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 calulate
  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(r,a,b,n2,t)
  75 BN_ULONG *r,*a,*b;
  76 int n2;
  77 BN_ULONG *t;
  78         {
  79         int n=n2/2,c1,c2;
  80         unsigned int neg,zero;
  81         BN_ULONG ln,lo,*p;
  82
  83 #ifdef BN_COUNT
  84 printf(" bn_mul_recursive %d * %d\n",n2,n2);
  85 #endif
  86 #ifdef BN_MUL_COMBA
  87 /*      if (n2 == 4)
  88                 {
  89                 bn_mul_comba4(r,a,b);
  90                 return;
  91                 }
  92         else */ if (n2 == 8)
  93                 {
  94                 bn_mul_comba8(r,a,b);
  95                 return;
  96                 }
  97 #endif
  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
 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(r,a,b,tn,n,t)
 221 BN_ULONG *r,*a,*b;
 222 int tn,n;
 223 BN_ULONG *t;
 224         {
 225         int i,j,n2=n*2;
 226         unsigned int c1;
 227         BN_ULONG ln,lo,*p;
 228
 229 #ifdef BN_COUNT
 230 printf(" bn_mul_part_recursive %d * %d\n",tn+n,tn+n);
 231 #endif
 232         if (n < 8)
 233                 {
 234                 i=tn+n;
 235                 bn_mul_normal(r,a,i,b,i);
 236                 return;
 237                 }
 238
 239         /* r=(a[0]-a[1])*(b[1]-b[0]) */
 240         bn_sub_words(t,      a,      &(a[n]),n); /* + */
 241         bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
 242
 243 /*      if (n == 4)
 244                 {
 245                 bn_mul_comba4(&(t[n2]),t,&(t[n]));
 246                 bn_mul_comba4(r,a,b);
 247                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
 248                 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
 249                 }
 250         else */ if (n == 8)
 251                 {
 252                 bn_mul_comba8(&(t[n2]),t,&(t[n]));
 253                 bn_mul_comba8(r,a,b);
 254                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
 255                 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
 256                 }
 257         else
 258                 {
 259                 p= &(t[n2*2]);
 260                 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
 261                 bn_mul_recursive(r,a,b,n,p);
 262                 i=n/2;
 263                 /* If there is only a bottom half to the number,
 264                  * just do it */
 265                 j=tn-i;
 266                 if (j == 0)
 267                         {
 268                         bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),i,p);
 269                         memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
 270                         }
 271                 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
 272                                 {
 273                                 bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
 274                                         j,i,p);
 275                                 memset(&(r[n2+tn*2]),0,
 276                                         sizeof(BN_ULONG)*(n2-tn*2));
 277                                 }
 278                 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
 279                         {
 280                         memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
 281                         if (tn < BN_MUL_RECURSIVE_SIZE_NORMAL)
 282                                 {
 283                                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
 284                                 }
 285                         else
 286                                 {
 287                                 for (;;)
 288                                         {
 289                                         i/=2;
 290                                         if (i < tn)
 291                                                 {
 292                                                 bn_mul_part_recursive(&(r[n2]),
 293                                                         &(a[n]),&(b[n]),
 294                                                         tn-i,i,p);
 295                                                 break;
 296                                                 }
 297                                         else if (i == tn)
 298                                                 {
 299                                                 bn_mul_recursive(&(r[n2]),
 300                                                         &(a[n]),&(b[n]),
 301                                                         i,p);
 302                                                 break;
 303                                                 }
 304                                         }
 305                                 }
 306                         }
 307                 }
 308
 309         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
 310          * r[10] holds (a[0]*b[0])
 311          * r[32] holds (b[1]*b[1])
 312          */
 313
 314         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
 315         c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
 316
 317         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
 318          * r[10] holds (a[0]*b[0])
 319          * r[32] holds (b[1]*b[1])
 320          * c1 holds the carry bits
 321          */
 322         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
 323         if (c1)
 324                 {
 325                 p= &(r[n+n2]);
 326                 lo= *p;
 327                 ln=(lo+c1)&BN_MASK2;
 328                 *p=ln;
 329
 330                 /* The overflow will stop before we over write
 331                  * words we should not overwrite */
 332                 if (ln < c1)
 333                         {
 334                         do      {
 335                                 p++;
 336                                 lo= *p;
 337                                 ln=(lo+1)&BN_MASK2;
 338                                 *p=ln;
 339                                 } while (ln == 0);
 340                         }
 341                 }
 342         }
 343
 344 /* a and b must be the same size, which is n2.
 345  * r needs to be n2 words and t needs to be n2*2
 346  */
 347 void bn_mul_low_recursive(r,a,b,n2,t)
 348 BN_ULONG *r,*a,*b;
 349 int n2;
 350 BN_ULONG *t;
 351         {
 352         int n=n2/2;
 353
 354 #ifdef BN_COUNT
 355 printf(" bn_mul_low_recursive %d * %d\n",n2,n2);
 356 #endif
 357
 358         bn_mul_recursive(r,a,b,n,&(t[0]));
 359         if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
 360                 {
 361                 bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
 362                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 363                 bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
 364                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 365                 }
 366         else
 367                 {
 368                 bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
 369                 bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
 370                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 371                 bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
 372                 }
 373         }
 374
 375 /* a and b must be the same size, which is n2.
 376  * r needs to be n2 words and t needs to be n2*2
 377  * l is the low words of the output.
 378  * t needs to be n2*3
 379  */
 380 void bn_mul_high(r,a,b,l,n2,t)
 381 BN_ULONG *r,*a,*b,*l;
 382 int n2;
 383 BN_ULONG *t;
 384         {
 385         int i,n;
 386         int c1,c2;
 387         int neg,oneg,zero;
 388         BN_ULONG ll,lc,*lp,*mp;
 389
 390 #ifdef BN_COUNT
 391 printf(" bn_mul_high %d * %d\n",n2,n2);
 392 #endif
 393         n=n2/2;
 394
 395         /* Calculate (al-ah)*(bh-bl) */
 396         neg=zero=0;
 397         c1=bn_cmp_words(&(a[0]),&(a[n]),n);
 398         c2=bn_cmp_words(&(b[n]),&(b[0]),n);
 399         switch (c1*3+c2)
 400                 {
 401         case -4:
 402                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
 403                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
 404                 break;
 405         case -3:
 406                 zero=1;
 407                 break;
 408         case -2:
 409                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
 410                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
 411                 neg=1;
 412                 break;
 413         case -1:
 414         case 0:
 415         case 1:
 416                 zero=1;
 417                 break;
 418         case 2:
 419                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
 420                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
 421                 neg=1;
 422                 break;
 423         case 3:
 424                 zero=1;
 425                 break;
 426         case 4:
 427                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
 428                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
 429                 break;
 430                 }
 431
 432         oneg=neg;
 433         /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
 434         /* r[10] = (a[1]*b[1]) */
 435 #ifdef BN_MUL_COMBA
 436         if (n == 8)
 437                 {
 438                 bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
 439                 bn_mul_comba8(r,&(a[n]),&(b[n]));
 440                 }
 441         else
 442 #endif
 443                 {
 444                 bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,&(t[n2]));
 445                 bn_mul_recursive(r,&(a[n]),&(b[n]),n,&(t[n2]));
 446                 }
 447
 448         /* s0 == low(al*bl)
 449          * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
 450          * We know s0 and s1 so the only unknown is high(al*bl)
 451          * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
 452          * high(al*bl) == s1 - (r[0]+l[0]+t[0])
 453          */
 454         if (l != NULL)
 455                 {
 456                 lp= &(t[n2+n]);
 457                 c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
 458                 }
 459         else
 460                 {
 461                 c1=0;
 462                 lp= &(r[0]);
 463                 }
 464
 465         if (neg)
 466                 neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
 467         else
 468                 {
 469                 bn_add_words(&(t[n2]),lp,&(t[0]),n);
 470                 neg=0;
 471                 }
 472
 473         if (l != NULL)
 474                 {
 475                 bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
 476                 }
 477         else
 478                 {
 479                 lp= &(t[n2+n]);
 480                 mp= &(t[n2]);
 481                 for (i=0; i<n; i++)
 482                         lp[i]=((~mp[i])+1)&BN_MASK2;
 483                 }
 484
 485         /* s[0] = low(al*bl)
 486          * t[3] = high(al*bl)
 487          * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
 488          * r[10] = (a[1]*b[1])
 489          */
 490         /* R[10] = al*bl
 491          * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
 492          * R[32] = ah*bh
 493          */
 494         /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
 495          * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
 496          * R[3]=r[1]+(carry/borrow)
 497          */
 498         if (l != NULL)
 499                 {
 500                 lp= &(t[n2]);
 501                 c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
 502                 }
 503         else
 504                 {
 505                 lp= &(t[n2+n]);
 506                 c1=0;
 507                 }
 508         c1+=(int)(bn_add_words(&(t[n2]),lp,  &(r[0]),n));
 509         if (oneg)
 510                 c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
 511         else
 512                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));
 513
 514         c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
 515         c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
 516         if (oneg)
 517                 c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
 518         else
 519                 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
 520
 521         if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
 522                 {
 523                 i=0;
 524                 if (c1 > 0)
 525                         {
 526                         lc=c1;
 527                         do      {
 528                                 ll=(r[i]+lc)&BN_MASK2;
 529                                 r[i++]=ll;
 530                                 lc=(lc > ll);
 531                                 } while (lc);
 532                         }
 533                 else
 534                         {
 535                         lc= -c1;
 536                         do      {
 537                                 ll=r[i];
 538                                 r[i++]=(ll-lc)&BN_MASK2;
 539                                 lc=(lc > ll);
 540                                 } while (lc);
 541                         }
 542                 }
 543         if (c2 != 0) /* Add starting at r[1] */
 544                 {
 545                 i=n;
 546                 if (c2 > 0)
 547                         {
 548                         lc=c2;
 549                         do      {
 550                                 ll=(r[i]+lc)&BN_MASK2;
 551                                 r[i++]=ll;
 552                                 lc=(lc > ll);
 553                                 } while (lc);
 554                         }
 555                 else
 556                         {
 557                         lc= -c2;
 558                         do      {
 559                                 ll=r[i];
 560                                 r[i++]=(ll-lc)&BN_MASK2;
 561                                 lc=(lc > ll);
 562                                 } while (lc);
 563                         }
 564                 }
 565         }
 566 #endif
 567
 568 int BN_mul(r,a,b,ctx)
 569 BIGNUM *r,*a,*b;
 570 BN_CTX *ctx;
 571         {
 572         int top,al,bl;
 573         BIGNUM *rr;
 574 #ifdef BN_RECURSION
 575         BIGNUM *t;
 576         int i,j,k;
 577 #endif
 578
 579 #ifdef BN_COUNT
 580 printf("BN_mul %d * %d\n",a->top,b->top);
 581 #endif
 582
 583         bn_check_top(a);
 584         bn_check_top(b);
 585         bn_check_top(r);
 586
 587         al=a->top;
 588         bl=b->top;
 589         r->neg=a->neg^b->neg;
 590
 591         if ((al == 0) || (bl == 0))
 592                 {
 593                 BN_zero(r);
 594                 return(1);
 595                 }
 596         top=al+bl;
 597
 598         if ((r == a) || (r == b))
 599                 rr= &(ctx->bn[ctx->tos+1]);
 600         else
 601                 rr=r;
 602
 603 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 604         if (al == bl)
 605                 {
 606 #  ifdef BN_MUL_COMBA
 607 /*              if (al == 4)
 608                         {
 609                         if (bn_wexpand(rr,8) == NULL) return(0);
 610                         r->top=8;
 611                         bn_mul_comba4(rr->d,a->d,b->d);
 612                         goto end;
 613                         }
 614                 else */ if (al == 8)
 615                         {
 616                         if (bn_wexpand(rr,16) == NULL) return(0);
 617                         r->top=16;
 618                         bn_mul_comba8(rr->d,a->d,b->d);
 619                         goto end;
 620                         }
 621                 else
 622 #  endif
 623 #ifdef BN_RECURSION
 624                 if (al < BN_MULL_SIZE_NORMAL)
 625 #endif
 626                         {
 627                         if (bn_wexpand(rr,top) == NULL) return(0);
 628                         rr->top=top;
 629                         bn_mul_normal(rr->d,a->d,al,b->d,bl);
 630                         goto end;
 631                         }
 632 #  ifdef BN_RECURSION
 633                 goto symetric;
 634 #  endif
 635                 }
 636 #endif
 637 #ifdef BN_RECURSION
 638         else if ((al < BN_MULL_SIZE_NORMAL) || (bl < BN_MULL_SIZE_NORMAL))
 639                 {
 640                 if (bn_wexpand(rr,top) == NULL) return(0);
 641                 rr->top=top;
 642                 bn_mul_normal(rr->d,a->d,al,b->d,bl);
 643                 goto end;
 644                 }
 645         else
 646                 {
 647                 i=(al-bl);
 648                 if ((i ==  1) && !BN_get_flags(b,BN_FLG_STATIC_DATA))
 649                         {
 650                         bn_wexpand(b,al);
 651                         b->d[bl]=0;
 652                         bl++;
 653                         goto symetric;
 654                         }
 655                 else if ((i ==  -1) && !BN_get_flags(a,BN_FLG_STATIC_DATA))
 656                         {
 657                         bn_wexpand(a,bl);
 658                         a->d[al]=0;
 659                         al++;
 660                         goto symetric;
 661                         }
 662                 }
 663 #endif
 664
 665         /* asymetric and >= 4 */
 666         if (bn_wexpand(rr,top) == NULL) return(0);
 667         rr->top=top;
 668         bn_mul_normal(rr->d,a->d,al,b->d,bl);
 669
 670 #ifdef BN_RECURSION
 671         if (0)
 672                 {
 673 symetric:
 674                 /* symetric and > 4 */
 675                 /* 16 or larger */
 676                 j=BN_num_bits_word((BN_ULONG)al);
 677                 j=1<<(j-1);
 678                 k=j+j;
 679                 t= &(ctx->bn[ctx->tos]);
 680                 if (al == j) /* exact multiple */
 681                         {
 682                         bn_wexpand(t,k*2);
 683                         bn_wexpand(rr,k*2);
 684                         bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
 685                         }
 686                 else
 687                         {
 688                         bn_wexpand(a,k);
 689                         bn_wexpand(b,k);
 690                         bn_wexpand(t,k*4);
 691                         bn_wexpand(rr,k*4);
 692                         for (i=a->top; i<k; i++)
 693                                 a->d[i]=0;
 694                         for (i=b->top; i<k; i++)
 695                                 b->d[i]=0;
 696                         bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
 697                         }
 698                 rr->top=top;
 699                 }
 700 #endif
 701 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 702 end:
 703 #endif
 704         bn_fix_top(rr);
 705         if (r != rr) BN_copy(r,rr);
 706         return(1);
 707         }
 708
 709 void bn_mul_normal(r,a,na,b,nb)
 710 BN_ULONG *r,*a;
 711 int na;
 712 BN_ULONG *b;
 713 int nb;
 714         {
 715         BN_ULONG *rr;
 716
 717 #ifdef BN_COUNT
 718 printf(" bn_mul_normal %d * %d\n",na,nb);
 719 #endif
 720
 721         if (na < nb)
 722                 {
 723                 int itmp;
 724                 BN_ULONG *ltmp;
 725
 726                 itmp=na; na=nb; nb=itmp;
 727                 ltmp=a;   a=b;   b=ltmp;
 728
 729                 }
 730         rr= &(r[na]);
 731         rr[0]=bn_mul_words(r,a,na,b[0]);
 732
 733         for (;;)
 734                 {
 735                 if (--nb <= 0) return;
 736                 rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
 737                 if (--nb <= 0) return;
 738                 rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
 739                 if (--nb <= 0) return;
 740                 rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
 741                 if (--nb <= 0) return;
 742                 rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
 743                 rr+=4;
 744                 r+=4;
 745                 b+=4;
 746                 }
 747         }
 748
 749 void bn_mul_low_normal(r,a,b,n)
 750 BN_ULONG *r,*a,*b;
 751 int n;
 752         {
 753 #ifdef BN_COUNT
 754 printf(" bn_mul_low_normal %d * %d\n",n,n);
 755 #endif
 756         bn_mul_words(r,a,n,b[0]);
 757
 758         for (;;)
 759                 {
 760                 if (--n <= 0) return;
 761                 bn_mul_add_words(&(r[1]),a,n,b[1]);
 762                 if (--n <= 0) return;
 763                 bn_mul_add_words(&(r[2]),a,n,b[2]);
 764                 if (--n <= 0) return;
 765                 bn_mul_add_words(&(r[3]),a,n,b[3]);
 766                 if (--n <= 0) return;
 767                 bn_mul_add_words(&(r[4]),a,n,b[4]);
 768                 r+=4;
 769                 b+=4;
 770                 }
 771         }
 772