * copied and put under another distribution licence
  56  * [including the GNU Public Licence.]
  57  */
  58
  59 #ifndef BN_DEBUG
  60 # undef NDEBUG /* avoid conflicting definitions */
  61 # define NDEBUG
  62 #endif
  63
  64 #include <stdio.h>
  65 #include <assert.h>
  66 #include "cryptlib.h"
  67 #include "bn_lcl.h"
  68
  69 #if defined(OPENSSL_NO_ASM) || !defined(OPENSSL_BN_ASM_PART_WORDS)
  70 /* Here follows specialised variants of bn_add_words() and
  71    bn_sub_words().  They have the property performing operations on
  72    arrays of different sizes.  The sizes of those arrays is expressed through
  73    cl, which is the common length ( basicall, min(len(a),len(b)) ), and dl,
  74    which is the delta between the two lengths, calculated as len(a)-len(b).
  75    All lengths are the number of BN_ULONGs...  For the operations that require
  76    a result array as parameter, it must have the length cl+abs(dl).
  77    These functions should probably end up in bn_asm.c as soon as there are
  78    assembler counterparts for the systems that use assembler files.  */
  79
  80 BN_ULONG bn_sub_part_words(BN_ULONG *r,
  81         const BN_ULONG *a, const BN_ULONG *b,
  82         int cl, int dl)
  83         {
  84         BN_ULONG c, t;
  85
  86         assert(cl >= 0);
  87         c = bn_sub_words(r, a, b, cl);
  88
  89         if (dl == 0)
  90                 return c;
  91
  92         r += cl;
  93         a += cl;
  94         b += cl;
  95
  96         if (dl < 0)
  97                 {
  98 #ifdef BN_COUNT
  99                 fprintf(stderr, "  bn_sub_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c);
 100 #endif
 101                 for (;;)
 102                         {
 103                         t = b[0];
 104                         r[0] = (0-t-c)&BN_MASK2;
 105                         if (t != 0) c=1;
 106                         if (++dl >= 0) break;
 107
 108                         t = b[1];
 109                         r[1] = (0-t-c)&BN_MASK2;
 110                         if (t != 0) c=1;
 111                         if (++dl >= 0) break;
 112
 113                         t = b[2];
 114                         r[2] = (0-t-c)&BN_MASK2;
 115                         if (t != 0) c=1;
 116                         if (++dl >= 0) break;
 117
 118                         t = b[3];
 119                         r[3] = (0-t-c)&BN_MASK2;
 120                         if (t != 0) c=1;
 121                         if (++dl >= 0) break;
 122
 123                         b += 4;
 124                         r += 4;
 125                         }
 126                 }
 127         else
 128                 {
 129                 int save_dl = dl;
 130 #ifdef BN_COUNT
 131                 fprintf(stderr, "  bn_sub_part_words %d + %d (dl > 0, c = %d)\n", cl, dl, c);
 132 #endif
 133                 while(c)
 134                         {
 135                         t = a[0];
 136                         r[0] = (t-c)&BN_MASK2;
 137                         if (t != 0) c=0;
 138                         if (--dl <= 0) break;
 139
 140                         t = a[1];
 141                         r[1] = (t-c)&BN_MASK2;
 142                         if (t != 0) c=0;
 143                         if (--dl <= 0) break;
 144
 145                         t = a[2];
 146                         r[2] = (t-c)&BN_MASK2;
 147                         if (t != 0) c=0;
 148                         if (--dl <= 0) break;
 149
 150                         t = a[3];
 151                         r[3] = (t-c)&BN_MASK2;
 152                         if (t != 0) c=0;
 153                         if (--dl <= 0) break;
 154
 155                         save_dl = dl;
 156                         a += 4;
 157                         r += 4;
 158                         }
 159                 if (dl > 0)
 160                         {
 161 #ifdef BN_COUNT
 162                         fprintf(stderr, "  bn_sub_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
 163 #endif
 164                         if (save_dl > dl)
 165                                 {
 166                                 switch (save_dl - dl)
 167                                         {
 168                                 case 1:
 169                                         r[1] = a[1];
 170                                         if (--dl <= 0) break;
 171                                 case 2:
 172                                         r[2] = a[2];
 173                                         if (--dl <= 0) break;
 174                                 case 3:
 175                                         r[3] = a[3];
 176                                         if (--dl <= 0) break;
 177                                         }
 178                                 a += 4;
 179                                 r += 4;
 180                                 }
 181                         }
 182                 if (dl > 0)
 183                         {
 184 #ifdef BN_COUNT
 185                         fprintf(stderr, "  bn_sub_part_words %d + %d (dl > 0, copy)\n", cl, dl);
 186 #endif
 187                         for(;;)
 188                                 {
 189                                 r[0] = a[0];
 190                                 if (--dl <= 0) break;
 191                                 r[1] = a[1];
 192                                 if (--dl <= 0) break;
 193                                 r[2] = a[2];
 194                                 if (--dl <= 0) break;
 195                                 r[3] = a[3];
 196                                 if (--dl <= 0) break;
 197
 198                                 a += 4;
 199                                 r += 4;
 200                                 }
 201                         }
 202                 }
 203         return c;
 204         }
 205 #endif
 206
 207 BN_ULONG bn_add_part_words(BN_ULONG *r,
 208         const BN_ULONG *a, const BN_ULONG *b,
 209         int cl, int dl)
 210         {
 211         BN_ULONG c, l, t;
 212
 213         assert(cl >= 0);
 214         c = bn_add_words(r, a, b, cl);
 215
 216         if (dl == 0)
 217                 return c;
 218
 219         r += cl;
 220         a += cl;
 221         b += cl;
 222
 223         if (dl < 0)
 224                 {
 225                 int save_dl = dl;
 226 #ifdef BN_COUNT
 227                 fprintf(stderr, "  bn_add_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c);
 228 #endif
 229                 while (c)
 230                         {
 231                         l=(c+b[0])&BN_MASK2;
 232                         c=(l < c);
 233                         r[0]=l;
 234                         if (++dl >= 0) break;
 235
 236                         l=(c+b[1])&BN_MASK2;
 237                         c=(l < c);
 238                         r[1]=l;
 239                         if (++dl >= 0) break;
 240
 241                         l=(c+b[2])&BN_MASK2;
 242                         c=(l < c);
 243                         r[2]=l;
 244                         if (++dl >= 0) break;
 245
 246                         l=(c+b[3])&BN_MASK2;
 247                         c=(l < c);
 248                         r[3]=l;
 249                         if (++dl >= 0) break;
 250
 251                         save_dl = dl;
 252                         b+=4;
 253                         r+=4;
 254                         }
 255                 if (dl < 0)
 256                         {
 257 #ifdef BN_COUNT
 258                         fprintf(stderr, "  bn_add_part_words %d + %d (dl < 0, c == 0)\n", cl, dl);
 259 #endif
 260                         if (save_dl < dl)
 261                                 {
 262                                 switch (dl - save_dl)
 263                                         {
 264                                 case 1:
 265                                         r[1] = b[1];
 266                                         if (++dl >= 0) break;
 267                                 case 2:
 268                                         r[2] = b[2];
 269                                         if (++dl >= 0) break;
 270                                 case 3:
 271                                         r[3] = b[3];
 272                                         if (++dl >= 0) break;
 273                                         }
 274                                 b += 4;
 275                                 r += 4;
 276                                 }
 277                         }
 278                 if (dl < 0)
 279                         {
 280 #ifdef BN_COUNT
 281                         fprintf(stderr, "  bn_add_part_words %d + %d (dl < 0, copy)\n", cl, dl);
 282 #endif
 283                         for(;;)
 284                                 {
 285                                 r[0] = b[0];
 286                                 if (++dl >= 0) break;
 287                                 r[1] = b[1];
 288                                 if (++dl >= 0) break;
 289                                 r[2] = b[2];
 290                                 if (++dl >= 0) break;
 291                                 r[3] = b[3];
 292                                 if (++dl >= 0) break;
 293
 294                                 b += 4;
 295                                 r += 4;
 296                                 }
 297                         }
 298                 }
 299         else
 300                 {
 301                 int save_dl = dl;
 302 #ifdef BN_COUNT
 303                 fprintf(stderr, "  bn_add_part_words %d + %d (dl > 0)\n", cl, dl);
 304 #endif
 305                 while (c)
 306                         {
 307                         t=(a[0]+c)&BN_MASK2;
 308                         c=(t < c);
 309                         r[0]=t;
 310                         if (--dl <= 0) break;
 311
 312                         t=(a[1]+c)&BN_MASK2;
 313                         c=(t < c);
 314                         r[1]=t;
 315                         if (--dl <= 0) break;
 316
 317                         t=(a[2]+c)&BN_MASK2;
 318                         c=(t < c);
 319                         r[2]=t;
 320                         if (--dl <= 0) break;
 321
 322                         t=(a[3]+c)&BN_MASK2;
 323                         c=(t < c);
 324                         r[3]=t;
 325                         if (--dl <= 0) break;
 326
 327                         save_dl = dl;
 328                         a+=4;
 329                         r+=4;
 330                         }
 331 #ifdef BN_COUNT
 332                 fprintf(stderr, "  bn_add_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
 333 #endif
 334                 if (dl > 0)
 335                         {
 336                         if (save_dl > dl)
 337                                 {
 338                                 switch (save_dl - dl)
 339                                         {
 340                                 case 1:
 341                                         r[1] = a[1];
 342                                         if (--dl <= 0) break;
 343                                 case 2:
 344                                         r[2] = a[2];
 345                                         if (--dl <= 0) break;
 346                                 case 3:
 347                                         r[3] = a[3];
 348                                         if (--dl <= 0) break;
 349                                         }
 350                                 a += 4;
 351                                 r += 4;
 352                                 }
 353                         }
 354                 if (dl > 0)
 355                         {
 356 #ifdef BN_COUNT
 357                         fprintf(stderr, "  bn_add_part_words %d + %d (dl > 0, copy)\n", cl, dl);
 358 #endif
 359                         for(;;)
 360                                 {
 361                                 r[0] = a[0];
 362                                 if (--dl <= 0) break;
 363                                 r[1] = a[1];
 364                                 if (--dl <= 0) break;
 365                                 r[2] = a[2];
 366                                 if (--dl <= 0) break;
 367                                 r[3] = a[3];
 368                                 if (--dl <= 0) break;
 369
 370                                 a += 4;
 371                                 r += 4;
 372                                 }
 373                         }
 374                 }
 375         return c;
 376         }
 377
 378 #ifdef BN_RECURSION
 379 /* Karatsuba recursive multiplication algorithm
 380  * (cf. Knuth, The Art of Computer Programming, Vol. 2) */
 381
 382 /* r is 2*n2 words in size,
 383  * a and b are both n2 words in size.
 384  * n2 must be a power of 2.
 385  * We multiply and return the result.
 386  * t must be 2*n2 words in size
 387  * We calculate
 388  * a[0]*b[0]
 389  * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
 390  * a[1]*b[1]
 391  */
 392 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
 393         int dna, int dnb, BN_ULONG *t)
 394         {
 395         int n=n2/2,c1,c2;
 396         int tna=n+dna, tnb=n+dnb;
 397         unsigned int neg,zero;
 398         BN_ULONG ln,lo,*p;
 399
 400 # ifdef BN_COUNT
 401         fprintf(stderr," bn_mul_recursive %d * %d\n",n2,n2);
 402 # endif
 403 # ifdef BN_MUL_COMBA
 404 #  if 0
 405         if (n2 == 4)
 406                 {
 407                 bn_mul_comba4(r,a,b);
 408                 return;
 409                 }
 410 #  endif
 411         /* Only call bn_mul_comba 8 if n2 == 8 and the
 412          * two arrays are complete [steve]
 413          */
 414         if (n2 == 8 && dna == 0 && dnb == 0)
 415                 {
 416                 bn_mul_comba8(r,a,b);
 417                 return;
 418                 }
 419 # endif /* BN_MUL_COMBA */
 420         /* Else do normal multiply */
 421         if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
 422                 {
 423                 bn_mul_normal(r,a,n2+dna,b,n2+dnb);
 424                 if ((dna + dnb) < 0)
 425                         memset(&r[2*n2 + dna + dnb], 0,
 426                                 sizeof(BN_ULONG) * -(dna + dnb));
 427                 return;
 428                 }
 429         /* r=(a[0]-a[1])*(b[1]-b[0]) */
 430         c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
 431         c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
 432         zero=neg=0;
 433         switch (c1*3+c2)
 434                 {
 435         case -4:
 436                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
 437                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
 438                 break;
 439         case -3:
 440                 zero=1;
 441                 break;
 442         case -2:
 443                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
 444                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n); /* + */
 445                 neg=1;
 446                 break;
 447         case -1:
 448         case 0:
 449         case 1:
 450                 zero=1;
 451                 break;
 452         case 2:
 453                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna); /* + */
 454                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
 455                 neg=1;
 456                 break;
 457         case 3:
 458                 zero=1;
 459                 break;
 460         case 4:
 461                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna);
 462                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n);
 463                 break;
 464                 }
 465
 466 # ifdef BN_MUL_COMBA
 467         if (n == 4 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba4 could take
 468                                                extra args to do this well */
 469                 {
 470                 if (!zero)
 471                         bn_mul_comba4(&(t[n2]),t,&(t[n]));
 472                 else
 473                         memset(&(t[n2]),0,8*sizeof(BN_ULONG));
 474
 475                 bn_mul_comba4(r,a,b);
 476                 bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
 477                 }
 478         else if (n == 8 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba8 could
 479                                                     take extra args to do this
 480                                                     well */
 481                 {
 482                 if (!zero)
 483                         bn_mul_comba8(&(t[n2]),t,&(t[n]));
 484                 else
 485                         memset(&(t[n2]),0,16*sizeof(BN_ULONG));
 486
 487                 bn_mul_comba8(r,a,b);
 488                 bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
 489                 }
 490         else
 491 # endif /* BN_MUL_COMBA */
 492                 {
 493                 p= &(t[n2*2]);
 494                 if (!zero)
 495                         bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
 496                 else
 497                         memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
 498                 bn_mul_recursive(r,a,b,n,0,0,p);
 499                 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,dna,dnb,p);
 500                 }
 501
 502         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
 503          * r[10] holds (a[0]*b[0])
 504          * r[32] holds (b[1]*b[1])
 505          */
 506
 507         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
 508
 509         if (neg) /* if t[32] is negative */
 510                 {
 511                 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
 512                 }
 513         else
 514                 {
 515                 /* Might have a carry */
 516                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
 517                 }
 518
 519         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
 520          * r[10] holds (a[0]*b[0])
 521          * r[32] holds (b[1]*b[1])
 522          * c1 holds the carry bits
 523          */
 524         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
 525         if (c1)
 526                 {
 527                 p= &(r[n+n2]);
 528                 lo= *p;
 529                 ln=(lo+c1)&BN_MASK2;
 530                 *p=ln;
 531
 532                 /* The overflow will stop before we over write
 533                  * words we should not overwrite */
 534                 if (ln < (BN_ULONG)c1)
 535                         {
 536                         do      {
 537                                 p++;
 538                                 lo= *p;
 539                                 ln=(lo+1)&BN_MASK2;
 540                                 *p=ln;
 541                                 } while (ln == 0);
 542                         }
 543                 }
 544         }
 545
 546 /* n+tn is the word length
 547  * t needs to be n*4 is size, as does r */
 548 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n,
 549              int tna, int tnb, BN_ULONG *t)
 550         {
 551         int i,j,n2=n*2;
 552         int c1,c2,neg,zero;
 553         BN_ULONG ln,lo,*p;
 554
 555 # ifdef BN_COUNT
 556         fprintf(stderr," bn_mul_part_recursive (%d+%d) * (%d+%d)\n",
 557                 tna, n, tnb, n);
 558 # endif
 559         if (n < 8)
 560                 {
 561                 bn_mul_normal(r,a,n+tna,b,n+tnb);
 562                 return;
 563                 }
 564
 565         /* r=(a[0]-a[1])*(b[1]-b[0]) */
 566         c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
 567         c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
 568         zero=neg=0;
 569         switch (c1*3+c2)
 570                 {
 571         case -4:
 572                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
 573                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
 574                 break;
 575         case -3:
 576                 zero=1;
 577                 /* break; */
 578         case -2:
 579                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
 580                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n); /* + */
 581                 neg=1;
 582                 break;
 583         case -1:
 584         case 0:
 585         case 1:
 586                 zero=1;
 587                 /* break; */
 588         case 2:
 589                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna); /* + */
 590                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
 591                 neg=1;
 592                 break;
 593         case 3:
 594                 zero=1;
 595                 /* break; */
 596         case 4:
 597                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna);
 598                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n);
 599                 break;
 600                 }
 601                 /* The zero case isn't yet implemented here. The speedup
 602                    would probably be negligible. */
 603 # if 0
 604         if (n == 4)
 605                 {
 606                 bn_mul_comba4(&(t[n2]),t,&(t[n]));
 607                 bn_mul_comba4(r,a,b);
 608                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
 609                 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
 610                 }
 611         else
 612 # endif
 613         if (n == 8)
 614                 {
 615                 bn_mul_comba8(&(t[n2]),t,&(t[n]));
 616                 bn_mul_comba8(r,a,b);
 617                 bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
 618                 memset(&(r[n2+tna+tnb]),0,sizeof(BN_ULONG)*(n2-tna-tnb));
 619                 }
 620         else
 621                 {
 622                 p= &(t[n2*2]);
 623                 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
 624                 bn_mul_recursive(r,a,b,n,0,0,p);
 625                 i=n/2;
 626                 /* If there is only a bottom half to the number,
 627                  * just do it */
 628                 if (tna > tnb)
 629                         j = tna - i;
 630                 else
 631                         j = tnb - i;
 632                 if (j == 0)
 633                         {
 634                         bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),
 635                                 i,tna-i,tnb-i,p);
 636                         memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
 637                         }
 638                 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
 639                                 {
 640                                 bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
 641                                         i,tna-i,tnb-i,p);
 642                                 memset(&(r[n2+tna+tnb]),0,
 643                                         sizeof(BN_ULONG)*(n2-tna-tnb));
 644                                 }
 645                 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
 646                         {
 647                         memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
 648                         if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL
 649                                 && tnb < BN_MUL_RECURSIVE_SIZE_NORMAL)
 650                                 {
 651                                 bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
 652                                 }
 653                         else
 654                                 {
 655                                 for (;;)
 656                                         {
 657                                         i/=2;
 658                                         if (i <= tna && tna == tnb)
 659                                                 {
 660                                                 bn_mul_recursive(&(r[n2]),
 661                                                         &(a[n]),&(b[n]),
 662                                                         i,tna-i,tnb-i,p);
 663                                                 break;
 664                                                 }
 665                                         else if (i < tna || i < tnb)
 666                                                 {
 667                                                 bn_mul_part_recursive(&(r[n2]),
 668                                                         &(a[n]),&(b[n]),
 669                                                         i,tna-i,tnb-i,p);
 670                                                 break;
 671                                                 }
 672                                         }
 673                                 }
 674                         }
 675                 }
 676
 677         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
 678          * r[10] holds (a[0]*b[0])
 679          * r[32] holds (b[1]*b[1])
 680          */
 681
 682         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
 683
 684         if (neg) /* if t[32] is negative */
 685                 {
 686                 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
 687                 }
 688         else
 689                 {
 690                 /* Might have a carry */
 691                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
 692                 }
 693
 694         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
 695          * r[10] holds (a[0]*b[0])
 696          * r[32] holds (b[1]*b[1])
 697          * c1 holds the carry bits
 698          */
 699         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
 700         if (c1)
 701                 {
 702                 p= &(r[n+n2]);
 703                 lo= *p;
 704                 ln=(lo+c1)&BN_MASK2;
 705                 *p=ln;
 706
 707                 /* The overflow will stop before we over write
 708                  * words we should not overwrite */
 709                 if (ln < (BN_ULONG)c1)
 710                         {
 711                         do      {
 712                                 p++;
 713                                 lo= *p;
 714                                 ln=(lo+1)&BN_MASK2;
 715                                 *p=ln;
 716                                 } while (ln == 0);
 717                         }
 718                 }
 719         }
 720
 721 /* a and b must be the same size, which is n2.
 722  * r needs to be n2 words and t needs to be n2*2
 723  */
 724 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
 725              BN_ULONG *t)
 726         {
 727         int n=n2/2;
 728
 729 # ifdef BN_COUNT
 730         fprintf(stderr," bn_mul_low_recursive %d * %d\n",n2,n2);
 731 # endif
 732
 733         bn_mul_recursive(r,a,b,n,0,0,&(t[0]));
 734         if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
 735                 {
 736                 bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
 737                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 738                 bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
 739                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 740                 }
 741         else
 742                 {
 743                 bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
 744                 bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
 745                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 746                 bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
 747                 }
 748         }
 749
 750 /* a and b must be the same size, which is n2.
 751  * r needs to be n2 words and t needs to be n2*2
 752  * l is the low words of the output.
 753  * t needs to be n2*3
 754  */
 755 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
 756              BN_ULONG *t)
 757         {
 758         int i,n;
 759         int c1,c2;
 760         int neg,oneg,zero;
 761         BN_ULONG ll,lc,*lp,*mp;
 762
 763 # ifdef BN_COUNT
 764         fprintf(stderr," bn_mul_high %d * %d\n",n2,n2);
 765 # endif
 766         n=n2/2;
 767
 768         /* Calculate (al-ah)*(bh-bl) */
 769         neg=zero=0;
 770         c1=bn_cmp_words(&(a[0]),&(a[n]),n);
 771         c2=bn_cmp_words(&(b[n]),&(b[0]),n);
 772         switch (c1*3+c2)
 773                 {
 774         case -4:
 775                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
 776                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
 777                 break;
 778         case -3:
 779                 zero=1;
 780                 break;
 781         case -2:
 782                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
 783                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
 784                 neg=1;
 785                 break;
 786         case -1:
 787         case 0:
 788         case 1:
 789                 zero=1;
 790                 break;
 791         case 2:
 792                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
 793                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
 794                 neg=1;
 795                 break;
 796         case 3:
 797                 zero=1;
 798                 break;
 799         case 4:
 800                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
 801                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
 802                 break;
 803                 }
 804
 805         oneg=neg;
 806         /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
 807         /* r[10] = (a[1]*b[1]) */
 808 # ifdef BN_MUL_COMBA
 809         if (n == 8)
 810                 {
 811                 bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
 812                 bn_mul_comba8(r,&(a[n]),&(b[n]));
 813                 }
 814         else
 815 # endif
 816                 {
 817                 bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,0,0,&(t[n2]));
 818                 bn_mul_recursive(r,&(a[n]),&(b[n]),n,0,0,&(t[n2]));
 819                 }
 820
 821         /* s0 == low(al*bl)
 822          * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
 823          * We know s0 and s1 so the only unknown is high(al*bl)
 824          * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
 825          * high(al*bl) == s1 - (r[0]+l[0]+t[0])
 826          */
 827         if (l != NULL)
 828                 {
 829                 lp= &(t[n2+n]);
 830                 c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
 831                 }
 832         else
 833                 {
 834                 c1=0;
 835                 lp= &(r[0]);
 836                 }
 837
 838         if (neg)
 839                 neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
 840         else
 841                 {
 842                 bn_add_words(&(t[n2]),lp,&(t[0]),n);
 843                 neg=0;
 844                 }
 845
 846         if (l != NULL)
 847                 {
 848                 bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
 849                 }
 850         else
 851                 {
 852                 lp= &(t[n2+n]);
 853                 mp= &(t[n2]);
 854                 for (i=0; i<n; i++)
 855                         lp[i]=((~mp[i])+1)&BN_MASK2;
 856                 }
 857
 858         /* s[0] = low(al*bl)
 859          * t[3] = high(al*bl)
 860          * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
 861          * r[10] = (a[1]*b[1])
 862          */
 863         /* R[10] = al*bl
 864          * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
 865          * R[32] = ah*bh
 866          */
 867         /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
 868          * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
 869          * R[3]=r[1]+(carry/borrow)
 870          */
 871         if (l != NULL)
 872                 {
 873                 lp= &(t[n2]);
 874                 c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
 875                 }
 876         else
 877                 {
 878                 lp= &(t[n2+n]);
 879                 c1=0;
 880                 }
 881         c1+=(int)(bn_add_words(&(t[n2]),lp,  &(r[0]),n));
 882         if (oneg)
 883                 c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
 884         else
 885                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));
 886
 887         c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
 888         c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
 889         if (oneg)
 890                 c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
 891         else
 892                 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
 893
 894         if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
 895                 {
 896                 i=0;
 897                 if (c1 > 0)
 898                         {
 899                         lc=c1;
 900                         do      {
 901                                 ll=(r[i]+lc)&BN_MASK2;
 902                                 r[i++]=ll;
 903                                 lc=(lc > ll);
 904                                 } while (lc);
 905                         }
 906                 else
 907                         {
 908                         lc= -c1;
 909                         do      {
 910                                 ll=r[i];
 911                                 r[i++]=(ll-lc)&BN_MASK2;
 912                                 lc=(lc > ll);
 913                                 } while (lc);
 914                         }
 915                 }
 916         if (c2 != 0) /* Add starting at r[1] */
 917                 {
 918                 i=n;
 919                 if (c2 > 0)
 920                         {
 921                         lc=c2;
 922                         do      {
 923                                 ll=(r[i]+lc)&BN_MASK2;
 924                                 r[i++]=ll;
 925                                 lc=(lc > ll);
 926                                 } while (lc);
 927                         }
 928                 else
 929                         {
 930                         lc= -c2;
 931                         do      {
 932                                 ll=r[i];
 933                                 r[i++]=(ll-lc)&BN_MASK2;
 934                                 lc=(lc > ll);
 935                                 } while (lc);
 936                         }
 937                 }
 938         }
 939 #endif /* BN_RECURSION */
 940
 941 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
 942         {
 943         int ret=0;
 944         int top,al,bl;
 945         BIGNUM *rr;
 946 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 947         int i;
 948 #endif
 949 #ifdef BN_RECURSION
 950         BIGNUM *t=NULL;
 951         int j=0,k;
 952 #endif
 953
 954 #ifdef BN_COUNT
 955         fprintf(stderr,"BN_mul %d * %d\n",a->top,b->top);
 956 #endif
 957
 958         bn_check_top(a);
 959         bn_check_top(b);
 960         bn_check_top(r);
 961
 962         al=a->top;
 963         bl=b->top;
 964
 965         if ((al == 0) || (bl == 0))
 966                 {
 967                 BN_zero(r);
 968                 return(1);
 969                 }
 970         top=al+bl;
 971
 972         BN_CTX_start(ctx);
 973         if ((r == a) || (r == b))
 974                 {
 975                 if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
 976                 }
 977         else
 978                 rr = r;
 979         rr->neg=a->neg^b->neg;
 980
 981 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 982         i = al-bl;
 983 #endif
 984 #ifdef BN_MUL_COMBA
 985         if (i == 0)
 986                 {
 987 # if 0
 988                 if (al == 4)
 989                         {
 990                         if (bn_wexpand(rr,8) == NULL) goto err;
 991                         rr->top=8;
 992                         bn_mul_comba4(rr->d,a->d,b->d);
 993                         goto end;
 994                         }
 995 # endif
 996                 if (al == 8)
 997                         {
 998                         if (bn_wexpand(rr,16) == NULL) goto err;
 999                         rr->top=16;
1000                         bn_mul_comba8(rr->d,a->d,b->d);
1001                         goto end;
1002                         }
1003                 }
1004 #endif /* BN_MUL_COMBA */
1005 #ifdef BN_RECURSION
1006         if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))
1007                 {
1008                 if (i >= -1 && i <= 1)
1009                         {
1010                         int sav_j =0;
1011                         /* Find out the power of two lower or equal
1012                            to the longest of the two numbers */
1013                         if (i >= 0)
1014                                 {
1015                                 j = BN_num_bits_word((BN_ULONG)al);
1016                                 }
1017                         if (i == -1)
1018                                 {
1019                                 j = BN_num_bits_word((BN_ULONG)bl);
1020                                 }
1021                         sav_j = j;
1022                         j = 1<<(j-1);
1023                         assert(j <= al || j <= bl);
1024                         k = j+j;
1025                         t = BN_CTX_get(ctx);
1026                         if (al > j || bl > j)
1027                                 {
1028                                 bn_wexpand(t,k*4);
1029                                 bn_wexpand(rr,k*4);
1030                                 bn_mul_part_recursive(rr->d,a->d,b->d,
1031                                         j,al-j,bl-j,t->d);
1032                                 }
1033                         else    /* al <= j || bl <= j */
1034                                 {
1035                                 bn_wexpand(t,k*2);
1036                                 bn_wexpand(rr,k*2);
1037                                 bn_mul_recursive(rr->d,a->d,b->d,
1038                                         j,al-j,bl-j,t->d);
1039                                 }
1040                         rr->top=top;
1041                         goto end;
1042                         }
1043 #if 0
1044                 if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
1045                         {
1046                         BIGNUM *tmp_bn = (BIGNUM *)b;
1047                         if (bn_wexpand(tmp_bn,al) == NULL) goto err;
1048                         tmp_bn->d[bl]=0;
1049                         bl++;
1050                         i--;
1051                         }
1052                 else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
1053                         {
1054                         BIGNUM *tmp_bn = (BIGNUM *)a;
1055                         if (bn_wexpand(tmp_bn,bl) == NULL) goto err;
1056                         tmp_bn->d[al]=0;
1057                         al++;
1058                         i++;
1059                         }
1060                 if (i == 0)
1061                         {
1062                         /* symmetric and > 4 */
1063                         /* 16 or larger */
1064                         j=BN_num_bits_word((BN_ULONG)al);
1065                         j=1<<(j-1);
1066                         k=j+j;
1067                         t = BN_CTX_get(ctx);
1068                         if (al == j) /* exact multiple */
1069                                 {
1070                                 if (bn_wexpand(t,k*2) == NULL) goto err;
1071                                 if (bn_wexpand(rr,k*2) == NULL) goto err;
1072                                 bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
1073                                 }
1074                         else
1075                                 {
1076                                 if (bn_wexpand(t,k*4) == NULL) goto err;
1077                                 if (bn_wexpand(rr,k*4) == NULL) goto err;
1078                                 bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
1079                                 }
1080                         rr->top=top;
1081                         goto end;
1082                         }
1083 #endif
1084                 }
1085 #endif /* BN_RECURSION */
1086         if (bn_wexpand(rr,top) == NULL) goto err;
1087         rr->top=top;
1088         bn_mul_normal(rr->d,a->d,al,b->d,bl);
1089
1090 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
1091 end:
1092 #endif
1093         bn_correct_top(rr);
1094         if (r != rr) BN_copy(r,rr);
1095         ret=1;
1096 err:
1097         bn_check_top(r);
1098         BN_CTX_end(ctx);
1099         return(ret);
1100         }
1101
1102 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
1103         {
1104         BN_ULONG *rr;
1105
1106 #ifdef BN_COUNT
1107         fprintf(stderr," bn_mul_normal %d * %d\n",na,nb);
1108 #endif
1109
1110         if (na < nb)
1111                 {
1112                 int itmp;
1113                 BN_ULONG *ltmp;
1114
1115                 itmp=na; na=nb; nb=itmp;
1116                 ltmp=a;   a=b;   b=ltmp;
1117
1118                 }
1119         rr= &(r[na]);
1120         if (nb <= 0)
1121                 {
1122                 (void)bn_mul_words(r,a,na,0);
1123                 return;
1124                 }
1125         else
1126                 rr[0]=bn_mul_words(r,a,na,b[0]);
1127
1128         for (;;)
1129                 {
1130                 if (--nb <= 0) return;
1131                 rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
1132                 if (--nb <= 0) return;
1133                 rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
1134                 if (--nb <= 0) return;
1135                 rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
1136                 if (--nb <= 0) return;
1137                 rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
1138                 rr+=4;
1139                 r+=4;
1140                 b+=4;
1141                 }
1142         }
1143
1144 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
1145         {
1146 #ifdef BN_COUNT
1147         fprintf(stderr," bn_mul_low_normal %d * %d\n",n,n);
1148 #endif
1149         bn_mul_words(r,a,n,b[0]);
1150
1151         for (;;)
1152                 {
1153                 if (--n <= 0) return;
1154                 bn_mul_add_words(&(r[1]),a,n,b[1]);
1155                 if (--n <= 0) return;
1156                 bn_mul_add_words(&(r[2]),a,n,b[2]);
1157                 if (--n <= 0) return;
1158                 bn_mul_add_words(&(r[3]),a,n,b[3]);
1159                 if (--n <= 0) return;
1160                 bn_mul_add_words(&(r[4]),a,n,b[4]);
1161                 r+=4;
1162                 b+=4;
1163                 }
1164         }