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 #include <stdio.h>
  60 #include "cryptlib.h"
  61 #include "bn_lcl.h"
  62
  63 #ifdef BN_RECURSION
  64 /* r is 2*n2 words in size,
  65  * a and b are both n2 words in size.
  66  * n2 must be a power of 2.
  67  * We multiply and return the result.
  68  * t must be 2*n2 words in size
  69  * We calculate
  70  * a[0]*b[0]
  71  * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
  72  * a[1]*b[1]
  73  */
  74 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
  75              BN_ULONG *t)
  76         {
  77         int n=n2/2,c1,c2;
  78         unsigned int neg,zero;
  79         BN_ULONG ln,lo,*p;
  80
  81 # ifdef BN_COUNT
  82         printf(" bn_mul_recursive %d * %d\n",n2,n2);
  83 # endif
  84 # ifdef BN_MUL_COMBA
  85 #  if 0
  86         if (n2 == 4)
  87                 {
  88                 bn_mul_comba4(r,a,b);
  89                 return;
  90                 }
  91 #  endif
  92         if (n2 == 8)
  93                 {
  94                 bn_mul_comba8(r,a,b);
  95                 return;
  96                 }
  97 # endif /* BN_MUL_COMBA */
  98         if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
  99                 {
 100                 /* This should not happen */
 101                 bn_mul_normal(r,a,n2,b,n2);
 102                 return;
 103                 }
 104         /* r=(a[0]-a[1])*(b[1]-b[0]) */
 105         c1=bn_cmp_words(a,&(a[n]),n);
 106         c2=bn_cmp_words(&(b[n]),b,n);
 107         zero=neg=0;
 108         switch (c1*3+c2)
 109                 {
 110         case -4:
 111                 bn_sub_words(t,      &(a[n]),a,      n); /* - */
 112                 bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
 113                 break;
 114         case -3:
 115                 zero=1;
 116                 break;
 117         case -2:
 118                 bn_sub_words(t,      &(a[n]),a,      n); /* - */
 119                 bn_sub_words(&(t[n]),&(b[n]),b,      n); /* + */
 120                 neg=1;
 121                 break;
 122         case -1:
 123         case 0:
 124         case 1:
 125                 zero=1;
 126                 break;
 127         case 2:
 128                 bn_sub_words(t,      a,      &(a[n]),n); /* + */
 129                 bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
 130                 neg=1;
 131                 break;
 132         case 3:
 133                 zero=1;
 134                 break;
 135         case 4:
 136                 bn_sub_words(t,      a,      &(a[n]),n);
 137                 bn_sub_words(&(t[n]),&(b[n]),b,      n);
 138                 break;
 139                 }
 140
 141 # ifdef BN_MUL_COMBA
 142         if (n == 4)
 143                 {
 144                 if (!zero)
 145                         bn_mul_comba4(&(t[n2]),t,&(t[n]));
 146                 else
 147                         memset(&(t[n2]),0,8*sizeof(BN_ULONG));
 148
 149                 bn_mul_comba4(r,a,b);
 150                 bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
 151                 }
 152         else if (n == 8)
 153                 {
 154                 if (!zero)
 155                         bn_mul_comba8(&(t[n2]),t,&(t[n]));
 156                 else
 157                         memset(&(t[n2]),0,16*sizeof(BN_ULONG));
 158
 159                 bn_mul_comba8(r,a,b);
 160                 bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
 161                 }
 162         else
 163 # endif /* BN_MUL_COMBA */
 164                 {
 165                 p= &(t[n2*2]);
 166                 if (!zero)
 167                         bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
 168                 else
 169                         memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
 170                 bn_mul_recursive(r,a,b,n,p);
 171                 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,p);
 172                 }
 173
 174         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
 175          * r[10] holds (a[0]*b[0])
 176          * r[32] holds (b[1]*b[1])
 177          */
 178
 179         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
 180
 181         if (neg) /* if t[32] is negative */
 182                 {
 183                 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
 184                 }
 185         else
 186                 {
 187                 /* Might have a carry */
 188                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
 189                 }
 190
 191         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
 192          * r[10] holds (a[0]*b[0])
 193          * r[32] holds (b[1]*b[1])
 194          * c1 holds the carry bits
 195          */
 196         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
 197         if (c1)
 198                 {
 199                 p= &(r[n+n2]);
 200                 lo= *p;
 201                 ln=(lo+c1)&BN_MASK2;
 202                 *p=ln;
 203
 204                 /* The overflow will stop before we over write
 205                  * words we should not overwrite */
 206                 if (ln < (BN_ULONG)c1)
 207                         {
 208                         do      {
 209                                 p++;
 210                                 lo= *p;
 211                                 ln=(lo+1)&BN_MASK2;
 212                                 *p=ln;
 213                                 } while (ln == 0);
 214                         }
 215                 }
 216         }
 217
 218 /* n+tn is the word length
 219  * t needs to be n*4 is size, as does r */
 220 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int tn,
 221              int n, BN_ULONG *t)
 222         {
 223         int i,j,n2=n*2;
 224         unsigned int c1;
 225         BN_ULONG ln,lo,*p;
 226
 227 # ifdef BN_COUNT
 228         printf(" bn_mul_part_recursive %d * %d\n",tn+n,tn+n);
 229 # endif
 230         if (n < 8)
 231                 {
 232                 i=tn+n;
 233                 bn_mul_normal(r,a,i,b,i);
 234                 return;
 235                 }
 236
 237         /* r=(a[0]-a[1])*(b[1]-b[0]) */
 238         bn_sub_words(t,      a,      &(a[n]),n); /* + */
 239         bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
 240
 241 # if 0
 242         if (n == 4)
 243                 {
 244                 bn_mul_comba4(&(t[n2]),t,&(t[n]));
 245                 bn_mul_comba4(r,a,b);
 246                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
 247                 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
 248                 }
 249         else
 250 # endif
 251         if (n == 8)
 252                 {
 253                 bn_mul_comba8(&(t[n2]),t,&(t[n]));
 254                 bn_mul_comba8(r,a,b);
 255                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
 256                 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
 257                 }
 258         else
 259                 {
 260                 p= &(t[n2*2]);
 261                 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
 262                 bn_mul_recursive(r,a,b,n,p);
 263                 i=n/2;
 264                 /* If there is only a bottom half to the number,
 265                  * just do it */
 266                 j=tn-i;
 267                 if (j == 0)
 268                         {
 269                         bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),i,p);
 270                         memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
 271                         }
 272                 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
 273                                 {
 274                                 bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
 275                                         j,i,p);
 276                                 memset(&(r[n2+tn*2]),0,
 277                                         sizeof(BN_ULONG)*(n2-tn*2));
 278                                 }
 279                 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
 280                         {
 281                         memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
 282                         if (tn < BN_MUL_RECURSIVE_SIZE_NORMAL)
 283                                 {
 284                                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
 285                                 }
 286                         else
 287                                 {
 288                                 for (;;)
 289                                         {
 290                                         i/=2;
 291                                         if (i < tn)
 292                                                 {
 293                                                 bn_mul_part_recursive(&(r[n2]),
 294                                                         &(a[n]),&(b[n]),
 295                                                         tn-i,i,p);
 296                                                 break;
 297                                                 }
 298                                         else if (i == tn)
 299                                                 {
 300                                                 bn_mul_recursive(&(r[n2]),
 301                                                         &(a[n]),&(b[n]),
 302                                                         i,p);
 303                                                 break;
 304                                                 }
 305                                         }
 306                                 }
 307                         }
 308                 }
 309
 310         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
 311          * r[10] holds (a[0]*b[0])
 312          * r[32] holds (b[1]*b[1])
 313          */
 314
 315         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
 316         c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
 317
 318         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
 319          * r[10] holds (a[0]*b[0])
 320          * r[32] holds (b[1]*b[1])
 321          * c1 holds the carry bits
 322          */
 323         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
 324         if (c1)
 325                 {
 326                 p= &(r[n+n2]);
 327                 lo= *p;
 328                 ln=(lo+c1)&BN_MASK2;
 329                 *p=ln;
 330
 331                 /* The overflow will stop before we over write
 332                  * words we should not overwrite */
 333                 if (ln < c1)
 334                         {
 335                         do      {
 336                                 p++;
 337                                 lo= *p;
 338                                 ln=(lo+1)&BN_MASK2;
 339                                 *p=ln;
 340                                 } while (ln == 0);
 341                         }
 342                 }
 343         }
 344
 345 /* a and b must be the same size, which is n2.
 346  * r needs to be n2 words and t needs to be n2*2
 347  */
 348 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
 349              BN_ULONG *t)
 350         {
 351         int n=n2/2;
 352
 353 # ifdef BN_COUNT
 354         printf(" bn_mul_low_recursive %d * %d\n",n2,n2);
 355 # endif
 356
 357         bn_mul_recursive(r,a,b,n,&(t[0]));
 358         if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
 359                 {
 360                 bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
 361                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 362                 bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
 363                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 364                 }
 365         else
 366                 {
 367                 bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
 368                 bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
 369                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 370                 bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
 371                 }
 372         }
 373
 374 /* a and b must be the same size, which is n2.
 375  * r needs to be n2 words and t needs to be n2*2
 376  * l is the low words of the output.
 377  * t needs to be n2*3
 378  */
 379 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
 380              BN_ULONG *t)
 381         {
 382         int i,n;
 383         int c1,c2;
 384         int neg,oneg,zero;
 385         BN_ULONG ll,lc,*lp,*mp;
 386
 387 # ifdef BN_COUNT
 388         printf(" bn_mul_high %d * %d\n",n2,n2);
 389 # endif
 390         n=n2/2;
 391
 392         /* Calculate (al-ah)*(bh-bl) */
 393         neg=zero=0;
 394         c1=bn_cmp_words(&(a[0]),&(a[n]),n);
 395         c2=bn_cmp_words(&(b[n]),&(b[0]),n);
 396         switch (c1*3+c2)
 397                 {
 398         case -4:
 399                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
 400                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
 401                 break;
 402         case -3:
 403                 zero=1;
 404                 break;
 405         case -2:
 406                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
 407                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
 408                 neg=1;
 409                 break;
 410         case -1:
 411         case 0:
 412         case 1:
 413                 zero=1;
 414                 break;
 415         case 2:
 416                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
 417                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
 418                 neg=1;
 419                 break;
 420         case 3:
 421                 zero=1;
 422                 break;
 423         case 4:
 424                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
 425                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
 426                 break;
 427                 }
 428
 429         oneg=neg;
 430         /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
 431         /* r[10] = (a[1]*b[1]) */
 432 # ifdef BN_MUL_COMBA
 433         if (n == 8)
 434                 {
 435                 bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
 436                 bn_mul_comba8(r,&(a[n]),&(b[n]));
 437                 }
 438         else
 439 # endif
 440                 {
 441                 bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,&(t[n2]));
 442                 bn_mul_recursive(r,&(a[n]),&(b[n]),n,&(t[n2]));
 443                 }
 444
 445         /* s0 == low(al*bl)
 446          * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
 447          * We know s0 and s1 so the only unknown is high(al*bl)
 448          * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
 449          * high(al*bl) == s1 - (r[0]+l[0]+t[0])
 450          */
 451         if (l != NULL)
 452                 {
 453                 lp= &(t[n2+n]);
 454                 c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
 455                 }
 456         else
 457                 {
 458                 c1=0;
 459                 lp= &(r[0]);
 460                 }
 461
 462         if (neg)
 463                 neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
 464         else
 465                 {
 466                 bn_add_words(&(t[n2]),lp,&(t[0]),n);
 467                 neg=0;
 468                 }
 469
 470         if (l != NULL)
 471                 {
 472                 bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
 473                 }
 474         else
 475                 {
 476                 lp= &(t[n2+n]);
 477                 mp= &(t[n2]);
 478                 for (i=0; i<n; i++)
 479                         lp[i]=((~mp[i])+1)&BN_MASK2;
 480                 }
 481
 482         /* s[0] = low(al*bl)
 483          * t[3] = high(al*bl)
 484          * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
 485          * r[10] = (a[1]*b[1])
 486          */
 487         /* R[10] = al*bl
 488          * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
 489          * R[32] = ah*bh
 490          */
 491         /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
 492          * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
 493          * R[3]=r[1]+(carry/borrow)
 494          */
 495         if (l != NULL)
 496                 {
 497                 lp= &(t[n2]);
 498                 c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
 499                 }
 500         else
 501                 {
 502                 lp= &(t[n2+n]);
 503                 c1=0;
 504                 }
 505         c1+=(int)(bn_add_words(&(t[n2]),lp,  &(r[0]),n));
 506         if (oneg)
 507                 c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
 508         else
 509                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));
 510
 511         c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
 512         c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
 513         if (oneg)
 514                 c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
 515         else
 516                 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
 517
 518         if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
 519                 {
 520                 i=0;
 521                 if (c1 > 0)
 522                         {
 523                         lc=c1;
 524                         do      {
 525                                 ll=(r[i]+lc)&BN_MASK2;
 526                                 r[i++]=ll;
 527                                 lc=(lc > ll);
 528                                 } while (lc);
 529                         }
 530                 else
 531                         {
 532                         lc= -c1;
 533                         do      {
 534                                 ll=r[i];
 535                                 r[i++]=(ll-lc)&BN_MASK2;
 536                                 lc=(lc > ll);
 537                                 } while (lc);
 538                         }
 539                 }
 540         if (c2 != 0) /* Add starting at r[1] */
 541                 {
 542                 i=n;
 543                 if (c2 > 0)
 544                         {
 545                         lc=c2;
 546                         do      {
 547                                 ll=(r[i]+lc)&BN_MASK2;
 548                                 r[i++]=ll;
 549                                 lc=(lc > ll);
 550                                 } while (lc);
 551                         }
 552                 else
 553                         {
 554                         lc= -c2;
 555                         do      {
 556                                 ll=r[i];
 557                                 r[i++]=(ll-lc)&BN_MASK2;
 558                                 lc=(lc > ll);
 559                                 } while (lc);
 560                         }
 561                 }
 562         }
 563 #endif /* BN_RECURSION */
 564
 565 int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
 566         {
 567         int top,al,bl;
 568         BIGNUM *rr;
 569         int ret = 0;
 570 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 571         int i;
 572 #endif
 573 #ifdef BN_RECURSION
 574         BIGNUM *t;
 575         int j,k;
 576 #endif
 577
 578 #ifdef BN_COUNT
 579         printf("BN_mul %d * %d\n",a->top,b->top);
 580 #endif
 581
 582         bn_check_top(a);
 583         bn_check_top(b);
 584         bn_check_top(r);
 585
 586         al=a->top;
 587         bl=b->top;
 588         r->neg=a->neg^b->neg;
 589
 590         if ((al == 0) || (bl == 0))
 591                 {
 592                 BN_zero(r);
 593                 return(1);
 594                 }
 595         top=al+bl;
 596
 597         BN_CTX_start(ctx);
 598         if ((r == a) || (r == b))
 599                 {
 600                 if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
 601                 }
 602         else
 603                 rr = r;
 604
 605 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 606         i = al-bl;
 607 #endif
 608 #ifdef BN_MUL_COMBA
 609         if (i == 0)
 610                 {
 611 # if 0
 612                 if (al == 4)
 613                         {
 614                         if (bn_wexpand(rr,8) == NULL) goto err;
 615                         rr->top=8;
 616                         bn_mul_comba4(rr->d,a->d,b->d);
 617                         goto end;
 618                         }
 619 # endif
 620                 if (al == 8)
 621                         {
 622                         if (bn_wexpand(rr,16) == NULL) goto err;
 623                         rr->top=16;
 624                         bn_mul_comba8(rr->d,a->d,b->d);
 625                         goto end;
 626                         }
 627                 }
 628 #endif /* BN_MUL_COMBA */
 629 #ifdef BN_RECURSION
 630         if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))
 631                 {
 632                 if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
 633                         {
 634                         bn_wexpand(b,al);
 635                         b->d[bl]=0;
 636                         bl++;
 637                         i--;
 638                         }
 639                 else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
 640                         {
 641                         bn_wexpand(a,bl);
 642                         a->d[al]=0;
 643                         al++;
 644                         i++;
 645                         }
 646                 if (i == 0)
 647                         {
 648                         /* symmetric and > 4 */
 649                         /* 16 or larger */
 650                         j=BN_num_bits_word((BN_ULONG)al);
 651                         j=1<<(j-1);
 652                         k=j+j;
 653                         t = BN_CTX_get(ctx);
 654                         if (al == j) /* exact multiple */
 655                                 {
 656                                 bn_wexpand(t,k*2);
 657                                 bn_wexpand(rr,k*2);
 658                                 bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
 659                                 }
 660                         else
 661                                 {
 662                                 bn_wexpand(a,k);
 663                                 bn_wexpand(b,k);
 664                                 bn_wexpand(t,k*4);
 665                                 bn_wexpand(rr,k*4);
 666                                 for (i=a->top; i<k; i++)
 667                                         a->d[i]=0;
 668                                 for (i=b->top; i<k; i++)
 669                                         b->d[i]=0;
 670                                 bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
 671                                 }
 672                         rr->top=top;
 673                         goto end;
 674                         }
 675                 }
 676 #endif /* BN_RECURSION */
 677
 678         if (bn_wexpand(rr,top) == NULL) goto err;
 679         rr->top=top;
 680         bn_mul_normal(rr->d,a->d,al,b->d,bl);
 681
 682 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 683 end:
 684 #endif
 685         bn_fix_top(rr);
 686         if (r != rr) BN_copy(r,rr);
 687         ret=1;
 688 err:
 689         BN_CTX_end(ctx);
 690         return(ret);
 691         }
 692
 693 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
 694         {
 695         BN_ULONG *rr;
 696
 697 #ifdef BN_COUNT
 698         printf(" bn_mul_normal %d * %d\n",na,nb);
 699 #endif
 700
 701         if (na < nb)
 702                 {
 703                 int itmp;
 704                 BN_ULONG *ltmp;
 705
 706                 itmp=na; na=nb; nb=itmp;
 707                 ltmp=a;   a=b;   b=ltmp;
 708
 709                 }
 710         rr= &(r[na]);
 711         rr[0]=bn_mul_words(r,a,na,b[0]);
 712
 713         for (;;)
 714                 {
 715                 if (--nb <= 0) return;
 716                 rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
 717                 if (--nb <= 0) return;
 718                 rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
 719                 if (--nb <= 0) return;
 720                 rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
 721                 if (--nb <= 0) return;
 722                 rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
 723                 rr+=4;
 724                 r+=4;
 725                 b+=4;
 726                 }
 727         }
 728
 729 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
 730         {
 731 #ifdef BN_COUNT
 732         printf(" bn_mul_low_normal %d * %d\n",n,n);
 733 #endif
 734         bn_mul_words(r,a,n,b[0]);
 735
 736         for (;;)
 737                 {
 738                 if (--n <= 0) return;
 739                 bn_mul_add_words(&(r[1]),a,n,b[1]);
 740                 if (--n <= 0) return;
 741                 bn_mul_add_words(&(r[2]),a,n,b[2]);
 742                 if (--n <= 0) return;
 743                 bn_mul_add_words(&(r[3]),a,n,b[3]);
 744                 if (--n <= 0) return;
 745                 bn_mul_add_words(&(r[4]),a,n,b[4]);
 746                 r+=4;
 747                 b+=4;
 748                 }
 749         }