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 int ret = 0; 71 BIGNUM *D; 72 73 bn_check_top(m); 74 bn_check_top(d); 75 if (BN_is_zero(d)) 76 { 77 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO); 78 return(0); 79 } 80 81 if (BN_ucmp(m,d) < 0) 82 { 83 if (rem != NULL) 84 { if (BN_copy(rem,m) == NULL) return(0); } 85 if (dv != NULL) BN_zero(dv); 86 return(1); 87 } 88 89 BN_CTX_start(ctx); 90 D = BN_CTX_get(ctx); 91 if (dv == NULL) dv = BN_CTX_get(ctx); 92 if (rem == NULL) rem = BN_CTX_get(ctx); 93 if (D == NULL || dv == NULL || rem == NULL) 94 goto end; 95 96 nd=BN_num_bits(d); 97 nm=BN_num_bits(m); 98 if (BN_copy(D,d) == NULL) goto end; 99 if (BN_copy(rem,m) == NULL) goto end; 100 101 /* The next 2 are needed so we can do a dv->d[0]|=1 later 102 * since BN_lshift1 will only work once there is a value :-) */ 103 BN_zero(dv); 104 bn_wexpand(dv,1); 105 dv->top=1; 106 107 if (!BN_lshift(D,D,nm-nd)) goto end; 108 for (i=nm-nd; i>=0; i--) 109 { 110 if (!BN_lshift1(dv,dv)) goto end; 111 if (BN_ucmp(rem,D) >= 0) 112 { 113 dv->d[0]|=1; 114 if (!BN_usub(rem,rem,D)) goto end; 115 } 116 /* CAN IMPROVE (and have now :=) */ 117 if (!BN_rshift1(D,D)) goto end; 118 } 119 rem->neg=BN_is_zero(rem)?0:m->neg; 120 dv->neg=m->neg^d->neg; 121 ret = 1; 122 end: 123 BN_CTX_end(ctx); 124 return(ret); 125 } 126 127 #else 128 129 #if !defined(NO_ASM) && !defined(NO_INLINE_ASM) && !defined(PEDANTIC) && !defined(BN_DIV3W) 130 # if defined(__GNUC__) && __GNUC__>=2 131 # if defined(__i386) 132 /* 133 * There were two reasons for implementing this template: 134 * - GNU C generates a call to a function (__udivdi3 to be exact) 135 * in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to 136 * understand why...); 137 * - divl doesn't only calculate quotient, but also leaves 138 * remainder in %edx which we can definitely use here:-) 139 * 140 * <appro@fy.chalmers.se> 141 */ 142 # define bn_div_words(n0,n1,d0) \ 143 ({ asm volatile ( \ 144 "divl %4" \ 145 : "=a"(q), "=d"(rem) \ 146 : "a"(n1), "d"(n0), "g"(d0) \ 147 : "cc"); \ 148 q; \ 149 }) 150 # define REMAINDER_IS_ALREADY_CALCULATED 151 # endif /* __<cpu> */ 152 # endif /* __GNUC__ */ 153 #endif /* NO_ASM */ 154 155 int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor, 156 BN_CTX *ctx) 157 { 158 int norm_shift,i,j,loop; 159 BIGNUM *tmp,wnum,*snum,*sdiv,*res; 160 BN_ULONG *resp,*wnump; 161 BN_ULONG d0,d1; 162 int num_n,div_n; 163 164 bn_check_top(num); 165 bn_check_top(divisor); 166 167 if (BN_is_zero(divisor)) 168 { 169 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO); 170 return(0); 171 } 172 173 if (BN_ucmp(num,divisor) < 0) 174 { 175 if (rm != NULL) 176 { if (BN_copy(rm,num) == NULL) return(0); } 177 if (dv != NULL) BN_zero(dv); 178 return(1); 179 } 180 181 BN_CTX_start(ctx); 182 tmp=BN_CTX_get(ctx); 183 tmp->neg=0; 184 snum=BN_CTX_get(ctx); 185 sdiv=BN_CTX_get(ctx); 186 if (dv == NULL) 187 res=BN_CTX_get(ctx); 188 else res=dv; 189 if (res == NULL) goto err; 190 191 /* First we normalise the numbers */ 192 norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2); 193 BN_lshift(sdiv,divisor,norm_shift); 194 sdiv->neg=0; 195 norm_shift+=BN_BITS2; 196 BN_lshift(snum,num,norm_shift); 197 snum->neg=0; 198 div_n=sdiv->top; 199 num_n=snum->top; 200 loop=num_n-div_n; 201 202 /* Lets setup a 'window' into snum 203 * This is the part that corresponds to the current 204 * 'area' being divided */ 205 BN_init(&wnum); 206 wnum.d= &(snum->d[loop]); 207 wnum.top= div_n; 208 wnum.dmax= snum->dmax+1; /* a bit of a lie */ 209 210 /* Get the top 2 words of sdiv */ 211 /* i=sdiv->top; */ 212 d0=sdiv->d[div_n-1]; 213 d1=(div_n == 1)?0:sdiv->d[div_n-2]; 214 215 /* pointer to the 'top' of snum */ 216 wnump= &(snum->d[num_n-1]); 217 218 /* Setup to 'res' */ 219 res->neg= (num->neg^divisor->neg); 220 if (!bn_wexpand(res,(loop+1))) goto err; 221 res->top=loop; 222 resp= &(res->d[loop-1]); 223 224 /* space for temp */ 225 if (!bn_wexpand(tmp,(div_n+1))) goto err; 226 227 if (BN_ucmp(&wnum,sdiv) >= 0) 228 { 229 if (!BN_usub(&wnum,&wnum,sdiv)) goto err; 230 *resp=1; 231 res->d[res->top-1]=1; 232 } 233 else 234 res->top--; 235 resp--; 236 237 for (i=0; i<loop-1; i++) 238 { 239 BN_ULONG q,l0; 240 #ifdef BN_DIV3W 241 q=bn_div_3_words(wnump,d1,d0); 242 #else 243 BN_ULONG n0,n1,rem=0; 244 245 n0=wnump[0]; 246 n1=wnump[-1]; 247 if (n0 == d0) 248 q=BN_MASK2; 249 else /* n0 < d0 */ 250 { 251 #ifdef BN_LLONG 252 BN_ULLONG t2; 253 254 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words) 255 q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0); 256 #else 257 q=bn_div_words(n0,n1,d0); 258 #endif 259 260 #ifndef REMAINDER_IS_ALREADY_CALCULATED 261 /* 262 * rem doesn't have to be BN_ULLONG. The least we 263 * know it's less that d0, isn't it? 264 */ 265 rem=(n1-q*d0)&BN_MASK2; 266 #endif 267 t2=(BN_ULLONG)d1*q; 268 269 for (;;) 270 { 271 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2])) 272 break; 273 q--; 274 rem += d0; 275 if (rem < d0) break; /* don't let rem overflow */ 276 t2 -= d1; 277 } 278 #else /* !BN_LLONG */ 279 BN_ULONG t2l,t2h,ql,qh; 280 281 q=bn_div_words(n0,n1,d0); 282 #ifndef REMAINDER_IS_ALREADY_CALCULATED 283 rem=(n1-q*d0)&BN_MASK2; 284 #endif 285 286 #ifdef BN_UMULT_HIGH 287 t2l = d1 * q; 288 t2h = BN_UMULT_HIGH(d1,q); 289 #else 290 t2l=LBITS(d1); t2h=HBITS(d1); 291 ql =LBITS(q); qh =HBITS(q); 292 mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */ 293 #endif 294 295 for (;;) 296 { 297 if ((t2h < rem) || 298 ((t2h == rem) && (t2l <= wnump[-2]))) 299 break; 300 q--; 301 rem += d0; 302 if (rem < d0) break; /* don't let rem overflow */ 303 if (t2l < d1) t2h--; t2l -= d1; 304 } 305 #endif /* !BN_LLONG */ 306 } 307 #endif /* !BN_DIV3W */ 308 309 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q); 310 wnum.d--; wnum.top++; 311 tmp->d[div_n]=l0; 312 for (j=div_n+1; j>0; j--) 313 if (tmp->d[j-1]) break; 314 tmp->top=j; 315 316 j=wnum.top; 317 BN_sub(&wnum,&wnum,tmp); 318 319 snum->top=snum->top+wnum.top-j; 320 321 if (wnum.neg) 322 { 323 q--; 324 j=wnum.top; 325 BN_add(&wnum,&wnum,sdiv); 326 snum->top+=wnum.top-j; 327 } 328 *(resp--)=q; 329 wnump--; 330 } 331 if (rm != NULL) 332 { 333 BN_rshift(rm,snum,norm_shift); 334 rm->neg=num->neg; 335 } 336 BN_CTX_end(ctx); 337 return(1); 338 err: 339 BN_CTX_end(ctx); 340 return(0); 341 } 342 343 #endif 344 345 /* rem != m */ 346 int BN_mod(BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx) 347 { 348 #if 0 /* The old slow way */ 349 int i,nm,nd; 350 BIGNUM *dv; 351 352 if (BN_ucmp(m,d) < 0) 353 return((BN_copy(rem,m) == NULL)?0:1); 354 355 BN_CTX_start(ctx); 356 dv=BN_CTX_get(ctx); 357 358 if (!BN_copy(rem,m)) goto err; 359 360 nm=BN_num_bits(rem); 361 nd=BN_num_bits(d); 362 if (!BN_lshift(dv,d,nm-nd)) goto err; 363 for (i=nm-nd; i>=0; i--) 364 { 365 if (BN_cmp(rem,dv) >= 0) 366 { 367 if (!BN_sub(rem,rem,dv)) goto err; 368 } 369 if (!BN_rshift1(dv,dv)) goto err; 370 } 371 BN_CTX_end(ctx); 372 return(1); 373 err: 374 BN_CTX_end(ctx); 375 return(0); 376 #else 377 return(BN_div(NULL,rem,m,d,ctx)); 378 #endif 379 } 380 381