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 388