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         if(bn_wexpand(dv,1) == NULL) goto end;
 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 #undef bn_div_words
 145 #  define bn_div_words(n0,n1,d0)                \
 146         ({  __asm volatile (                    \
 147                 "divl   %4"                     \
 148                 : "=a"(q), "=d"(rem)            \
 149                 : "a"(n1), "d"(n0), "g"(d0)     \
 150                 : "cc");                        \
 151             q;                                  \
 152         })
 153 #  define REMAINDER_IS_ALREADY_CALCULATED
 154 #  elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
 155    /*
 156     * Same story here, but it's 128-bit by 64-bit division. Wow!
 157     *                                   <appro@fy.chalmers.se>
 158     */
 159 #  undef bn_div_words
 160 #  define bn_div_words(n0,n1,d0)                \
 161         ({  __asm volatile (                    \
 162                 "divq   %4"                     \
 163                 : "=a"(q), "=d"(rem)            \
 164                 : "a"(n1), "d"(n0), "g"(d0)     \
 165                 : "cc");                        \
 166             q;                                  \
 167         })
 168 #  define REMAINDER_IS_ALREADY_CALCULATED
 169 #  endif /* __<cpu> */
 170 # endif /* __GNUC__ */
 171 #endif /* OPENSSL_NO_ASM */
 172 
 173 
 174 /* BN_div computes  dv := num / divisor,  rounding towards
 175  * zero, and sets up rm  such that  dv*divisor + rm = num  holds.
 176  * Thus:
 177  *     dv->neg == num->neg ^ divisor->neg  (unless the result is zero)
 178  *     rm->neg == num->neg                 (unless the remainder is zero)
 179  * If 'dv' or 'rm' is NULL, the respective value is not returned.
 180  */
 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         int no_branch=0;
 190 
 191         /* Invalid zero-padding would have particularly bad consequences
 192          * in the case of 'num', so don't just rely on bn_check_top() for this one
 193          * (bn_check_top() works only for BN_DEBUG builds) */
 194         if (num->top > 0 && num->d[num->top - 1] == 0)
 195                 {
 196                 BNerr(BN_F_BN_DIV,BN_R_NOT_INITIALIZED);
 197                 return 0;
 198                 }
 199 
 200         bn_check_top(num);
 201 
 202         if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0))
 203                 {
 204                 no_branch=1;
 205                 }
 206 
 207         bn_check_top(dv);
 208         bn_check_top(rm);
 209         /* bn_check_top(num); */ /* 'num' has been checked already */
 210         bn_check_top(divisor);
 211 
 212         if (BN_is_zero(divisor))
 213                 {
 214                 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
 215                 return(0);
 216                 }
 217 
 218         if (!no_branch && BN_ucmp(num,divisor) < 0)
 219                 {
 220                 if (rm != NULL)
 221                         { if (BN_copy(rm,num) == NULL) return(0); }
 222                 if (dv != NULL) BN_zero(dv);
 223                 return(1);
 224                 }
 225 
 226         BN_CTX_start(ctx);
 227         tmp=BN_CTX_get(ctx);
 228         snum=BN_CTX_get(ctx);
 229         sdiv=BN_CTX_get(ctx);
 230         if (dv == NULL)
 231                 res=BN_CTX_get(ctx);
 232         else    res=dv;
 233         if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)
 234                 goto err;
 235 
 236         /* First we normalise the numbers */
 237         norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
 238         if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
 239         sdiv->neg=0;
 240         norm_shift+=BN_BITS2;
 241         if (!(BN_lshift(snum,num,norm_shift))) goto err;
 242         snum->neg=0;
 243 
 244         if (no_branch)
 245                 {
 246                 /* Since we don't know whether snum is larger than sdiv,
 247                  * we pad snum with enough zeroes without changing its
 248                  * value.
 249                  */
 250                 if (snum->top <= sdiv->top+1)
 251                         {
 252                         if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err;
 253                         for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0;
 254                         snum->top = sdiv->top + 2;
 255                         }
 256                 else
 257                         {
 258                         if (bn_wexpand(snum, snum->top + 1) == NULL) goto err;
 259                         snum->d[snum->top] = 0;
 260                         snum->top ++;
 261                         }
 262                 }
 263 
 264         div_n=sdiv->top;
 265         num_n=snum->top;
 266         loop=num_n-div_n;
 267         /* Lets setup a 'window' into snum
 268          * This is the part that corresponds to the current
 269          * 'area' being divided */
 270         wnum.neg   = 0;
 271         wnum.d     = &(snum->d[loop]);
 272         wnum.top   = div_n;
 273         /* only needed when BN_ucmp messes up the values between top and max */
 274         wnum.dmax  = snum->dmax - loop; /* so we don't step out of bounds */
 275 
 276         /* Get the top 2 words of sdiv */
 277         /* div_n=sdiv->top; */
 278         d0=sdiv->d[div_n-1];
 279         d1=(div_n == 1)?0:sdiv->d[div_n-2];
 280 
 281         /* pointer to the 'top' of snum */
 282         wnump= &(snum->d[num_n-1]);
 283 
 284         /* Setup to 'res' */
 285         res->neg= (num->neg^divisor->neg);
 286         if (!bn_wexpand(res,(loop+1))) goto err;
 287         res->top=loop-no_branch;
 288         resp= &(res->d[loop-1]);
 289 
 290         /* space for temp */
 291         if (!bn_wexpand(tmp,(div_n+1))) goto err;
 292 
 293         if (!no_branch)
 294                 {
 295                 if (BN_ucmp(&wnum,sdiv) >= 0)
 296                         {
 297                         /* If BN_DEBUG_RAND is defined BN_ucmp changes (via
 298                          * bn_pollute) the const bignum arguments =>
 299                          * clean the values between top and max again */
 300                         bn_clear_top2max(&wnum);
 301                         bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
 302                         *resp=1;
 303                         }
 304                 else
 305                         res->top--;
 306                 }
 307 
 308         /* if res->top == 0 then clear the neg value otherwise decrease
 309          * the resp pointer */
 310         if (res->top == 0)
 311                 res->neg = 0;
 312         else
 313                 resp--;
 314 
 315         for (i=0; i<loop-1; i++, wnump--, resp--)
 316                 {
 317                 BN_ULONG q,l0;
 318                 /* the first part of the loop uses the top two words of
 319                  * snum and sdiv to calculate a BN_ULONG q such that
 320                  * | wnum - sdiv * q | < sdiv */
 321 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
 322                 BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
 323                 q=bn_div_3_words(wnump,d1,d0);
 324 #else
 325                 BN_ULONG n0,n1,rem=0;
 326 
 327                 n0=wnump[0];
 328                 n1=wnump[-1];
 329                 if (n0 == d0)
 330                         q=BN_MASK2;
 331                 else                    /* n0 < d0 */
 332                         {
 333 #ifdef BN_LLONG
 334                         BN_ULLONG t2;
 335 
 336 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
 337                         q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
 338 #else
 339                         q=bn_div_words(n0,n1,d0);
 340 #ifdef BN_DEBUG_LEVITTE
 341                         fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
 342 X) -> 0x%08X\n",
 343                                 n0, n1, d0, q);
 344 #endif
 345 #endif
 346 
 347 #ifndef REMAINDER_IS_ALREADY_CALCULATED
 348                         /*
 349                          * rem doesn't have to be BN_ULLONG. The least we
 350                          * know it's less that d0, isn't it?
 351                          */
 352                         rem=(n1-q*d0)&BN_MASK2;
 353 #endif
 354                         t2=(BN_ULLONG)d1*q;
 355 
 356                         for (;;)
 357                                 {
 358                                 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
 359                                         break;
 360                                 q--;
 361                                 rem += d0;
 362                                 if (rem < d0) break; /* don't let rem overflow */
 363                                 t2 -= d1;
 364                                 }
 365 #else /* !BN_LLONG */
 366                         BN_ULONG t2l,t2h;
 367 
 368                         q=bn_div_words(n0,n1,d0);
 369 #ifdef BN_DEBUG_LEVITTE
 370                         fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
 371 X) -> 0x%08X\n",
 372                                 n0, n1, d0, q);
 373 #endif
 374 #ifndef REMAINDER_IS_ALREADY_CALCULATED
 375                         rem=(n1-q*d0)&BN_MASK2;
 376 #endif
 377 
 378 #if defined(BN_UMULT_LOHI)
 379                         BN_UMULT_LOHI(t2l,t2h,d1,q);
 380 #elif defined(BN_UMULT_HIGH)
 381                         t2l = d1 * q;
 382                         t2h = BN_UMULT_HIGH(d1,q);
 383 #else
 384                         {
 385                         BN_ULONG ql, qh;
 386                         t2l=LBITS(d1); t2h=HBITS(d1);
 387                         ql =LBITS(q);  qh =HBITS(q);
 388                         mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
 389                         }
 390 #endif
 391 
 392                         for (;;)
 393                                 {
 394                                 if ((t2h < rem) ||
 395                                         ((t2h == rem) && (t2l <= wnump[-2])))
 396                                         break;
 397                                 q--;
 398                                 rem += d0;
 399                                 if (rem < d0) break; /* don't let rem overflow */
 400                                 if (t2l < d1) t2h--; t2l -= d1;
 401                                 }
 402 #endif /* !BN_LLONG */
 403                         }
 404 #endif /* !BN_DIV3W */
 405 
 406                 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
 407                 tmp->d[div_n]=l0;
 408                 wnum.d--;
 409                 /* ingore top values of the bignums just sub the two
 410                  * BN_ULONG arrays with bn_sub_words */
 411                 if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
 412                         {
 413                         /* Note: As we have considered only the leading
 414                          * two BN_ULONGs in the calculation of q, sdiv * q
 415                          * might be greater than wnum (but then (q-1) * sdiv
 416                          * is less or equal than wnum)
 417                          */
 418                         q--;
 419                         if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
 420                                 /* we can't have an overflow here (assuming
 421                                  * that q != 0, but if q == 0 then tmp is
 422                                  * zero anyway) */
 423                                 (*wnump)++;
 424                         }
 425                 /* store part of the result */
 426                 *resp = q;
 427                 }
 428         bn_correct_top(snum);
 429         if (rm != NULL)
 430                 {
 431                 /* Keep a copy of the neg flag in num because if rm==num
 432                  * BN_rshift() will overwrite it.
 433                  */
 434                 int neg = num->neg;
 435                 BN_rshift(rm,snum,norm_shift);
 436                 if (!BN_is_zero(rm))
 437                         rm->neg = neg;
 438                 bn_check_top(rm);
 439                 }
 440         if (no_branch)  bn_correct_top(res);
 441         BN_CTX_end(ctx);
 442         return(1);
 443 err:
 444         bn_check_top(rm);
 445         BN_CTX_end(ctx);
 446         return(0);
 447         }
 448 #endif