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
  60
  61 #include <openssl/bn.h>
  62 #include "cryptlib.h"
  63 #include "bn_lcl.h"
  64
  65
  66 /* The old slow way */
  67 #if 0
  68 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
  69            BN_CTX *ctx)
  70         {
  71         int i,nm,nd;
  72         int ret = 0;
  73         BIGNUM *D;
  74
  75         bn_check_top(m);
  76         bn_check_top(d);
  77         if (BN_is_zero(d))
  78                 {
  79                 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
  80                 return(0);
  81                 }
  82
  83         if (BN_ucmp(m,d) < 0)
  84                 {
  85                 if (rem != NULL)
  86                         { if (BN_copy(rem,m) == NULL) return(0); }
  87                 if (dv != NULL) BN_zero(dv);
  88                 return(1);
  89                 }
  90
  91         BN_CTX_start(ctx);
  92         D = BN_CTX_get(ctx);
  93         if (dv == NULL) dv = BN_CTX_get(ctx);
  94         if (rem == NULL) rem = BN_CTX_get(ctx);
  95         if (D == NULL || dv == NULL || rem == NULL)
  96                 goto end;
  97
  98         nd=BN_num_bits(d);
  99         nm=BN_num_bits(m);
 100         if (BN_copy(D,d) == NULL) goto end;
 101         if (BN_copy(rem,m) == NULL) goto end;
 102
 103         /* The next 2 are needed so we can do a dv->d[0]|=1 later
 104          * since BN_lshift1 will only work once there is a value :-) */
 105         BN_zero(dv);
 106         if(bn_wexpand(dv,1) == NULL) goto end;
 107         dv->top=1;
 108
 109         if (!BN_lshift(D,D,nm-nd)) goto end;
 110         for (i=nm-nd; i>=0; i--)
 111                 {
 112                 if (!BN_lshift1(dv,dv)) goto end;
 113                 if (BN_ucmp(rem,D) >= 0)
 114                         {
 115                         dv->d[0]|=1;
 116                         if (!BN_usub(rem,rem,D)) goto end;
 117                         }
 118 /* CAN IMPROVE (and have now :=) */
 119                 if (!BN_rshift1(D,D)) goto end;
 120                 }
 121         rem->neg=BN_is_zero(rem)?0:m->neg;
 122         dv->neg=m->neg^d->neg;
 123         ret = 1;
 124  end:
 125         BN_CTX_end(ctx);
 126         return(ret);
 127         }
 128
 129 #else
 130
 131 #if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
 132     && !defined(PEDANTIC) && !defined(BN_DIV3W)
 133 # if defined(__GNUC__) && __GNUC__>=2
 134 #  if defined(__i386) || defined (__i386__)
 135    /*-
 136     * There were two reasons for implementing this template:
 137     * - GNU C generates a call to a function (__udivdi3 to be exact)
 138     *   in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
 139     *   understand why...);
 140     * - divl doesn't only calculate quotient, but also leaves
 141     *   remainder in %edx which we can definitely use here:-)
 142     *
 143     *                                   <appro@fy.chalmers.se>
 144     */
 145 #undef bn_div_words
 146 #  define bn_div_words(n0,n1,d0)                \
 147         ({  asm volatile (                      \
 148                 "divl   %4"                     \
 149                 : "=a"(q), "=d"(rem)            \
 150                 : "a"(n1), "d"(n0), "g"(d0)     \
 151                 : "cc");                        \
 152             q;                                  \
 153         })
 154 #  define REMAINDER_IS_ALREADY_CALCULATED
 155 #  elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
 156    /*
 157     * Same story here, but it's 128-bit by 64-bit division. Wow!
 158     *                                   <appro@fy.chalmers.se>
 159     */
 160 #  undef bn_div_words
 161 #  define bn_div_words(n0,n1,d0)                \
 162         ({  asm volatile (                      \
 163                 "divq   %4"                     \
 164                 : "=a"(q), "=d"(rem)            \
 165                 : "a"(n1), "d"(n0), "g"(d0)     \
 166                 : "cc");                        \
 167             q;                                  \
 168         })
 169 #  define REMAINDER_IS_ALREADY_CALCULATED
 170 #  endif /* __<cpu> */
 171 # endif /* __GNUC__ */
 172 #endif /* OPENSSL_NO_ASM */
 173
 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          * so don't just rely on bn_check_top() here
 195          * (bn_check_top() works only for BN_DEBUG builds) */
 196         if ((num->top > 0 && num->d[num->top - 1] == 0) ||
 197                 (divisor->top > 0 && divisor->d[divisor->top - 1] == 0))
 198                 {
 199                 BNerr(BN_F_BN_DIV,BN_R_NOT_INITIALIZED);
 200                 return 0;
 201                 }
 202
 203         bn_check_top(num);
 204         bn_check_top(divisor);
 205
 206         if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0))
 207                 {
 208                 no_branch=1;
 209                 }
 210
 211         bn_check_top(dv);
 212         bn_check_top(rm);
 213         /* bn_check_top(num); */ /* 'num' has been checked already */
 214         /* bn_check_top(divisor); */ /* 'divisor' has been checked already */
 215
 216         if (BN_is_zero(divisor))
 217                 {
 218                 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
 219                 return(0);
 220                 }
 221
 222         if (!no_branch && BN_ucmp(num,divisor) < 0)
 223                 {
 224                 if (rm != NULL)
 225                         { if (BN_copy(rm,num) == NULL) return(0); }
 226                 if (dv != NULL) BN_zero(dv);
 227                 return(1);
 228                 }
 229
 230         BN_CTX_start(ctx);
 231         tmp=BN_CTX_get(ctx);
 232         snum=BN_CTX_get(ctx);
 233         sdiv=BN_CTX_get(ctx);
 234         if (dv == NULL)
 235                 res=BN_CTX_get(ctx);
 236         else    res=dv;
 237         if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)
 238                 goto err;
 239
 240         /* First we normalise the numbers */
 241         norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
 242         if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
 243         sdiv->neg=0;
 244         norm_shift+=BN_BITS2;
 245         if (!(BN_lshift(snum,num,norm_shift))) goto err;
 246         snum->neg=0;
 247
 248         if (no_branch)
 249                 {
 250                 /* Since we don't know whether snum is larger than sdiv,
 251                  * we pad snum with enough zeroes without changing its
 252                  * value.
 253                  */
 254                 if (snum->top <= sdiv->top+1)
 255                         {
 256                         if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err;
 257                         for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0;
 258                         snum->top = sdiv->top + 2;
 259                         }
 260                 else
 261                         {
 262                         if (bn_wexpand(snum, snum->top + 1) == NULL) goto err;
 263                         snum->d[snum->top] = 0;
 264                         snum->top ++;
 265                         }
 266                 }
 267
 268         div_n=sdiv->top;
 269         num_n=snum->top;
 270         loop=num_n-div_n;
 271         /* Lets setup a 'window' into snum
 272          * This is the part that corresponds to the current
 273          * 'area' being divided */
 274         wnum.neg   = 0;
 275         wnum.d     = &(snum->d[loop]);
 276         wnum.top   = div_n;
 277         /* only needed when BN_ucmp messes up the values between top and max */
 278         wnum.dmax  = snum->dmax - loop; /* so we don't step out of bounds */
 279
 280         /* Get the top 2 words of sdiv */
 281         /* div_n=sdiv->top; */
 282         d0=sdiv->d[div_n-1];
 283         d1=(div_n == 1)?0:sdiv->d[div_n-2];
 284
 285         /* pointer to the 'top' of snum */
 286         wnump= &(snum->d[num_n-1]);
 287
 288         /* Setup to 'res' */
 289         res->neg= (num->neg^divisor->neg);
 290         if (!bn_wexpand(res,(loop+1))) goto err;
 291         res->top=loop-no_branch;
 292         resp= &(res->d[loop-1]);
 293
 294         /* space for temp */
 295         if (!bn_wexpand(tmp,(div_n+1))) goto err;
 296
 297         if (!no_branch)
 298                 {
 299                 if (BN_ucmp(&wnum,sdiv) >= 0)
 300                         {
 301                         /* If BN_DEBUG_RAND is defined BN_ucmp changes (via
 302                          * bn_pollute) the const bignum arguments =>
 303                          * clean the values between top and max again */
 304                         bn_clear_top2max(&wnum);
 305                         bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
 306                         *resp=1;
 307                         }
 308                 else
 309                         res->top--;
 310                 }
 311
 312         /* if res->top == 0 then clear the neg value otherwise decrease
 313          * the resp pointer */
 314         if (res->top == 0)
 315                 res->neg = 0;
 316         else
 317                 resp--;
 318
 319         for (i=0; i<loop-1; i++, wnump--, resp--)
 320                 {
 321                 BN_ULONG q,l0;
 322                 /* the first part of the loop uses the top two words of
 323                  * snum and sdiv to calculate a BN_ULONG q such that
 324                  * | wnum - sdiv * q | < sdiv */
 325 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
 326                 BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
 327                 q=bn_div_3_words(wnump,d1,d0);
 328 #else
 329                 BN_ULONG n0,n1,rem=0;
 330
 331                 n0=wnump[0];
 332                 n1=wnump[-1];
 333                 if (n0 == d0)
 334                         q=BN_MASK2;
 335                 else                    /* n0 < d0 */
 336                         {
 337 #ifdef BN_LLONG
 338                         BN_ULLONG t2;
 339
 340 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
 341                         q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
 342 #else
 343                         q=bn_div_words(n0,n1,d0);
 344 #ifdef BN_DEBUG_LEVITTE
 345                         fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
 346 X) -> 0x%08X\n",
 347                                 n0, n1, d0, q);
 348 #endif
 349 #endif
 350
 351 #ifndef REMAINDER_IS_ALREADY_CALCULATED
 352                         /*
 353                          * rem doesn't have to be BN_ULLONG. The least we
 354                          * know it's less that d0, isn't it?
 355                          */
 356                         rem=(n1-q*d0)&BN_MASK2;
 357 #endif
 358                         t2=(BN_ULLONG)d1*q;
 359
 360                         for (;;)
 361                                 {
 362                                 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
 363                                         break;
 364                                 q--;
 365                                 rem += d0;
 366                                 if (rem < d0) break; /* don't let rem overflow */
 367                                 t2 -= d1;
 368                                 }
 369 #else /* !BN_LLONG */
 370                         BN_ULONG t2l,t2h;
 371
 372                         q=bn_div_words(n0,n1,d0);
 373 #ifdef BN_DEBUG_LEVITTE
 374                         fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
 375 X) -> 0x%08X\n",
 376                                 n0, n1, d0, q);
 377 #endif
 378 #ifndef REMAINDER_IS_ALREADY_CALCULATED
 379                         rem=(n1-q*d0)&BN_MASK2;
 380 #endif
 381
 382 #if defined(BN_UMULT_LOHI)
 383                         BN_UMULT_LOHI(t2l,t2h,d1,q);
 384 #elif defined(BN_UMULT_HIGH)
 385                         t2l = d1 * q;
 386                         t2h = BN_UMULT_HIGH(d1,q);
 387 #else
 388                         {
 389                         BN_ULONG ql, qh;
 390                         t2l=LBITS(d1); t2h=HBITS(d1);
 391                         ql =LBITS(q);  qh =HBITS(q);
 392                         mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
 393                         }
 394 #endif
 395
 396                         for (;;)
 397                                 {
 398                                 if ((t2h < rem) ||
 399                                         ((t2h == rem) && (t2l <= wnump[-2])))
 400                                         break;
 401                                 q--;
 402                                 rem += d0;
 403                                 if (rem < d0) break; /* don't let rem overflow */
 404                                 if (t2l < d1) t2h--; t2l -= d1;
 405                                 }
 406 #endif /* !BN_LLONG */
 407                         }
 408 #endif /* !BN_DIV3W */
 409
 410                 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
 411                 tmp->d[div_n]=l0;
 412                 wnum.d--;
 413                 /* ingore top values of the bignums just sub the two
 414                  * BN_ULONG arrays with bn_sub_words */
 415                 if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
 416                         {
 417                         /* Note: As we have considered only the leading
 418                          * two BN_ULONGs in the calculation of q, sdiv * q
 419                          * might be greater than wnum (but then (q-1) * sdiv
 420                          * is less or equal than wnum)
 421                          */
 422                         q--;
 423                         if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
 424                                 /* we can't have an overflow here (assuming
 425                                  * that q != 0, but if q == 0 then tmp is
 426                                  * zero anyway) */
 427                                 (*wnump)++;
 428                         }
 429                 /* store part of the result */
 430                 *resp = q;
 431                 }
 432         bn_correct_top(snum);
 433         if (rm != NULL)
 434                 {
 435                 /* Keep a copy of the neg flag in num because if rm==num
 436                  * BN_rshift() will overwrite it.
 437                  */
 438                 int neg = num->neg;
 439                 BN_rshift(rm,snum,norm_shift);
 440                 if (!BN_is_zero(rm))
 441                         rm->neg = neg;
 442                 bn_check_top(rm);
 443                 }
 444         if (no_branch)  bn_correct_top(res);
 445         BN_CTX_end(ctx);
 446         return(1);
 447 err:
 448         bn_check_top(rm);
 449         BN_CTX_end(ctx);
 450         return(0);
 451         }
 452 #endif