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(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 (n2 == 4)
  86                 {
  87                 bn_mul_comba4(r,a,b);
  88                 return;
  89                 }
  90         else */ if (n2 == 8)
  91                 {
  92                 bn_mul_comba8(r,a,b);
  93                 return;
  94                 }
  95 #endif
  96         if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
  97                 {
  98                 /* This should not happen */
  99                 bn_mul_normal(r,a,n2,b,n2);
 100                 return;
 101                 }
 102         /* r=(a[0]-a[1])*(b[1]-b[0]) */
 103         c1=bn_cmp_words(a,&(a[n]),n);
 104         c2=bn_cmp_words(&(b[n]),b,n);
 105         zero=neg=0;
 106         switch (c1*3+c2)
 107                 {
 108         case -4:
 109                 bn_sub_words(t,      &(a[n]),a,      n); /* - */
 110                 bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
 111                 break;
 112         case -3:
 113                 zero=1;
 114                 break;
 115         case -2:
 116                 bn_sub_words(t,      &(a[n]),a,      n); /* - */
 117                 bn_sub_words(&(t[n]),&(b[n]),b,      n); /* + */
 118                 neg=1;
 119                 break;
 120         case -1:
 121         case 0:
 122         case 1:
 123                 zero=1;
 124                 break;
 125         case 2:
 126                 bn_sub_words(t,      a,      &(a[n]),n); /* + */
 127                 bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
 128                 neg=1;
 129                 break;
 130         case 3:
 131                 zero=1;
 132                 break;
 133         case 4:
 134                 bn_sub_words(t,      a,      &(a[n]),n);
 135                 bn_sub_words(&(t[n]),&(b[n]),b,      n);
 136                 break;
 137                 }
 138
 139 #ifdef BN_MUL_COMBA
 140         if (n == 4)
 141                 {
 142                 if (!zero)
 143                         bn_mul_comba4(&(t[n2]),t,&(t[n]));
 144                 else
 145                         memset(&(t[n2]),0,8*sizeof(BN_ULONG));
 146
 147                 bn_mul_comba4(r,a,b);
 148                 bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
 149                 }
 150         else if (n == 8)
 151                 {
 152                 if (!zero)
 153                         bn_mul_comba8(&(t[n2]),t,&(t[n]));
 154                 else
 155                         memset(&(t[n2]),0,16*sizeof(BN_ULONG));
 156
 157                 bn_mul_comba8(r,a,b);
 158                 bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
 159                 }
 160         else
 161 #endif
 162                 {
 163                 p= &(t[n2*2]);
 164                 if (!zero)
 165                         bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
 166                 else
 167                         memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
 168                 bn_mul_recursive(r,a,b,n,p);
 169                 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,p);
 170                 }
 171
 172         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
 173          * r[10] holds (a[0]*b[0])
 174          * r[32] holds (b[1]*b[1])
 175          */
 176
 177         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
 178
 179         if (neg) /* if t[32] is negative */
 180                 {
 181                 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
 182                 }
 183         else
 184                 {
 185                 /* Might have a carry */
 186                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
 187                 }
 188
 189         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
 190          * r[10] holds (a[0]*b[0])
 191          * r[32] holds (b[1]*b[1])
 192          * c1 holds the carry bits
 193          */
 194         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
 195         if (c1)
 196                 {
 197                 p= &(r[n+n2]);
 198                 lo= *p;
 199                 ln=(lo+c1)&BN_MASK2;
 200                 *p=ln;
 201
 202                 /* The overflow will stop before we over write
 203                  * words we should not overwrite */
 204                 if (ln < (BN_ULONG)c1)
 205                         {
 206                         do      {
 207                                 p++;
 208                                 lo= *p;
 209                                 ln=(lo+1)&BN_MASK2;
 210                                 *p=ln;
 211                                 } while (ln == 0);
 212                         }
 213                 }
 214         }
 215
 216 /* n+tn is the word length
 217  * t needs to be n*4 is size, as does r */
 218 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int tn,
 219              int n, BN_ULONG *t)
 220         {
 221         int i,j,n2=n*2;
 222         unsigned int c1;
 223         BN_ULONG ln,lo,*p;
 224
 225 #ifdef BN_COUNT
 226 printf(" bn_mul_part_recursive %d * %d\n",tn+n,tn+n);
 227 #endif
 228         if (n < 8)
 229                 {
 230                 i=tn+n;
 231                 bn_mul_normal(r,a,i,b,i);
 232                 return;
 233                 }
 234
 235         /* r=(a[0]-a[1])*(b[1]-b[0]) */
 236         bn_sub_words(t,      a,      &(a[n]),n); /* + */
 237         bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
 238
 239 /*      if (n == 4)
 240                 {
 241                 bn_mul_comba4(&(t[n2]),t,&(t[n]));
 242                 bn_mul_comba4(r,a,b);
 243                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
 244                 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
 245                 }
 246         else */ if (n == 8)
 247                 {
 248                 bn_mul_comba8(&(t[n2]),t,&(t[n]));
 249                 bn_mul_comba8(r,a,b);
 250                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
 251                 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
 252                 }
 253         else
 254                 {
 255                 p= &(t[n2*2]);
 256                 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
 257                 bn_mul_recursive(r,a,b,n,p);
 258                 i=n/2;
 259                 /* If there is only a bottom half to the number,
 260                  * just do it */
 261                 j=tn-i;
 262                 if (j == 0)
 263                         {
 264                         bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),i,p);
 265                         memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
 266                         }
 267                 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
 268                                 {
 269                                 bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
 270                                         j,i,p);
 271                                 memset(&(r[n2+tn*2]),0,
 272                                         sizeof(BN_ULONG)*(n2-tn*2));
 273                                 }
 274                 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
 275                         {
 276                         memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
 277                         if (tn < BN_MUL_RECURSIVE_SIZE_NORMAL)
 278                                 {
 279                                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
 280                                 }
 281                         else
 282                                 {
 283                                 for (;;)
 284                                         {
 285                                         i/=2;
 286                                         if (i < tn)
 287                                                 {
 288                                                 bn_mul_part_recursive(&(r[n2]),
 289                                                         &(a[n]),&(b[n]),
 290                                                         tn-i,i,p);
 291                                                 break;
 292                                                 }
 293                                         else if (i == tn)
 294                                                 {
 295                                                 bn_mul_recursive(&(r[n2]),
 296                                                         &(a[n]),&(b[n]),
 297                                                         i,p);
 298                                                 break;
 299                                                 }
 300                                         }
 301                                 }
 302                         }
 303                 }
 304
 305         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
 306          * r[10] holds (a[0]*b[0])
 307          * r[32] holds (b[1]*b[1])
 308          */
 309
 310         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
 311         c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
 312
 313         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
 314          * r[10] holds (a[0]*b[0])
 315          * r[32] holds (b[1]*b[1])
 316          * c1 holds the carry bits
 317          */
 318         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
 319         if (c1)
 320                 {
 321                 p= &(r[n+n2]);
 322                 lo= *p;
 323                 ln=(lo+c1)&BN_MASK2;
 324                 *p=ln;
 325
 326                 /* The overflow will stop before we over write
 327                  * words we should not overwrite */
 328                 if (ln < c1)
 329                         {
 330                         do      {
 331                                 p++;
 332                                 lo= *p;
 333                                 ln=(lo+1)&BN_MASK2;
 334                                 *p=ln;
 335                                 } while (ln == 0);
 336                         }
 337                 }
 338         }
 339
 340 /* a and b must be the same size, which is n2.
 341  * r needs to be n2 words and t needs to be n2*2
 342  */
 343 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
 344              BN_ULONG *t)
 345         {
 346         int n=n2/2;
 347
 348 #ifdef BN_COUNT
 349 printf(" bn_mul_low_recursive %d * %d\n",n2,n2);
 350 #endif
 351
 352         bn_mul_recursive(r,a,b,n,&(t[0]));
 353         if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
 354                 {
 355                 bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
 356                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 357                 bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
 358                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 359                 }
 360         else
 361                 {
 362                 bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
 363                 bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
 364                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 365                 bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
 366                 }
 367         }
 368
 369 /* a and b must be the same size, which is n2.
 370  * r needs to be n2 words and t needs to be n2*2
 371  * l is the low words of the output.
 372  * t needs to be n2*3
 373  */
 374 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
 375              BN_ULONG *t)
 376         {
 377         int i,n;
 378         int c1,c2;
 379         int neg,oneg,zero;
 380         BN_ULONG ll,lc,*lp,*mp;
 381
 382 #ifdef BN_COUNT
 383 printf(" bn_mul_high %d * %d\n",n2,n2);
 384 #endif
 385         n=n2/2;
 386
 387         /* Calculate (al-ah)*(bh-bl) */
 388         neg=zero=0;
 389         c1=bn_cmp_words(&(a[0]),&(a[n]),n);
 390         c2=bn_cmp_words(&(b[n]),&(b[0]),n);
 391         switch (c1*3+c2)
 392                 {
 393         case -4:
 394                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
 395                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
 396                 break;
 397         case -3:
 398                 zero=1;
 399                 break;
 400         case -2:
 401                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
 402                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
 403                 neg=1;
 404                 break;
 405         case -1:
 406         case 0:
 407         case 1:
 408                 zero=1;
 409                 break;
 410         case 2:
 411                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
 412                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
 413                 neg=1;
 414                 break;
 415         case 3:
 416                 zero=1;
 417                 break;
 418         case 4:
 419                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
 420                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
 421                 break;
 422                 }
 423
 424         oneg=neg;
 425         /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
 426         /* r[10] = (a[1]*b[1]) */
 427 #ifdef BN_MUL_COMBA
 428         if (n == 8)
 429                 {
 430                 bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
 431                 bn_mul_comba8(r,&(a[n]),&(b[n]));
 432                 }
 433         else
 434 #endif
 435                 {
 436                 bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,&(t[n2]));
 437                 bn_mul_recursive(r,&(a[n]),&(b[n]),n,&(t[n2]));
 438                 }
 439
 440         /* s0 == low(al*bl)
 441          * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
 442          * We know s0 and s1 so the only unknown is high(al*bl)
 443          * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
 444          * high(al*bl) == s1 - (r[0]+l[0]+t[0])
 445          */
 446         if (l != NULL)
 447                 {
 448                 lp= &(t[n2+n]);
 449                 c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
 450                 }
 451         else
 452                 {
 453                 c1=0;
 454                 lp= &(r[0]);
 455                 }
 456
 457         if (neg)
 458                 neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
 459         else
 460                 {
 461                 bn_add_words(&(t[n2]),lp,&(t[0]),n);
 462                 neg=0;
 463                 }
 464
 465         if (l != NULL)
 466                 {
 467                 bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
 468                 }
 469         else
 470                 {
 471                 lp= &(t[n2+n]);
 472                 mp= &(t[n2]);
 473                 for (i=0; i<n; i++)
 474                         lp[i]=((~mp[i])+1)&BN_MASK2;
 475                 }
 476
 477         /* s[0] = low(al*bl)
 478          * t[3] = high(al*bl)
 479          * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
 480          * r[10] = (a[1]*b[1])
 481          */
 482         /* R[10] = al*bl
 483          * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
 484          * R[32] = ah*bh
 485          */
 486         /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
 487          * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
 488          * R[3]=r[1]+(carry/borrow)
 489          */
 490         if (l != NULL)
 491                 {
 492                 lp= &(t[n2]);
 493                 c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
 494                 }
 495         else
 496                 {
 497                 lp= &(t[n2+n]);
 498                 c1=0;
 499                 }
 500         c1+=(int)(bn_add_words(&(t[n2]),lp,  &(r[0]),n));
 501         if (oneg)
 502                 c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
 503         else
 504                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));
 505
 506         c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
 507         c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
 508         if (oneg)
 509                 c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
 510         else
 511                 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
 512
 513         if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
 514                 {
 515                 i=0;
 516                 if (c1 > 0)
 517                         {
 518                         lc=c1;
 519                         do      {
 520                                 ll=(r[i]+lc)&BN_MASK2;
 521                                 r[i++]=ll;
 522                                 lc=(lc > ll);
 523                                 } while (lc);
 524                         }
 525                 else
 526                         {
 527                         lc= -c1;
 528                         do      {
 529                                 ll=r[i];
 530                                 r[i++]=(ll-lc)&BN_MASK2;
 531                                 lc=(lc > ll);
 532                                 } while (lc);
 533                         }
 534                 }
 535         if (c2 != 0) /* Add starting at r[1] */
 536                 {
 537                 i=n;
 538                 if (c2 > 0)
 539                         {
 540                         lc=c2;
 541                         do      {
 542                                 ll=(r[i]+lc)&BN_MASK2;
 543                                 r[i++]=ll;
 544                                 lc=(lc > ll);
 545                                 } while (lc);
 546                         }
 547                 else
 548                         {
 549                         lc= -c2;
 550                         do      {
 551                                 ll=r[i];
 552                                 r[i++]=(ll-lc)&BN_MASK2;
 553                                 lc=(lc > ll);
 554                                 } while (lc);
 555                         }
 556                 }
 557         }
 558 #endif
 559
 560 int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
 561         {
 562         int top,al,bl;
 563         BIGNUM *rr;
 564 #ifdef BN_RECURSION
 565         BIGNUM *t;
 566         int i,j,k;
 567 #endif
 568
 569 #ifdef BN_COUNT
 570 printf("BN_mul %d * %d\n",a->top,b->top);
 571 #endif
 572
 573         bn_check_top(a);
 574         bn_check_top(b);
 575         bn_check_top(r);
 576
 577         al=a->top;
 578         bl=b->top;
 579         r->neg=a->neg^b->neg;
 580
 581         if ((al == 0) || (bl == 0))
 582                 {
 583                 BN_zero(r);
 584                 return(1);
 585                 }
 586         top=al+bl;
 587
 588         if ((r == a) || (r == b))
 589                 rr= &(ctx->bn[ctx->tos+1]);
 590         else
 591                 rr=r;
 592
 593 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 594         if (al == bl)
 595                 {
 596 #  ifdef BN_MUL_COMBA
 597 /*              if (al == 4)
 598                         {
 599                         if (bn_wexpand(rr,8) == NULL) return(0);
 600                         r->top=8;
 601                         bn_mul_comba4(rr->d,a->d,b->d);
 602                         goto end;
 603                         }
 604                 else */ if (al == 8)
 605                         {
 606                         if (bn_wexpand(rr,16) == NULL) return(0);
 607                         r->top=16;
 608                         bn_mul_comba8(rr->d,a->d,b->d);
 609                         goto end;
 610                         }
 611                 else
 612 #  endif
 613 #ifdef BN_RECURSION
 614                 if (al < BN_MULL_SIZE_NORMAL)
 615 #endif
 616                         {
 617                         if (bn_wexpand(rr,top) == NULL) return(0);
 618                         rr->top=top;
 619                         bn_mul_normal(rr->d,a->d,al,b->d,bl);
 620                         goto end;
 621                         }
 622 #  ifdef BN_RECURSION
 623                 goto symetric;
 624 #  endif
 625                 }
 626 #endif
 627 #ifdef BN_RECURSION
 628         else if ((al < BN_MULL_SIZE_NORMAL) || (bl < BN_MULL_SIZE_NORMAL))
 629                 {
 630                 if (bn_wexpand(rr,top) == NULL) return(0);
 631                 rr->top=top;
 632                 bn_mul_normal(rr->d,a->d,al,b->d,bl);
 633                 goto end;
 634                 }
 635         else
 636                 {
 637                 i=(al-bl);
 638                 if ((i ==  1) && !BN_get_flags(b,BN_FLG_STATIC_DATA))
 639                         {
 640                         bn_wexpand(b,al);
 641                         b->d[bl]=0;
 642                         bl++;
 643                         goto symetric;
 644                         }
 645                 else if ((i ==  -1) && !BN_get_flags(a,BN_FLG_STATIC_DATA))
 646                         {
 647                         bn_wexpand(a,bl);
 648                         a->d[al]=0;
 649                         al++;
 650                         goto symetric;
 651                         }
 652                 }
 653 #endif
 654
 655         /* asymetric and >= 4 */
 656         if (bn_wexpand(rr,top) == NULL) return(0);
 657         rr->top=top;
 658         bn_mul_normal(rr->d,a->d,al,b->d,bl);
 659
 660 #ifdef BN_RECURSION
 661         if (0)
 662                 {
 663 symetric:
 664                 /* symetric and > 4 */
 665                 /* 16 or larger */
 666                 j=BN_num_bits_word((BN_ULONG)al);
 667                 j=1<<(j-1);
 668                 k=j+j;
 669                 t= &(ctx->bn[ctx->tos]);
 670                 if (al == j) /* exact multiple */
 671                         {
 672                         bn_wexpand(t,k*2);
 673                         bn_wexpand(rr,k*2);
 674                         bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
 675                         }
 676                 else
 677                         {
 678                         bn_wexpand(a,k);
 679                         bn_wexpand(b,k);
 680                         bn_wexpand(t,k*4);
 681                         bn_wexpand(rr,k*4);
 682                         for (i=a->top; i<k; i++)
 683                                 a->d[i]=0;
 684                         for (i=b->top; i<k; i++)
 685                                 b->d[i]=0;
 686                         bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
 687                         }
 688                 rr->top=top;
 689                 }
 690 #endif
 691 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 692 end:
 693 #endif
 694         bn_fix_top(rr);
 695         if (r != rr) BN_copy(r,rr);
 696         return(1);
 697         }
 698
 699 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
 700         {
 701         BN_ULONG *rr;
 702
 703 #ifdef BN_COUNT
 704 printf(" bn_mul_normal %d * %d\n",na,nb);
 705 #endif
 706
 707         if (na < nb)
 708                 {
 709                 int itmp;
 710                 BN_ULONG *ltmp;
 711
 712                 itmp=na; na=nb; nb=itmp;
 713                 ltmp=a;   a=b;   b=ltmp;
 714
 715                 }
 716         rr= &(r[na]);
 717         rr[0]=bn_mul_words(r,a,na,b[0]);
 718
 719         for (;;)
 720                 {
 721                 if (--nb <= 0) return;
 722                 rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
 723                 if (--nb <= 0) return;
 724                 rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
 725                 if (--nb <= 0) return;
 726                 rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
 727                 if (--nb <= 0) return;
 728                 rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
 729                 rr+=4;
 730                 r+=4;
 731                 b+=4;
 732                 }
 733         }
 734
 735 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
 736         {
 737 #ifdef BN_COUNT
 738 printf(" bn_mul_low_normal %d * %d\n",n,n);
 739 #endif
 740         bn_mul_words(r,a,n,b[0]);
 741
 742         for (;;)
 743                 {
 744                 if (--n <= 0) return;
 745                 bn_mul_add_words(&(r[1]),a,n,b[1]);
 746                 if (--n <= 0) return;
 747                 bn_mul_add_words(&(r[2]),a,n,b[2]);
 748                 if (--n <= 0) return;
 749                 bn_mul_add_words(&(r[3]),a,n,b[3]);
 750                 if (--n <= 0) return;
 751                 bn_mul_add_words(&(r[4]),a,n,b[4]);
 752                 r+=4;
 753                 b+=4;
 754                 }
 755         }
 756