crypto/openssl/crypto/bn/bn_div.c

   1 /* crypto/bn/bn_div.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 <openssl/bn.h>
  61 #include "cryptlib.h"
  62 #include "bn_lcl.h"
  63
  64
  65 /* The old slow way */
  66 #if 0
  67 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
  68            BN_CTX *ctx)
  69         {
  70         int i,nm,nd;
  71         int ret = 0;
  72         BIGNUM *D;
  73
  74         bn_check_top(m);
  75         bn_check_top(d);
  76         if (BN_is_zero(d))
  77                 {
  78                 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
  79                 return(0);
  80                 }
  81
  82         if (BN_ucmp(m,d) < 0)
  83                 {
  84                 if (rem != NULL)
  85                         { if (BN_copy(rem,m) == NULL) return(0); }
  86                 if (dv != NULL) BN_zero(dv);
  87                 return(1);
  88                 }
  89
  90         BN_CTX_start(ctx);
  91         D = BN_CTX_get(ctx);
  92         if (dv == NULL) dv = BN_CTX_get(ctx);
  93         if (rem == NULL) rem = BN_CTX_get(ctx);
  94         if (D == NULL || dv == NULL || rem == NULL)
  95                 goto end;
  96
  97         nd=BN_num_bits(d);
  98         nm=BN_num_bits(m);
  99         if (BN_copy(D,d) == NULL) goto end;
 100         if (BN_copy(rem,m) == NULL) goto end;
 101
 102         /* The next 2 are needed so we can do a dv->d[0]|=1 later
 103          * since BN_lshift1 will only work once there is a value :-) */
 104         BN_zero(dv);
 105         bn_wexpand(dv,1);
 106         dv->top=1;
 107
 108         if (!BN_lshift(D,D,nm-nd)) goto end;
 109         for (i=nm-nd; i>=0; i--)
 110                 {
 111                 if (!BN_lshift1(dv,dv)) goto end;
 112                 if (BN_ucmp(rem,D) >= 0)
 113                         {
 114                         dv->d[0]|=1;
 115                         if (!BN_usub(rem,rem,D)) goto end;
 116                         }
 117 /* CAN IMPROVE (and have now :=) */
 118                 if (!BN_rshift1(D,D)) goto end;
 119                 }
 120         rem->neg=BN_is_zero(rem)?0:m->neg;
 121         dv->neg=m->neg^d->neg;
 122         ret = 1;
 123  end:
 124         BN_CTX_end(ctx);
 125         return(ret);
 126         }
 127
 128 #else
 129
 130 #if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
 131     && !defined(PEDANTIC) && !defined(BN_DIV3W)
 132 # if defined(__GNUC__) && __GNUC__>=2
 133 #  if defined(__i386) || defined (__i386__)
 134    /*
 135     * There were two reasons for implementing this template:
 136     * - GNU C generates a call to a function (__udivdi3 to be exact)
 137     *   in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
 138     *   understand why...);
 139     * - divl doesn't only calculate quotient, but also leaves
 140     *   remainder in %edx which we can definitely use here:-)
 141     *
 142     *                                   <appro@fy.chalmers.se>
 143     */
 144 #  define bn_div_words(n0,n1,d0)                \
 145         ({  asm volatile (                      \
 146                 "divl   %4"                     \
 147                 : "=a"(q), "=d"(rem)            \
 148                 : "a"(n1), "d"(n0), "g"(d0)     \
 149                 : "cc");                        \
 150             q;                                  \
 151         })
 152 #  define REMAINDER_IS_ALREADY_CALCULATED
 153 #  elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
 154    /*
 155     * Same story here, but it's 128-bit by 64-bit division. Wow!
 156     *                                   <appro@fy.chalmers.se>
 157     */
 158 #  define bn_div_words(n0,n1,d0)                \
 159         ({  asm volatile (                      \
 160                 "divq   %4"                     \
 161                 : "=a"(q), "=d"(rem)            \
 162                 : "a"(n1), "d"(n0), "g"(d0)     \
 163                 : "cc");                        \
 164             q;                                  \
 165         })
 166 #  define REMAINDER_IS_ALREADY_CALCULATED
 167 #  endif /* __<cpu> */
 168 # endif /* __GNUC__ */
 169 #endif /* OPENSSL_NO_ASM */
 170
 171
 172 /* BN_div[_no_branch] computes  dv := num / divisor,  rounding towards
 173  * zero, and sets up rm  such that  dv*divisor + rm = num  holds.
 174  * Thus:
 175  *     dv->neg == num->neg ^ divisor->neg  (unless the result is zero)
 176  *     rm->neg == num->neg                 (unless the remainder is zero)
 177  * If 'dv' or 'rm' is NULL, the respective value is not returned.
 178  */
 179 static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,
 180         const BIGNUM *divisor, BN_CTX *ctx);
 181 int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
 182            BN_CTX *ctx)
 183         {
 184         int norm_shift,i,loop;
 185         BIGNUM *tmp,wnum,*snum,*sdiv,*res;
 186         BN_ULONG *resp,*wnump;
 187         BN_ULONG d0,d1;
 188         int num_n,div_n;
 189
 190         /* Invalid zero-padding would have particularly bad consequences
 191          * in the case of 'num', so don't just rely on bn_check_top() for this one
 192          * (bn_check_top() works only for BN_DEBUG builds) */
 193         if (num->top > 0 && num->d[num->top - 1] == 0)
 194                 {
 195                 BNerr(BN_F_BN_DIV,BN_R_NOT_INITIALIZED);
 196                 return 0;
 197                 }
 198
 199         bn_check_top(num);
 200
 201         if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0))
 202                 {
 203                 return BN_div_no_branch(dv, rm, num, divisor, ctx);
 204                 }
 205
 206         bn_check_top(dv);
 207         bn_check_top(rm);
 208         /* bn_check_top(num); */ /* 'num' has been checked already */
 209         bn_check_top(divisor);
 210
 211         if (BN_is_zero(divisor))
 212                 {
 213                 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
 214                 return(0);
 215                 }
 216
 217         if (BN_ucmp(num,divisor) < 0)
 218                 {
 219                 if (rm != NULL)
 220                         { if (BN_copy(rm,num) == NULL) return(0); }
 221                 if (dv != NULL) BN_zero(dv);
 222                 return(1);
 223                 }
 224
 225         BN_CTX_start(ctx);
 226         tmp=BN_CTX_get(ctx);
 227         snum=BN_CTX_get(ctx);
 228         sdiv=BN_CTX_get(ctx);
 229         if (dv == NULL)
 230                 res=BN_CTX_get(ctx);
 231         else    res=dv;
 232         if (sdiv == NULL || res == NULL) goto err;
 233
 234         /* First we normalise the numbers */
 235         norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
 236         if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
 237         sdiv->neg=0;
 238         norm_shift+=BN_BITS2;
 239         if (!(BN_lshift(snum,num,norm_shift))) goto err;
 240         snum->neg=0;
 241         div_n=sdiv->top;
 242         num_n=snum->top;
 243         loop=num_n-div_n;
 244         /* Lets setup a 'window' into snum
 245          * This is the part that corresponds to the current
 246          * 'area' being divided */
 247         wnum.neg   = 0;
 248         wnum.d     = &(snum->d[loop]);
 249         wnum.top   = div_n;
 250         /* only needed when BN_ucmp messes up the values between top and max */
 251         wnum.dmax  = snum->dmax - loop; /* so we don't step out of bounds */
 252
 253         /* Get the top 2 words of sdiv */
 254         /* div_n=sdiv->top; */
 255         d0=sdiv->d[div_n-1];
 256         d1=(div_n == 1)?0:sdiv->d[div_n-2];
 257
 258         /* pointer to the 'top' of snum */
 259         wnump= &(snum->d[num_n-1]);
 260
 261         /* Setup to 'res' */
 262         res->neg= (num->neg^divisor->neg);
 263         if (!bn_wexpand(res,(loop+1))) goto err;
 264         res->top=loop;
 265         resp= &(res->d[loop-1]);
 266
 267         /* space for temp */
 268         if (!bn_wexpand(tmp,(div_n+1))) goto err;
 269
 270         if (BN_ucmp(&wnum,sdiv) >= 0)
 271                 {
 272                 /* If BN_DEBUG_RAND is defined BN_ucmp changes (via
 273                  * bn_pollute) the const bignum arguments =>
 274                  * clean the values between top and max again */
 275                 bn_clear_top2max(&wnum);
 276                 bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
 277                 *resp=1;
 278                 }
 279         else
 280                 res->top--;
 281         /* if res->top == 0 then clear the neg value otherwise decrease
 282          * the resp pointer */
 283         if (res->top == 0)
 284                 res->neg = 0;
 285         else
 286                 resp--;
 287
 288         for (i=0; i<loop-1; i++, wnump--, resp--)
 289                 {
 290                 BN_ULONG q,l0;
 291                 /* the first part of the loop uses the top two words of
 292                  * snum and sdiv to calculate a BN_ULONG q such that
 293                  * | wnum - sdiv * q | < sdiv */
 294 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
 295                 BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
 296                 q=bn_div_3_words(wnump,d1,d0);
 297 #else
 298                 BN_ULONG n0,n1,rem=0;
 299
 300                 n0=wnump[0];
 301                 n1=wnump[-1];
 302                 if (n0 == d0)
 303                         q=BN_MASK2;
 304                 else                    /* n0 < d0 */
 305                         {
 306 #ifdef BN_LLONG
 307                         BN_ULLONG t2;
 308
 309 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
 310                         q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
 311 #else
 312                         q=bn_div_words(n0,n1,d0);
 313 #ifdef BN_DEBUG_LEVITTE
 314                         fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
 315 X) -> 0x%08X\n",
 316                                 n0, n1, d0, q);
 317 #endif
 318 #endif
 319
 320 #ifndef REMAINDER_IS_ALREADY_CALCULATED
 321                         /*
 322                          * rem doesn't have to be BN_ULLONG. The least we
 323                          * know it's less that d0, isn't it?
 324                          */
 325                         rem=(n1-q*d0)&BN_MASK2;
 326 #endif
 327                         t2=(BN_ULLONG)d1*q;
 328
 329                         for (;;)
 330                                 {
 331                                 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
 332                                         break;
 333                                 q--;
 334                                 rem += d0;
 335                                 if (rem < d0) break; /* don't let rem overflow */
 336                                 t2 -= d1;
 337                                 }
 338 #else /* !BN_LLONG */
 339                         BN_ULONG t2l,t2h,ql,qh;
 340
 341                         q=bn_div_words(n0,n1,d0);
 342 #ifdef BN_DEBUG_LEVITTE
 343                         fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
 344 X) -> 0x%08X\n",
 345                                 n0, n1, d0, q);
 346 #endif
 347 #ifndef REMAINDER_IS_ALREADY_CALCULATED
 348                         rem=(n1-q*d0)&BN_MASK2;
 349 #endif
 350
 351 #if defined(BN_UMULT_LOHI)
 352                         BN_UMULT_LOHI(t2l,t2h,d1,q);
 353 #elif defined(BN_UMULT_HIGH)
 354                         t2l = d1 * q;
 355                         t2h = BN_UMULT_HIGH(d1,q);
 356 #else
 357                         t2l=LBITS(d1); t2h=HBITS(d1);
 358                         ql =LBITS(q);  qh =HBITS(q);
 359                         mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
 360 #endif
 361
 362                         for (;;)
 363                                 {
 364                                 if ((t2h < rem) ||
 365                                         ((t2h == rem) && (t2l <= wnump[-2])))
 366                                         break;
 367                                 q--;
 368                                 rem += d0;
 369                                 if (rem < d0) break; /* don't let rem overflow */
 370                                 if (t2l < d1) t2h--; t2l -= d1;
 371                                 }
 372 #endif /* !BN_LLONG */
 373                         }
 374 #endif /* !BN_DIV3W */
 375
 376                 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
 377                 tmp->d[div_n]=l0;
 378                 wnum.d--;
 379                 /* ingore top values of the bignums just sub the two
 380                  * BN_ULONG arrays with bn_sub_words */
 381                 if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
 382                         {
 383                         /* Note: As we have considered only the leading
 384                          * two BN_ULONGs in the calculation of q, sdiv * q
 385                          * might be greater than wnum (but then (q-1) * sdiv
 386                          * is less or equal than wnum)
 387                          */
 388                         q--;
 389                         if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
 390                                 /* we can't have an overflow here (assuming
 391                                  * that q != 0, but if q == 0 then tmp is
 392                                  * zero anyway) */
 393                                 (*wnump)++;
 394                         }
 395                 /* store part of the result */
 396                 *resp = q;
 397                 }
 398         bn_correct_top(snum);
 399         if (rm != NULL)
 400                 {
 401                 /* Keep a copy of the neg flag in num because if rm==num
 402                  * BN_rshift() will overwrite it.
 403                  */
 404                 int neg = num->neg;
 405                 BN_rshift(rm,snum,norm_shift);
 406                 if (!BN_is_zero(rm))
 407                         rm->neg = neg;
 408                 bn_check_top(rm);
 409                 }
 410         BN_CTX_end(ctx);
 411         return(1);
 412 err:
 413         bn_check_top(rm);
 414         BN_CTX_end(ctx);
 415         return(0);
 416         }
 417
 418
 419 /* BN_div_no_branch is a special version of BN_div. It does not contain
 420  * branches that may leak sensitive information.
 421  */
 422 static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,
 423         const BIGNUM *divisor, BN_CTX *ctx)
 424         {
 425         int norm_shift,i,loop;
 426         BIGNUM *tmp,wnum,*snum,*sdiv,*res;
 427         BN_ULONG *resp,*wnump;
 428         BN_ULONG d0,d1;
 429         int num_n,div_n;
 430
 431         bn_check_top(dv);
 432         bn_check_top(rm);
 433         /* bn_check_top(num); */ /* 'num' has been checked in BN_div() */
 434         bn_check_top(divisor);
 435
 436         if (BN_is_zero(divisor))
 437                 {
 438                 BNerr(BN_F_BN_DIV_NO_BRANCH,BN_R_DIV_BY_ZERO);
 439                 return(0);
 440                 }
 441
 442         BN_CTX_start(ctx);
 443         tmp=BN_CTX_get(ctx);
 444         snum=BN_CTX_get(ctx);
 445         sdiv=BN_CTX_get(ctx);
 446         if (dv == NULL)
 447                 res=BN_CTX_get(ctx);
 448         else    res=dv;
 449         if (sdiv == NULL || res == NULL) goto err;
 450
 451         /* First we normalise the numbers */
 452         norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
 453         if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
 454         sdiv->neg=0;
 455         norm_shift+=BN_BITS2;
 456         if (!(BN_lshift(snum,num,norm_shift))) goto err;
 457         snum->neg=0;
 458
 459         /* Since we don't know whether snum is larger than sdiv,
 460          * we pad snum with enough zeroes without changing its
 461          * value.
 462          */
 463         if (snum->top <= sdiv->top+1)
 464                 {
 465                 if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err;
 466                 for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0;
 467                 snum->top = sdiv->top + 2;
 468                 }
 469         else
 470                 {
 471                 if (bn_wexpand(snum, snum->top + 1) == NULL) goto err;
 472                 snum->d[snum->top] = 0;
 473                 snum->top ++;
 474                 }
 475
 476         div_n=sdiv->top;
 477         num_n=snum->top;
 478         loop=num_n-div_n;
 479         /* Lets setup a 'window' into snum
 480          * This is the part that corresponds to the current
 481          * 'area' being divided */
 482         wnum.neg   = 0;
 483         wnum.d     = &(snum->d[loop]);
 484         wnum.top   = div_n;
 485         /* only needed when BN_ucmp messes up the values between top and max */
 486         wnum.dmax  = snum->dmax - loop; /* so we don't step out of bounds */
 487
 488         /* Get the top 2 words of sdiv */
 489         /* div_n=sdiv->top; */
 490         d0=sdiv->d[div_n-1];
 491         d1=(div_n == 1)?0:sdiv->d[div_n-2];
 492
 493         /* pointer to the 'top' of snum */
 494         wnump= &(snum->d[num_n-1]);
 495
 496         /* Setup to 'res' */
 497         res->neg= (num->neg^divisor->neg);
 498         if (!bn_wexpand(res,(loop+1))) goto err;
 499         res->top=loop-1;
 500         resp= &(res->d[loop-1]);
 501
 502         /* space for temp */
 503         if (!bn_wexpand(tmp,(div_n+1))) goto err;
 504
 505         /* if res->top == 0 then clear the neg value otherwise decrease
 506          * the resp pointer */
 507         if (res->top == 0)
 508                 res->neg = 0;
 509         else
 510                 resp--;
 511
 512         for (i=0; i<loop-1; i++, wnump--, resp--)
 513                 {
 514                 BN_ULONG q,l0;
 515                 /* the first part of the loop uses the top two words of
 516                  * snum and sdiv to calculate a BN_ULONG q such that
 517                  * | wnum - sdiv * q | < sdiv */
 518 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
 519                 BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
 520                 q=bn_div_3_words(wnump,d1,d0);
 521 #else
 522                 BN_ULONG n0,n1,rem=0;
 523
 524                 n0=wnump[0];
 525                 n1=wnump[-1];
 526                 if (n0 == d0)
 527                         q=BN_MASK2;
 528                 else                    /* n0 < d0 */
 529                         {
 530 #ifdef BN_LLONG
 531                         BN_ULLONG t2;
 532
 533 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
 534                         q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
 535 #else
 536                         q=bn_div_words(n0,n1,d0);
 537 #ifdef BN_DEBUG_LEVITTE
 538                         fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
 539 X) -> 0x%08X\n",
 540                                 n0, n1, d0, q);
 541 #endif
 542 #endif
 543
 544 #ifndef REMAINDER_IS_ALREADY_CALCULATED
 545                         /*
 546                          * rem doesn't have to be BN_ULLONG. The least we
 547                          * know it's less that d0, isn't it?
 548                          */
 549                         rem=(n1-q*d0)&BN_MASK2;
 550 #endif
 551                         t2=(BN_ULLONG)d1*q;
 552
 553                         for (;;)
 554                                 {
 555                                 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
 556                                         break;
 557                                 q--;
 558                                 rem += d0;
 559                                 if (rem < d0) break; /* don't let rem overflow */
 560                                 t2 -= d1;
 561                                 }
 562 #else /* !BN_LLONG */
 563                         BN_ULONG t2l,t2h,ql,qh;
 564
 565                         q=bn_div_words(n0,n1,d0);
 566 #ifdef BN_DEBUG_LEVITTE
 567                         fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
 568 X) -> 0x%08X\n",
 569                                 n0, n1, d0, q);
 570 #endif
 571 #ifndef REMAINDER_IS_ALREADY_CALCULATED
 572                         rem=(n1-q*d0)&BN_MASK2;
 573 #endif
 574
 575 #if defined(BN_UMULT_LOHI)
 576                         BN_UMULT_LOHI(t2l,t2h,d1,q);
 577 #elif defined(BN_UMULT_HIGH)
 578                         t2l = d1 * q;
 579                         t2h = BN_UMULT_HIGH(d1,q);
 580 #else
 581                         t2l=LBITS(d1); t2h=HBITS(d1);
 582                         ql =LBITS(q);  qh =HBITS(q);
 583                         mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
 584 #endif
 585
 586                         for (;;)
 587                                 {
 588                                 if ((t2h < rem) ||
 589                                         ((t2h == rem) && (t2l <= wnump[-2])))
 590                                         break;
 591                                 q--;
 592                                 rem += d0;
 593                                 if (rem < d0) break; /* don't let rem overflow */
 594                                 if (t2l < d1) t2h--; t2l -= d1;
 595                                 }
 596 #endif /* !BN_LLONG */
 597                         }
 598 #endif /* !BN_DIV3W */
 599
 600                 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
 601                 tmp->d[div_n]=l0;
 602                 wnum.d--;
 603                 /* ingore top values of the bignums just sub the two
 604                  * BN_ULONG arrays with bn_sub_words */
 605                 if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
 606                         {
 607                         /* Note: As we have considered only the leading
 608                          * two BN_ULONGs in the calculation of q, sdiv * q
 609                          * might be greater than wnum (but then (q-1) * sdiv
 610                          * is less or equal than wnum)
 611                          */
 612                         q--;
 613                         if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
 614                                 /* we can't have an overflow here (assuming
 615                                  * that q != 0, but if q == 0 then tmp is
 616                                  * zero anyway) */
 617                                 (*wnump)++;
 618                         }
 619                 /* store part of the result */
 620                 *resp = q;
 621                 }
 622         bn_correct_top(snum);
 623         if (rm != NULL)
 624                 {
 625                 /* Keep a copy of the neg flag in num because if rm==num
 626                  * BN_rshift() will overwrite it.
 627                  */
 628                 int neg = num->neg;
 629                 BN_rshift(rm,snum,norm_shift);
 630                 if (!BN_is_zero(rm))
 631                         rm->neg = neg;
 632                 bn_check_top(rm);
 633                 }
 634         bn_correct_top(res);
 635         BN_CTX_end(ctx);
 636         return(1);
 637 err:
 638         bn_check_top(rm);
 639         BN_CTX_end(ctx);
 640         return(0);
 641         }
 642
 643 #endif