crypto/openssl-0.9.7e/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,j,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         bn_check_top(num);
 189         bn_check_top(divisor);
 190
 191         if (BN_is_zero(divisor))
 192                 {
 193                 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
 194                 return(0);
 195                 }
 196
 197         if (BN_ucmp(num,divisor) < 0)
 198                 {
 199                 if (rm != NULL)
 200                         { if (BN_copy(rm,num) == NULL) return(0); }
 201                 if (dv != NULL) BN_zero(dv);
 202                 return(1);
 203                 }
 204
 205         BN_CTX_start(ctx);
 206         tmp=BN_CTX_get(ctx);
 207         snum=BN_CTX_get(ctx);
 208         sdiv=BN_CTX_get(ctx);
 209         if (dv == NULL)
 210                 res=BN_CTX_get(ctx);
 211         else    res=dv;
 212         if (sdiv == NULL || res == NULL) goto err;
 213         tmp->neg=0;
 214
 215         /* First we normalise the numbers */
 216         norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
 217         if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
 218         sdiv->neg=0;
 219         norm_shift+=BN_BITS2;
 220         if (!(BN_lshift(snum,num,norm_shift))) goto err;
 221         snum->neg=0;
 222         div_n=sdiv->top;
 223         num_n=snum->top;
 224         loop=num_n-div_n;
 225
 226         /* Lets setup a 'window' into snum
 227          * This is the part that corresponds to the current
 228          * 'area' being divided */
 229         BN_init(&wnum);
 230         wnum.d=  &(snum->d[loop]);
 231         wnum.top= div_n;
 232         wnum.dmax= snum->dmax+1; /* a bit of a lie */
 233
 234         /* Get the top 2 words of sdiv */
 235         /* i=sdiv->top; */
 236         d0=sdiv->d[div_n-1];
 237         d1=(div_n == 1)?0:sdiv->d[div_n-2];
 238
 239         /* pointer to the 'top' of snum */
 240         wnump= &(snum->d[num_n-1]);
 241
 242         /* Setup to 'res' */
 243         res->neg= (num->neg^divisor->neg);
 244         if (!bn_wexpand(res,(loop+1))) goto err;
 245         res->top=loop;
 246         resp= &(res->d[loop-1]);
 247
 248         /* space for temp */
 249         if (!bn_wexpand(tmp,(div_n+1))) goto err;
 250
 251         if (BN_ucmp(&wnum,sdiv) >= 0)
 252                 {
 253                 if (!BN_usub(&wnum,&wnum,sdiv)) goto err;
 254                 *resp=1;
 255                 res->d[res->top-1]=1;
 256                 }
 257         else
 258                 res->top--;
 259         if (res->top == 0)
 260                 res->neg = 0;
 261         resp--;
 262
 263         for (i=0; i<loop-1; i++)
 264                 {
 265                 BN_ULONG q,l0;
 266 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
 267                 BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
 268                 q=bn_div_3_words(wnump,d1,d0);
 269 #else
 270                 BN_ULONG n0,n1,rem=0;
 271
 272                 n0=wnump[0];
 273                 n1=wnump[-1];
 274                 if (n0 == d0)
 275                         q=BN_MASK2;
 276                 else                    /* n0 < d0 */
 277                         {
 278 #ifdef BN_LLONG
 279                         BN_ULLONG t2;
 280
 281 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
 282                         q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
 283 #else
 284                         q=bn_div_words(n0,n1,d0);
 285 #ifdef BN_DEBUG_LEVITTE
 286                         fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
 287 X) -> 0x%08X\n",
 288                                 n0, n1, d0, q);
 289 #endif
 290 #endif
 291
 292 #ifndef REMAINDER_IS_ALREADY_CALCULATED
 293                         /*
 294                          * rem doesn't have to be BN_ULLONG. The least we
 295                          * know it's less that d0, isn't it?
 296                          */
 297                         rem=(n1-q*d0)&BN_MASK2;
 298 #endif
 299                         t2=(BN_ULLONG)d1*q;
 300
 301                         for (;;)
 302                                 {
 303                                 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
 304                                         break;
 305                                 q--;
 306                                 rem += d0;
 307                                 if (rem < d0) break; /* don't let rem overflow */
 308                                 t2 -= d1;
 309                                 }
 310 #else /* !BN_LLONG */
 311                         BN_ULONG t2l,t2h,ql,qh;
 312
 313                         q=bn_div_words(n0,n1,d0);
 314 #ifdef BN_DEBUG_LEVITTE
 315                         fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
 316 X) -> 0x%08X\n",
 317                                 n0, n1, d0, q);
 318 #endif
 319 #ifndef REMAINDER_IS_ALREADY_CALCULATED
 320                         rem=(n1-q*d0)&BN_MASK2;
 321 #endif
 322
 323 #if defined(BN_UMULT_LOHI)
 324                         BN_UMULT_LOHI(t2l,t2h,d1,q);
 325 #elif defined(BN_UMULT_HIGH)
 326                         t2l = d1 * q;
 327                         t2h = BN_UMULT_HIGH(d1,q);
 328 #else
 329                         t2l=LBITS(d1); t2h=HBITS(d1);
 330                         ql =LBITS(q);  qh =HBITS(q);
 331                         mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
 332 #endif
 333
 334                         for (;;)
 335                                 {
 336                                 if ((t2h < rem) ||
 337                                         ((t2h == rem) && (t2l <= wnump[-2])))
 338                                         break;
 339                                 q--;
 340                                 rem += d0;
 341                                 if (rem < d0) break; /* don't let rem overflow */
 342                                 if (t2l < d1) t2h--; t2l -= d1;
 343                                 }
 344 #endif /* !BN_LLONG */
 345                         }
 346 #endif /* !BN_DIV3W */
 347
 348                 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
 349                 wnum.d--; wnum.top++;
 350                 tmp->d[div_n]=l0;
 351                 for (j=div_n+1; j>0; j--)
 352                         if (tmp->d[j-1]) break;
 353                 tmp->top=j;
 354
 355                 j=wnum.top;
 356                 if (!BN_sub(&wnum,&wnum,tmp)) goto err;
 357
 358                 snum->top=snum->top+wnum.top-j;
 359
 360                 if (wnum.neg)
 361                         {
 362                         q--;
 363                         j=wnum.top;
 364                         if (!BN_add(&wnum,&wnum,sdiv)) goto err;
 365                         snum->top+=wnum.top-j;
 366                         }
 367                 *(resp--)=q;
 368                 wnump--;
 369                 }
 370         if (rm != NULL)
 371                 {
 372                 /* Keep a copy of the neg flag in num because if rm==num
 373                  * BN_rshift() will overwrite it.
 374                  */
 375                 int neg = num->neg;
 376                 BN_rshift(rm,snum,norm_shift);
 377                 if (!BN_is_zero(rm))
 378                         rm->neg = neg;
 379                 }
 380         BN_CTX_end(ctx);
 381         return(1);
 382 err:
 383         BN_CTX_end(ctx);
 384         return(0);
 385         }
 386
 387 #endif