| 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 "bn_lcl.h" |
| 61 | |
| 62 | #define NO_ASM |
| 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 | return(0); |
| 78 | } |
| 79 | |
| 80 | if (BN_ucmp(m,d) < 0) |
| 81 | { |
| 82 | if (rem != NULL) |
| 83 | { if (BN_copy(rem,m) == NULL) return(0); } |
| 84 | if (dv != NULL) BN_zero(dv); |
| 85 | return(1); |
| 86 | } |
| 87 | |
| 88 | BN_CTX_start(ctx); |
| 89 | D = BN_CTX_get(ctx); |
| 90 | if (dv == NULL) dv = BN_CTX_get(ctx); |
| 91 | if (rem == NULL) rem = BN_CTX_get(ctx); |
| 92 | if (D == NULL || dv == NULL || rem == NULL) |
| 93 | goto end; |
| 94 | |
| 95 | nd=BN_num_bits(d); |
| 96 | nm=BN_num_bits(m); |
| 97 | if (BN_copy(D,d) == NULL) goto end; |
| 98 | if (BN_copy(rem,m) == NULL) goto end; |
| 99 | |
| 100 | /* The next 2 are needed so we can do a dv->d[0]|=1 later |
| 101 | * since BN_lshift1 will only work once there is a value :-) */ |
| 102 | BN_zero(dv); |
| 103 | bn_wexpand(dv,1); |
| 104 | dv->top=1; |
| 105 | |
| 106 | if (!BN_lshift(D,D,nm-nd)) goto end; |
| 107 | for (i=nm-nd; i>=0; i--) |
| 108 | { |
| 109 | if (!BN_lshift1(dv,dv)) goto end; |
| 110 | if (BN_ucmp(rem,D) >= 0) |
| 111 | { |
| 112 | dv->d[0]|=1; |
| 113 | if (!BN_usub(rem,rem,D)) goto end; |
| 114 | } |
| 115 | /* CAN IMPROVE (and have now :=) */ |
| 116 | if (!BN_rshift1(D,D)) goto end; |
| 117 | } |
| 118 | rem->neg=BN_is_zero(rem)?0:m->neg; |
| 119 | dv->neg=m->neg^d->neg; |
| 120 | ret = 1; |
| 121 | end: |
| 122 | BN_CTX_end(ctx); |
| 123 | return(ret); |
| 124 | } |
| 125 | |
| 126 | #else |
| 127 | |
| 128 | #if !defined(NO_ASM) && !defined(NO_INLINE_ASM) && !defined(PEDANTIC) && !defined(BN_DIV3W) |
| 129 | # if defined(__GNUC__) && __GNUC__>=2 |
| 130 | # if defined(__i386) |
| 131 | /* |
| 132 | * There were two reasons for implementing this template: |
| 133 | * - GNU C generates a call to a function (__udivdi3 to be exact) |
| 134 | * in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to |
| 135 | * understand why...); |
| 136 | * - divl doesn't only calculate quotient, but also leaves |
| 137 | * remainder in %edx which we can definitely use here:-) |
| 138 | * |
| 139 | * <appro@fy.chalmers.se> |
| 140 | */ |
| 141 | # define bn_div_words(n0,n1,d0) \ |
| 142 | ({ asm volatile ( \ |
| 143 | "divl %4" \ |
| 144 | : "=a"(q), "=d"(rem) \ |
| 145 | : "a"(n1), "d"(n0), "g"(d0) \ |
| 146 | : "cc"); \ |
| 147 | q; \ |
| 148 | }) |
| 149 | # define REMAINDER_IS_ALREADY_CALCULATED |
| 150 | # endif /* __<cpu> */ |
| 151 | # endif /* __GNUC__ */ |
| 152 | #endif /* NO_ASM */ |
| 153 | |
| 154 | int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor, |
| 155 | BN_CTX *ctx) |
| 156 | { |
| 157 | int norm_shift,i,j,loop; |
| 158 | BIGNUM *tmp,wnum,*snum,*sdiv,*res; |
| 159 | BN_ULONG *resp,*wnump; |
| 160 | BN_ULONG d0,d1; |
| 161 | int num_n,div_n; |
| 162 | |
| 163 | bn_check_top(num); |
| 164 | bn_check_top(divisor); |
| 165 | |
| 166 | if (BN_is_zero(divisor)) |
| 167 | { |
| 168 | return(0); |
| 169 | } |
| 170 | |
| 171 | if (BN_ucmp(num,divisor) < 0) |
| 172 | { |
| 173 | if (rm != NULL) |
| 174 | { if (BN_copy(rm,num) == NULL) return(0); } |
| 175 | if (dv != NULL) BN_zero(dv); |
| 176 | return(1); |
| 177 | } |
| 178 | |
| 179 | BN_CTX_start(ctx); |
| 180 | tmp=BN_CTX_get(ctx); |
| 181 | tmp->neg=0; |
| 182 | snum=BN_CTX_get(ctx); |
| 183 | sdiv=BN_CTX_get(ctx); |
| 184 | if (dv == NULL) |
| 185 | res=BN_CTX_get(ctx); |
| 186 | else res=dv; |
| 187 | if (res == NULL) goto err; |
| 188 | |
| 189 | /* First we normalise the numbers */ |
| 190 | norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2); |
| 191 | BN_lshift(sdiv,divisor,norm_shift); |
| 192 | sdiv->neg=0; |
| 193 | norm_shift+=BN_BITS2; |
| 194 | BN_lshift(snum,num,norm_shift); |
| 195 | snum->neg=0; |
| 196 | div_n=sdiv->top; |
| 197 | num_n=snum->top; |
| 198 | loop=num_n-div_n; |
| 199 | |
| 200 | /* Lets setup a 'window' into snum |
| 201 | * This is the part that corresponds to the current |
| 202 | * 'area' being divided */ |
| 203 | BN_init(&wnum); |
| 204 | wnum.d= &(snum->d[loop]); |
| 205 | wnum.top= div_n; |
| 206 | wnum.dmax= snum->dmax+1; /* a bit of a lie */ |
| 207 | |
| 208 | /* Get the top 2 words of sdiv */ |
| 209 | /* i=sdiv->top; */ |
| 210 | d0=sdiv->d[div_n-1]; |
| 211 | d1=(div_n == 1)?0:sdiv->d[div_n-2]; |
| 212 | |
| 213 | /* pointer to the 'top' of snum */ |
| 214 | wnump= &(snum->d[num_n-1]); |
| 215 | |
| 216 | /* Setup to 'res' */ |
| 217 | res->neg= (num->neg^divisor->neg); |
| 218 | if (!bn_wexpand(res,(loop+1))) goto err; |
| 219 | res->top=loop; |
| 220 | resp= &(res->d[loop-1]); |
| 221 | |
| 222 | /* space for temp */ |
| 223 | if (!bn_wexpand(tmp,(div_n+1))) goto err; |
| 224 | |
| 225 | if (BN_ucmp(&wnum,sdiv) >= 0) |
| 226 | { |
| 227 | if (!BN_usub(&wnum,&wnum,sdiv)) goto err; |
| 228 | *resp=1; |
| 229 | res->d[res->top-1]=1; |
| 230 | } |
| 231 | else |
| 232 | res->top--; |
| 233 | resp--; |
| 234 | |
| 235 | for (i=0; i<loop-1; i++) |
| 236 | { |
| 237 | BN_ULONG q,l0; |
| 238 | #ifdef BN_DIV3W |
| 239 | q=bn_div_3_words(wnump,d1,d0); |
| 240 | #else |
| 241 | BN_ULONG n0,n1,rem=0; |
| 242 | |
| 243 | n0=wnump[0]; |
| 244 | n1=wnump[-1]; |
| 245 | if (n0 == d0) |
| 246 | q=BN_MASK2; |
| 247 | else /* n0 < d0 */ |
| 248 | { |
| 249 | #ifdef BN_LLONG |
| 250 | BN_ULLONG t2; |
| 251 | |
| 252 | #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words) |
| 253 | q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0); |
| 254 | #else |
| 255 | q=bn_div_words(n0,n1,d0); |
| 256 | #endif |
| 257 | |
| 258 | #ifndef REMAINDER_IS_ALREADY_CALCULATED |
| 259 | /* |
| 260 | * rem doesn't have to be BN_ULLONG. The least we |
| 261 | * know it's less that d0, isn't it? |
| 262 | */ |
| 263 | rem=(n1-q*d0)&BN_MASK2; |
| 264 | #endif |
| 265 | t2=(BN_ULLONG)d1*q; |
| 266 | |
| 267 | for (;;) |
| 268 | { |
| 269 | if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2])) |
| 270 | break; |
| 271 | q--; |
| 272 | rem += d0; |
| 273 | if (rem < d0) break; /* don't let rem overflow */ |
| 274 | t2 -= d1; |
| 275 | } |
| 276 | #else /* !BN_LLONG */ |
| 277 | BN_ULONG t2l,t2h,ql,qh; |
| 278 | |
| 279 | q=bn_div_words(n0,n1,d0); |
| 280 | #ifndef REMAINDER_IS_ALREADY_CALCULATED |
| 281 | rem=(n1-q*d0)&BN_MASK2; |
| 282 | #endif |
| 283 | |
| 284 | #ifdef BN_UMULT_HIGH |
| 285 | t2l = d1 * q; |
| 286 | t2h = BN_UMULT_HIGH(d1,q); |
| 287 | #else |
| 288 | t2l=LBITS(d1); t2h=HBITS(d1); |
| 289 | ql =LBITS(q); qh =HBITS(q); |
| 290 | mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */ |
| 291 | #endif |
| 292 | |
| 293 | for (;;) |
| 294 | { |
| 295 | if ((t2h < rem) || |
| 296 | ((t2h == rem) && (t2l <= wnump[-2]))) |
| 297 | break; |
| 298 | q--; |
| 299 | rem += d0; |
| 300 | if (rem < d0) break; /* don't let rem overflow */ |
| 301 | if (t2l < d1) t2h--; t2l -= d1; |
| 302 | } |
| 303 | #endif /* !BN_LLONG */ |
| 304 | } |
| 305 | #endif /* !BN_DIV3W */ |
| 306 | |
| 307 | l0=bn_mul_words(tmp->d,sdiv->d,div_n,q); |
| 308 | wnum.d--; wnum.top++; |
| 309 | tmp->d[div_n]=l0; |
| 310 | for (j=div_n+1; j>0; j--) |
| 311 | if (tmp->d[j-1]) break; |
| 312 | tmp->top=j; |
| 313 | |
| 314 | j=wnum.top; |
| 315 | BN_sub(&wnum,&wnum,tmp); |
| 316 | |
| 317 | snum->top=snum->top+wnum.top-j; |
| 318 | |
| 319 | if (wnum.neg) |
| 320 | { |
| 321 | q--; |
| 322 | j=wnum.top; |
| 323 | BN_add(&wnum,&wnum,sdiv); |
| 324 | snum->top+=wnum.top-j; |
| 325 | } |
| 326 | *(resp--)=q; |
| 327 | wnump--; |
| 328 | } |
| 329 | if (rm != NULL) |
| 330 | { |
| 331 | BN_rshift(rm,snum,norm_shift); |
| 332 | rm->neg=num->neg; |
| 333 | } |
| 334 | BN_CTX_end(ctx); |
| 335 | return(1); |
| 336 | err: |
| 337 | BN_CTX_end(ctx); |
| 338 | return(0); |
| 339 | } |
| 340 | |
| 341 | #endif |
| 342 | |
| 343 | /* rem != m */ |
| 344 | int BN_mod(BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx) |
| 345 | { |
| 346 | #if 0 /* The old slow way */ |
| 347 | int i,nm,nd; |
| 348 | BIGNUM *dv; |
| 349 | |
| 350 | if (BN_ucmp(m,d) < 0) |
| 351 | return((BN_copy(rem,m) == NULL)?0:1); |
| 352 | |
| 353 | BN_CTX_start(ctx); |
| 354 | dv=BN_CTX_get(ctx); |
| 355 | |
| 356 | if (!BN_copy(rem,m)) goto err; |
| 357 | |
| 358 | nm=BN_num_bits(rem); |
| 359 | nd=BN_num_bits(d); |
| 360 | if (!BN_lshift(dv,d,nm-nd)) goto err; |
| 361 | for (i=nm-nd; i>=0; i--) |
| 362 | { |
| 363 | if (BN_cmp(rem,dv) >= 0) |
| 364 | { |
| 365 | if (!BN_sub(rem,rem,dv)) goto err; |
| 366 | } |
| 367 | if (!BN_rshift1(dv,dv)) goto err; |
| 368 | } |
| 369 | BN_CTX_end(ctx); |
| 370 | return(1); |
| 371 | err: |
| 372 | BN_CTX_end(ctx); |
| 373 | return(0); |
| 374 | #else |
| 375 | return(BN_div(NULL,rem,m,d,ctx)); |
| 376 | #endif |
| 377 | } |
| 378 | |
| 379 | |
