release/src/router/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 /* The old slow way */
  65 #if 0
  66 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
  67            BN_CTX *ctx)
  68 {
  69     int i, nm, nd;
  70     int ret = 0;
  71     BIGNUM *D;
  72
  73     bn_check_top(m);
  74     bn_check_top(d);
  75     if (BN_is_zero(d)) {
  76         BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);
  77         return (0);
  78     }
  79
  80     if (BN_ucmp(m, d) < 0) {
  81         if (rem != NULL) {
  82             if (BN_copy(rem, m) == NULL)
  83                 return (0);
  84         }
  85         if (dv != NULL)
  86             BN_zero(dv);
  87         return (1);
  88     }
  89
  90     BN_CTX_start(ctx);
  91     D = BN_CTX_get(ctx);
  92     if (dv == NULL)
  93         dv = BN_CTX_get(ctx);
  94     if (rem == NULL)
  95         rem = BN_CTX_get(ctx);
  96     if (D == NULL || dv == NULL || rem == NULL)
  97         goto end;
  98
  99     nd = BN_num_bits(d);
 100     nm = BN_num_bits(m);
 101     if (BN_copy(D, d) == NULL)
 102         goto end;
 103     if (BN_copy(rem, m) == NULL)
 104         goto end;
 105
 106     /*
 107      * The next 2 are needed so we can do a dv->d[0]|=1 later since
 108      * BN_lshift1 will only work once there is a value :-)
 109      */
 110     BN_zero(dv);
 111     if (bn_wexpand(dv, 1) == NULL)
 112         goto end;
 113     dv->top = 1;
 114
 115     if (!BN_lshift(D, D, nm - nd))
 116         goto end;
 117     for (i = nm - nd; i >= 0; i--) {
 118         if (!BN_lshift1(dv, dv))
 119             goto end;
 120         if (BN_ucmp(rem, D) >= 0) {
 121             dv->d[0] |= 1;
 122             if (!BN_usub(rem, rem, D))
 123                 goto end;
 124         }
 125 /* CAN IMPROVE (and have now :=) */
 126         if (!BN_rshift1(D, D))
 127             goto end;
 128     }
 129     rem->neg = BN_is_zero(rem) ? 0 : m->neg;
 130     dv->neg = m->neg ^ d->neg;
 131     ret = 1;
 132  end:
 133     BN_CTX_end(ctx);
 134     return (ret);
 135 }
 136
 137 #else
 138
 139 # if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
 140     && !defined(PEDANTIC) && !defined(BN_DIV3W)
 141 #  if defined(__GNUC__) && __GNUC__>=2
 142 #   if defined(__i386) || defined (__i386__)
 143    /*-
 144     * There were two reasons for implementing this template:
 145     * - GNU C generates a call to a function (__udivdi3 to be exact)
 146     *   in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
 147     *   understand why...);
 148     * - divl doesn't only calculate quotient, but also leaves
 149     *   remainder in %edx which we can definitely use here:-)
 150     *
 151     *                                   <appro@fy.chalmers.se>
 152     */
 153 #    undef bn_div_words
 154 #    define bn_div_words(n0,n1,d0)                \
 155         ({  asm volatile (                      \
 156                 "divl   %4"                     \
 157                 : "=a"(q), "=d"(rem)            \
 158                 : "a"(n1), "d"(n0), "g"(d0)     \
 159                 : "cc");                        \
 160             q;                                  \
 161         })
 162 #    define REMAINDER_IS_ALREADY_CALCULATED
 163 #   elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
 164    /*
 165     * Same story here, but it's 128-bit by 64-bit division. Wow!
 166     *                                   <appro@fy.chalmers.se>
 167     */
 168 #    undef bn_div_words
 169 #    define bn_div_words(n0,n1,d0)                \
 170         ({  asm volatile (                      \
 171                 "divq   %4"                     \
 172                 : "=a"(q), "=d"(rem)            \
 173                 : "a"(n1), "d"(n0), "g"(d0)     \
 174                 : "cc");                        \
 175             q;                                  \
 176         })
 177 #    define REMAINDER_IS_ALREADY_CALCULATED
 178 #   endif                       /* __<cpu> */
 179 #  endif                        /* __GNUC__ */
 180 # endif                         /* OPENSSL_NO_ASM */
 181
 182 /*-
 183  * BN_div computes  dv := num / divisor,  rounding towards
 184  * zero, and sets up rm  such that  dv*divisor + rm = num  holds.
 185  * Thus:
 186  *     dv->neg == num->neg ^ divisor->neg  (unless the result is zero)
 187  *     rm->neg == num->neg                 (unless the remainder is zero)
 188  * If 'dv' or 'rm' is NULL, the respective value is not returned.
 189  */
 190 int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
 191            BN_CTX *ctx)
 192 {
 193     int norm_shift, i, loop;
 194     BIGNUM *tmp, wnum, *snum, *sdiv, *res;
 195     BN_ULONG *resp, *wnump;
 196     BN_ULONG d0, d1;
 197     int num_n, div_n;
 198     int no_branch = 0;
 199
 200     /*
 201      * Invalid zero-padding would have particularly bad consequences so don't
 202      * just rely on bn_check_top() here (bn_check_top() works only for
 203      * BN_DEBUG builds)
 204      */
 205     if ((num->top > 0 && num->d[num->top - 1] == 0) ||
 206         (divisor->top > 0 && divisor->d[divisor->top - 1] == 0)) {
 207         BNerr(BN_F_BN_DIV, BN_R_NOT_INITIALIZED);
 208         return 0;
 209     }
 210
 211     bn_check_top(num);
 212     bn_check_top(divisor);
 213
 214     if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0)
 215         || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0)) {
 216         no_branch = 1;
 217     }
 218
 219     bn_check_top(dv);
 220     bn_check_top(rm);
 221     /*- bn_check_top(num); *//*
 222      * 'num' has been checked already
 223      */
 224     /*- bn_check_top(divisor); *//*
 225      * 'divisor' has been checked already
 226      */
 227
 228     if (BN_is_zero(divisor)) {
 229         BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);
 230         return (0);
 231     }
 232
 233     if (!no_branch && BN_ucmp(num, divisor) < 0) {
 234         if (rm != NULL) {
 235             if (BN_copy(rm, num) == NULL)
 236                 return (0);
 237         }
 238         if (dv != NULL)
 239             BN_zero(dv);
 240         return (1);
 241     }
 242
 243     BN_CTX_start(ctx);
 244     tmp = BN_CTX_get(ctx);
 245     snum = BN_CTX_get(ctx);
 246     sdiv = BN_CTX_get(ctx);
 247     if (dv == NULL)
 248         res = BN_CTX_get(ctx);
 249     else
 250         res = dv;
 251     if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)
 252         goto err;
 253
 254     /* First we normalise the numbers */
 255     norm_shift = BN_BITS2 - ((BN_num_bits(divisor)) % BN_BITS2);
 256     if (!(BN_lshift(sdiv, divisor, norm_shift)))
 257         goto err;
 258     sdiv->neg = 0;
 259     norm_shift += BN_BITS2;
 260     if (!(BN_lshift(snum, num, norm_shift)))
 261         goto err;
 262     snum->neg = 0;
 263
 264     if (no_branch) {
 265         /*
 266          * Since we don't know whether snum is larger than sdiv, we pad snum
 267          * with enough zeroes without changing its value.
 268          */
 269         if (snum->top <= sdiv->top + 1) {
 270             if (bn_wexpand(snum, sdiv->top + 2) == NULL)
 271                 goto err;
 272             for (i = snum->top; i < sdiv->top + 2; i++)
 273                 snum->d[i] = 0;
 274             snum->top = sdiv->top + 2;
 275         } else {
 276             if (bn_wexpand(snum, snum->top + 1) == NULL)
 277                 goto err;
 278             snum->d[snum->top] = 0;
 279             snum->top++;
 280         }
 281     }
 282
 283     div_n = sdiv->top;
 284     num_n = snum->top;
 285     loop = num_n - div_n;
 286     /*
 287      * Lets setup a 'window' into snum This is the part that corresponds to
 288      * the current 'area' being divided
 289      */
 290     wnum.neg = 0;
 291     wnum.d = &(snum->d[loop]);
 292     wnum.top = div_n;
 293     /*
 294      * only needed when BN_ucmp messes up the values between top and max
 295      */
 296     wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
 297
 298     /* Get the top 2 words of sdiv */
 299     /* div_n=sdiv->top; */
 300     d0 = sdiv->d[div_n - 1];
 301     d1 = (div_n == 1) ? 0 : sdiv->d[div_n - 2];
 302
 303     /* pointer to the 'top' of snum */
 304     wnump = &(snum->d[num_n - 1]);
 305
 306     /* Setup to 'res' */
 307     res->neg = (num->neg ^ divisor->neg);
 308     if (!bn_wexpand(res, (loop + 1)))
 309         goto err;
 310     res->top = loop - no_branch;
 311     resp = &(res->d[loop - 1]);
 312
 313     /* space for temp */
 314     if (!bn_wexpand(tmp, (div_n + 1)))
 315         goto err;
 316
 317     if (!no_branch) {
 318         if (BN_ucmp(&wnum, sdiv) >= 0) {
 319             /*
 320              * If BN_DEBUG_RAND is defined BN_ucmp changes (via bn_pollute)
 321              * the const bignum arguments => clean the values between top and
 322              * max again
 323              */
 324             bn_clear_top2max(&wnum);
 325             bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
 326             *resp = 1;
 327         } else
 328             res->top--;
 329     }
 330
 331     /*
 332      * if res->top == 0 then clear the neg value otherwise decrease the resp
 333      * pointer
 334      */
 335     if (res->top == 0)
 336         res->neg = 0;
 337     else
 338         resp--;
 339
 340     for (i = 0; i < loop - 1; i++, wnump--, resp--) {
 341         BN_ULONG q, l0;
 342         /*
 343          * the first part of the loop uses the top two words of snum and sdiv
 344          * to calculate a BN_ULONG q such that | wnum - sdiv * q | < sdiv
 345          */
 346 # if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
 347         BN_ULONG bn_div_3_words(BN_ULONG *, BN_ULONG, BN_ULONG);
 348         q = bn_div_3_words(wnump, d1, d0);
 349 # else
 350         BN_ULONG n0, n1, rem = 0;
 351
 352         n0 = wnump[0];
 353         n1 = wnump[-1];
 354         if (n0 == d0)
 355             q = BN_MASK2;
 356         else {                  /* n0 < d0 */
 357
 358 #  ifdef BN_LLONG
 359             BN_ULLONG t2;
 360
 361 #   if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
 362             q = (BN_ULONG)(((((BN_ULLONG) n0) << BN_BITS2) | n1) / d0);
 363 #   else
 364             q = bn_div_words(n0, n1, d0);
 365 #    ifdef BN_DEBUG_LEVITTE
 366             fprintf(stderr, "DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
 367 X) -> 0x%08X\n", n0, n1, d0, q);
 368 #    endif
 369 #   endif
 370
 371 #   ifndef REMAINDER_IS_ALREADY_CALCULATED
 372             /*
 373              * rem doesn't have to be BN_ULLONG. The least we
 374              * know it's less that d0, isn't it?
 375              */
 376             rem = (n1 - q * d0) & BN_MASK2;
 377 #   endif
 378             t2 = (BN_ULLONG) d1 *q;
 379
 380             for (;;) {
 381                 if (t2 <= ((((BN_ULLONG) rem) << BN_BITS2) | wnump[-2]))
 382                     break;
 383                 q--;
 384                 rem += d0;
 385                 if (rem < d0)
 386                     break;      /* don't let rem overflow */
 387                 t2 -= d1;
 388             }
 389 #  else                         /* !BN_LLONG */
 390             BN_ULONG t2l, t2h;
 391
 392             q = bn_div_words(n0, n1, d0);
 393 #   ifdef BN_DEBUG_LEVITTE
 394             fprintf(stderr, "DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
 395 X) -> 0x%08X\n", n0, n1, d0, q);
 396 #   endif
 397 #   ifndef REMAINDER_IS_ALREADY_CALCULATED
 398             rem = (n1 - q * d0) & BN_MASK2;
 399 #   endif
 400
 401 #   if defined(BN_UMULT_LOHI)
 402             BN_UMULT_LOHI(t2l, t2h, d1, q);
 403 #   elif defined(BN_UMULT_HIGH)
 404             t2l = d1 * q;
 405             t2h = BN_UMULT_HIGH(d1, q);
 406 #   else
 407             {
 408                 BN_ULONG ql, qh;
 409                 t2l = LBITS(d1);
 410                 t2h = HBITS(d1);
 411                 ql = LBITS(q);
 412                 qh = HBITS(q);
 413                 mul64(t2l, t2h, ql, qh); /* t2=(BN_ULLONG)d1*q; */
 414             }
 415 #   endif
 416
 417             for (;;) {
 418                 if ((t2h < rem) || ((t2h == rem) && (t2l <= wnump[-2])))
 419                     break;
 420                 q--;
 421                 rem += d0;
 422                 if (rem < d0)
 423                     break;      /* don't let rem overflow */
 424                 if (t2l < d1)
 425                     t2h--;
 426                 t2l -= d1;
 427             }
 428 #  endif                        /* !BN_LLONG */
 429         }
 430 # endif                         /* !BN_DIV3W */
 431
 432         l0 = bn_mul_words(tmp->d, sdiv->d, div_n, q);
 433         tmp->d[div_n] = l0;
 434         wnum.d--;
 435         /*
 436          * ingore top values of the bignums just sub the two BN_ULONG arrays
 437          * with bn_sub_words
 438          */
 439         if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n + 1)) {
 440             /*
 441              * Note: As we have considered only the leading two BN_ULONGs in
 442              * the calculation of q, sdiv * q might be greater than wnum (but
 443              * then (q-1) * sdiv is less or equal than wnum)
 444              */
 445             q--;
 446             if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
 447                 /*
 448                  * we can't have an overflow here (assuming that q != 0, but
 449                  * if q == 0 then tmp is zero anyway)
 450                  */
 451                 (*wnump)++;
 452         }
 453         /* store part of the result */
 454         *resp = q;
 455     }
 456     bn_correct_top(snum);
 457     if (rm != NULL) {
 458         /*
 459          * Keep a copy of the neg flag in num because if rm==num BN_rshift()
 460          * will overwrite it.
 461          */
 462         int neg = num->neg;
 463         BN_rshift(rm, snum, norm_shift);
 464         if (!BN_is_zero(rm))
 465             rm->neg = neg;
 466         bn_check_top(rm);
 467     }
 468     if (no_branch)
 469         bn_correct_top(res);
 470     BN_CTX_end(ctx);
 471     return (1);
 472  err:
 473     bn_check_top(rm);
 474     BN_CTX_end(ctx);
 475     return (0);
 476 }
 477 #endif