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
  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         bn_wexpand(dv,1);
 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 #  define bn_div_words(n0,n1,d0)                \
 145         ({  asm volatile (                      \
 146                 "divl   %4"                     \
 147                 : "=a"(q), "=d"(rem)            \
 148                 : "a"(n1), "d"(n0), "g"(d0)     \
 149                 : "cc");                        \
 150             q;                                  \
 151         })
 152 #  define REMAINDER_IS_ALREADY_CALCULATED
 153 #  elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
 154    /*
 155     * Same story here, but it's 128-bit by 64-bit division. Wow!
 156     *                                   <appro@fy.chalmers.se>
 157     */
 158 #  define bn_div_words(n0,n1,d0)                \
 159         ({  asm volatile (                      \
 160                 "divq   %4"                     \
 161                 : "=a"(q), "=d"(rem)            \
 162                 : "a"(n1), "d"(n0), "g"(d0)     \
 163                 : "cc");                        \
 164             q;                                  \
 165         })
 166 #  define REMAINDER_IS_ALREADY_CALCULATED
 167 #  endif /* __<cpu> */
 168 # endif /* __GNUC__ */
 169 #endif /* OPENSSL_NO_ASM */
 170
 171
 172 /* BN_div computes  dv := num / divisor,  rounding towards zero, and sets up
 173  * rm  such that  dv*divisor + rm = num  holds.
 174  * Thus:
 175  *     dv->neg == num->neg ^ divisor->neg  (unless the result is zero)
 176  *     rm->neg == num->neg                 (unless the remainder is zero)
 177  * If 'dv' or 'rm' is NULL, the respective value is not returned.
 178  */
 179 int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
 180            BN_CTX *ctx)
 181         {
 182         int norm_shift,i,loop;
 183         BIGNUM *tmp,wnum,*snum,*sdiv,*res;
 184         BN_ULONG *resp,*wnump;
 185         BN_ULONG d0,d1;
 186         int num_n,div_n;
 187
 188         if (dv)
 189                 bn_check_top(dv);
 190         if (rm)
 191                 bn_check_top(rm);
 192         bn_check_top(num);
 193         bn_check_top(divisor);
 194
 195         if (BN_is_zero(divisor))
 196                 {
 197                 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
 198                 return(0);
 199                 }
 200
 201         if (BN_ucmp(num,divisor) < 0)
 202                 {
 203                 if (rm != NULL)
 204                         { if (BN_copy(rm,num) == NULL) return(0); }
 205                 if (dv != NULL) BN_zero(dv);
 206                 return(1);
 207                 }
 208
 209         BN_CTX_start(ctx);
 210         tmp=BN_CTX_get(ctx);
 211         snum=BN_CTX_get(ctx);
 212         sdiv=BN_CTX_get(ctx);
 213         if (dv == NULL)
 214                 res=BN_CTX_get(ctx);
 215         else    res=dv;
 216         if (sdiv == NULL || res == NULL) goto err;
 217         tmp->neg=0;
 218
 219         /* First we normalise the numbers */
 220         norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
 221         if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
 222         sdiv->neg=0;
 223         norm_shift+=BN_BITS2;
 224         if (!(BN_lshift(snum,num,norm_shift))) goto err;
 225         snum->neg=0;
 226         div_n=sdiv->top;
 227         num_n=snum->top;
 228         loop=num_n-div_n;
 229         /* Lets setup a 'window' into snum
 230          * This is the part that corresponds to the current
 231          * 'area' being divided */
 232         wnum.neg   = 0;
 233         wnum.d     = &(snum->d[loop]);
 234         wnum.top   = div_n;
 235 #ifdef BN_DEBUG_RAND
 236         /* only needed when BN_ucmp messes up the values between top and max */
 237         wnum.dmax  = snum->dmax - loop; /* so we don't step out of bounds */
 238 #endif
 239
 240         /* Get the top 2 words of sdiv */
 241         /* div_n=sdiv->top; */
 242         d0=sdiv->d[div_n-1];
 243         d1=(div_n == 1)?0:sdiv->d[div_n-2];
 244
 245         /* pointer to the 'top' of snum */
 246         wnump= &(snum->d[num_n-1]);
 247
 248         /* Setup to 'res' */
 249         res->neg= (num->neg^divisor->neg);
 250         if (!bn_wexpand(res,(loop+1))) goto err;
 251         res->top=loop;
 252         resp= &(res->d[loop-1]);
 253
 254         /* space for temp */
 255         if (!bn_wexpand(tmp,(div_n+1))) goto err;
 256
 257         if (BN_ucmp(&wnum,sdiv) >= 0)
 258                 {
 259 #ifdef BN_DEBUG_RAND
 260                 /* If BN_DEBUG_RAND is defined BN_ucmp changes (via
 261                  * bn_pollute) the const bignum arguments =>
 262                  * clean the values between top and max again */
 263                 bn_clear_top2max(&wnum);
 264 #endif
 265                 bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
 266                 *resp=1;
 267                 }
 268         else
 269                 res->top--;
 270         /* if res->top == 0 then clear the neg value otherwise decrease
 271          * the resp pointer */
 272         if (res->top == 0)
 273                 res->neg = 0;
 274         else
 275                 resp--;
 276
 277         for (i=0; i<loop-1; i++, wnump--, resp--)
 278                 {
 279                 BN_ULONG q,l0;
 280                 /* the first part of the loop uses the top two words of
 281                  * snum and sdiv to calculate a BN_ULONG q such that
 282                  * | wnum - sdiv * q | < sdiv */
 283 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
 284                 BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
 285                 q=bn_div_3_words(wnump,d1,d0);
 286 #else
 287                 BN_ULONG n0,n1,rem=0;
 288
 289                 n0=wnump[0];
 290                 n1=wnump[-1];
 291                 if (n0 == d0)
 292                         q=BN_MASK2;
 293                 else                    /* n0 < d0 */
 294                         {
 295 #ifdef BN_LLONG
 296                         BN_ULLONG t2;
 297
 298 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
 299                         q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
 300 #else
 301                         q=bn_div_words(n0,n1,d0);
 302 #ifdef BN_DEBUG_LEVITTE
 303                         fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
 304 X) -> 0x%08X\n",
 305                                 n0, n1, d0, q);
 306 #endif
 307 #endif
 308
 309 #ifndef REMAINDER_IS_ALREADY_CALCULATED
 310                         /*
 311                          * rem doesn't have to be BN_ULLONG. The least we
 312                          * know it's less that d0, isn't it?
 313                          */
 314                         rem=(n1-q*d0)&BN_MASK2;
 315 #endif
 316                         t2=(BN_ULLONG)d1*q;
 317
 318                         for (;;)
 319                                 {
 320                                 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
 321                                         break;
 322                                 q--;
 323                                 rem += d0;
 324                                 if (rem < d0) break; /* don't let rem overflow */
 325                                 t2 -= d1;
 326                                 }
 327 #else /* !BN_LLONG */
 328                         BN_ULONG t2l,t2h,ql,qh;
 329
 330                         q=bn_div_words(n0,n1,d0);
 331 #ifdef BN_DEBUG_LEVITTE
 332                         fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
 333 X) -> 0x%08X\n",
 334                                 n0, n1, d0, q);
 335 #endif
 336 #ifndef REMAINDER_IS_ALREADY_CALCULATED
 337                         rem=(n1-q*d0)&BN_MASK2;
 338 #endif
 339
 340 #if defined(BN_UMULT_LOHI)
 341                         BN_UMULT_LOHI(t2l,t2h,d1,q);
 342 #elif defined(BN_UMULT_HIGH)
 343                         t2l = d1 * q;
 344                         t2h = BN_UMULT_HIGH(d1,q);
 345 #else
 346                         t2l=LBITS(d1); t2h=HBITS(d1);
 347                         ql =LBITS(q);  qh =HBITS(q);
 348                         mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
 349 #endif
 350
 351                         for (;;)
 352                                 {
 353                                 if ((t2h < rem) ||
 354                                         ((t2h == rem) && (t2l <= wnump[-2])))
 355                                         break;
 356                                 q--;
 357                                 rem += d0;
 358                                 if (rem < d0) break; /* don't let rem overflow */
 359                                 if (t2l < d1) t2h--; t2l -= d1;
 360                                 }
 361 #endif /* !BN_LLONG */
 362                         }
 363 #endif /* !BN_DIV3W */
 364
 365                 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
 366                 tmp->d[div_n]=l0;
 367                 wnum.d--;
 368                 /* ingore top values of the bignums just sub the two
 369                  * BN_ULONG arrays with bn_sub_words */
 370                 if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
 371                         {
 372                         /* Note: As we have considered only the leading
 373                          * two BN_ULONGs in the calculation of q, sdiv * q
 374                          * might be greater than wnum (but then (q-1) * sdiv
 375                          * is less or equal than wnum)
 376                          */
 377                         q--;
 378                         if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
 379                                 /* we can't have an overflow here (assuming
 380                                  * that q != 0, but if q == 0 then tmp is
 381                                  * zero anyway) */
 382                                 (*wnump)++;
 383                         }
 384                 /* store part of the result */
 385                 *resp = q;
 386                 }
 387         if (rm != NULL)
 388                 {
 389                 /* Keep a copy of the neg flag in num because if rm==num
 390                  * BN_rshift() will overwrite it.
 391                  */
 392                 int neg = num->neg;
 393                 bn_correct_top(snum);
 394                 BN_rshift(rm,snum,norm_shift);
 395                 if (!BN_is_zero(rm))
 396                         rm->neg = neg;
 397                 bn_check_top(rm);
 398                 }
 399         BN_CTX_end(ctx);
 400         return(1);
 401 err:
 402         if (rm)
 403                 bn_check_top(rm);
 404         BN_CTX_end(ctx);
 405         return(0);
 406         }
 407
 408 #endif