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(NO_ASM) && !defined(NO_INLINE_ASM) && !defined(PEDANTIC) && !defined(BN_DIV3W)
 131 # if defined(__GNUC__) && __GNUC__>=2
 132 #  if defined(__i386)
 133    /*
 134     * There were two reasons for implementing this template:
 135     * - GNU C generates a call to a function (__udivdi3 to be exact)
 136     *   in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
 137     *   understand why...);
 138     * - divl doesn't only calculate quotient, but also leaves
 139     *   remainder in %edx which we can definitely use here:-)
 140     *
 141     *                                   <appro@fy.chalmers.se>
 142     */
 143 #  define bn_div_words(n0,n1,d0)                \
 144         ({  asm volatile (                      \
 145                 "divl   %4"                     \
 146                 : "=a"(q), "=d"(rem)            \
 147                 : "a"(n1), "d"(n0), "g"(d0)     \
 148                 : "cc");                        \
 149             q;                                  \
 150         })
 151 #  define REMAINDER_IS_ALREADY_CALCULATED
 152 #  endif /* __<cpu> */
 153 # endif /* __GNUC__ */
 154 #endif /* NO_ASM */
 155
 156
 157 /* BN_div computes  dv := num / divisor,  rounding towards zero, and sets up
 158  * rm  such that  dv*divisor + rm = num  holds.
 159  * Thus:
 160  *     dv->neg == num->neg ^ divisor->neg  (unless the result is zero)
 161  *     rm->neg == num->neg                 (unless the remainder is zero)
 162  * If 'dv' or 'rm' is NULL, the respective value is not returned.
 163  */
 164 int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
 165            BN_CTX *ctx)
 166         {
 167         int norm_shift,i,j,loop;
 168         BIGNUM *tmp,wnum,*snum,*sdiv,*res;
 169         BN_ULONG *resp,*wnump;
 170         BN_ULONG d0,d1;
 171         int num_n,div_n;
 172
 173         bn_check_top(num);
 174         bn_check_top(divisor);
 175
 176         if (BN_is_zero(divisor))
 177                 {
 178                 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
 179                 return(0);
 180                 }
 181
 182         if (BN_ucmp(num,divisor) < 0)
 183                 {
 184                 if (rm != NULL)
 185                         { if (BN_copy(rm,num) == NULL) return(0); }
 186                 if (dv != NULL) BN_zero(dv);
 187                 return(1);
 188                 }
 189
 190         BN_CTX_start(ctx);
 191         tmp=BN_CTX_get(ctx);
 192         snum=BN_CTX_get(ctx);
 193         sdiv=BN_CTX_get(ctx);
 194         if (dv == NULL)
 195                 res=BN_CTX_get(ctx);
 196         else    res=dv;
 197         if (sdiv == NULL || res == NULL) goto err;
 198         tmp->neg=0;
 199
 200         /* First we normalise the numbers */
 201         norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
 202         BN_lshift(sdiv,divisor,norm_shift);
 203         sdiv->neg=0;
 204         norm_shift+=BN_BITS2;
 205         BN_lshift(snum,num,norm_shift);
 206         snum->neg=0;
 207         div_n=sdiv->top;
 208         num_n=snum->top;
 209         loop=num_n-div_n;
 210
 211         /* Lets setup a 'window' into snum
 212          * This is the part that corresponds to the current
 213          * 'area' being divided */
 214         BN_init(&wnum);
 215         wnum.d=  &(snum->d[loop]);
 216         wnum.top= div_n;
 217         wnum.dmax= snum->dmax+1; /* a bit of a lie */
 218
 219         /* Get the top 2 words of sdiv */
 220         /* i=sdiv->top; */
 221         d0=sdiv->d[div_n-1];
 222         d1=(div_n == 1)?0:sdiv->d[div_n-2];
 223
 224         /* pointer to the 'top' of snum */
 225         wnump= &(snum->d[num_n-1]);
 226
 227         /* Setup to 'res' */
 228         res->neg= (num->neg^divisor->neg);
 229         if (!bn_wexpand(res,(loop+1))) goto err;
 230         res->top=loop;
 231         resp= &(res->d[loop-1]);
 232
 233         /* space for temp */
 234         if (!bn_wexpand(tmp,(div_n+1))) goto err;
 235
 236         if (BN_ucmp(&wnum,sdiv) >= 0)
 237                 {
 238                 if (!BN_usub(&wnum,&wnum,sdiv)) goto err;
 239                 *resp=1;
 240                 res->d[res->top-1]=1;
 241                 }
 242         else
 243                 res->top--;
 244         if (res->top == 0)
 245                 res->neg = 0;
 246         resp--;
 247
 248         for (i=0; i<loop-1; i++)
 249                 {
 250                 BN_ULONG q,l0;
 251 #if defined(BN_DIV3W) && !defined(NO_ASM)
 252                 q=bn_div_3_words(wnump,d1,d0);
 253 #else
 254                 BN_ULONG n0,n1,rem=0;
 255
 256                 n0=wnump[0];
 257                 n1=wnump[-1];
 258                 if (n0 == d0)
 259                         q=BN_MASK2;
 260                 else                    /* n0 < d0 */
 261                         {
 262 #ifdef BN_LLONG
 263                         BN_ULLONG t2;
 264
 265 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
 266                         q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
 267 #else
 268                         q=bn_div_words(n0,n1,d0);
 269 #endif
 270
 271 #ifndef REMAINDER_IS_ALREADY_CALCULATED
 272                         /*
 273                          * rem doesn't have to be BN_ULLONG. The least we
 274                          * know it's less that d0, isn't it?
 275                          */
 276                         rem=(n1-q*d0)&BN_MASK2;
 277 #endif
 278                         t2=(BN_ULLONG)d1*q;
 279
 280                         for (;;)
 281                                 {
 282                                 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
 283                                         break;
 284                                 q--;
 285                                 rem += d0;
 286                                 if (rem < d0) break; /* don't let rem overflow */
 287                                 t2 -= d1;
 288                                 }
 289 #else /* !BN_LLONG */
 290                         BN_ULONG t2l,t2h,ql,qh;
 291
 292                         q=bn_div_words(n0,n1,d0);
 293 #ifndef REMAINDER_IS_ALREADY_CALCULATED
 294                         rem=(n1-q*d0)&BN_MASK2;
 295 #endif
 296
 297 #ifdef BN_UMULT_HIGH
 298                         t2l = d1 * q;
 299                         t2h = BN_UMULT_HIGH(d1,q);
 300 #else
 301                         t2l=LBITS(d1); t2h=HBITS(d1);
 302                         ql =LBITS(q);  qh =HBITS(q);
 303                         mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
 304 #endif
 305
 306                         for (;;)
 307                                 {
 308                                 if ((t2h < rem) ||
 309                                         ((t2h == rem) && (t2l <= wnump[-2])))
 310                                         break;
 311                                 q--;
 312                                 rem += d0;
 313                                 if (rem < d0) break; /* don't let rem overflow */
 314                                 if (t2l < d1) t2h--; t2l -= d1;
 315                                 }
 316 #endif /* !BN_LLONG */
 317                         }
 318 #endif /* !BN_DIV3W */
 319
 320                 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
 321                 wnum.d--; wnum.top++;
 322                 tmp->d[div_n]=l0;
 323                 for (j=div_n+1; j>0; j--)
 324                         if (tmp->d[j-1]) break;
 325                 tmp->top=j;
 326
 327                 j=wnum.top;
 328                 BN_sub(&wnum,&wnum,tmp);
 329
 330                 snum->top=snum->top+wnum.top-j;
 331
 332                 if (wnum.neg)
 333                         {
 334                         q--;
 335                         j=wnum.top;
 336                         BN_add(&wnum,&wnum,sdiv);
 337                         snum->top+=wnum.top-j;
 338                         }
 339                 *(resp--)=q;
 340                 wnump--;
 341                 }
 342         if (rm != NULL)
 343                 {
 344                 BN_rshift(rm,snum,norm_shift);
 345                 if (!BN_is_zero(rm))
 346                         rm->neg = num->neg;
 347                 }
 348         BN_CTX_end(ctx);
 349         return(1);
 350 err:
 351         BN_CTX_end(ctx);
 352         return(0);
 353         }
 354
 355 #endif