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| 1 /* |
| 2 * mplogic.c |
| 3 * |
| 4 * Bitwise logical operations on MPI values |
| 5 * |
| 6 * ***** BEGIN LICENSE BLOCK ***** |
| 7 * Version: MPL 1.1/GPL 2.0/LGPL 2.1 |
| 8 * |
| 9 * The contents of this file are subject to the Mozilla Public License Version |
| 10 * 1.1 (the "License"); you may not use this file except in compliance with |
| 11 * the License. You may obtain a copy of the License at |
| 12 * http://www.mozilla.org/MPL/ |
| 13 * |
| 14 * Software distributed under the License is distributed on an "AS IS" basis, |
| 15 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License |
| 16 * for the specific language governing rights and limitations under the |
| 17 * License. |
| 18 * |
| 19 * The Original Code is the MPI Arbitrary Precision Integer Arithmetic library. |
| 20 * |
| 21 * The Initial Developer of the Original Code is |
| 22 * Michael J. Fromberger. |
| 23 * Portions created by the Initial Developer are Copyright (C) 1998 |
| 24 * the Initial Developer. All Rights Reserved. |
| 25 * |
| 26 * Contributor(s): |
| 27 * |
| 28 * Alternatively, the contents of this file may be used under the terms of |
| 29 * either the GNU General Public License Version 2 or later (the "GPL"), or |
| 30 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), |
| 31 * in which case the provisions of the GPL or the LGPL are applicable instead |
| 32 * of those above. If you wish to allow use of your version of this file only |
| 33 * under the terms of either the GPL or the LGPL, and not to allow others to |
| 34 * use your version of this file under the terms of the MPL, indicate your |
| 35 * decision by deleting the provisions above and replace them with the notice |
| 36 * and other provisions required by the GPL or the LGPL. If you do not delete |
| 37 * the provisions above, a recipient may use your version of this file under |
| 38 * the terms of any one of the MPL, the GPL or the LGPL. |
| 39 * |
| 40 * ***** END LICENSE BLOCK ***** */ |
| 41 /* $Id: mplogic.c,v 1.15 2004/04/27 23:04:36 gerv%gerv.net Exp $ */ |
| 42 |
| 43 #define MP_API_COMPATIBLE 1 |
| 44 #include "mpi-priv.h" |
| 45 #include "mplogic.h" |
| 46 |
| 47 /* {{{ Lookup table for population count */ |
| 48 |
| 49 static unsigned char bitc[] = { |
| 50 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, |
| 51 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, |
| 52 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, |
| 53 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, |
| 54 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, |
| 55 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, |
| 56 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, |
| 57 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, |
| 58 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, |
| 59 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, |
| 60 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, |
| 61 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, |
| 62 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, |
| 63 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, |
| 64 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, |
| 65 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8 |
| 66 }; |
| 67 |
| 68 /* }}} */ |
| 69 |
| 70 /*------------------------------------------------------------------------*/ |
| 71 /* |
| 72 mpl_not(a, b) - compute b = ~a |
| 73 mpl_and(a, b, c) - compute c = a & b |
| 74 mpl_or(a, b, c) - compute c = a | b |
| 75 mpl_xor(a, b, c) - compute c = a ^ b |
| 76 */ |
| 77 |
| 78 /* {{{ mpl_not(a, b) */ |
| 79 |
| 80 mp_err mpl_not(mp_int *a, mp_int *b) |
| 81 { |
| 82 mp_err res; |
| 83 unsigned int ix; |
| 84 |
| 85 ARGCHK(a != NULL && b != NULL, MP_BADARG); |
| 86 |
| 87 if((res = mp_copy(a, b)) != MP_OKAY) |
| 88 return res; |
| 89 |
| 90 /* This relies on the fact that the digit type is unsigned */ |
| 91 for(ix = 0; ix < USED(b); ix++) |
| 92 DIGIT(b, ix) = ~DIGIT(b, ix); |
| 93 |
| 94 s_mp_clamp(b); |
| 95 |
| 96 return MP_OKAY; |
| 97 |
| 98 } /* end mpl_not() */ |
| 99 |
| 100 /* }}} */ |
| 101 |
| 102 /* {{{ mpl_and(a, b, c) */ |
| 103 |
| 104 mp_err mpl_and(mp_int *a, mp_int *b, mp_int *c) |
| 105 { |
| 106 mp_int *which, *other; |
| 107 mp_err res; |
| 108 unsigned int ix; |
| 109 |
| 110 ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); |
| 111 |
| 112 if(USED(a) <= USED(b)) { |
| 113 which = a; |
| 114 other = b; |
| 115 } else { |
| 116 which = b; |
| 117 other = a; |
| 118 } |
| 119 |
| 120 if((res = mp_copy(which, c)) != MP_OKAY) |
| 121 return res; |
| 122 |
| 123 for(ix = 0; ix < USED(which); ix++) |
| 124 DIGIT(c, ix) &= DIGIT(other, ix); |
| 125 |
| 126 s_mp_clamp(c); |
| 127 |
| 128 return MP_OKAY; |
| 129 |
| 130 } /* end mpl_and() */ |
| 131 |
| 132 /* }}} */ |
| 133 |
| 134 /* {{{ mpl_or(a, b, c) */ |
| 135 |
| 136 mp_err mpl_or(mp_int *a, mp_int *b, mp_int *c) |
| 137 { |
| 138 mp_int *which, *other; |
| 139 mp_err res; |
| 140 unsigned int ix; |
| 141 |
| 142 ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); |
| 143 |
| 144 if(USED(a) >= USED(b)) { |
| 145 which = a; |
| 146 other = b; |
| 147 } else { |
| 148 which = b; |
| 149 other = a; |
| 150 } |
| 151 |
| 152 if((res = mp_copy(which, c)) != MP_OKAY) |
| 153 return res; |
| 154 |
| 155 for(ix = 0; ix < USED(which); ix++) |
| 156 DIGIT(c, ix) |= DIGIT(other, ix); |
| 157 |
| 158 return MP_OKAY; |
| 159 |
| 160 } /* end mpl_or() */ |
| 161 |
| 162 /* }}} */ |
| 163 |
| 164 /* {{{ mpl_xor(a, b, c) */ |
| 165 |
| 166 mp_err mpl_xor(mp_int *a, mp_int *b, mp_int *c) |
| 167 { |
| 168 mp_int *which, *other; |
| 169 mp_err res; |
| 170 unsigned int ix; |
| 171 |
| 172 ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG); |
| 173 |
| 174 if(USED(a) >= USED(b)) { |
| 175 which = a; |
| 176 other = b; |
| 177 } else { |
| 178 which = b; |
| 179 other = a; |
| 180 } |
| 181 |
| 182 if((res = mp_copy(which, c)) != MP_OKAY) |
| 183 return res; |
| 184 |
| 185 for(ix = 0; ix < USED(which); ix++) |
| 186 DIGIT(c, ix) ^= DIGIT(other, ix); |
| 187 |
| 188 s_mp_clamp(c); |
| 189 |
| 190 return MP_OKAY; |
| 191 |
| 192 } /* end mpl_xor() */ |
| 193 |
| 194 /* }}} */ |
| 195 |
| 196 /*------------------------------------------------------------------------*/ |
| 197 /* |
| 198 mpl_rsh(a, b, d) - b = a >> d |
| 199 mpl_lsh(a, b, d) - b = a << d |
| 200 */ |
| 201 |
| 202 /* {{{ mpl_rsh(a, b, d) */ |
| 203 |
| 204 mp_err mpl_rsh(const mp_int *a, mp_int *b, mp_digit d) |
| 205 { |
| 206 mp_err res; |
| 207 |
| 208 ARGCHK(a != NULL && b != NULL, MP_BADARG); |
| 209 |
| 210 if((res = mp_copy(a, b)) != MP_OKAY) |
| 211 return res; |
| 212 |
| 213 s_mp_div_2d(b, d); |
| 214 |
| 215 return MP_OKAY; |
| 216 |
| 217 } /* end mpl_rsh() */ |
| 218 |
| 219 /* }}} */ |
| 220 |
| 221 /* {{{ mpl_lsh(a, b, d) */ |
| 222 |
| 223 mp_err mpl_lsh(const mp_int *a, mp_int *b, mp_digit d) |
| 224 { |
| 225 mp_err res; |
| 226 |
| 227 ARGCHK(a != NULL && b != NULL, MP_BADARG); |
| 228 |
| 229 if((res = mp_copy(a, b)) != MP_OKAY) |
| 230 return res; |
| 231 |
| 232 return s_mp_mul_2d(b, d); |
| 233 |
| 234 } /* end mpl_lsh() */ |
| 235 |
| 236 /* }}} */ |
| 237 |
| 238 /*------------------------------------------------------------------------*/ |
| 239 /* |
| 240 mpl_num_set(a, num) |
| 241 |
| 242 Count the number of set bits in the binary representation of a. |
| 243 Returns MP_OKAY and sets 'num' to be the number of such bits, if |
| 244 possible. If num is NULL, the result is thrown away, but it is |
| 245 not considered an error. |
| 246 |
| 247 mpl_num_clear() does basically the same thing for clear bits. |
| 248 */ |
| 249 |
| 250 /* {{{ mpl_num_set(a, num) */ |
| 251 |
| 252 mp_err mpl_num_set(mp_int *a, int *num) |
| 253 { |
| 254 unsigned int ix; |
| 255 int db, nset = 0; |
| 256 mp_digit cur; |
| 257 unsigned char reg; |
| 258 |
| 259 ARGCHK(a != NULL, MP_BADARG); |
| 260 |
| 261 for(ix = 0; ix < USED(a); ix++) { |
| 262 cur = DIGIT(a, ix); |
| 263 |
| 264 for(db = 0; db < sizeof(mp_digit); db++) { |
| 265 reg = (unsigned char)(cur >> (CHAR_BIT * db)); |
| 266 |
| 267 nset += bitc[reg]; |
| 268 } |
| 269 } |
| 270 |
| 271 if(num) |
| 272 *num = nset; |
| 273 |
| 274 return MP_OKAY; |
| 275 |
| 276 } /* end mpl_num_set() */ |
| 277 |
| 278 /* }}} */ |
| 279 |
| 280 /* {{{ mpl_num_clear(a, num) */ |
| 281 |
| 282 mp_err mpl_num_clear(mp_int *a, int *num) |
| 283 { |
| 284 unsigned int ix; |
| 285 int db, nset = 0; |
| 286 mp_digit cur; |
| 287 unsigned char reg; |
| 288 |
| 289 ARGCHK(a != NULL, MP_BADARG); |
| 290 |
| 291 for(ix = 0; ix < USED(a); ix++) { |
| 292 cur = DIGIT(a, ix); |
| 293 |
| 294 for(db = 0; db < sizeof(mp_digit); db++) { |
| 295 reg = (unsigned char)(cur >> (CHAR_BIT * db)); |
| 296 |
| 297 nset += bitc[UCHAR_MAX - reg]; |
| 298 } |
| 299 } |
| 300 |
| 301 if(num) |
| 302 *num = nset; |
| 303 |
| 304 return MP_OKAY; |
| 305 |
| 306 |
| 307 } /* end mpl_num_clear() */ |
| 308 |
| 309 /* }}} */ |
| 310 |
| 311 /*------------------------------------------------------------------------*/ |
| 312 /* |
| 313 mpl_parity(a) |
| 314 |
| 315 Determines the bitwise parity of the value given. Returns MP_EVEN |
| 316 if an even number of digits are set, MP_ODD if an odd number are |
| 317 set. |
| 318 */ |
| 319 |
| 320 /* {{{ mpl_parity(a) */ |
| 321 |
| 322 mp_err mpl_parity(mp_int *a) |
| 323 { |
| 324 unsigned int ix; |
| 325 int par = 0; |
| 326 mp_digit cur; |
| 327 |
| 328 ARGCHK(a != NULL, MP_BADARG); |
| 329 |
| 330 for(ix = 0; ix < USED(a); ix++) { |
| 331 int shft = (sizeof(mp_digit) * CHAR_BIT) / 2; |
| 332 |
| 333 cur = DIGIT(a, ix); |
| 334 |
| 335 /* Compute parity for current digit */ |
| 336 while(shft != 0) { |
| 337 cur ^= (cur >> shft); |
| 338 shft >>= 1; |
| 339 } |
| 340 cur &= 1; |
| 341 |
| 342 /* XOR with running parity so far */ |
| 343 par ^= cur; |
| 344 } |
| 345 |
| 346 if(par) |
| 347 return MP_ODD; |
| 348 else |
| 349 return MP_EVEN; |
| 350 |
| 351 } /* end mpl_parity() */ |
| 352 |
| 353 /* }}} */ |
| 354 |
| 355 /* |
| 356 mpl_set_bit |
| 357 |
| 358 Returns MP_OKAY or some error code. |
| 359 Grows a if needed to set a bit to 1. |
| 360 */ |
| 361 mp_err mpl_set_bit(mp_int *a, mp_size bitNum, mp_size value) |
| 362 { |
| 363 mp_size ix; |
| 364 mp_err rv; |
| 365 mp_digit mask; |
| 366 |
| 367 ARGCHK(a != NULL, MP_BADARG); |
| 368 |
| 369 ix = bitNum / MP_DIGIT_BIT; |
| 370 if (ix + 1 > MP_USED(a)) { |
| 371 rv = s_mp_pad(a, ix + 1); |
| 372 if (rv != MP_OKAY) |
| 373 return rv; |
| 374 } |
| 375 |
| 376 bitNum = bitNum % MP_DIGIT_BIT; |
| 377 mask = (mp_digit)1 << bitNum; |
| 378 if (value) |
| 379 MP_DIGIT(a,ix) |= mask; |
| 380 else |
| 381 MP_DIGIT(a,ix) &= ~mask; |
| 382 s_mp_clamp(a); |
| 383 return MP_OKAY; |
| 384 } |
| 385 |
| 386 /* |
| 387 mpl_get_bit |
| 388 |
| 389 returns 0 or 1 or some (negative) error code. |
| 390 */ |
| 391 mp_err mpl_get_bit(const mp_int *a, mp_size bitNum) |
| 392 { |
| 393 mp_size bit, ix; |
| 394 mp_err rv; |
| 395 |
| 396 ARGCHK(a != NULL, MP_BADARG); |
| 397 |
| 398 ix = bitNum / MP_DIGIT_BIT; |
| 399 ARGCHK(ix <= MP_USED(a) - 1, MP_RANGE); |
| 400 |
| 401 bit = bitNum % MP_DIGIT_BIT; |
| 402 rv = (mp_err)(MP_DIGIT(a, ix) >> bit) & 1; |
| 403 return rv; |
| 404 } |
| 405 |
| 406 /* |
| 407 mpl_get_bits |
| 408 - Extracts numBits bits from a, where the least significant extracted bit |
| 409 is bit lsbNum. Returns a negative value if error occurs. |
| 410 - Because sign bit is used to indicate error, maximum number of bits to |
| 411 be returned is the lesser of (a) the number of bits in an mp_digit, or |
| 412 (b) one less than the number of bits in an mp_err. |
| 413 - lsbNum + numbits can be greater than the number of significant bits in |
| 414 integer a, as long as bit lsbNum is in the high order digit of a. |
| 415 */ |
| 416 mp_err mpl_get_bits(const mp_int *a, mp_size lsbNum, mp_size numBits) |
| 417 { |
| 418 mp_size rshift = (lsbNum % MP_DIGIT_BIT); |
| 419 mp_size lsWndx = (lsbNum / MP_DIGIT_BIT); |
| 420 mp_digit * digit = MP_DIGITS(a) + lsWndx; |
| 421 mp_digit mask = ((1 << numBits) - 1); |
| 422 |
| 423 ARGCHK(numBits < CHAR_BIT * sizeof mask, MP_BADARG); |
| 424 ARGCHK(MP_HOWMANY(lsbNum, MP_DIGIT_BIT) <= MP_USED(a), MP_RANGE); |
| 425 |
| 426 if ((numBits + lsbNum % MP_DIGIT_BIT <= MP_DIGIT_BIT) || |
| 427 (lsWndx + 1 >= MP_USED(a))) { |
| 428 mask &= (digit[0] >> rshift); |
| 429 } else { |
| 430 mask &= ((digit[0] >> rshift) | (digit[1] << (MP_DIGIT_BIT - rshift))); |
| 431 } |
| 432 return (mp_err)mask; |
| 433 } |
| 434 |
| 435 /* |
| 436 mpl_significant_bits |
| 437 returns number of significnant bits in abs(a). |
| 438 returns 1 if value is zero. |
| 439 */ |
| 440 mp_err mpl_significant_bits(const mp_int *a) |
| 441 { |
| 442 mp_err bits = 0; |
| 443 int ix; |
| 444 |
| 445 ARGCHK(a != NULL, MP_BADARG); |
| 446 |
| 447 ix = MP_USED(a); |
| 448 for (ix = MP_USED(a); ix > 0; ) { |
| 449 mp_digit d; |
| 450 d = MP_DIGIT(a, --ix); |
| 451 if (d) { |
| 452 while (d) { |
| 453 ++bits; |
| 454 d >>= 1; |
| 455 } |
| 456 break; |
| 457 } |
| 458 } |
| 459 bits += ix * MP_DIGIT_BIT; |
| 460 if (!bits) |
| 461 bits = 1; |
| 462 return bits; |
| 463 } |
| 464 |
| 465 /*------------------------------------------------------------------------*/ |
| 466 /* HERE THERE BE DRAGONS */ |
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