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 /* Karatsuba recursive multiplication algorithm
  65  * (cf. Knuth, The Art of Computer Programming, Vol. 2) */
  66
  67 /* r is 2*n2 words in size,
  68  * a and b are both n2 words in size.
  69  * n2 must be a power of 2.
  70  * We multiply and return the result.
  71  * t must be 2*n2 words in size
  72  * We calculate
  73  * a[0]*b[0]
  74  * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
  75  * a[1]*b[1]
  76  */
  77 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
  78              BN_ULONG *t)
  79         {
  80         int n=n2/2,c1,c2;
  81         unsigned int neg,zero;
  82         BN_ULONG ln,lo,*p;
  83
  84 # ifdef BN_COUNT
  85         printf(" bn_mul_recursive %d * %d\n",n2,n2);
  86 # endif
  87 # ifdef BN_MUL_COMBA
  88 #  if 0
  89         if (n2 == 4)
  90                 {
  91                 bn_mul_comba4(r,a,b);
  92                 return;
  93                 }
  94 #  endif
  95         if (n2 == 8)
  96                 {
  97                 bn_mul_comba8(r,a,b);
  98                 return;
  99                 }
 100 # endif /* BN_MUL_COMBA */
 101         if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
 102                 {
 103                 /* This should not happen */
 104                 bn_mul_normal(r,a,n2,b,n2);
 105                 return;
 106                 }
 107         /* r=(a[0]-a[1])*(b[1]-b[0]) */
 108         c1=bn_cmp_words(a,&(a[n]),n);
 109         c2=bn_cmp_words(&(b[n]),b,n);
 110         zero=neg=0;
 111         switch (c1*3+c2)
 112                 {
 113         case -4:
 114                 bn_sub_words(t,      &(a[n]),a,      n); /* - */
 115                 bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
 116                 break;
 117         case -3:
 118                 zero=1;
 119                 break;
 120         case -2:
 121                 bn_sub_words(t,      &(a[n]),a,      n); /* - */
 122                 bn_sub_words(&(t[n]),&(b[n]),b,      n); /* + */
 123                 neg=1;
 124                 break;
 125         case -1:
 126         case 0:
 127         case 1:
 128                 zero=1;
 129                 break;
 130         case 2:
 131                 bn_sub_words(t,      a,      &(a[n]),n); /* + */
 132                 bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
 133                 neg=1;
 134                 break;
 135         case 3:
 136                 zero=1;
 137                 break;
 138         case 4:
 139                 bn_sub_words(t,      a,      &(a[n]),n);
 140                 bn_sub_words(&(t[n]),&(b[n]),b,      n);
 141                 break;
 142                 }
 143
 144 # ifdef BN_MUL_COMBA
 145         if (n == 4)
 146                 {
 147                 if (!zero)
 148                         bn_mul_comba4(&(t[n2]),t,&(t[n]));
 149                 else
 150                         memset(&(t[n2]),0,8*sizeof(BN_ULONG));
 151
 152                 bn_mul_comba4(r,a,b);
 153                 bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
 154                 }
 155         else if (n == 8)
 156                 {
 157                 if (!zero)
 158                         bn_mul_comba8(&(t[n2]),t,&(t[n]));
 159                 else
 160                         memset(&(t[n2]),0,16*sizeof(BN_ULONG));
 161
 162                 bn_mul_comba8(r,a,b);
 163                 bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
 164                 }
 165         else
 166 # endif /* BN_MUL_COMBA */
 167                 {
 168                 p= &(t[n2*2]);
 169                 if (!zero)
 170                         bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
 171                 else
 172                         memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
 173                 bn_mul_recursive(r,a,b,n,p);
 174                 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,p);
 175                 }
 176
 177         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
 178          * r[10] holds (a[0]*b[0])
 179          * r[32] holds (b[1]*b[1])
 180          */
 181
 182         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
 183
 184         if (neg) /* if t[32] is negative */
 185                 {
 186                 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
 187                 }
 188         else
 189                 {
 190                 /* Might have a carry */
 191                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
 192                 }
 193
 194         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
 195          * r[10] holds (a[0]*b[0])
 196          * r[32] holds (b[1]*b[1])
 197          * c1 holds the carry bits
 198          */
 199         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
 200         if (c1)
 201                 {
 202                 p= &(r[n+n2]);
 203                 lo= *p;
 204                 ln=(lo+c1)&BN_MASK2;
 205                 *p=ln;
 206
 207                 /* The overflow will stop before we over write
 208                  * words we should not overwrite */
 209                 if (ln < (BN_ULONG)c1)
 210                         {
 211                         do      {
 212                                 p++;
 213                                 lo= *p;
 214                                 ln=(lo+1)&BN_MASK2;
 215                                 *p=ln;
 216                                 } while (ln == 0);
 217                         }
 218                 }
 219         }
 220
 221 /* n+tn is the word length
 222  * t needs to be n*4 is size, as does r */
 223 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int tn,
 224              int n, BN_ULONG *t)
 225         {
 226         int i,j,n2=n*2;
 227         unsigned int c1,c2,neg,zero;
 228         BN_ULONG ln,lo,*p;
 229
 230 # ifdef BN_COUNT
 231         printf(" bn_mul_part_recursive %d * %d\n",tn+n,tn+n);
 232 # endif
 233         if (n < 8)
 234                 {
 235                 i=tn+n;
 236                 bn_mul_normal(r,a,i,b,i);
 237                 return;
 238                 }
 239
 240         /* r=(a[0]-a[1])*(b[1]-b[0]) */
 241         c1=bn_cmp_words(a,&(a[n]),n);
 242         c2=bn_cmp_words(&(b[n]),b,n);
 243         zero=neg=0;
 244         switch (c1*3+c2)
 245                 {
 246         case -4:
 247                 bn_sub_words(t,      &(a[n]),a,      n); /* - */
 248                 bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
 249                 break;
 250         case -3:
 251                 zero=1;
 252                 /* break; */
 253         case -2:
 254                 bn_sub_words(t,      &(a[n]),a,      n); /* - */
 255                 bn_sub_words(&(t[n]),&(b[n]),b,      n); /* + */
 256                 neg=1;
 257                 break;
 258         case -1:
 259         case 0:
 260         case 1:
 261                 zero=1;
 262                 /* break; */
 263         case 2:
 264                 bn_sub_words(t,      a,      &(a[n]),n); /* + */
 265                 bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
 266                 neg=1;
 267                 break;
 268         case 3:
 269                 zero=1;
 270                 /* break; */
 271         case 4:
 272                 bn_sub_words(t,      a,      &(a[n]),n);
 273                 bn_sub_words(&(t[n]),&(b[n]),b,      n);
 274                 break;
 275                 }
 276                 /* The zero case isn't yet implemented here. The speedup
 277                    would probably be negligible. */
 278 # if 0
 279         if (n == 4)
 280                 {
 281                 bn_mul_comba4(&(t[n2]),t,&(t[n]));
 282                 bn_mul_comba4(r,a,b);
 283                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
 284                 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
 285                 }
 286         else
 287 # endif
 288         if (n == 8)
 289                 {
 290                 bn_mul_comba8(&(t[n2]),t,&(t[n]));
 291                 bn_mul_comba8(r,a,b);
 292                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
 293                 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
 294                 }
 295         else
 296                 {
 297                 p= &(t[n2*2]);
 298                 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
 299                 bn_mul_recursive(r,a,b,n,p);
 300                 i=n/2;
 301                 /* If there is only a bottom half to the number,
 302                  * just do it */
 303                 j=tn-i;
 304                 if (j == 0)
 305                         {
 306                         bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),i,p);
 307                         memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
 308                         }
 309                 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
 310                                 {
 311                                 bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
 312                                         j,i,p);
 313                                 memset(&(r[n2+tn*2]),0,
 314                                         sizeof(BN_ULONG)*(n2-tn*2));
 315                                 }
 316                 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
 317                         {
 318                         memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
 319                         if (tn < BN_MUL_RECURSIVE_SIZE_NORMAL)
 320                                 {
 321                                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
 322                                 }
 323                         else
 324                                 {
 325                                 for (;;)
 326                                         {
 327                                         i/=2;
 328                                         if (i < tn)
 329                                                 {
 330                                                 bn_mul_part_recursive(&(r[n2]),
 331                                                         &(a[n]),&(b[n]),
 332                                                         tn-i,i,p);
 333                                                 break;
 334                                                 }
 335                                         else if (i == tn)
 336                                                 {
 337                                                 bn_mul_recursive(&(r[n2]),
 338                                                         &(a[n]),&(b[n]),
 339                                                         i,p);
 340                                                 break;
 341                                                 }
 342                                         }
 343                                 }
 344                         }
 345                 }
 346
 347         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
 348          * r[10] holds (a[0]*b[0])
 349          * r[32] holds (b[1]*b[1])
 350          */
 351
 352         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
 353
 354         if (neg) /* if t[32] is negative */
 355                 {
 356                 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
 357                 }
 358         else
 359                 {
 360                 /* Might have a carry */
 361                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
 362                 }
 363
 364         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
 365          * r[10] holds (a[0]*b[0])
 366          * r[32] holds (b[1]*b[1])
 367          * c1 holds the carry bits
 368          */
 369         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
 370         if (c1)
 371                 {
 372                 p= &(r[n+n2]);
 373                 lo= *p;
 374                 ln=(lo+c1)&BN_MASK2;
 375                 *p=ln;
 376
 377                 /* The overflow will stop before we over write
 378                  * words we should not overwrite */
 379                 if (ln < c1)
 380                         {
 381                         do      {
 382                                 p++;
 383                                 lo= *p;
 384                                 ln=(lo+1)&BN_MASK2;
 385                                 *p=ln;
 386                                 } while (ln == 0);
 387                         }
 388                 }
 389         }
 390
 391 /* a and b must be the same size, which is n2.
 392  * r needs to be n2 words and t needs to be n2*2
 393  */
 394 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
 395              BN_ULONG *t)
 396         {
 397         int n=n2/2;
 398
 399 # ifdef BN_COUNT
 400         printf(" bn_mul_low_recursive %d * %d\n",n2,n2);
 401 # endif
 402
 403         bn_mul_recursive(r,a,b,n,&(t[0]));
 404         if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
 405                 {
 406                 bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
 407                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 408                 bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
 409                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 410                 }
 411         else
 412                 {
 413                 bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
 414                 bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
 415                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
 416                 bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
 417                 }
 418         }
 419
 420 /* a and b must be the same size, which is n2.
 421  * r needs to be n2 words and t needs to be n2*2
 422  * l is the low words of the output.
 423  * t needs to be n2*3
 424  */
 425 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
 426              BN_ULONG *t)
 427         {
 428         int i,n;
 429         int c1,c2;
 430         int neg,oneg,zero;
 431         BN_ULONG ll,lc,*lp,*mp;
 432
 433 # ifdef BN_COUNT
 434         printf(" bn_mul_high %d * %d\n",n2,n2);
 435 # endif
 436         n=n2/2;
 437
 438         /* Calculate (al-ah)*(bh-bl) */
 439         neg=zero=0;
 440         c1=bn_cmp_words(&(a[0]),&(a[n]),n);
 441         c2=bn_cmp_words(&(b[n]),&(b[0]),n);
 442         switch (c1*3+c2)
 443                 {
 444         case -4:
 445                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
 446                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
 447                 break;
 448         case -3:
 449                 zero=1;
 450                 break;
 451         case -2:
 452                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
 453                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
 454                 neg=1;
 455                 break;
 456         case -1:
 457         case 0:
 458         case 1:
 459                 zero=1;
 460                 break;
 461         case 2:
 462                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
 463                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
 464                 neg=1;
 465                 break;
 466         case 3:
 467                 zero=1;
 468                 break;
 469         case 4:
 470                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
 471                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
 472                 break;
 473                 }
 474
 475         oneg=neg;
 476         /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
 477         /* r[10] = (a[1]*b[1]) */
 478 # ifdef BN_MUL_COMBA
 479         if (n == 8)
 480                 {
 481                 bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
 482                 bn_mul_comba8(r,&(a[n]),&(b[n]));
 483                 }
 484         else
 485 # endif
 486                 {
 487                 bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,&(t[n2]));
 488                 bn_mul_recursive(r,&(a[n]),&(b[n]),n,&(t[n2]));
 489                 }
 490
 491         /* s0 == low(al*bl)
 492          * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
 493          * We know s0 and s1 so the only unknown is high(al*bl)
 494          * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
 495          * high(al*bl) == s1 - (r[0]+l[0]+t[0])
 496          */
 497         if (l != NULL)
 498                 {
 499                 lp= &(t[n2+n]);
 500                 c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
 501                 }
 502         else
 503                 {
 504                 c1=0;
 505                 lp= &(r[0]);
 506                 }
 507
 508         if (neg)
 509                 neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
 510         else
 511                 {
 512                 bn_add_words(&(t[n2]),lp,&(t[0]),n);
 513                 neg=0;
 514                 }
 515
 516         if (l != NULL)
 517                 {
 518                 bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
 519                 }
 520         else
 521                 {
 522                 lp= &(t[n2+n]);
 523                 mp= &(t[n2]);
 524                 for (i=0; i<n; i++)
 525                         lp[i]=((~mp[i])+1)&BN_MASK2;
 526                 }
 527
 528         /* s[0] = low(al*bl)
 529          * t[3] = high(al*bl)
 530          * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
 531          * r[10] = (a[1]*b[1])
 532          */
 533         /* R[10] = al*bl
 534          * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
 535          * R[32] = ah*bh
 536          */
 537         /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
 538          * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
 539          * R[3]=r[1]+(carry/borrow)
 540          */
 541         if (l != NULL)
 542                 {
 543                 lp= &(t[n2]);
 544                 c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
 545                 }
 546         else
 547                 {
 548                 lp= &(t[n2+n]);
 549                 c1=0;
 550                 }
 551         c1+=(int)(bn_add_words(&(t[n2]),lp,  &(r[0]),n));
 552         if (oneg)
 553                 c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
 554         else
 555                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));
 556
 557         c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
 558         c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
 559         if (oneg)
 560                 c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
 561         else
 562                 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
 563
 564         if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
 565                 {
 566                 i=0;
 567                 if (c1 > 0)
 568                         {
 569                         lc=c1;
 570                         do      {
 571                                 ll=(r[i]+lc)&BN_MASK2;
 572                                 r[i++]=ll;
 573                                 lc=(lc > ll);
 574                                 } while (lc);
 575                         }
 576                 else
 577                         {
 578                         lc= -c1;
 579                         do      {
 580                                 ll=r[i];
 581                                 r[i++]=(ll-lc)&BN_MASK2;
 582                                 lc=(lc > ll);
 583                                 } while (lc);
 584                         }
 585                 }
 586         if (c2 != 0) /* Add starting at r[1] */
 587                 {
 588                 i=n;
 589                 if (c2 > 0)
 590                         {
 591                         lc=c2;
 592                         do      {
 593                                 ll=(r[i]+lc)&BN_MASK2;
 594                                 r[i++]=ll;
 595                                 lc=(lc > ll);
 596                                 } while (lc);
 597                         }
 598                 else
 599                         {
 600                         lc= -c2;
 601                         do      {
 602                                 ll=r[i];
 603                                 r[i++]=(ll-lc)&BN_MASK2;
 604                                 lc=(lc > ll);
 605                                 } while (lc);
 606                         }
 607                 }
 608         }
 609 #endif /* BN_RECURSION */
 610
 611 int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
 612         {
 613         int top,al,bl;
 614         BIGNUM *rr;
 615         int ret = 0;
 616 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 617         int i;
 618 #endif
 619 #ifdef BN_RECURSION
 620         BIGNUM *t;
 621         int j,k;
 622 #endif
 623
 624 #ifdef BN_COUNT
 625         printf("BN_mul %d * %d\n",a->top,b->top);
 626 #endif
 627
 628         bn_check_top(a);
 629         bn_check_top(b);
 630         bn_check_top(r);
 631
 632         al=a->top;
 633         bl=b->top;
 634         r->neg=a->neg^b->neg;
 635
 636         if ((al == 0) || (bl == 0))
 637                 {
 638                 BN_zero(r);
 639                 return(1);
 640                 }
 641         top=al+bl;
 642
 643         BN_CTX_start(ctx);
 644         if ((r == a) || (r == b))
 645                 {
 646                 if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
 647                 }
 648         else
 649                 rr = r;
 650
 651 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 652         i = al-bl;
 653 #endif
 654 #ifdef BN_MUL_COMBA
 655         if (i == 0)
 656                 {
 657 # if 0
 658                 if (al == 4)
 659                         {
 660                         if (bn_wexpand(rr,8) == NULL) goto err;
 661                         rr->top=8;
 662                         bn_mul_comba4(rr->d,a->d,b->d);
 663                         goto end;
 664                         }
 665 # endif
 666                 if (al == 8)
 667                         {
 668                         if (bn_wexpand(rr,16) == NULL) goto err;
 669                         rr->top=16;
 670                         bn_mul_comba8(rr->d,a->d,b->d);
 671                         goto end;
 672                         }
 673                 }
 674 #endif /* BN_MUL_COMBA */
 675 #ifdef BN_RECURSION
 676         if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))
 677                 {
 678                 if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
 679                         {
 680                         bn_wexpand(b,al);
 681                         b->d[bl]=0;
 682                         bl++;
 683                         i--;
 684                         }
 685                 else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
 686                         {
 687                         bn_wexpand(a,bl);
 688                         a->d[al]=0;
 689                         al++;
 690                         i++;
 691                         }
 692                 if (i == 0)
 693                         {
 694                         /* symmetric and > 4 */
 695                         /* 16 or larger */
 696                         j=BN_num_bits_word((BN_ULONG)al);
 697                         j=1<<(j-1);
 698                         k=j+j;
 699                         t = BN_CTX_get(ctx);
 700                         if (al == j) /* exact multiple */
 701                                 {
 702                                 bn_wexpand(t,k*2);
 703                                 bn_wexpand(rr,k*2);
 704                                 bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
 705                                 }
 706                         else
 707                                 {
 708                                 bn_wexpand(a,k);
 709                                 bn_wexpand(b,k);
 710                                 bn_wexpand(t,k*4);
 711                                 bn_wexpand(rr,k*4);
 712                                 for (i=a->top; i<k; i++)
 713                                         a->d[i]=0;
 714                                 for (i=b->top; i<k; i++)
 715                                         b->d[i]=0;
 716                                 bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
 717                                 }
 718                         rr->top=top;
 719                         goto end;
 720                         }
 721                 }
 722 #endif /* BN_RECURSION */
 723         if (bn_wexpand(rr,top) == NULL) goto err;
 724         rr->top=top;
 725         bn_mul_normal(rr->d,a->d,al,b->d,bl);
 726
 727 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
 728 end:
 729 #endif
 730         bn_fix_top(rr);
 731         if (r != rr) BN_copy(r,rr);
 732         ret=1;
 733 err:
 734         BN_CTX_end(ctx);
 735         return(ret);
 736         }
 737
 738 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
 739         {
 740         BN_ULONG *rr;
 741
 742 #ifdef BN_COUNT
 743         printf(" bn_mul_normal %d * %d\n",na,nb);
 744 #endif
 745
 746         if (na < nb)
 747                 {
 748                 int itmp;
 749                 BN_ULONG *ltmp;
 750
 751                 itmp=na; na=nb; nb=itmp;
 752                 ltmp=a;   a=b;   b=ltmp;
 753
 754                 }
 755         rr= &(r[na]);
 756         rr[0]=bn_mul_words(r,a,na,b[0]);
 757
 758         for (;;)
 759                 {
 760                 if (--nb <= 0) return;
 761                 rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
 762                 if (--nb <= 0) return;
 763                 rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
 764                 if (--nb <= 0) return;
 765                 rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
 766                 if (--nb <= 0) return;
 767                 rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
 768                 rr+=4;
 769                 r+=4;
 770                 b+=4;
 771                 }
 772         }
 773
 774 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
 775         {
 776 #ifdef BN_COUNT
 777         printf(" bn_mul_low_normal %d * %d\n",n,n);
 778 #endif
 779         bn_mul_words(r,a,n,b[0]);
 780
 781         for (;;)
 782                 {
 783                 if (--n <= 0) return;
 784                 bn_mul_add_words(&(r[1]),a,n,b[1]);
 785                 if (--n <= 0) return;
 786                 bn_mul_add_words(&(r[2]),a,n,b[2]);
 787                 if (--n <= 0) return;
 788                 bn_mul_add_words(&(r[3]),a,n,b[3]);
 789                 if (--n <= 0) return;
 790                 bn_mul_add_words(&(r[4]),a,n,b[4]);
 791                 r+=4;
 792                 b+=4;
 793                 }
 794         }