1 /* crypto/bn/bn_div.c */ 2 /* Copyright (C) 1995-1998 Eric Young (eay (at) cryptsoft.com) 3 * All rights reserved. 4 * 5 * This package is an SSL implementation written 6 * by Eric Young (eay (at) 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 (at) 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 (at) 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 (at) 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 if(bn_wexpand(dv,1) == NULL) goto end; 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 (at) 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 (at) 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 173 * zero, and sets up 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,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 int no_branch=0; 188 189 /* Invalid zero-padding would have particularly bad consequences 190 * in the case of 'num', so don't just rely on bn_check_top() for this one 191 * (bn_check_top() works only for BN_DEBUG builds) */ 192 if (num->top > 0 && num->d[num->top - 1] == 0) 193 { 194 BNerr(BN_F_BN_DIV,BN_R_NOT_INITIALIZED); 195 return 0; 196 } 197 198 bn_check_top(num); 199 200 if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0)) 201 { 202 no_branch=1; 203 } 204 205 bn_check_top(dv); 206 bn_check_top(rm); 207 /* bn_check_top(num); */ /* 'num' has been checked already */ 208 bn_check_top(divisor); 209 210 if (BN_is_zero(divisor)) 211 { 212 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO); 213 return(0); 214 } 215 216 if (!no_branch && BN_ucmp(num,divisor) < 0) 217 { 218 if (rm != NULL) 219 { if (BN_copy(rm,num) == NULL) return(0); } 220 if (dv != NULL) BN_zero(dv); 221 return(1); 222 } 223 224 BN_CTX_start(ctx); 225 tmp=BN_CTX_get(ctx); 226 snum=BN_CTX_get(ctx); 227 sdiv=BN_CTX_get(ctx); 228 if (dv == NULL) 229 res=BN_CTX_get(ctx); 230 else res=dv; 231 if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL) 232 goto err; 233 234 /* First we normalise the numbers */ 235 norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2); 236 if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err; 237 sdiv->neg=0; 238 norm_shift+=BN_BITS2; 239 if (!(BN_lshift(snum,num,norm_shift))) goto err; 240 snum->neg=0; 241 242 if (no_branch) 243 { 244 /* Since we don't know whether snum is larger than sdiv, 245 * we pad snum with enough zeroes without changing its 246 * value. 247 */ 248 if (snum->top <= sdiv->top+1) 249 { 250 if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err; 251 for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0; 252 snum->top = sdiv->top + 2; 253 } 254 else 255 { 256 if (bn_wexpand(snum, snum->top + 1) == NULL) goto err; 257 snum->d[snum->top] = 0; 258 snum->top ++; 259 } 260 } 261 262 div_n=sdiv->top; 263 num_n=snum->top; 264 loop=num_n-div_n; 265 /* Lets setup a 'window' into snum 266 * This is the part that corresponds to the current 267 * 'area' being divided */ 268 wnum.neg = 0; 269 wnum.d = &(snum->d[loop]); 270 wnum.top = div_n; 271 /* only needed when BN_ucmp messes up the values between top and max */ 272 wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */ 273 274 /* Get the top 2 words of sdiv */ 275 /* div_n=sdiv->top; */ 276 d0=sdiv->d[div_n-1]; 277 d1=(div_n == 1)?0:sdiv->d[div_n-2]; 278 279 /* pointer to the 'top' of snum */ 280 wnump= &(snum->d[num_n-1]); 281 282 /* Setup to 'res' */ 283 res->neg= (num->neg^divisor->neg); 284 if (!bn_wexpand(res,(loop+1))) goto err; 285 res->top=loop-no_branch; 286 resp= &(res->d[loop-1]); 287 288 /* space for temp */ 289 if (!bn_wexpand(tmp,(div_n+1))) goto err; 290 291 if (!no_branch) 292 { 293 if (BN_ucmp(&wnum,sdiv) >= 0) 294 { 295 /* If BN_DEBUG_RAND is defined BN_ucmp changes (via 296 * bn_pollute) the const bignum arguments => 297 * clean the values between top and max again */ 298 bn_clear_top2max(&wnum); 299 bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n); 300 *resp=1; 301 } 302 else 303 res->top--; 304 } 305 306 /* if res->top == 0 then clear the neg value otherwise decrease 307 * the resp pointer */ 308 if (res->top == 0) 309 res->neg = 0; 310 else 311 resp--; 312 313 for (i=0; i<loop-1; i++, wnump--, resp--) 314 { 315 BN_ULONG q,l0; 316 /* the first part of the loop uses the top two words of 317 * snum and sdiv to calculate a BN_ULONG q such that 318 * | wnum - sdiv * q | < sdiv */ 319 #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM) 320 BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG); 321 q=bn_div_3_words(wnump,d1,d0); 322 #else 323 BN_ULONG n0,n1,rem=0; 324 325 n0=wnump[0]; 326 n1=wnump[-1]; 327 if (n0 == d0) 328 q=BN_MASK2; 329 else /* n0 < d0 */ 330 { 331 #ifdef BN_LLONG 332 BN_ULLONG t2; 333 334 #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words) 335 q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0); 336 #else 337 q=bn_div_words(n0,n1,d0); 338 #ifdef BN_DEBUG_LEVITTE 339 fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\ 340 X) -> 0x%08X\n", 341 n0, n1, d0, q); 342 #endif 343 #endif 344 345 #ifndef REMAINDER_IS_ALREADY_CALCULATED 346 /* 347 * rem doesn't have to be BN_ULLONG. The least we 348 * know it's less that d0, isn't it? 349 */ 350 rem=(n1-q*d0)&BN_MASK2; 351 #endif 352 t2=(BN_ULLONG)d1*q; 353 354 for (;;) 355 { 356 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2])) 357 break; 358 q--; 359 rem += d0; 360 if (rem < d0) break; /* don't let rem overflow */ 361 t2 -= d1; 362 } 363 #else /* !BN_LLONG */ 364 BN_ULONG t2l,t2h; 365 366 q=bn_div_words(n0,n1,d0); 367 #ifdef BN_DEBUG_LEVITTE 368 fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\ 369 X) -> 0x%08X\n", 370 n0, n1, d0, q); 371 #endif 372 #ifndef REMAINDER_IS_ALREADY_CALCULATED 373 rem=(n1-q*d0)&BN_MASK2; 374 #endif 375 376 #if defined(BN_UMULT_LOHI) 377 BN_UMULT_LOHI(t2l,t2h,d1,q); 378 #elif defined(BN_UMULT_HIGH) 379 t2l = d1 * q; 380 t2h = BN_UMULT_HIGH(d1,q); 381 #else 382 { 383 BN_ULONG ql, qh; 384 t2l=LBITS(d1); t2h=HBITS(d1); 385 ql =LBITS(q); qh =HBITS(q); 386 mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */ 387 } 388 #endif 389 390 for (;;) 391 { 392 if ((t2h < rem) || 393 ((t2h == rem) && (t2l <= wnump[-2]))) 394 break; 395 q--; 396 rem += d0; 397 if (rem < d0) break; /* don't let rem overflow */ 398 if (t2l < d1) t2h--; t2l -= d1; 399 } 400 #endif /* !BN_LLONG */ 401 } 402 #endif /* !BN_DIV3W */ 403 404 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q); 405 tmp->d[div_n]=l0; 406 wnum.d--; 407 /* ingore top values of the bignums just sub the two 408 * BN_ULONG arrays with bn_sub_words */ 409 if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1)) 410 { 411 /* Note: As we have considered only the leading 412 * two BN_ULONGs in the calculation of q, sdiv * q 413 * might be greater than wnum (but then (q-1) * sdiv 414 * is less or equal than wnum) 415 */ 416 q--; 417 if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n)) 418 /* we can't have an overflow here (assuming 419 * that q != 0, but if q == 0 then tmp is 420 * zero anyway) */ 421 (*wnump)++; 422 } 423 /* store part of the result */ 424 *resp = q; 425 } 426 bn_correct_top(snum); 427 if (rm != NULL) 428 { 429 /* Keep a copy of the neg flag in num because if rm==num 430 * BN_rshift() will overwrite it. 431 */ 432 int neg = num->neg; 433 BN_rshift(rm,snum,norm_shift); 434 if (!BN_is_zero(rm)) 435 rm->neg = neg; 436 bn_check_top(rm); 437 } 438 if (no_branch) bn_correct_top(res); 439 BN_CTX_end(ctx); 440 return(1); 441 err: 442 bn_check_top(rm); 443 BN_CTX_end(ctx); 444 return(0); 445 } 446 #endif 447
