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 /* The old slow way */
  65 #if 0
  66 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
  67            BN_CTX *ctx)
  68         {
  69         int i,nm,nd;
  70         BIGNUM *D;
  71
  72         bn_check_top(m);
  73         bn_check_top(d);
  74         if (BN_is_zero(d))
  75                 {
  76                 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
  77                 return(0);
  78                 }
  79
  80         if (BN_ucmp(m,d) < 0)
  81                 {
  82                 if (rem != NULL)
  83                         { if (BN_copy(rem,m) == NULL) return(0); }
  84                 if (dv != NULL) BN_zero(dv);
  85                 return(1);
  86                 }
  87
  88         D= &(ctx->bn[ctx->tos]);
  89         if (dv == NULL) dv= &(ctx->bn[ctx->tos+1]);
  90         if (rem == NULL) rem= &(ctx->bn[ctx->tos+2]);
  91
  92         nd=BN_num_bits(d);
  93         nm=BN_num_bits(m);
  94         if (BN_copy(D,d) == NULL) return(0);
  95         if (BN_copy(rem,m) == NULL) return(0);
  96
  97         /* The next 2 are needed so we can do a dv->d[0]|=1 later
  98          * since BN_lshift1 will only work once there is a value :-) */
  99         BN_zero(dv);
 100         bn_wexpand(dv,1);
 101         dv->top=1;
 102
 103         if (!BN_lshift(D,D,nm-nd)) return(0);
 104         for (i=nm-nd; i>=0; i--)
 105                 {
 106                 if (!BN_lshift1(dv,dv)) return(0);
 107                 if (BN_ucmp(rem,D) >= 0)
 108                         {
 109                         dv->d[0]|=1;
 110                         if (!BN_usub(rem,rem,D)) return(0);
 111                         }
 112 /* CAN IMPROVE (and have now :=) */
 113                 if (!BN_rshift1(D,D)) return(0);
 114                 }
 115         rem->neg=BN_is_zero(rem)?0:m->neg;
 116         dv->neg=m->neg^d->neg;
 117         return(1);
 118         }
 119
 120 #else
 121
 122 int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
 123            BN_CTX *ctx)
 124         {
 125         int norm_shift,i,j,loop;
 126         BIGNUM *tmp,wnum,*snum,*sdiv,*res;
 127         BN_ULONG *resp,*wnump;
 128         BN_ULONG d0,d1;
 129         int num_n,div_n;
 130
 131         bn_check_top(num);
 132         bn_check_top(divisor);
 133
 134         if (BN_is_zero(divisor))
 135                 {
 136                 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
 137                 return(0);
 138                 }
 139
 140         if (BN_ucmp(num,divisor) < 0)
 141                 {
 142                 if (rm != NULL)
 143                         { if (BN_copy(rm,num) == NULL) return(0); }
 144                 if (dv != NULL) BN_zero(dv);
 145                 return(1);
 146                 }
 147
 148         tmp= &(ctx->bn[ctx->tos]);
 149         tmp->neg=0;
 150         snum= &(ctx->bn[ctx->tos+1]);
 151         sdiv= &(ctx->bn[ctx->tos+2]);
 152         if (dv == NULL)
 153                 res= &(ctx->bn[ctx->tos+3]);
 154         else    res=dv;
 155
 156         /* First we normalise the numbers */
 157         norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
 158         BN_lshift(sdiv,divisor,norm_shift);
 159         sdiv->neg=0;
 160         norm_shift+=BN_BITS2;
 161         BN_lshift(snum,num,norm_shift);
 162         snum->neg=0;
 163         div_n=sdiv->top;
 164         num_n=snum->top;
 165         loop=num_n-div_n;
 166
 167         /* Lets setup a 'window' into snum
 168          * This is the part that corresponds to the current
 169          * 'area' being divided */
 170         BN_init(&wnum);
 171         wnum.d=  &(snum->d[loop]);
 172         wnum.top= div_n;
 173         wnum.max= snum->max+1; /* a bit of a lie */
 174
 175         /* Get the top 2 words of sdiv */
 176         /* i=sdiv->top; */
 177         d0=sdiv->d[div_n-1];
 178         d1=(div_n == 1)?0:sdiv->d[div_n-2];
 179
 180         /* pointer to the 'top' of snum */
 181         wnump= &(snum->d[num_n-1]);
 182
 183         /* Setup to 'res' */
 184         res->neg= (num->neg^divisor->neg);
 185         if (!bn_wexpand(res,(loop+1))) goto err;
 186         res->top=loop;
 187         resp= &(res->d[loop-1]);
 188
 189         /* space for temp */
 190         if (!bn_wexpand(tmp,(div_n+1))) goto err;
 191
 192         if (BN_ucmp(&wnum,sdiv) >= 0)
 193                 {
 194                 if (!BN_usub(&wnum,&wnum,sdiv)) goto err;
 195                 *resp=1;
 196                 res->d[res->top-1]=1;
 197                 }
 198         else
 199                 res->top--;
 200         resp--;
 201
 202         for (i=0; i<loop-1; i++)
 203                 {
 204                 BN_ULONG q,l0;
 205 #ifdef BN_DIV3W
 206                 q=bn_div_3_words(wnump,d1,d0);
 207 #else
 208
 209 #if !defined(NO_ASM) && !defined(PEDANTIC)
 210 # if defined(__GNUC__) && __GNUC__>=2
 211 #  if defined(__i386)
 212    /*
 213     * There were two reasons for implementing this template:
 214     * - GNU C generates a call to a function (__udivdi3 to be exact)
 215     *   in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
 216     *   understand why...);
 217     * - divl doesn't only calculate quotient, but also leaves
 218     *   remainder in %edx which we can definitely use here:-)
 219     *
 220     *                                   <appro@fy.chalmers.se>
 221     */
 222 #  define bn_div_words(n0,n1,d0)                \
 223         ({  asm volatile (                      \
 224                 "divl   %4"                     \
 225                 : "=a"(q), "=d"(rem)            \
 226                 : "a"(n1), "d"(n0), "g"(d0)     \
 227                 : "cc");                        \
 228             q;                                  \
 229         })
 230 #  define REMAINDER_IS_ALREADY_CALCULATED
 231 #  endif /* __<cpu> */
 232 # endif /* __GNUC__ */
 233 #endif /* NO_ASM */
 234                 BN_ULONG n0,n1,rem=0;
 235
 236                 n0=wnump[0];
 237                 n1=wnump[-1];
 238                 if (n0 == d0)
 239                         {
 240                         q=BN_MASK2;
 241 #ifdef REMAINDER_IS_ALREADY_CALCULATED /* in this case it isn't */
 242                         rem=(n1-q*d0)&BN_MASK2;
 243 #endif
 244                         }
 245                 else /* n0 < d0 */
 246 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
 247                         q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
 248 #else
 249                         q=bn_div_words(n0,n1,d0);
 250 #endif
 251                 {
 252 #ifdef BN_LLONG
 253                 BN_ULLONG t2;
 254
 255 #ifndef REMAINDER_IS_ALREADY_CALCULATED
 256                 /*
 257                  * rem doesn't have to be BN_ULLONG. The least we
 258                  * know it's less that d0, isn't it?
 259                  */
 260                 rem=(n1-q*d0)&BN_MASK2;
 261 #endif
 262                 t2=(BN_ULLONG)d1*q;
 263
 264                 for (;;)
 265                         {
 266                         if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
 267                                 break;
 268                         q--;
 269                         rem += d0;
 270                         if (rem < d0) break; /* don't let rem overflow */
 271                         t2 -= d1;
 272                         }
 273 #else
 274                 BN_ULONG t2l,t2h,ql,qh;
 275
 276 #ifndef REMAINDER_IS_ALREADY_CALCULATED
 277                 /*
 278                  * It's more than enough with the only multiplication.
 279                  * See the comment above in BN_LLONG section...
 280                  */
 281                 rem=(n1-q*d0)&BN_MASK2;
 282 #endif
 283 #ifdef BN_UMULT_HIGH
 284                 t2l = d1 * q;
 285                 t2h = BN_UMULT_HIGH(d1,q);
 286 #else
 287                 t2l=LBITS(d1); t2h=HBITS(d1);
 288                 ql =LBITS(q);  qh =HBITS(q);
 289                 mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
 290 #endif
 291
 292                 for (;;)
 293                         {
 294                         if ((t2h < rem) ||
 295                                 ((t2h == rem) && (t2l <= wnump[-2])))
 296                                 break;
 297                         q--;
 298                         rem += d0;
 299                         if (rem < d0) break; /* don't let rem overflow */
 300                         if (t2l < d1) t2h--; t2l -= d1;
 301                         }
 302 #endif
 303                 }
 304 #endif /* !BN_DIV3W */
 305                 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
 306                 wnum.d--; wnum.top++;
 307                 tmp->d[div_n]=l0;
 308                 for (j=div_n+1; j>0; j--)
 309                         if (tmp->d[j-1]) break;
 310                 tmp->top=j;
 311
 312                 j=wnum.top;
 313                 BN_sub(&wnum,&wnum,tmp);
 314
 315                 snum->top=snum->top+wnum.top-j;
 316
 317                 if (wnum.neg)
 318                         {
 319                         q--;
 320                         j=wnum.top;
 321                         BN_add(&wnum,&wnum,sdiv);
 322                         snum->top+=wnum.top-j;
 323                         }
 324                 *(resp--)=q;
 325                 wnump--;
 326                 }
 327         if (rm != NULL)
 328                 {
 329                 BN_rshift(rm,snum,norm_shift);
 330                 rm->neg=num->neg;
 331                 }
 332         return(1);
 333 err:
 334         return(0);
 335         }
 336
 337 #endif
 338
 339 /* rem != m */
 340 int BN_mod(BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)
 341         {
 342 #if 0 /* The old slow way */
 343         int i,nm,nd;
 344         BIGNUM *dv;
 345
 346         if (BN_ucmp(m,d) < 0)
 347                 return((BN_copy(rem,m) == NULL)?0:1);
 348
 349         dv= &(ctx->bn[ctx->tos]);
 350
 351         if (!BN_copy(rem,m)) return(0);
 352
 353         nm=BN_num_bits(rem);
 354         nd=BN_num_bits(d);
 355         if (!BN_lshift(dv,d,nm-nd)) return(0);
 356         for (i=nm-nd; i>=0; i--)
 357                 {
 358                 if (BN_cmp(rem,dv) >= 0)
 359                         {
 360                         if (!BN_sub(rem,rem,dv)) return(0);
 361                         }
 362                 if (!BN_rshift1(dv,dv)) return(0);
 363                 }
 364         return(1);
 365 #else
 366         return(BN_div(NULL,rem,m,d,ctx));
 367 #endif
 368         }
 369