Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 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 | 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 | # 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 | |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 172 | /* BN_div[_no_branch] computes dv := num / divisor, rounding towards |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 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 | */ |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 179 | static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, |
| 180 | const BIGNUM *divisor, BN_CTX *ctx); |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 181 | int 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; |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 189 | |
| 190 | /* Invalid zero-padding would have particularly bad consequences |
| 191 | * in the case of 'num', so don't just rely on bn_check_top() for this one |
| 192 | * (bn_check_top() works only for BN_DEBUG builds) */ |
| 193 | if (num->top > 0 && num->d[num->top - 1] == 0) |
| 194 | { |
| 195 | BNerr(BN_F_BN_DIV,BN_R_NOT_INITIALIZED); |
| 196 | return 0; |
| 197 | } |
| 198 | |
| 199 | bn_check_top(num); |
| 200 | |
| 201 | if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0)) |
| 202 | { |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 203 | return BN_div_no_branch(dv, rm, num, divisor, ctx); |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 204 | } |
| 205 | |
| 206 | bn_check_top(dv); |
| 207 | bn_check_top(rm); |
| 208 | /* bn_check_top(num); */ /* 'num' has been checked already */ |
| 209 | bn_check_top(divisor); |
| 210 | |
| 211 | if (BN_is_zero(divisor)) |
| 212 | { |
| 213 | BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO); |
| 214 | return(0); |
| 215 | } |
| 216 | |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 217 | if (BN_ucmp(num,divisor) < 0) |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 218 | { |
| 219 | if (rm != NULL) |
| 220 | { if (BN_copy(rm,num) == NULL) return(0); } |
| 221 | if (dv != NULL) BN_zero(dv); |
| 222 | return(1); |
| 223 | } |
| 224 | |
| 225 | BN_CTX_start(ctx); |
| 226 | tmp=BN_CTX_get(ctx); |
| 227 | snum=BN_CTX_get(ctx); |
| 228 | sdiv=BN_CTX_get(ctx); |
| 229 | if (dv == NULL) |
| 230 | res=BN_CTX_get(ctx); |
| 231 | else res=dv; |
| 232 | if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL) |
| 233 | goto err; |
| 234 | |
| 235 | /* First we normalise the numbers */ |
| 236 | norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2); |
| 237 | if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err; |
| 238 | sdiv->neg=0; |
| 239 | norm_shift+=BN_BITS2; |
| 240 | if (!(BN_lshift(snum,num,norm_shift))) goto err; |
| 241 | snum->neg=0; |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 242 | div_n=sdiv->top; |
| 243 | num_n=snum->top; |
| 244 | loop=num_n-div_n; |
| 245 | /* Lets setup a 'window' into snum |
| 246 | * This is the part that corresponds to the current |
| 247 | * 'area' being divided */ |
| 248 | wnum.neg = 0; |
| 249 | wnum.d = &(snum->d[loop]); |
| 250 | wnum.top = div_n; |
| 251 | /* only needed when BN_ucmp messes up the values between top and max */ |
| 252 | wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */ |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 253 | |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 254 | /* Get the top 2 words of sdiv */ |
| 255 | /* div_n=sdiv->top; */ |
| 256 | d0=sdiv->d[div_n-1]; |
| 257 | d1=(div_n == 1)?0:sdiv->d[div_n-2]; |
| 258 | |
| 259 | /* pointer to the 'top' of snum */ |
| 260 | wnump= &(snum->d[num_n-1]); |
| 261 | |
| 262 | /* Setup to 'res' */ |
| 263 | res->neg= (num->neg^divisor->neg); |
| 264 | if (!bn_wexpand(res,(loop+1))) goto err; |
| 265 | res->top=loop; |
| 266 | resp= &(res->d[loop-1]); |
| 267 | |
| 268 | /* space for temp */ |
| 269 | if (!bn_wexpand(tmp,(div_n+1))) goto err; |
| 270 | |
| 271 | if (BN_ucmp(&wnum,sdiv) >= 0) |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 272 | { |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 273 | /* If BN_DEBUG_RAND is defined BN_ucmp changes (via |
| 274 | * bn_pollute) the const bignum arguments => |
| 275 | * clean the values between top and max again */ |
| 276 | bn_clear_top2max(&wnum); |
| 277 | bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n); |
| 278 | *resp=1; |
| 279 | } |
| 280 | else |
| 281 | res->top--; |
| 282 | /* if res->top == 0 then clear the neg value otherwise decrease |
| 283 | * the resp pointer */ |
| 284 | if (res->top == 0) |
| 285 | res->neg = 0; |
| 286 | else |
| 287 | resp--; |
| 288 | |
| 289 | for (i=0; i<loop-1; i++, wnump--, resp--) |
| 290 | { |
| 291 | BN_ULONG q,l0; |
| 292 | /* the first part of the loop uses the top two words of |
| 293 | * snum and sdiv to calculate a BN_ULONG q such that |
| 294 | * | wnum - sdiv * q | < sdiv */ |
| 295 | #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM) |
| 296 | BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG); |
| 297 | q=bn_div_3_words(wnump,d1,d0); |
| 298 | #else |
| 299 | BN_ULONG n0,n1,rem=0; |
| 300 | |
| 301 | n0=wnump[0]; |
| 302 | n1=wnump[-1]; |
| 303 | if (n0 == d0) |
| 304 | q=BN_MASK2; |
| 305 | else /* n0 < d0 */ |
| 306 | { |
| 307 | #ifdef BN_LLONG |
| 308 | BN_ULLONG t2; |
| 309 | |
| 310 | #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words) |
| 311 | q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0); |
| 312 | #else |
| 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 | #endif |
| 320 | |
| 321 | #ifndef REMAINDER_IS_ALREADY_CALCULATED |
| 322 | /* |
| 323 | * rem doesn't have to be BN_ULLONG. The least we |
| 324 | * know it's less that d0, isn't it? |
| 325 | */ |
| 326 | rem=(n1-q*d0)&BN_MASK2; |
| 327 | #endif |
| 328 | t2=(BN_ULLONG)d1*q; |
| 329 | |
| 330 | for (;;) |
| 331 | { |
| 332 | if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2])) |
| 333 | break; |
| 334 | q--; |
| 335 | rem += d0; |
| 336 | if (rem < d0) break; /* don't let rem overflow */ |
| 337 | t2 -= d1; |
| 338 | } |
| 339 | #else /* !BN_LLONG */ |
| 340 | BN_ULONG t2l,t2h; |
| 341 | |
| 342 | q=bn_div_words(n0,n1,d0); |
| 343 | #ifdef BN_DEBUG_LEVITTE |
| 344 | fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\ |
| 345 | X) -> 0x%08X\n", |
| 346 | n0, n1, d0, q); |
| 347 | #endif |
| 348 | #ifndef REMAINDER_IS_ALREADY_CALCULATED |
| 349 | rem=(n1-q*d0)&BN_MASK2; |
| 350 | #endif |
| 351 | |
| 352 | #if defined(BN_UMULT_LOHI) |
| 353 | BN_UMULT_LOHI(t2l,t2h,d1,q); |
| 354 | #elif defined(BN_UMULT_HIGH) |
| 355 | t2l = d1 * q; |
| 356 | t2h = BN_UMULT_HIGH(d1,q); |
| 357 | #else |
| 358 | { |
| 359 | BN_ULONG ql, qh; |
| 360 | t2l=LBITS(d1); t2h=HBITS(d1); |
| 361 | ql =LBITS(q); qh =HBITS(q); |
| 362 | mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */ |
| 363 | } |
| 364 | #endif |
| 365 | |
| 366 | for (;;) |
| 367 | { |
| 368 | if ((t2h < rem) || |
| 369 | ((t2h == rem) && (t2l <= wnump[-2]))) |
| 370 | break; |
| 371 | q--; |
| 372 | rem += d0; |
| 373 | if (rem < d0) break; /* don't let rem overflow */ |
| 374 | if (t2l < d1) t2h--; t2l -= d1; |
| 375 | } |
| 376 | #endif /* !BN_LLONG */ |
| 377 | } |
| 378 | #endif /* !BN_DIV3W */ |
| 379 | |
| 380 | l0=bn_mul_words(tmp->d,sdiv->d,div_n,q); |
| 381 | tmp->d[div_n]=l0; |
| 382 | wnum.d--; |
| 383 | /* ingore top values of the bignums just sub the two |
| 384 | * BN_ULONG arrays with bn_sub_words */ |
| 385 | if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1)) |
| 386 | { |
| 387 | /* Note: As we have considered only the leading |
| 388 | * two BN_ULONGs in the calculation of q, sdiv * q |
| 389 | * might be greater than wnum (but then (q-1) * sdiv |
| 390 | * is less or equal than wnum) |
| 391 | */ |
| 392 | q--; |
| 393 | if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n)) |
| 394 | /* we can't have an overflow here (assuming |
| 395 | * that q != 0, but if q == 0 then tmp is |
| 396 | * zero anyway) */ |
| 397 | (*wnump)++; |
| 398 | } |
| 399 | /* store part of the result */ |
| 400 | *resp = q; |
| 401 | } |
| 402 | bn_correct_top(snum); |
| 403 | if (rm != NULL) |
| 404 | { |
| 405 | /* Keep a copy of the neg flag in num because if rm==num |
| 406 | * BN_rshift() will overwrite it. |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 407 | */ |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 408 | int neg = num->neg; |
| 409 | BN_rshift(rm,snum,norm_shift); |
| 410 | if (!BN_is_zero(rm)) |
| 411 | rm->neg = neg; |
| 412 | bn_check_top(rm); |
| 413 | } |
| 414 | BN_CTX_end(ctx); |
| 415 | return(1); |
| 416 | err: |
| 417 | bn_check_top(rm); |
| 418 | BN_CTX_end(ctx); |
| 419 | return(0); |
| 420 | } |
| 421 | |
| 422 | |
| 423 | /* BN_div_no_branch is a special version of BN_div. It does not contain |
| 424 | * branches that may leak sensitive information. |
| 425 | */ |
| 426 | static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, |
| 427 | const BIGNUM *divisor, BN_CTX *ctx) |
| 428 | { |
| 429 | int norm_shift,i,loop; |
| 430 | BIGNUM *tmp,wnum,*snum,*sdiv,*res; |
| 431 | BN_ULONG *resp,*wnump; |
| 432 | BN_ULONG d0,d1; |
| 433 | int num_n,div_n; |
| 434 | |
| 435 | bn_check_top(dv); |
| 436 | bn_check_top(rm); |
| 437 | /* bn_check_top(num); */ /* 'num' has been checked in BN_div() */ |
| 438 | bn_check_top(divisor); |
| 439 | |
| 440 | if (BN_is_zero(divisor)) |
| 441 | { |
| 442 | BNerr(BN_F_BN_DIV_NO_BRANCH,BN_R_DIV_BY_ZERO); |
| 443 | return(0); |
| 444 | } |
| 445 | |
| 446 | BN_CTX_start(ctx); |
| 447 | tmp=BN_CTX_get(ctx); |
| 448 | snum=BN_CTX_get(ctx); |
| 449 | sdiv=BN_CTX_get(ctx); |
| 450 | if (dv == NULL) |
| 451 | res=BN_CTX_get(ctx); |
| 452 | else res=dv; |
| 453 | if (sdiv == NULL || res == NULL) goto err; |
| 454 | |
| 455 | /* First we normalise the numbers */ |
| 456 | norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2); |
| 457 | if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err; |
| 458 | sdiv->neg=0; |
| 459 | norm_shift+=BN_BITS2; |
| 460 | if (!(BN_lshift(snum,num,norm_shift))) goto err; |
| 461 | snum->neg=0; |
| 462 | |
| 463 | /* Since we don't know whether snum is larger than sdiv, |
| 464 | * we pad snum with enough zeroes without changing its |
| 465 | * value. |
| 466 | */ |
| 467 | if (snum->top <= sdiv->top+1) |
| 468 | { |
| 469 | if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err; |
| 470 | for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0; |
| 471 | snum->top = sdiv->top + 2; |
| 472 | } |
| 473 | else |
| 474 | { |
| 475 | if (bn_wexpand(snum, snum->top + 1) == NULL) goto err; |
| 476 | snum->d[snum->top] = 0; |
| 477 | snum->top ++; |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 478 | } |
| 479 | |
| 480 | div_n=sdiv->top; |
| 481 | num_n=snum->top; |
| 482 | loop=num_n-div_n; |
| 483 | /* Lets setup a 'window' into snum |
| 484 | * This is the part that corresponds to the current |
| 485 | * 'area' being divided */ |
| 486 | wnum.neg = 0; |
| 487 | wnum.d = &(snum->d[loop]); |
| 488 | wnum.top = div_n; |
| 489 | /* only needed when BN_ucmp messes up the values between top and max */ |
| 490 | wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */ |
| 491 | |
| 492 | /* Get the top 2 words of sdiv */ |
| 493 | /* div_n=sdiv->top; */ |
| 494 | d0=sdiv->d[div_n-1]; |
| 495 | d1=(div_n == 1)?0:sdiv->d[div_n-2]; |
| 496 | |
| 497 | /* pointer to the 'top' of snum */ |
| 498 | wnump= &(snum->d[num_n-1]); |
| 499 | |
| 500 | /* Setup to 'res' */ |
| 501 | res->neg= (num->neg^divisor->neg); |
| 502 | if (!bn_wexpand(res,(loop+1))) goto err; |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 503 | res->top=loop-1; |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 504 | resp= &(res->d[loop-1]); |
| 505 | |
| 506 | /* space for temp */ |
| 507 | if (!bn_wexpand(tmp,(div_n+1))) goto err; |
| 508 | |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 509 | /* if res->top == 0 then clear the neg value otherwise decrease |
| 510 | * the resp pointer */ |
| 511 | if (res->top == 0) |
| 512 | res->neg = 0; |
| 513 | else |
| 514 | resp--; |
| 515 | |
| 516 | for (i=0; i<loop-1; i++, wnump--, resp--) |
| 517 | { |
| 518 | BN_ULONG q,l0; |
| 519 | /* the first part of the loop uses the top two words of |
| 520 | * snum and sdiv to calculate a BN_ULONG q such that |
| 521 | * | wnum - sdiv * q | < sdiv */ |
| 522 | #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM) |
| 523 | BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG); |
| 524 | q=bn_div_3_words(wnump,d1,d0); |
| 525 | #else |
| 526 | BN_ULONG n0,n1,rem=0; |
| 527 | |
| 528 | n0=wnump[0]; |
| 529 | n1=wnump[-1]; |
| 530 | if (n0 == d0) |
| 531 | q=BN_MASK2; |
| 532 | else /* n0 < d0 */ |
| 533 | { |
| 534 | #ifdef BN_LLONG |
| 535 | BN_ULLONG t2; |
| 536 | |
| 537 | #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words) |
| 538 | q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0); |
| 539 | #else |
| 540 | q=bn_div_words(n0,n1,d0); |
| 541 | #ifdef BN_DEBUG_LEVITTE |
| 542 | fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\ |
| 543 | X) -> 0x%08X\n", |
| 544 | n0, n1, d0, q); |
| 545 | #endif |
| 546 | #endif |
| 547 | |
| 548 | #ifndef REMAINDER_IS_ALREADY_CALCULATED |
| 549 | /* |
| 550 | * rem doesn't have to be BN_ULLONG. The least we |
| 551 | * know it's less that d0, isn't it? |
| 552 | */ |
| 553 | rem=(n1-q*d0)&BN_MASK2; |
| 554 | #endif |
| 555 | t2=(BN_ULLONG)d1*q; |
| 556 | |
| 557 | for (;;) |
| 558 | { |
| 559 | if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2])) |
| 560 | break; |
| 561 | q--; |
| 562 | rem += d0; |
| 563 | if (rem < d0) break; /* don't let rem overflow */ |
| 564 | t2 -= d1; |
| 565 | } |
| 566 | #else /* !BN_LLONG */ |
| 567 | BN_ULONG t2l,t2h; |
| 568 | |
| 569 | q=bn_div_words(n0,n1,d0); |
| 570 | #ifdef BN_DEBUG_LEVITTE |
| 571 | fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\ |
| 572 | X) -> 0x%08X\n", |
| 573 | n0, n1, d0, q); |
| 574 | #endif |
| 575 | #ifndef REMAINDER_IS_ALREADY_CALCULATED |
| 576 | rem=(n1-q*d0)&BN_MASK2; |
| 577 | #endif |
| 578 | |
| 579 | #if defined(BN_UMULT_LOHI) |
| 580 | BN_UMULT_LOHI(t2l,t2h,d1,q); |
| 581 | #elif defined(BN_UMULT_HIGH) |
| 582 | t2l = d1 * q; |
| 583 | t2h = BN_UMULT_HIGH(d1,q); |
| 584 | #else |
| 585 | { |
| 586 | BN_ULONG ql, qh; |
| 587 | t2l=LBITS(d1); t2h=HBITS(d1); |
| 588 | ql =LBITS(q); qh =HBITS(q); |
| 589 | mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */ |
| 590 | } |
| 591 | #endif |
| 592 | |
| 593 | for (;;) |
| 594 | { |
| 595 | if ((t2h < rem) || |
| 596 | ((t2h == rem) && (t2l <= wnump[-2]))) |
| 597 | break; |
| 598 | q--; |
| 599 | rem += d0; |
| 600 | if (rem < d0) break; /* don't let rem overflow */ |
| 601 | if (t2l < d1) t2h--; t2l -= d1; |
| 602 | } |
| 603 | #endif /* !BN_LLONG */ |
| 604 | } |
| 605 | #endif /* !BN_DIV3W */ |
| 606 | |
| 607 | l0=bn_mul_words(tmp->d,sdiv->d,div_n,q); |
| 608 | tmp->d[div_n]=l0; |
| 609 | wnum.d--; |
| 610 | /* ingore top values of the bignums just sub the two |
| 611 | * BN_ULONG arrays with bn_sub_words */ |
| 612 | if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1)) |
| 613 | { |
| 614 | /* Note: As we have considered only the leading |
| 615 | * two BN_ULONGs in the calculation of q, sdiv * q |
| 616 | * might be greater than wnum (but then (q-1) * sdiv |
| 617 | * is less or equal than wnum) |
| 618 | */ |
| 619 | q--; |
| 620 | if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n)) |
| 621 | /* we can't have an overflow here (assuming |
| 622 | * that q != 0, but if q == 0 then tmp is |
| 623 | * zero anyway) */ |
| 624 | (*wnump)++; |
| 625 | } |
| 626 | /* store part of the result */ |
| 627 | *resp = q; |
| 628 | } |
| 629 | bn_correct_top(snum); |
| 630 | if (rm != NULL) |
| 631 | { |
| 632 | /* Keep a copy of the neg flag in num because if rm==num |
| 633 | * BN_rshift() will overwrite it. |
| 634 | */ |
| 635 | int neg = num->neg; |
| 636 | BN_rshift(rm,snum,norm_shift); |
| 637 | if (!BN_is_zero(rm)) |
| 638 | rm->neg = neg; |
| 639 | bn_check_top(rm); |
| 640 | } |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 641 | bn_correct_top(res); |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 642 | BN_CTX_end(ctx); |
| 643 | return(1); |
| 644 | err: |
| 645 | bn_check_top(rm); |
| 646 | BN_CTX_end(ctx); |
| 647 | return(0); |
| 648 | } |
Alexandre Savard | 7541067 | 2012-08-08 09:50:01 -0400 | [diff] [blame] | 649 | |
Alexandre Savard | 1b09e31 | 2012-08-07 20:33:29 -0400 | [diff] [blame] | 650 | #endif |