crypto/bn/bn_div.c

   1 /*
   2  * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
   3  *
   4  * Licensed under the OpenSSL license (the "License").  You may not use
   5  * this file except in compliance with the License.  You can obtain a copy
   6  * in the file LICENSE in the source distribution or at
   7  * https://www.openssl.org/source/license.html
   8  */
   9
  10 #include <openssl/bn.h>
  11 #include "internal/cryptlib.h"
  12 #include "bn_lcl.h"
  13
  14 /* The old slow way */
  15 #if 0
  16 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
  17            BN_CTX *ctx)
  18 {
  19     int i, nm, nd;
  20     int ret = 0;
  21     BIGNUM *D;
  22
  23     bn_check_top(m);
  24     bn_check_top(d);
  25     if (BN_is_zero(d)) {
  26         BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);
  27         return (0);
  28     }
  29
  30     if (BN_ucmp(m, d) < 0) {
  31         if (rem != NULL) {
  32             if (BN_copy(rem, m) == NULL)
  33                 return (0);
  34         }
  35         if (dv != NULL)
  36             BN_zero(dv);
  37         return (1);
  38     }
  39
  40     BN_CTX_start(ctx);
  41     D = BN_CTX_get(ctx);
  42     if (dv == NULL)
  43         dv = BN_CTX_get(ctx);
  44     if (rem == NULL)
  45         rem = BN_CTX_get(ctx);
  46     if (D == NULL || dv == NULL || rem == NULL)
  47         goto end;
  48
  49     nd = BN_num_bits(d);
  50     nm = BN_num_bits(m);
  51     if (BN_copy(D, d) == NULL)
  52         goto end;
  53     if (BN_copy(rem, m) == NULL)
  54         goto end;
  55
  56     /*
  57      * The next 2 are needed so we can do a dv->d[0]|=1 later since
  58      * BN_lshift1 will only work once there is a value :-)
  59      */
  60     BN_zero(dv);
  61     if (bn_wexpand(dv, 1) == NULL)
  62         goto end;
  63     dv->top = 1;
  64
  65     if (!BN_lshift(D, D, nm - nd))
  66         goto end;
  67     for (i = nm - nd; i >= 0; i--) {
  68         if (!BN_lshift1(dv, dv))
  69             goto end;
  70         if (BN_ucmp(rem, D) >= 0) {
  71             dv->d[0] |= 1;
  72             if (!BN_usub(rem, rem, D))
  73                 goto end;
  74         }
  75 /* CAN IMPROVE (and have now :=) */
  76         if (!BN_rshift1(D, D))
  77             goto end;
  78     }
  79     rem->neg = BN_is_zero(rem) ? 0 : m->neg;
  80     dv->neg = m->neg ^ d->neg;
  81     ret = 1;
  82  end:
  83     BN_CTX_end(ctx);
  84     return (ret);
  85 }
  86
  87 #else
  88
  89 # if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
  90     && !defined(PEDANTIC) && !defined(BN_DIV3W)
  91 #  if defined(__GNUC__) && __GNUC__>=2
  92 #   if defined(__i386) || defined (__i386__)
  93    /*-
  94     * There were two reasons for implementing this template:
  95     * - GNU C generates a call to a function (__udivdi3 to be exact)
  96     *   in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
  97     *   understand why...);
  98     * - divl doesn't only calculate quotient, but also leaves
  99     *   remainder in %edx which we can definitely use here:-)
 100     *
 101     *                                   <appro@fy.chalmers.se>
 102     */
 103 #    undef bn_div_words
 104 #    define bn_div_words(n0,n1,d0)                \
 105         ({  asm volatile (                      \
 106                 "divl   %4"                     \
 107                 : "=a"(q), "=d"(rem)            \
 108                 : "a"(n1), "d"(n0), "g"(d0)     \
 109                 : "cc");                        \
 110             q;                                  \
 111         })
 112 #    define REMAINDER_IS_ALREADY_CALCULATED
 113 #   elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
 114    /*
 115     * Same story here, but it's 128-bit by 64-bit division. Wow!
 116     *                                   <appro@fy.chalmers.se>
 117     */
 118 #    undef bn_div_words
 119 #    define bn_div_words(n0,n1,d0)                \
 120         ({  asm volatile (                      \
 121                 "divq   %4"                     \
 122                 : "=a"(q), "=d"(rem)            \
 123                 : "a"(n1), "d"(n0), "g"(d0)     \
 124                 : "cc");                        \
 125             q;                                  \
 126         })
 127 #    define REMAINDER_IS_ALREADY_CALCULATED
 128 #   endif                       /* __<cpu> */
 129 #  endif                        /* __GNUC__ */
 130 # endif                         /* OPENSSL_NO_ASM */
 131
 132 /*-
 133  * BN_div computes  dv := num / divisor,  rounding towards
 134  * zero, and sets up rm  such that  dv*divisor + rm = num  holds.
 135  * Thus:
 136  *     dv->neg == num->neg ^ divisor->neg  (unless the result is zero)
 137  *     rm->neg == num->neg                 (unless the remainder is zero)
 138  * If 'dv' or 'rm' is NULL, the respective value is not returned.
 139  */
 140 int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
 141            BN_CTX *ctx)
 142 {
 143     int norm_shift, i, loop;
 144     BIGNUM *tmp, wnum, *snum, *sdiv, *res;
 145     BN_ULONG *resp, *wnump;
 146     BN_ULONG d0, d1;
 147     int num_n, div_n;
 148     int no_branch = 0;
 149
 150     /*
 151      * Invalid zero-padding would have particularly bad consequences so don't
 152      * just rely on bn_check_top() here (bn_check_top() works only for
 153      * BN_DEBUG builds)
 154      */
 155     if ((num->top > 0 && num->d[num->top - 1] == 0) ||
 156         (divisor->top > 0 && divisor->d[divisor->top - 1] == 0)) {
 157         BNerr(BN_F_BN_DIV, BN_R_NOT_INITIALIZED);
 158         return 0;
 159     }
 160
 161     bn_check_top(num);
 162     bn_check_top(divisor);
 163
 164     if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0)
 165         || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0)) {
 166         no_branch = 1;
 167     }
 168
 169     bn_check_top(dv);
 170     bn_check_top(rm);
 171     /*- bn_check_top(num); *//*
 172      * 'num' has been checked already
 173      */
 174     /*- bn_check_top(divisor); *//*
 175      * 'divisor' has been checked already
 176      */
 177
 178     if (BN_is_zero(divisor)) {
 179         BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);
 180         return (0);
 181     }
 182
 183     if (!no_branch && BN_ucmp(num, divisor) < 0) {
 184         if (rm != NULL) {
 185             if (BN_copy(rm, num) == NULL)
 186                 return (0);
 187         }
 188         if (dv != NULL)
 189             BN_zero(dv);
 190         return (1);
 191     }
 192
 193     BN_CTX_start(ctx);
 194     tmp = BN_CTX_get(ctx);
 195     snum = BN_CTX_get(ctx);
 196     sdiv = BN_CTX_get(ctx);
 197     if (dv == NULL)
 198         res = BN_CTX_get(ctx);
 199     else
 200         res = dv;
 201     if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)
 202         goto err;
 203
 204     /* First we normalise the numbers */
 205     norm_shift = BN_BITS2 - ((BN_num_bits(divisor)) % BN_BITS2);
 206     if (!(BN_lshift(sdiv, divisor, norm_shift)))
 207         goto err;
 208     sdiv->neg = 0;
 209     norm_shift += BN_BITS2;
 210     if (!(BN_lshift(snum, num, norm_shift)))
 211         goto err;
 212     snum->neg = 0;
 213
 214     if (no_branch) {
 215         /*
 216          * Since we don't know whether snum is larger than sdiv, we pad snum
 217          * with enough zeroes without changing its value.
 218          */
 219         if (snum->top <= sdiv->top + 1) {
 220             if (bn_wexpand(snum, sdiv->top + 2) == NULL)
 221                 goto err;
 222             for (i = snum->top; i < sdiv->top + 2; i++)
 223                 snum->d[i] = 0;
 224             snum->top = sdiv->top + 2;
 225         } else {
 226             if (bn_wexpand(snum, snum->top + 1) == NULL)
 227                 goto err;
 228             snum->d[snum->top] = 0;
 229             snum->top++;
 230         }
 231     }
 232
 233     div_n = sdiv->top;
 234     num_n = snum->top;
 235     loop = num_n - div_n;
 236     /*
 237      * Lets setup a 'window' into snum This is the part that corresponds to
 238      * the current 'area' being divided
 239      */
 240     wnum.neg = 0;
 241     wnum.d = &(snum->d[loop]);
 242     wnum.top = div_n;
 243     /*
 244      * only needed when BN_ucmp messes up the values between top and max
 245      */
 246     wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
 247
 248     /* Get the top 2 words of sdiv */
 249     /* div_n=sdiv->top; */
 250     d0 = sdiv->d[div_n - 1];
 251     d1 = (div_n == 1) ? 0 : sdiv->d[div_n - 2];
 252
 253     /* pointer to the 'top' of snum */
 254     wnump = &(snum->d[num_n - 1]);
 255
 256     /* Setup to 'res' */
 257     res->neg = (num->neg ^ divisor->neg);
 258     if (!bn_wexpand(res, (loop + 1)))
 259         goto err;
 260     res->top = loop - no_branch;
 261     resp = &(res->d[loop - 1]);
 262
 263     /* space for temp */
 264     if (!bn_wexpand(tmp, (div_n + 1)))
 265         goto err;
 266
 267     if (!no_branch) {
 268         if (BN_ucmp(&wnum, sdiv) >= 0) {
 269             /*
 270              * If BN_DEBUG_RAND is defined BN_ucmp changes (via bn_pollute)
 271              * the const bignum arguments => clean the values between top and
 272              * max again
 273              */
 274             bn_clear_top2max(&wnum);
 275             bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
 276             *resp = 1;
 277         } else
 278             res->top--;
 279     }
 280
 281     /*
 282      * if res->top == 0 then clear the neg value otherwise decrease the resp
 283      * pointer
 284      */
 285     if (res->top == 0)
 286         res->neg = 0;
 287     else
 288         resp--;
 289
 290     for (i = 0; i < loop - 1; i++, wnump--, resp--) {
 291         BN_ULONG q, l0;
 292         /*
 293          * the first part of the loop uses the top two words of snum and sdiv
 294          * to calculate a BN_ULONG q such that | wnum - sdiv * q | < sdiv
 295          */
 296 # if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
 297         BN_ULONG bn_div_3_words(BN_ULONG *, BN_ULONG, BN_ULONG);
 298         q = bn_div_3_words(wnump, d1, d0);
 299 # else
 300         BN_ULONG n0, n1, rem = 0;
 301
 302         n0 = wnump[0];
 303         n1 = wnump[-1];
 304         if (n0 == d0)
 305             q = BN_MASK2;
 306         else {                  /* n0 < d0 */
 307
 308 #  ifdef BN_LLONG
 309             BN_ULLONG t2;
 310
 311 #   if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
 312             q = (BN_ULONG)(((((BN_ULLONG) n0) << BN_BITS2) | n1) / d0);
 313 #   else
 314             q = bn_div_words(n0, n1, d0);
 315 #   endif
 316
 317 #   ifndef REMAINDER_IS_ALREADY_CALCULATED
 318             /*
 319              * rem doesn't have to be BN_ULLONG. The least we
 320              * know it's less that d0, isn't it?
 321              */
 322             rem = (n1 - q * d0) & BN_MASK2;
 323 #   endif
 324             t2 = (BN_ULLONG) d1 *q;
 325
 326             for (;;) {
 327                 if (t2 <= ((((BN_ULLONG) rem) << BN_BITS2) | wnump[-2]))
 328                     break;
 329                 q--;
 330                 rem += d0;
 331                 if (rem < d0)
 332                     break;      /* don't let rem overflow */
 333                 t2 -= d1;
 334             }
 335 #  else                         /* !BN_LLONG */
 336             BN_ULONG t2l, t2h;
 337
 338             q = bn_div_words(n0, n1, d0);
 339 #   ifndef REMAINDER_IS_ALREADY_CALCULATED
 340             rem = (n1 - q * d0) & BN_MASK2;
 341 #   endif
 342
 343 #   if defined(BN_UMULT_LOHI)
 344             BN_UMULT_LOHI(t2l, t2h, d1, q);
 345 #   elif defined(BN_UMULT_HIGH)
 346             t2l = d1 * q;
 347             t2h = BN_UMULT_HIGH(d1, q);
 348 #   else
 349             {
 350                 BN_ULONG ql, qh;
 351                 t2l = LBITS(d1);
 352                 t2h = HBITS(d1);
 353                 ql = LBITS(q);
 354                 qh = HBITS(q);
 355                 mul64(t2l, t2h, ql, qh); /* t2=(BN_ULLONG)d1*q; */
 356             }
 357 #   endif
 358
 359             for (;;) {
 360                 if ((t2h < rem) || ((t2h == rem) && (t2l <= wnump[-2])))
 361                     break;
 362                 q--;
 363                 rem += d0;
 364                 if (rem < d0)
 365                     break;      /* don't let rem overflow */
 366                 if (t2l < d1)
 367                     t2h--;
 368                 t2l -= d1;
 369             }
 370 #  endif                        /* !BN_LLONG */
 371         }
 372 # endif                         /* !BN_DIV3W */
 373
 374         l0 = bn_mul_words(tmp->d, sdiv->d, div_n, q);
 375         tmp->d[div_n] = l0;
 376         wnum.d--;
 377         /*
 378          * ingore top values of the bignums just sub the two BN_ULONG arrays
 379          * with bn_sub_words
 380          */
 381         if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n + 1)) {
 382             /*
 383              * Note: As we have considered only the leading two BN_ULONGs in
 384              * the calculation of q, sdiv * q might be greater than wnum (but
 385              * then (q-1) * sdiv is less or equal than wnum)
 386              */
 387             q--;
 388             if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
 389                 /*
 390                  * we can't have an overflow here (assuming that q != 0, but
 391                  * if q == 0 then tmp is zero anyway)
 392                  */
 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 BN_rshift()
 402          * 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     if (no_branch)
 411         bn_correct_top(res);
 412     BN_CTX_end(ctx);
 413     return (1);
 414  err:
 415     bn_check_top(rm);
 416     BN_CTX_end(ctx);
 417     return (0);
 418 }
 419 #endif