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 67int 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@fy.chalmers.se> 143 */ 144#undef bn_div_words 145# define bn_div_words(n0,n1,d0) \ 146 ({ asm volatile ( \ 147 "divl %4" \ 148 : "=a"(q), "=d"(rem) \ 149 : "a"(n1), "d"(n0), "g"(d0) \ 150 : "cc"); \ 151 q; \ 152 }) 153# define REMAINDER_IS_ALREADY_CALCULATED 154# elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG) 155 /* 156 * Same story here, but it's 128-bit by 64-bit division. Wow! 157 * <appro@fy.chalmers.se> 158 */ 159# undef bn_div_words 160# define bn_div_words(n0,n1,d0) \ 161 ({ asm volatile ( \ 162 "divq %4" \ 163 : "=a"(q), "=d"(rem) \ 164 : "a"(n1), "d"(n0), "g"(d0) \ 165 : "cc"); \ 166 q; \ 167 }) 168# define REMAINDER_IS_ALREADY_CALCULATED 169# endif /* __<cpu> */ 170# endif /* __GNUC__ */ 171#endif /* OPENSSL_NO_ASM */ 172 173 174/* BN_div computes dv := num / divisor, rounding towards 175 * zero, and sets up rm such that dv*divisor + rm = num holds. 176 * Thus: 177 * dv->neg == num->neg ^ divisor->neg (unless the result is zero) 178 * rm->neg == num->neg (unless the remainder is zero) 179 * If 'dv' or 'rm' is NULL, the respective value is not returned. 180 */ 181int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor, 182 BN_CTX *ctx) 183 { 184 int norm_shift,i,loop; 185 BIGNUM *tmp,wnum,*snum,*sdiv,*res; 186 BN_ULONG *resp,*wnump; 187 BN_ULONG d0,d1; 188 int num_n,div_n; 189 int no_branch=0; 190 191 /* Invalid zero-padding would have particularly bad consequences 192 * in the case of 'num', so don't just rely on bn_check_top() for this one 193 * (bn_check_top() works only for BN_DEBUG builds) */ 194 if (num->top > 0 && num->d[num->top - 1] == 0) 195 { 196 BNerr(BN_F_BN_DIV,BN_R_NOT_INITIALIZED); 197 return 0; 198 } 199 200 bn_check_top(num); 201 202 if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0)) 203 { 204 no_branch=1; 205 } 206 207 bn_check_top(dv); 208 bn_check_top(rm); 209 /* bn_check_top(num); */ /* 'num' has been checked already */ 210 bn_check_top(divisor); 211 212 if (BN_is_zero(divisor)) 213 { 214 BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO); 215 return(0); 216 } 217 218 if (!no_branch && BN_ucmp(num,divisor) < 0) 219 { 220 if (rm != NULL) 221 { if (BN_copy(rm,num) == NULL) return(0); } 222 if (dv != NULL) BN_zero(dv); 223 return(1); 224 } 225 226 BN_CTX_start(ctx); 227 tmp=BN_CTX_get(ctx); 228 snum=BN_CTX_get(ctx); 229 sdiv=BN_CTX_get(ctx); 230 if (dv == NULL) 231 res=BN_CTX_get(ctx); 232 else res=dv; 233 if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL) 234 goto err; 235 236 /* First we normalise the numbers */ 237 norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2); 238 if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err; 239 sdiv->neg=0; 240 norm_shift+=BN_BITS2; 241 if (!(BN_lshift(snum,num,norm_shift))) goto err; 242 snum->neg=0; 243 244 if (no_branch) 245 { 246 /* Since we don't know whether snum is larger than sdiv, 247 * we pad snum with enough zeroes without changing its 248 * value. 249 */ 250 if (snum->top <= sdiv->top+1) 251 { 252 if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err; 253 for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0; 254 snum->top = sdiv->top + 2; 255 } 256 else 257 { 258 if (bn_wexpand(snum, snum->top + 1) == NULL) goto err; 259 snum->d[snum->top] = 0; 260 snum->top ++; 261 } 262 } 263 264 div_n=sdiv->top; 265 num_n=snum->top; 266 loop=num_n-div_n; 267 /* Lets setup a 'window' into snum 268 * This is the part that corresponds to the current 269 * 'area' being divided */ 270 wnum.neg = 0; 271 wnum.d = &(snum->d[loop]); 272 wnum.top = div_n; 273 /* only needed when BN_ucmp messes up the values between top and max */ 274 wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */ 275 276 /* Get the top 2 words of sdiv */ 277 /* div_n=sdiv->top; */ 278 d0=sdiv->d[div_n-1]; 279 d1=(div_n == 1)?0:sdiv->d[div_n-2]; 280 281 /* pointer to the 'top' of snum */ 282 wnump= &(snum->d[num_n-1]); 283 284 /* Setup to 'res' */ 285 res->neg= (num->neg^divisor->neg); 286 if (!bn_wexpand(res,(loop+1))) goto err; 287 res->top=loop-no_branch; 288 resp= &(res->d[loop-1]); 289 290 /* space for temp */ 291 if (!bn_wexpand(tmp,(div_n+1))) goto err; 292 293 if (!no_branch) 294 { 295 if (BN_ucmp(&wnum,sdiv) >= 0) 296 { 297 /* If BN_DEBUG_RAND is defined BN_ucmp changes (via 298 * bn_pollute) the const bignum arguments => 299 * clean the values between top and max again */ 300 bn_clear_top2max(&wnum); 301 bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n); 302 *resp=1; 303 } 304 else 305 res->top--; 306 } 307 308 /* if res->top == 0 then clear the neg value otherwise decrease 309 * the resp pointer */ 310 if (res->top == 0) 311 res->neg = 0; 312 else 313 resp--; 314 315 for (i=0; i<loop-1; i++, wnump--, resp--) 316 { 317 BN_ULONG q,l0; 318 /* the first part of the loop uses the top two words of 319 * snum and sdiv to calculate a BN_ULONG q such that 320 * | wnum - sdiv * q | < sdiv */ 321#if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM) 322 BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG); 323 q=bn_div_3_words(wnump,d1,d0); 324#else 325 BN_ULONG n0,n1,rem=0; 326 327 n0=wnump[0]; 328 n1=wnump[-1]; 329 if (n0 == d0) 330 q=BN_MASK2; 331 else /* n0 < d0 */ 332 { 333#ifdef BN_LLONG 334 BN_ULLONG t2; 335 336#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words) 337 q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0); 338#else 339 q=bn_div_words(n0,n1,d0); 340#ifdef BN_DEBUG_LEVITTE 341 fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\ 342X) -> 0x%08X\n", 343 n0, n1, d0, q); 344#endif 345#endif 346 347#ifndef REMAINDER_IS_ALREADY_CALCULATED 348 /* 349 * rem doesn't have to be BN_ULLONG. The least we 350 * know it's less that d0, isn't it? 351 */ 352 rem=(n1-q*d0)&BN_MASK2; 353#endif 354 t2=(BN_ULLONG)d1*q; 355 356 for (;;) 357 { 358 if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2])) 359 break; 360 q--; 361 rem += d0; 362 if (rem < d0) break; /* don't let rem overflow */ 363 t2 -= d1; 364 } 365#else /* !BN_LLONG */ 366 BN_ULONG t2l,t2h; 367 368 q=bn_div_words(n0,n1,d0); 369#ifdef BN_DEBUG_LEVITTE 370 fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\ 371X) -> 0x%08X\n", 372 n0, n1, d0, q); 373#endif 374#ifndef REMAINDER_IS_ALREADY_CALCULATED 375 rem=(n1-q*d0)&BN_MASK2; 376#endif 377 378#if defined(BN_UMULT_LOHI) 379 BN_UMULT_LOHI(t2l,t2h,d1,q); 380#elif defined(BN_UMULT_HIGH) 381 t2l = d1 * q; 382 t2h = BN_UMULT_HIGH(d1,q); 383#else 384 { 385 BN_ULONG ql, qh; 386 t2l=LBITS(d1); t2h=HBITS(d1); 387 ql =LBITS(q); qh =HBITS(q); 388 mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */ 389 } 390#endif 391 392 for (;;) 393 { 394 if ((t2h < rem) || 395 ((t2h == rem) && (t2l <= wnump[-2]))) 396 break; 397 q--; 398 rem += d0; 399 if (rem < d0) break; /* don't let rem overflow */ 400 if (t2l < d1) t2h--; t2l -= d1; 401 } 402#endif /* !BN_LLONG */ 403 } 404#endif /* !BN_DIV3W */ 405 406 l0=bn_mul_words(tmp->d,sdiv->d,div_n,q); 407 tmp->d[div_n]=l0; 408 wnum.d--; 409 /* ingore top values of the bignums just sub the two 410 * BN_ULONG arrays with bn_sub_words */ 411 if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1)) 412 { 413 /* Note: As we have considered only the leading 414 * two BN_ULONGs in the calculation of q, sdiv * q 415 * might be greater than wnum (but then (q-1) * sdiv 416 * is less or equal than wnum) 417 */ 418 q--; 419 if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n)) 420 /* we can't have an overflow here (assuming 421 * that q != 0, but if q == 0 then tmp is 422 * zero anyway) */ 423 (*wnump)++; 424 } 425 /* store part of the result */ 426 *resp = q; 427 } 428 bn_correct_top(snum); 429 if (rm != NULL) 430 { 431 /* Keep a copy of the neg flag in num because if rm==num 432 * BN_rshift() will overwrite it. 433 */ 434 int neg = num->neg; 435 BN_rshift(rm,snum,norm_shift); 436 if (!BN_is_zero(rm)) 437 rm->neg = neg; 438 bn_check_top(rm); 439 } 440 if (no_branch) bn_correct_top(res); 441 BN_CTX_end(ctx); 442 return(1); 443err: 444 bn_check_top(rm); 445 BN_CTX_end(ctx); 446 return(0); 447 } 448#endif 449