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, BIGNUM *m, BIGNUM *d, BN_CTX *ctx)
  67         {
  68         int i,nm,nd;
  69         BIGNUM *D;
  70
  71         bn_check_top(m);
  72         bn_check_top(d);
  73         if (BN_is_zero(d))
  74                 {
  75                 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
  76                 return(0);
  77                 }
  78
  79         if (BN_ucmp(m,d) < 0)
  80                 {
  81                 if (rem != NULL)
  82                         { if (BN_copy(rem,m) == NULL) return(0); }
  83                 if (dv != NULL) BN_zero(dv);
  84                 return(1);
  85                 }
  86
  87         D= &(ctx->bn[ctx->tos]);
  88         if (dv == NULL) dv= &(ctx->bn[ctx->tos+1]);
  89         if (rem == NULL) rem= &(ctx->bn[ctx->tos+2]);
  90
  91         nd=BN_num_bits(d);
  92         nm=BN_num_bits(m);
  93         if (BN_copy(D,d) == NULL) return(0);
  94         if (BN_copy(rem,m) == NULL) return(0);
  95
  96         /* The next 2 are needed so we can do a dv->d[0]|=1 later
  97          * since BN_lshift1 will only work once there is a value :-) */
  98         BN_zero(dv);
  99         bn_wexpand(dv,1);
 100         dv->top=1;
 101
 102         if (!BN_lshift(D,D,nm-nd)) return(0);
 103         for (i=nm-nd; i>=0; i--)
 104                 {
 105                 if (!BN_lshift1(dv,dv)) return(0);
 106                 if (BN_ucmp(rem,D) >= 0)
 107                         {
 108                         dv->d[0]|=1;
 109                         if (!BN_usub(rem,rem,D)) return(0);
 110                         }
 111 /* CAN IMPROVE (and have now :=) */
 112                 if (!BN_rshift1(D,D)) return(0);
 113                 }
 114         rem->neg=BN_is_zero(rem)?0:m->neg;
 115         dv->neg=m->neg^d->neg;
 116         return(1);
 117         }
 118
 119 #else
 120
 121 int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
 122            BN_CTX *ctx)
 123         {
 124         int norm_shift,i,j,loop;
 125         BIGNUM *tmp,wnum,*snum,*sdiv,*res;
 126         BN_ULONG *resp,*wnump;
 127         BN_ULONG d0,d1;
 128         int num_n,div_n;
 129
 130         bn_check_top(num);
 131         bn_check_top(divisor);
 132
 133         if (BN_is_zero(divisor))
 134                 {
 135                 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
 136                 return(0);
 137                 }
 138
 139         if (BN_ucmp(num,divisor) < 0)
 140                 {
 141                 if (rm != NULL)
 142                         { if (BN_copy(rm,num) == NULL) return(0); }
 143                 if (dv != NULL) BN_zero(dv);
 144                 return(1);
 145                 }
 146
 147         tmp= &(ctx->bn[ctx->tos]);
 148         tmp->neg=0;
 149         snum= &(ctx->bn[ctx->tos+1]);
 150         sdiv= &(ctx->bn[ctx->tos+2]);
 151         if (dv == NULL)
 152                 res= &(ctx->bn[ctx->tos+3]);
 153         else    res=dv;
 154
 155         /* First we normalise the numbers */
 156         norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
 157         BN_lshift(sdiv,divisor,norm_shift);
 158         sdiv->neg=0;
 159         norm_shift+=BN_BITS2;
 160         BN_lshift(snum,num,norm_shift);
 161         snum->neg=0;
 162         div_n=sdiv->top;
 163         num_n=snum->top;
 164         loop=num_n-div_n;
 165
 166         /* Lets setup a 'window' into snum
 167          * This is the part that corresponds to the current
 168          * 'area' being divided */
 169         BN_init(&wnum);
 170         wnum.d=  &(snum->d[loop]);
 171         wnum.top= div_n;
 172         wnum.max= snum->max+1; /* a bit of a lie */
 173
 174         /* Get the top 2 words of sdiv */
 175         /* i=sdiv->top; */
 176         d0=sdiv->d[div_n-1];
 177         d1=(div_n == 1)?0:sdiv->d[div_n-2];
 178
 179         /* pointer to the 'top' of snum */
 180         wnump= &(snum->d[num_n-1]);
 181
 182         /* Setup to 'res' */
 183         res->neg= (num->neg^divisor->neg);
 184         if (!bn_wexpand(res,(loop+1))) goto err;
 185         res->top=loop;
 186         resp= &(res->d[loop-1]);
 187
 188         /* space for temp */
 189         if (!bn_wexpand(tmp,(div_n+1))) goto err;
 190
 191         if (BN_ucmp(&wnum,sdiv) >= 0)
 192                 {
 193                 if (!BN_usub(&wnum,&wnum,sdiv)) goto err;
 194                 *resp=1;
 195                 res->d[res->top-1]=1;
 196                 }
 197         else
 198                 res->top--;
 199         resp--;
 200
 201         for (i=0; i<loop-1; i++)
 202                 {
 203                 BN_ULONG q,n0,n1;
 204                 BN_ULONG l0;
 205
 206                 wnum.d--; wnum.top++;
 207                 n0=wnump[0];
 208                 n1=wnump[-1];
 209                 if (n0 == d0)
 210                         q=BN_MASK2;
 211                 else
 212                         q=bn_div_words(n0,n1,d0);
 213                 {
 214 #ifdef BN_LLONG
 215                 BN_ULLONG t1,t2,rem;
 216                 t1=((BN_ULLONG)n0<<BN_BITS2)|n1;
 217                 for (;;)
 218                         {
 219                         rem=t1-(BN_ULLONG)q*d0;
 220                         t2=(BN_ULLONG)d1*q;
 221                         if ((rem>>BN_BITS2) ||
 222                                 (t2 <= ((rem<<BN_BITS2)|wnump[-2])))
 223                                 break;
 224                         q--;
 225                         }
 226 #else
 227                 BN_ULONG t1l,t1h,t2l,t2h,t3l,t3h,ql,qh,t3t;
 228                 t1h=n0;
 229                 t1l=n1;
 230                 for (;;)
 231                         {
 232                         t2l=LBITS(d1); t2h=HBITS(d1);
 233                         ql =LBITS(q);  qh =HBITS(q);
 234                         mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
 235
 236                         t3t=LBITS(d0); t3h=HBITS(d0);
 237                         mul64(t3t,t3h,ql,qh); /* t3=t1-(BN_ULLONG)q*d0; */
 238                         t3l=(t1l-t3t)&BN_MASK2;
 239                         if (t3l > t1l) t3h++;
 240                         t3h=(t1h-t3h)&BN_MASK2;
 241
 242                         /*if ((t3>>BN_BITS2) ||
 243                                 (t2 <= ((t3<<BN_BITS2)+wnump[-2])))
 244                                 break; */
 245                         if (t3h) break;
 246                         if (t2h < t3l) break;
 247                         if ((t2h == t3l) && (t2l <= wnump[-2])) break;
 248
 249                         q--;
 250                         }
 251 #endif
 252                 }
 253                 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
 254                 tmp->d[div_n]=l0;
 255                 for (j=div_n+1; j>0; j--)
 256                         if (tmp->d[j-1]) break;
 257                 tmp->top=j;
 258
 259                 j=wnum.top;
 260                 BN_sub(&wnum,&wnum,tmp);
 261
 262                 snum->top=snum->top+wnum.top-j;
 263
 264                 if (wnum.neg)
 265                         {
 266                         q--;
 267                         j=wnum.top;
 268                         BN_add(&wnum,&wnum,sdiv);
 269                         snum->top+=wnum.top-j;
 270                         }
 271                 *(resp--)=q;
 272                 wnump--;
 273                 }
 274         if (rm != NULL)
 275                 {
 276                 BN_rshift(rm,snum,norm_shift);
 277                 rm->neg=num->neg;
 278                 }
 279         return(1);
 280 err:
 281         return(0);
 282         }
 283
 284 #endif
 285
 286 /* rem != m */
 287 int BN_mod(BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)
 288         {
 289 #if 0 /* The old slow way */
 290         int i,nm,nd;
 291         BIGNUM *dv;
 292
 293         if (BN_ucmp(m,d) < 0)
 294                 return((BN_copy(rem,m) == NULL)?0:1);
 295
 296         dv= &(ctx->bn[ctx->tos]);
 297
 298         if (!BN_copy(rem,m)) return(0);
 299
 300         nm=BN_num_bits(rem);
 301         nd=BN_num_bits(d);
 302         if (!BN_lshift(dv,d,nm-nd)) return(0);
 303         for (i=nm-nd; i>=0; i--)
 304                 {
 305                 if (BN_cmp(rem,dv) >= 0)
 306                         {
 307                         if (!BN_sub(rem,rem,dv)) return(0);
 308                         }
 309                 if (!BN_rshift1(dv,dv)) return(0);
 310                 }
 311         return(1);
 312 #else
 313         return(BN_div(NULL,rem,m,d,ctx));
 314 #endif
 315         }
 316