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 #define OPENSSL_FIPSAPI
  60
  61 #include <stdio.h>
  62 #include <openssl/bn.h>
  63 #include "cryptlib.h"
  64 #include "bn_lcl.h"
  65
  66
  67 /* The old slow way */
  68 #if 0
  69 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
  70            BN_CTX *ctx)
  71         {
  72         int i,nm,nd;
  73         int ret = 0;
  74         BIGNUM *D;
  75
  76         bn_check_top(m);
  77         bn_check_top(d);
  78         if (BN_is_zero(d))
  79                 {
  80                 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
  81                 return(0);
  82                 }
  83
  84         if (BN_ucmp(m,d) < 0)
  85                 {
  86                 if (rem != NULL)
  87                         { if (BN_copy(rem,m) == NULL) return(0); }
  88                 if (dv != NULL) BN_zero(dv);
  89                 return(1);
  90                 }
  91
  92         BN_CTX_start(ctx);
  93         D = BN_CTX_get(ctx);
  94         if (dv == NULL) dv = BN_CTX_get(ctx);
  95         if (rem == NULL) 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) goto end;
 102         if (BN_copy(rem,m) == NULL) goto end;
 103
 104         /* The next 2 are needed so we can do a dv->d[0]|=1 later
 105          * since BN_lshift1 will only work once there is a value :-) */
 106         BN_zero(dv);
 107         if(bn_wexpand(dv,1) == NULL) goto end;
 108         dv->top=1;
 109
 110         if (!BN_lshift(D,D,nm-nd)) goto end;
 111         for (i=nm-nd; i>=0; i--)
 112                 {
 113                 if (!BN_lshift1(dv,dv)) goto end;
 114                 if (BN_ucmp(rem,D) >= 0)
 115                         {
 116                         dv->d[0]|=1;
 117                         if (!BN_usub(rem,rem,D)) goto end;
 118                         }
 119 /* CAN IMPROVE (and have now :=) */
 120                 if (!BN_rshift1(D,D)) goto end;
 121                 }
 122         rem->neg=BN_is_zero(rem)?0:m->neg;
 123         dv->neg=m->neg^d->neg;
 124         ret = 1;
 125  end:
 126         BN_CTX_end(ctx);
 127         return(ret);
 128         }
 129
 130 #else
 131
 132 #if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
 133     && !defined(PEDANTIC) && !defined(BN_DIV3W)
 134 # if defined(__GNUC__) && __GNUC__>=2
 135 #  if defined(__i386) || defined (__i386__)
 136    /*
 137     * There were two reasons for implementing this template:
 138     * - GNU C generates a call to a function (__udivdi3 to be exact)
 139     *   in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
 140     *   understand why...);
 141     * - divl doesn't only calculate quotient, but also leaves
 142     *   remainder in %edx which we can definitely use here:-)
 143     *
 144     *                                   <appro@fy.chalmers.se>
 145     */
 146 #undef bn_div_words
 147 #  define bn_div_words(n0,n1,d0)                \
 148         ({  asm volatile (                      \
 149                 "divl   %4"                     \
 150                 : "=a"(q), "=d"(rem)            \
 151                 : "a"(n1), "d"(n0), "g"(d0)     \
 152                 : "cc");                        \
 153             q;                                  \
 154         })
 155 #  define REMAINDER_IS_ALREADY_CALCULATED
 156 #  elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
 157    /*
 158     * Same story here, but it's 128-bit by 64-bit division. Wow!
 159     *                                   <appro@fy.chalmers.se>
 160     */
 161 #  undef bn_div_words
 162 #  define bn_div_words(n0,n1,d0)                \
 163         ({  asm volatile (                      \
 164                 "divq   %4"                     \
 165                 : "=a"(q), "=d"(rem)            \
 166                 : "a"(n1), "d"(n0), "g"(d0)     \
 167                 : "cc");                        \
 168             q;                                  \
 169         })
 170 #  define REMAINDER_IS_ALREADY_CALCULATED
 171 #  endif /* __<cpu> */
 172 # endif /* __GNUC__ */
 173 #endif /* OPENSSL_NO_ASM */
 174
 175
 176 /* BN_div computes  dv := num / divisor,  rounding towards
 177  * zero, and sets up rm  such that  dv*divisor + rm = num  holds.
 178  * Thus:
 179  *     dv->neg == num->neg ^ divisor->neg  (unless the result is zero)
 180  *     rm->neg == num->neg                 (unless the remainder is zero)
 181  * If 'dv' or 'rm' is NULL, the respective value is not returned.
 182  */
 183 int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
 184            BN_CTX *ctx)
 185         {
 186         int norm_shift,i,loop;
 187         BIGNUM *tmp,wnum,*snum,*sdiv,*res;
 188         BN_ULONG *resp,*wnump;
 189         BN_ULONG d0,d1;
 190         int num_n,div_n;
 191         int no_branch=0;
 192
 193         /* Invalid zero-padding would have particularly bad consequences
 194          * in the case of 'num', so don't just rely on bn_check_top() for this one
 195          * (bn_check_top() works only for BN_DEBUG builds) */
 196         if (num->top > 0 && num->d[num->top - 1] == 0)
 197                 {
 198                 BNerr(BN_F_BN_DIV,BN_R_NOT_INITIALIZED);
 199                 return 0;
 200                 }
 201
 202         bn_check_top(num);
 203
 204         if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0))
 205                 {
 206                 no_branch=1;
 207                 }
 208
 209         bn_check_top(dv);
 210         bn_check_top(rm);
 211         /* bn_check_top(num); */ /* 'num' has been checked already */
 212         bn_check_top(divisor);
 213
 214         if (BN_is_zero(divisor))
 215                 {
 216                 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
 217                 return(0);
 218                 }
 219
 220         if (!no_branch && BN_ucmp(num,divisor) < 0)
 221                 {
 222                 if (rm != NULL)
 223                         { if (BN_copy(rm,num) == NULL) return(0); }
 224                 if (dv != NULL) BN_zero(dv);
 225                 return(1);
 226                 }
 227
 228         BN_CTX_start(ctx);
 229         tmp=BN_CTX_get(ctx);
 230         snum=BN_CTX_get(ctx);
 231         sdiv=BN_CTX_get(ctx);
 232         if (dv == NULL)
 233                 res=BN_CTX_get(ctx);
 234         else    res=dv;
 235         if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)
 236                 goto err;
 237
 238         /* First we normalise the numbers */
 239         norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
 240         if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
 241         sdiv->neg=0;
 242         norm_shift+=BN_BITS2;
 243         if (!(BN_lshift(snum,num,norm_shift))) goto err;
 244         snum->neg=0;
 245
 246         if (no_branch)
 247                 {
 248                 /* Since we don't know whether snum is larger than sdiv,
 249                  * we pad snum with enough zeroes without changing its
 250                  * value.
 251                  */
 252                 if (snum->top <= sdiv->top+1)
 253                         {
 254                         if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err;
 255                         for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0;
 256                         snum->top = sdiv->top + 2;
 257                         }
 258                 else
 259                         {
 260                         if (bn_wexpand(snum, snum->top + 1) == NULL) goto err;
 261                         snum->d[snum->top] = 0;
 262                         snum->top ++;
 263                         }
 264                 }
 265
 266         div_n=sdiv->top;
 267         num_n=snum->top;
 268         loop=num_n-div_n;
 269         /* Lets setup a 'window' into snum
 270          * This is the part that corresponds to the current
 271          * 'area' being divided */
 272         wnum.neg   = 0;
 273         wnum.d     = &(snum->d[loop]);
 274         wnum.top   = div_n;
 275         /* only needed when BN_ucmp messes up the values between top and max */
 276         wnum.dmax  = snum->dmax - loop; /* so we don't step out of bounds */
 277
 278         /* Get the top 2 words of sdiv */
 279         /* div_n=sdiv->top; */
 280         d0=sdiv->d[div_n-1];
 281         d1=(div_n == 1)?0:sdiv->d[div_n-2];
 282
 283         /* pointer to the 'top' of snum */
 284         wnump= &(snum->d[num_n-1]);
 285
 286         /* Setup to 'res' */
 287         res->neg= (num->neg^divisor->neg);
 288         if (!bn_wexpand(res,(loop+1))) goto err;
 289         res->top=loop-no_branch;
 290         resp= &(res->d[loop-1]);
 291
 292         /* space for temp */
 293         if (!bn_wexpand(tmp,(div_n+1))) goto err;
 294
 295         if (!no_branch)
 296                 {
 297                 if (BN_ucmp(&wnum,sdiv) >= 0)
 298                         {
 299                         /* If BN_DEBUG_RAND is defined BN_ucmp changes (via
 300                          * bn_pollute) the const bignum arguments =>
 301                          * clean the values between top and max again */
 302                         bn_clear_top2max(&wnum);
 303                         bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
 304                         *resp=1;
 305                         }
 306                 else
 307                         res->top--;
 308                 }
 309
 310         /* if res->top == 0 then clear the neg value otherwise decrease
 311          * the resp pointer */
 312         if (res->top == 0)
 313                 res->neg = 0;
 314         else
 315                 resp--;
 316
 317         for (i=0; i<loop-1; i++, wnump--, resp--)
 318                 {
 319                 BN_ULONG q,l0;
 320                 /* the first part of the loop uses the top two words of
 321                  * snum and sdiv to calculate a BN_ULONG q such that
 322                  * | wnum - sdiv * q | < sdiv */
 323 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
 324                 BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
 325                 q=bn_div_3_words(wnump,d1,d0);
 326 #else
 327                 BN_ULONG n0,n1,rem=0;
 328
 329                 n0=wnump[0];
 330                 n1=wnump[-1];
 331                 if (n0 == d0)
 332                         q=BN_MASK2;
 333                 else                    /* n0 < d0 */
 334                         {
 335 #ifdef BN_LLONG
 336                         BN_ULLONG t2;
 337
 338 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
 339                         q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
 340 #else
 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 #endif
 348
 349 #ifndef REMAINDER_IS_ALREADY_CALCULATED
 350                         /*
 351                          * rem doesn't have to be BN_ULLONG. The least we
 352                          * know it's less that d0, isn't it?
 353                          */
 354                         rem=(n1-q*d0)&BN_MASK2;
 355 #endif
 356                         t2=(BN_ULLONG)d1*q;
 357
 358                         for (;;)
 359                                 {
 360                                 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
 361                                         break;
 362                                 q--;
 363                                 rem += d0;
 364                                 if (rem < d0) break; /* don't let rem overflow */
 365                                 t2 -= d1;
 366                                 }
 367 #else /* !BN_LLONG */
 368                         BN_ULONG t2l,t2h;
 369
 370                         q=bn_div_words(n0,n1,d0);
 371 #ifdef BN_DEBUG_LEVITTE
 372                         fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
 373 X) -> 0x%08X\n",
 374                                 n0, n1, d0, q);
 375 #endif
 376 #ifndef REMAINDER_IS_ALREADY_CALCULATED
 377                         rem=(n1-q*d0)&BN_MASK2;
 378 #endif
 379
 380 #if defined(BN_UMULT_LOHI)
 381                         BN_UMULT_LOHI(t2l,t2h,d1,q);
 382 #elif defined(BN_UMULT_HIGH)
 383                         t2l = d1 * q;
 384                         t2h = BN_UMULT_HIGH(d1,q);
 385 #else
 386                         {
 387                         BN_ULONG ql, qh;
 388                         t2l=LBITS(d1); t2h=HBITS(d1);
 389                         ql =LBITS(q);  qh =HBITS(q);
 390                         mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
 391                         }
 392 #endif
 393
 394                         for (;;)
 395                                 {
 396                                 if ((t2h < rem) ||
 397                                         ((t2h == rem) && (t2l <= wnump[-2])))
 398                                         break;
 399                                 q--;
 400                                 rem += d0;
 401                                 if (rem < d0) break; /* don't let rem overflow */
 402                                 if (t2l < d1) t2h--; t2l -= d1;
 403                                 }
 404 #endif /* !BN_LLONG */
 405                         }
 406 #endif /* !BN_DIV3W */
 407
 408                 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
 409                 tmp->d[div_n]=l0;
 410                 wnum.d--;
 411                 /* ingore top values of the bignums just sub the two
 412                  * BN_ULONG arrays with bn_sub_words */
 413                 if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
 414                         {
 415                         /* Note: As we have considered only the leading
 416                          * two BN_ULONGs in the calculation of q, sdiv * q
 417                          * might be greater than wnum (but then (q-1) * sdiv
 418                          * is less or equal than wnum)
 419                          */
 420                         q--;
 421                         if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
 422                                 /* we can't have an overflow here (assuming
 423                                  * that q != 0, but if q == 0 then tmp is
 424                                  * zero anyway) */
 425                                 (*wnump)++;
 426                         }
 427                 /* store part of the result */
 428                 *resp = q;
 429                 }
 430         bn_correct_top(snum);
 431         if (rm != NULL)
 432                 {
 433                 /* Keep a copy of the neg flag in num because if rm==num
 434                  * BN_rshift() will overwrite it.
 435                  */
 436                 int neg = num->neg;
 437                 BN_rshift(rm,snum,norm_shift);
 438                 if (!BN_is_zero(rm))
 439                         rm->neg = neg;
 440                 bn_check_top(rm);
 441                 }
 442         if (no_branch)  bn_correct_top(res);
 443         BN_CTX_end(ctx);
 444         return(1);
 445 err:
 446         bn_check_top(rm);
 447         BN_CTX_end(ctx);
 448         return(0);
 449         }
 450 #endif