| 1 | /* |
| 2 | * Copyright 2015 INRIA Paris-Rocquencourt |
| 3 | * |
| 4 | * Use of this software is governed by the MIT license |
| 5 | * |
| 6 | * Written by Michael Kruse, INRIA Paris-Rocquencourt, |
| 7 | * Domaine de Voluceau, Rocquenqourt, B.P. 105, |
| 8 | * 78153 Le Chesnay Cedex France |
| 9 | */ |
| 10 | #ifndef ISL_INT_SIOIMATH_H |
| 11 | #define ISL_INT_SIOIMATH_H |
| 12 | |
| 13 | #include <inttypes.h> |
| 14 | #include <limits.h> |
| 15 | #include <stdint.h> |
| 16 | #include <stdlib.h> |
| 17 | |
| 18 | #include <isl_imath.h> |
| 19 | #include <isl/hash.h> |
| 20 | |
| 21 | #define ARRAY_SIZE(array) (sizeof(array)/sizeof(*array)) |
| 22 | |
| 23 | /* Visual Studio before VS2015 does not support the inline keyword when |
| 24 | * compiling in C mode because it was introduced in C99 which it does not |
| 25 | * officially support. Instead, it has a proprietary extension using __inline. |
| 26 | */ |
| 27 | #if defined(_MSC_VER) && (_MSC_VER < 1900) |
| 28 | #define inline __inline |
| 29 | #endif |
| 30 | |
| 31 | /* The type to represent integers optimized for small values. It is either a |
| 32 | * pointer to an mp_int ( = mpz_t*; big representation) or an int32_t (small |
| 33 | * represenation) with a discriminator at the least significant bit. In big |
| 34 | * representation it will be always zero because of heap alignment. It is set |
| 35 | * to 1 for small representation and use the 32 most significant bits for the |
| 36 | * int32_t. |
| 37 | * |
| 38 | * Structure on 64 bit machines, with 8-byte aligment (3 bits): |
| 39 | * |
| 40 | * Big representation: |
| 41 | * MSB LSB |
| 42 | * |------------------------------------------------------------000 |
| 43 | * | mpz_t* | |
| 44 | * | != NULL | |
| 45 | * |
| 46 | * Small representation: |
| 47 | * MSB 32 LSB |
| 48 | * |------------------------------|00000000000000000000000000000001 |
| 49 | * | int32_t | |
| 50 | * | 2147483647 ... -2147483647 | |
| 51 | * ^ |
| 52 | * | |
| 53 | * discriminator bit |
| 54 | * |
| 55 | * On 32 bit machines isl_sioimath type is blown up to 8 bytes, i.e. |
| 56 | * isl_sioimath is guaranteed to be at least 8 bytes. This is to ensure the |
| 57 | * int32_t can be hidden in that type without data loss. In the future we might |
| 58 | * optimize this to use 31 hidden bits in a 32 bit pointer. We may also use 63 |
| 59 | * bits on 64 bit machines, but this comes with the cost of additional overflow |
| 60 | * checks because there is no standardized 128 bit integer we could expand to. |
| 61 | * |
| 62 | * We use native integer types and avoid union structures to avoid assumptions |
| 63 | * on the machine's endianness. |
| 64 | * |
| 65 | * This implementation makes the following assumptions: |
| 66 | * - long can represent any int32_t |
| 67 | * - mp_small is signed long |
| 68 | * - mp_usmall is unsigned long |
| 69 | * - adresses returned by malloc are aligned to 2-byte boundaries (leastmost |
| 70 | * bit is zero) |
| 71 | */ |
| 72 | #if UINT64_MAX > UINTPTR_MAX |
| 73 | typedef uint64_t isl_sioimath; |
| 74 | #else |
| 75 | typedef uintptr_t isl_sioimath; |
| 76 | #endif |
| 77 | |
| 78 | /* The negation of the smallest possible number in int32_t, INT32_MIN |
| 79 | * (0x80000000u, -2147483648), cannot be represented in an int32_t, therefore |
| 80 | * every operation that may produce this value needs to special-case it. |
| 81 | * The operations are: |
| 82 | * abs(INT32_MIN) |
| 83 | * -INT32_MIN (negation) |
| 84 | * -1 * INT32_MIN (multiplication) |
| 85 | * INT32_MIN/-1 (any division: divexact, fdiv, cdiv, tdiv) |
| 86 | * To avoid checking these cases, we exclude INT32_MIN from small |
| 87 | * representation. |
| 88 | */ |
| 89 | #define ISL_SIOIMATH_SMALL_MIN (-INT32_MAX) |
| 90 | |
| 91 | /* Largest possible number in small representation */ |
| 92 | #define ISL_SIOIMATH_SMALL_MAX INT32_MAX |
| 93 | |
| 94 | /* Used for function parameters the function modifies. */ |
| 95 | typedef isl_sioimath *isl_sioimath_ptr; |
| 96 | |
| 97 | /* Used for function parameters that are read-only. */ |
| 98 | typedef isl_sioimath isl_sioimath_src; |
| 99 | |
| 100 | /* Return whether the argument is stored in small representation. |
| 101 | */ |
| 102 | inline int isl_sioimath_is_small(isl_sioimath val) |
| 103 | { |
| 104 | return val & 0x00000001; |
| 105 | } |
| 106 | |
| 107 | /* Return whether the argument is stored in big representation. |
| 108 | */ |
| 109 | inline int isl_sioimath_is_big(isl_sioimath val) |
| 110 | { |
| 111 | return !isl_sioimath_is_small(val); |
| 112 | } |
| 113 | |
| 114 | /* Get the number of an isl_int in small representation. Result is undefined if |
| 115 | * val is not stored in that format. |
| 116 | */ |
| 117 | inline int32_t isl_sioimath_get_small(isl_sioimath val) |
| 118 | { |
| 119 | return val >> 32; |
| 120 | } |
| 121 | |
| 122 | /* Get the number of an in isl_int in big representation. Result is undefined if |
| 123 | * val is not stored in that format. |
| 124 | */ |
| 125 | inline mp_int isl_sioimath_get_big(isl_sioimath val) |
| 126 | { |
| 127 | return (mp_int)(uintptr_t) val; |
| 128 | } |
| 129 | |
| 130 | /* Return 1 if val is stored in small representation and store its value to |
| 131 | * small. We rely on the compiler to optimize the isl_sioimath_get_small such |
| 132 | * that the shift is moved into the branch that executes in case of small |
| 133 | * representation. If there is no such branch, then a single shift is still |
| 134 | * cheaper than introducing branching code. |
| 135 | */ |
| 136 | inline int isl_sioimath_decode_small(isl_sioimath val, int32_t *small) |
| 137 | { |
| 138 | *small = isl_sioimath_get_small(val); |
| 139 | return isl_sioimath_is_small(val); |
| 140 | } |
| 141 | |
| 142 | /* Return 1 if val is stored in big representation and store its value to big. |
| 143 | */ |
| 144 | inline int isl_sioimath_decode_big(isl_sioimath val, mp_int *big) |
| 145 | { |
| 146 | *big = isl_sioimath_get_big(val); |
| 147 | return isl_sioimath_is_big(val); |
| 148 | } |
| 149 | |
| 150 | /* Encode a small representation into an isl_int. |
| 151 | */ |
| 152 | inline isl_sioimath isl_sioimath_encode_small(int32_t val) |
| 153 | { |
| 154 | return ((isl_sioimath) val) << 32 | 0x00000001; |
| 155 | } |
| 156 | |
| 157 | /* Encode a big representation. |
| 158 | */ |
| 159 | inline isl_sioimath isl_sioimath_encode_big(mp_int val) |
| 160 | { |
| 161 | return (isl_sioimath)(uintptr_t) val; |
| 162 | } |
| 163 | |
| 164 | /* A common situation is to call an IMath function with at least one argument |
| 165 | * that is currently in small representation or an integer parameter, i.e. a big |
| 166 | * representation of the same number is required. Promoting the original |
| 167 | * argument comes with multiple problems, such as modifying a read-only |
| 168 | * argument, the responsibility of deallocation and the execution cost. Instead, |
| 169 | * we make a copy by 'faking' the IMath internal structure. |
| 170 | * |
| 171 | * We reserve the maximum number of required digits on the stack to avoid heap |
| 172 | * allocations. |
| 173 | * |
| 174 | * mp_digit can be uint32_t or uint16_t. This code must work for little and big |
| 175 | * endian digits. The structure for an uint64_t argument and 32-bit mp_digits is |
| 176 | * sketched below. |
| 177 | * |
| 178 | * |----------------------------| |
| 179 | * uint64_t |
| 180 | * |
| 181 | * |-------------||-------------| |
| 182 | * mp_digit mp_digit |
| 183 | * digits[1] digits[0] |
| 184 | * Most sig digit Least sig digit |
| 185 | */ |
| 186 | typedef struct { |
| 187 | mpz_t big; |
| 188 | mp_digit digits[(sizeof(uintmax_t) + sizeof(mp_digit) - 1) / |
| 189 | sizeof(mp_digit)]; |
| 190 | } isl_sioimath_scratchspace_t; |
| 191 | |
| 192 | /* Convert a native integer to IMath's digit representation. A native integer |
| 193 | * might be big- or little endian, but IMath always stores the least significant |
| 194 | * digit in the lowest array indices. memcpy therefore is not possible. |
| 195 | * |
| 196 | * We also have to consider that long and mp_digit can be of different sizes, |
| 197 | * depending on the compiler (LP64, LLP64) and IMath's USE_64BIT_WORDS. This |
| 198 | * macro should work for all of them. |
| 199 | * |
| 200 | * "used" is set to the number of written digits. It must be minimal (IMath |
| 201 | * checks zeroness using the used field), but always at least one. Also note |
| 202 | * that the result of num>>(sizeof(num)*CHAR_BIT) is undefined. |
| 203 | */ |
| 204 | #define ISL_SIOIMATH_TO_DIGITS(num, digits, used) \ |
| 205 | do { \ |
| 206 | int i = 0; \ |
| 207 | do { \ |
| 208 | (digits)[i] = \ |
| 209 | ((num) >> (sizeof(mp_digit) * CHAR_BIT * i)); \ |
| 210 | i += 1; \ |
| 211 | if (i >= (sizeof(num) + sizeof(mp_digit) - 1) / \ |
| 212 | sizeof(mp_digit)) \ |
| 213 | break; \ |
| 214 | if (((num) >> (sizeof(mp_digit) * CHAR_BIT * i)) == 0) \ |
| 215 | break; \ |
| 216 | } while (1); \ |
| 217 | (used) = i; \ |
| 218 | } while (0) |
| 219 | |
| 220 | inline void isl_siomath_uint32_to_digits(uint32_t num, mp_digit *digits, |
| 221 | mp_size *used) |
| 222 | { |
| 223 | ISL_SIOIMATH_TO_DIGITS(num, digits, *used); |
| 224 | } |
| 225 | |
| 226 | inline void isl_siomath_ulong_to_digits(unsigned long num, mp_digit *digits, |
| 227 | mp_size *used) |
| 228 | { |
| 229 | ISL_SIOIMATH_TO_DIGITS(num, digits, *used); |
| 230 | } |
| 231 | |
| 232 | inline void isl_siomath_uint64_to_digits(uint64_t num, mp_digit *digits, |
| 233 | mp_size *used) |
| 234 | { |
| 235 | ISL_SIOIMATH_TO_DIGITS(num, digits, *used); |
| 236 | } |
| 237 | |
| 238 | /* Get the IMath representation of an isl_int without modifying it. |
| 239 | * For the case it is not in big representation yet, pass some scratch space we |
| 240 | * can use to store the big representation in. |
| 241 | * In order to avoid requiring init and free on the scratch space, we directly |
| 242 | * modify the internal representation. |
| 243 | * |
| 244 | * The name derives from its indented use: getting the big representation of an |
| 245 | * input (src) argument. |
| 246 | */ |
| 247 | inline mp_int isl_sioimath_bigarg_src(isl_sioimath arg, |
| 248 | isl_sioimath_scratchspace_t *scratch) |
| 249 | { |
| 250 | mp_int big; |
| 251 | int32_t small; |
| 252 | uint32_t num; |
| 253 | |
| 254 | if (isl_sioimath_decode_big(val: arg, big: &big)) |
| 255 | return big; |
| 256 | |
| 257 | small = isl_sioimath_get_small(val: arg); |
| 258 | scratch->big.digits = scratch->digits; |
| 259 | scratch->big.alloc = ARRAY_SIZE(scratch->digits); |
| 260 | if (small >= 0) { |
| 261 | scratch->big.sign = MP_ZPOS; |
| 262 | num = small; |
| 263 | } else { |
| 264 | scratch->big.sign = MP_NEG; |
| 265 | num = -small; |
| 266 | } |
| 267 | |
| 268 | isl_siomath_uint32_to_digits(num, digits: scratch->digits, used: &scratch->big.used); |
| 269 | return &scratch->big; |
| 270 | } |
| 271 | |
| 272 | /* Create a temporary IMath mp_int for a signed long. |
| 273 | */ |
| 274 | inline mp_int isl_sioimath_siarg_src(signed long arg, |
| 275 | isl_sioimath_scratchspace_t *scratch) |
| 276 | { |
| 277 | unsigned long num; |
| 278 | |
| 279 | scratch->big.digits = scratch->digits; |
| 280 | scratch->big.alloc = ARRAY_SIZE(scratch->digits); |
| 281 | if (arg >= 0) { |
| 282 | scratch->big.sign = MP_ZPOS; |
| 283 | num = arg; |
| 284 | } else { |
| 285 | scratch->big.sign = MP_NEG; |
| 286 | num = (arg == LONG_MIN) ? ((unsigned long) LONG_MAX) + 1 : -arg; |
| 287 | } |
| 288 | |
| 289 | isl_siomath_ulong_to_digits(num, digits: scratch->digits, used: &scratch->big.used); |
| 290 | return &scratch->big; |
| 291 | } |
| 292 | |
| 293 | /* Create a temporary IMath mp_int for an int64_t. |
| 294 | */ |
| 295 | inline mp_int isl_sioimath_si64arg_src(int64_t arg, |
| 296 | isl_sioimath_scratchspace_t *scratch) |
| 297 | { |
| 298 | uint64_t num; |
| 299 | |
| 300 | scratch->big.digits = scratch->digits; |
| 301 | scratch->big.alloc = ARRAY_SIZE(scratch->digits); |
| 302 | if (arg >= 0) { |
| 303 | scratch->big.sign = MP_ZPOS; |
| 304 | num = arg; |
| 305 | } else { |
| 306 | scratch->big.sign = MP_NEG; |
| 307 | num = (arg == INT64_MIN) ? ((uint64_t) INT64_MAX) + 1 : -arg; |
| 308 | } |
| 309 | |
| 310 | isl_siomath_uint64_to_digits(num, digits: scratch->digits, used: &scratch->big.used); |
| 311 | return &scratch->big; |
| 312 | } |
| 313 | |
| 314 | /* Create a temporary IMath mp_int for an unsigned long. |
| 315 | */ |
| 316 | inline mp_int isl_sioimath_uiarg_src(unsigned long arg, |
| 317 | isl_sioimath_scratchspace_t *scratch) |
| 318 | { |
| 319 | scratch->big.digits = scratch->digits; |
| 320 | scratch->big.alloc = ARRAY_SIZE(scratch->digits); |
| 321 | scratch->big.sign = MP_ZPOS; |
| 322 | |
| 323 | isl_siomath_ulong_to_digits(num: arg, digits: scratch->digits, used: &scratch->big.used); |
| 324 | return &scratch->big; |
| 325 | } |
| 326 | |
| 327 | /* Ensure big representation. Does not preserve the current number. |
| 328 | * Callers may use the fact that the value _is_ preserved if the presentation |
| 329 | * was big before. |
| 330 | */ |
| 331 | inline mp_int isl_sioimath_reinit_big(isl_sioimath_ptr ptr) |
| 332 | { |
| 333 | if (isl_sioimath_is_small(val: *ptr)) |
| 334 | *ptr = isl_sioimath_encode_big(val: mp_int_alloc()); |
| 335 | return isl_sioimath_get_big(val: *ptr); |
| 336 | } |
| 337 | |
| 338 | /* Set ptr to a number in small representation. |
| 339 | */ |
| 340 | inline void isl_sioimath_set_small(isl_sioimath_ptr ptr, int32_t val) |
| 341 | { |
| 342 | if (isl_sioimath_is_big(val: *ptr)) |
| 343 | mp_int_free(z: isl_sioimath_get_big(val: *ptr)); |
| 344 | *ptr = isl_sioimath_encode_small(val); |
| 345 | } |
| 346 | |
| 347 | /* Set ptr to val, choosing small representation if possible. |
| 348 | */ |
| 349 | inline void isl_sioimath_set_int32(isl_sioimath_ptr ptr, int32_t val) |
| 350 | { |
| 351 | if (ISL_SIOIMATH_SMALL_MIN <= val && val <= ISL_SIOIMATH_SMALL_MAX) { |
| 352 | isl_sioimath_set_small(ptr, val); |
| 353 | return; |
| 354 | } |
| 355 | |
| 356 | mp_int_init_value(z: isl_sioimath_reinit_big(ptr), value: val); |
| 357 | } |
| 358 | |
| 359 | /* Assign an int64_t number using small representation if possible. |
| 360 | */ |
| 361 | inline void isl_sioimath_set_int64(isl_sioimath_ptr ptr, int64_t val) |
| 362 | { |
| 363 | if (ISL_SIOIMATH_SMALL_MIN <= val && val <= ISL_SIOIMATH_SMALL_MAX) { |
| 364 | isl_sioimath_set_small(ptr, val); |
| 365 | return; |
| 366 | } |
| 367 | |
| 368 | isl_sioimath_scratchspace_t scratch; |
| 369 | mp_int_copy(a: isl_sioimath_si64arg_src(arg: val, scratch: &scratch), |
| 370 | c: isl_sioimath_reinit_big(ptr)); |
| 371 | } |
| 372 | |
| 373 | /* Convert to big representation while preserving the current number. |
| 374 | */ |
| 375 | inline void isl_sioimath_promote(isl_sioimath_ptr dst) |
| 376 | { |
| 377 | int32_t small; |
| 378 | |
| 379 | if (isl_sioimath_is_big(val: *dst)) |
| 380 | return; |
| 381 | |
| 382 | small = isl_sioimath_get_small(val: *dst); |
| 383 | mp_int_set_value(z: isl_sioimath_reinit_big(ptr: dst), value: small); |
| 384 | } |
| 385 | |
| 386 | /* Convert to small representation while preserving the current number. Does |
| 387 | * nothing if dst doesn't fit small representation. |
| 388 | */ |
| 389 | inline void isl_sioimath_try_demote(isl_sioimath_ptr dst) |
| 390 | { |
| 391 | mp_small small; |
| 392 | |
| 393 | if (isl_sioimath_is_small(val: *dst)) |
| 394 | return; |
| 395 | |
| 396 | if (mp_int_to_int(z: isl_sioimath_get_big(val: *dst), out: &small) != MP_OK) |
| 397 | return; |
| 398 | |
| 399 | if (ISL_SIOIMATH_SMALL_MIN <= small && small <= ISL_SIOIMATH_SMALL_MAX) |
| 400 | isl_sioimath_set_small(ptr: dst, val: small); |
| 401 | } |
| 402 | |
| 403 | /* Initialize an isl_int. The implicit value is 0 in small representation. |
| 404 | */ |
| 405 | inline void isl_sioimath_init(isl_sioimath_ptr dst) |
| 406 | { |
| 407 | *dst = isl_sioimath_encode_small(val: 0); |
| 408 | } |
| 409 | |
| 410 | /* Free the resources taken by an isl_int. |
| 411 | */ |
| 412 | inline void isl_sioimath_clear(isl_sioimath_ptr dst) |
| 413 | { |
| 414 | if (isl_sioimath_is_small(val: *dst)) |
| 415 | return; |
| 416 | |
| 417 | mp_int_free(z: isl_sioimath_get_big(val: *dst)); |
| 418 | } |
| 419 | |
| 420 | /* Copy the value of one isl_int to another. |
| 421 | */ |
| 422 | inline void isl_sioimath_set(isl_sioimath_ptr dst, isl_sioimath_src val) |
| 423 | { |
| 424 | if (isl_sioimath_is_small(val)) { |
| 425 | isl_sioimath_set_small(ptr: dst, val: isl_sioimath_get_small(val)); |
| 426 | return; |
| 427 | } |
| 428 | |
| 429 | mp_int_copy(a: isl_sioimath_get_big(val), c: isl_sioimath_reinit_big(ptr: dst)); |
| 430 | } |
| 431 | |
| 432 | /* Store a signed long into an isl_int. |
| 433 | */ |
| 434 | inline void isl_sioimath_set_si(isl_sioimath_ptr dst, long val) |
| 435 | { |
| 436 | if (ISL_SIOIMATH_SMALL_MIN <= val && val <= ISL_SIOIMATH_SMALL_MAX) { |
| 437 | isl_sioimath_set_small(ptr: dst, val); |
| 438 | return; |
| 439 | } |
| 440 | |
| 441 | mp_int_set_value(z: isl_sioimath_reinit_big(ptr: dst), value: val); |
| 442 | } |
| 443 | |
| 444 | /* Store an unsigned long into an isl_int. |
| 445 | */ |
| 446 | inline void isl_sioimath_set_ui(isl_sioimath_ptr dst, unsigned long val) |
| 447 | { |
| 448 | if (val <= ISL_SIOIMATH_SMALL_MAX) { |
| 449 | isl_sioimath_set_small(ptr: dst, val); |
| 450 | return; |
| 451 | } |
| 452 | |
| 453 | mp_int_set_uvalue(z: isl_sioimath_reinit_big(ptr: dst), uvalue: val); |
| 454 | } |
| 455 | |
| 456 | /* Return whether a number can be represented by a signed long. |
| 457 | */ |
| 458 | inline int isl_sioimath_fits_slong(isl_sioimath_src val) |
| 459 | { |
| 460 | mp_small dummy; |
| 461 | |
| 462 | if (isl_sioimath_is_small(val)) |
| 463 | return 1; |
| 464 | |
| 465 | return mp_int_to_int(z: isl_sioimath_get_big(val), out: &dummy) == MP_OK; |
| 466 | } |
| 467 | |
| 468 | /* Return a number as signed long. Result is undefined if the number cannot be |
| 469 | * represented as long. |
| 470 | */ |
| 471 | inline long isl_sioimath_get_si(isl_sioimath_src val) |
| 472 | { |
| 473 | mp_small result; |
| 474 | |
| 475 | if (isl_sioimath_is_small(val)) |
| 476 | return isl_sioimath_get_small(val); |
| 477 | |
| 478 | mp_int_to_int(z: isl_sioimath_get_big(val), out: &result); |
| 479 | return result; |
| 480 | } |
| 481 | |
| 482 | /* Return whether a number can be represented as unsigned long. |
| 483 | */ |
| 484 | inline int isl_sioimath_fits_ulong(isl_sioimath_src val) |
| 485 | { |
| 486 | mp_usmall dummy; |
| 487 | |
| 488 | if (isl_sioimath_is_small(val)) |
| 489 | return isl_sioimath_get_small(val) >= 0; |
| 490 | |
| 491 | return mp_int_to_uint(z: isl_sioimath_get_big(val), out: &dummy) == MP_OK; |
| 492 | } |
| 493 | |
| 494 | /* Return a number as unsigned long. Result is undefined if the number cannot be |
| 495 | * represented as unsigned long. |
| 496 | */ |
| 497 | inline unsigned long isl_sioimath_get_ui(isl_sioimath_src val) |
| 498 | { |
| 499 | mp_usmall result; |
| 500 | |
| 501 | if (isl_sioimath_is_small(val)) |
| 502 | return isl_sioimath_get_small(val); |
| 503 | |
| 504 | mp_int_to_uint(z: isl_sioimath_get_big(val), out: &result); |
| 505 | return result; |
| 506 | } |
| 507 | |
| 508 | /* Return a number as floating point value. |
| 509 | */ |
| 510 | inline double isl_sioimath_get_d(isl_sioimath_src val) |
| 511 | { |
| 512 | mp_int big; |
| 513 | double result = 0; |
| 514 | int i; |
| 515 | |
| 516 | if (isl_sioimath_is_small(val)) |
| 517 | return isl_sioimath_get_small(val); |
| 518 | |
| 519 | big = isl_sioimath_get_big(val); |
| 520 | for (i = 0; i < big->used; ++i) |
| 521 | result = result * (double) ((uintmax_t) MP_DIGIT_MAX + 1) + |
| 522 | (double) big->digits[i]; |
| 523 | |
| 524 | if (big->sign == MP_NEG) |
| 525 | result = -result; |
| 526 | |
| 527 | return result; |
| 528 | } |
| 529 | |
| 530 | /* Format a number as decimal string. |
| 531 | * |
| 532 | * The largest possible string from small representation is 12 characters |
| 533 | * ("-2147483647"). |
| 534 | */ |
| 535 | inline char *isl_sioimath_get_str(isl_sioimath_src val) |
| 536 | { |
| 537 | char *result; |
| 538 | |
| 539 | if (isl_sioimath_is_small(val)) { |
| 540 | result = malloc(size: 12); |
| 541 | snprintf(s: result, maxlen: 12, format: "%" PRIi32, isl_sioimath_get_small(val)); |
| 542 | return result; |
| 543 | } |
| 544 | |
| 545 | return impz_get_str(NULL, radix: 10, op: isl_sioimath_get_big(val)); |
| 546 | } |
| 547 | |
| 548 | /* Return the absolute value. |
| 549 | */ |
| 550 | inline void isl_sioimath_abs(isl_sioimath_ptr dst, isl_sioimath_src arg) |
| 551 | { |
| 552 | if (isl_sioimath_is_small(val: arg)) { |
| 553 | isl_sioimath_set_small(ptr: dst, val: labs(x: isl_sioimath_get_small(val: arg))); |
| 554 | return; |
| 555 | } |
| 556 | |
| 557 | mp_int_abs(a: isl_sioimath_get_big(val: arg), c: isl_sioimath_reinit_big(ptr: dst)); |
| 558 | } |
| 559 | |
| 560 | /* Return the negation of a number. |
| 561 | */ |
| 562 | inline void isl_sioimath_neg(isl_sioimath_ptr dst, isl_sioimath_src arg) |
| 563 | { |
| 564 | if (isl_sioimath_is_small(val: arg)) { |
| 565 | isl_sioimath_set_small(ptr: dst, val: -isl_sioimath_get_small(val: arg)); |
| 566 | return; |
| 567 | } |
| 568 | |
| 569 | mp_int_neg(a: isl_sioimath_get_big(val: arg), c: isl_sioimath_reinit_big(ptr: dst)); |
| 570 | } |
| 571 | |
| 572 | /* Swap two isl_ints. |
| 573 | * |
| 574 | * isl_sioimath can be copied bytewise; nothing depends on its address. It can |
| 575 | * also be stored in a CPU register. |
| 576 | */ |
| 577 | inline void isl_sioimath_swap(isl_sioimath_ptr lhs, isl_sioimath_ptr rhs) |
| 578 | { |
| 579 | isl_sioimath tmp = *lhs; |
| 580 | *lhs = *rhs; |
| 581 | *rhs = tmp; |
| 582 | } |
| 583 | |
| 584 | /* Add an unsigned long to the number. |
| 585 | * |
| 586 | * On LP64 unsigned long exceeds the range of an int64_t, therefore we check in |
| 587 | * advance whether small representation possibly overflows. |
| 588 | */ |
| 589 | inline void isl_sioimath_add_ui(isl_sioimath_ptr dst, isl_sioimath lhs, |
| 590 | unsigned long rhs) |
| 591 | { |
| 592 | int32_t smalllhs; |
| 593 | isl_sioimath_scratchspace_t lhsscratch; |
| 594 | |
| 595 | if (isl_sioimath_decode_small(val: lhs, small: &smalllhs) && |
| 596 | (rhs <= (uint64_t) INT64_MAX - (uint64_t) ISL_SIOIMATH_SMALL_MAX)) { |
| 597 | isl_sioimath_set_int64(ptr: dst, val: (int64_t) smalllhs + rhs); |
| 598 | return; |
| 599 | } |
| 600 | |
| 601 | impz_add_ui(rop: isl_sioimath_reinit_big(ptr: dst), |
| 602 | op1: isl_sioimath_bigarg_src(arg: lhs, scratch: &lhsscratch), op2: rhs); |
| 603 | isl_sioimath_try_demote(dst); |
| 604 | } |
| 605 | |
| 606 | /* Subtract an unsigned long. |
| 607 | * |
| 608 | * On LP64 unsigned long exceeds the range of an int64_t. If |
| 609 | * ISL_SIOIMATH_SMALL_MIN-rhs>=INT64_MIN we can do the calculation using int64_t |
| 610 | * without risking an overflow. |
| 611 | */ |
| 612 | inline void isl_sioimath_sub_ui(isl_sioimath_ptr dst, isl_sioimath lhs, |
| 613 | unsigned long rhs) |
| 614 | { |
| 615 | int32_t smalllhs; |
| 616 | isl_sioimath_scratchspace_t lhsscratch; |
| 617 | |
| 618 | if (isl_sioimath_decode_small(val: lhs, small: &smalllhs) && |
| 619 | (rhs < (uint64_t) INT64_MIN - (uint64_t) ISL_SIOIMATH_SMALL_MIN)) { |
| 620 | isl_sioimath_set_int64(ptr: dst, val: (int64_t) smalllhs - rhs); |
| 621 | return; |
| 622 | } |
| 623 | |
| 624 | impz_sub_ui(rop: isl_sioimath_reinit_big(ptr: dst), |
| 625 | op1: isl_sioimath_bigarg_src(arg: lhs, scratch: &lhsscratch), op2: rhs); |
| 626 | isl_sioimath_try_demote(dst); |
| 627 | } |
| 628 | |
| 629 | /* Sum of two isl_ints. |
| 630 | */ |
| 631 | inline void isl_sioimath_add(isl_sioimath_ptr dst, isl_sioimath_src lhs, |
| 632 | isl_sioimath_src rhs) |
| 633 | { |
| 634 | isl_sioimath_scratchspace_t scratchlhs, scratchrhs; |
| 635 | int32_t smalllhs, smallrhs; |
| 636 | |
| 637 | if (isl_sioimath_decode_small(val: lhs, small: &smalllhs) && |
| 638 | isl_sioimath_decode_small(val: rhs, small: &smallrhs)) { |
| 639 | isl_sioimath_set_int64( |
| 640 | ptr: dst, val: (int64_t) smalllhs + (int64_t) smallrhs); |
| 641 | return; |
| 642 | } |
| 643 | |
| 644 | mp_int_add(a: isl_sioimath_bigarg_src(arg: lhs, scratch: &scratchlhs), |
| 645 | b: isl_sioimath_bigarg_src(arg: rhs, scratch: &scratchrhs), |
| 646 | c: isl_sioimath_reinit_big(ptr: dst)); |
| 647 | isl_sioimath_try_demote(dst); |
| 648 | } |
| 649 | |
| 650 | /* Subtract two isl_ints. |
| 651 | */ |
| 652 | inline void isl_sioimath_sub(isl_sioimath_ptr dst, isl_sioimath_src lhs, |
| 653 | isl_sioimath_src rhs) |
| 654 | { |
| 655 | isl_sioimath_scratchspace_t scratchlhs, scratchrhs; |
| 656 | int32_t smalllhs, smallrhs; |
| 657 | |
| 658 | if (isl_sioimath_decode_small(val: lhs, small: &smalllhs) && |
| 659 | isl_sioimath_decode_small(val: rhs, small: &smallrhs)) { |
| 660 | isl_sioimath_set_int64( |
| 661 | ptr: dst, val: (int64_t) smalllhs - (int64_t) smallrhs); |
| 662 | return; |
| 663 | } |
| 664 | |
| 665 | mp_int_sub(a: isl_sioimath_bigarg_src(arg: lhs, scratch: &scratchlhs), |
| 666 | b: isl_sioimath_bigarg_src(arg: rhs, scratch: &scratchrhs), |
| 667 | c: isl_sioimath_reinit_big(ptr: dst)); |
| 668 | isl_sioimath_try_demote(dst); |
| 669 | } |
| 670 | |
| 671 | /* Multiply two isl_ints. |
| 672 | */ |
| 673 | inline void isl_sioimath_mul(isl_sioimath_ptr dst, isl_sioimath_src lhs, |
| 674 | isl_sioimath_src rhs) |
| 675 | { |
| 676 | isl_sioimath_scratchspace_t scratchlhs, scratchrhs; |
| 677 | int32_t smalllhs, smallrhs; |
| 678 | |
| 679 | if (isl_sioimath_decode_small(val: lhs, small: &smalllhs) && |
| 680 | isl_sioimath_decode_small(val: rhs, small: &smallrhs)) { |
| 681 | isl_sioimath_set_int64( |
| 682 | ptr: dst, val: (int64_t) smalllhs * (int64_t) smallrhs); |
| 683 | return; |
| 684 | } |
| 685 | |
| 686 | mp_int_mul(a: isl_sioimath_bigarg_src(arg: lhs, scratch: &scratchlhs), |
| 687 | b: isl_sioimath_bigarg_src(arg: rhs, scratch: &scratchrhs), |
| 688 | c: isl_sioimath_reinit_big(ptr: dst)); |
| 689 | isl_sioimath_try_demote(dst); |
| 690 | } |
| 691 | |
| 692 | /* Shift lhs by rhs bits to the left and store the result in dst. Effectively, |
| 693 | * this operation computes 'lhs * 2^rhs'. |
| 694 | */ |
| 695 | inline void isl_sioimath_mul_2exp(isl_sioimath_ptr dst, isl_sioimath lhs, |
| 696 | unsigned long rhs) |
| 697 | { |
| 698 | isl_sioimath_scratchspace_t scratchlhs; |
| 699 | int32_t smalllhs; |
| 700 | |
| 701 | if (isl_sioimath_decode_small(val: lhs, small: &smalllhs) && (rhs <= 32ul)) { |
| 702 | isl_sioimath_set_int64(ptr: dst, val: ((int64_t) smalllhs) << rhs); |
| 703 | return; |
| 704 | } |
| 705 | |
| 706 | mp_int_mul_pow2(a: isl_sioimath_bigarg_src(arg: lhs, scratch: &scratchlhs), p2: rhs, |
| 707 | c: isl_sioimath_reinit_big(ptr: dst)); |
| 708 | } |
| 709 | |
| 710 | /* Multiply an isl_int and a signed long. |
| 711 | */ |
| 712 | inline void isl_sioimath_mul_si(isl_sioimath_ptr dst, isl_sioimath lhs, |
| 713 | signed long rhs) |
| 714 | { |
| 715 | isl_sioimath_scratchspace_t scratchlhs, scratchrhs; |
| 716 | int32_t smalllhs; |
| 717 | |
| 718 | if (isl_sioimath_decode_small(val: lhs, small: &smalllhs) && (rhs > LONG_MIN) && |
| 719 | (labs(x: rhs) <= UINT32_MAX)) { |
| 720 | isl_sioimath_set_int64(ptr: dst, val: (int64_t) smalllhs * (int64_t) rhs); |
| 721 | return; |
| 722 | } |
| 723 | |
| 724 | mp_int_mul(a: isl_sioimath_bigarg_src(arg: lhs, scratch: &scratchlhs), |
| 725 | b: isl_sioimath_siarg_src(arg: rhs, scratch: &scratchrhs), |
| 726 | c: isl_sioimath_reinit_big(ptr: dst)); |
| 727 | isl_sioimath_try_demote(dst); |
| 728 | } |
| 729 | |
| 730 | /* Multiply an isl_int and an unsigned long. |
| 731 | */ |
| 732 | inline void isl_sioimath_mul_ui(isl_sioimath_ptr dst, isl_sioimath lhs, |
| 733 | unsigned long rhs) |
| 734 | { |
| 735 | isl_sioimath_scratchspace_t scratchlhs, scratchrhs; |
| 736 | int32_t smalllhs; |
| 737 | |
| 738 | if (isl_sioimath_decode_small(val: lhs, small: &smalllhs) && (rhs <= UINT32_MAX)) { |
| 739 | isl_sioimath_set_int64(ptr: dst, val: (int64_t) smalllhs * (int64_t) rhs); |
| 740 | return; |
| 741 | } |
| 742 | |
| 743 | mp_int_mul(a: isl_sioimath_bigarg_src(arg: lhs, scratch: &scratchlhs), |
| 744 | b: isl_sioimath_uiarg_src(arg: rhs, scratch: &scratchrhs), |
| 745 | c: isl_sioimath_reinit_big(ptr: dst)); |
| 746 | isl_sioimath_try_demote(dst); |
| 747 | } |
| 748 | |
| 749 | /* Compute the power of an isl_int to an unsigned long. |
| 750 | * Always let IMath do it; the result is unlikely to be small except in some |
| 751 | * special cases. |
| 752 | * Note: 0^0 == 1 |
| 753 | */ |
| 754 | inline void isl_sioimath_pow_ui(isl_sioimath_ptr dst, isl_sioimath_src lhs, |
| 755 | unsigned long rhs) |
| 756 | { |
| 757 | isl_sioimath_scratchspace_t scratchlhs, scratchrhs; |
| 758 | int32_t smalllhs; |
| 759 | |
| 760 | switch (rhs) { |
| 761 | case 0: |
| 762 | isl_sioimath_set_small(ptr: dst, val: 1); |
| 763 | return; |
| 764 | case 1: |
| 765 | isl_sioimath_set(dst, val: lhs); |
| 766 | return; |
| 767 | case 2: |
| 768 | isl_sioimath_mul(dst, lhs, rhs: lhs); |
| 769 | return; |
| 770 | } |
| 771 | |
| 772 | if (isl_sioimath_decode_small(val: lhs, small: &smalllhs)) { |
| 773 | switch (smalllhs) { |
| 774 | case 0: |
| 775 | isl_sioimath_set_small(ptr: dst, val: 0); |
| 776 | return; |
| 777 | case 1: |
| 778 | isl_sioimath_set_small(ptr: dst, val: 1); |
| 779 | return; |
| 780 | case 2: |
| 781 | isl_sioimath_set_small(ptr: dst, val: 1); |
| 782 | isl_sioimath_mul_2exp(dst, lhs: *dst, rhs); |
| 783 | return; |
| 784 | default: |
| 785 | if ((MP_SMALL_MIN <= rhs) && (rhs <= MP_SMALL_MAX)) { |
| 786 | mp_int_expt_value(a: smalllhs, b: rhs, |
| 787 | c: isl_sioimath_reinit_big(ptr: dst)); |
| 788 | isl_sioimath_try_demote(dst); |
| 789 | return; |
| 790 | } |
| 791 | } |
| 792 | } |
| 793 | |
| 794 | mp_int_expt_full(a: isl_sioimath_bigarg_src(arg: lhs, scratch: &scratchlhs), |
| 795 | b: isl_sioimath_uiarg_src(arg: rhs, scratch: &scratchrhs), |
| 796 | c: isl_sioimath_reinit_big(ptr: dst)); |
| 797 | isl_sioimath_try_demote(dst); |
| 798 | } |
| 799 | |
| 800 | /* Fused multiply-add. |
| 801 | */ |
| 802 | inline void isl_sioimath_addmul(isl_sioimath_ptr dst, isl_sioimath_src lhs, |
| 803 | isl_sioimath_src rhs) |
| 804 | { |
| 805 | isl_sioimath tmp; |
| 806 | isl_sioimath_init(dst: &tmp); |
| 807 | isl_sioimath_mul(dst: &tmp, lhs, rhs); |
| 808 | isl_sioimath_add(dst, lhs: *dst, rhs: tmp); |
| 809 | isl_sioimath_clear(dst: &tmp); |
| 810 | } |
| 811 | |
| 812 | /* Fused multiply-add with an unsigned long. |
| 813 | */ |
| 814 | inline void isl_sioimath_addmul_ui(isl_sioimath_ptr dst, isl_sioimath_src lhs, |
| 815 | unsigned long rhs) |
| 816 | { |
| 817 | isl_sioimath tmp; |
| 818 | isl_sioimath_init(dst: &tmp); |
| 819 | isl_sioimath_mul_ui(dst: &tmp, lhs, rhs); |
| 820 | isl_sioimath_add(dst, lhs: *dst, rhs: tmp); |
| 821 | isl_sioimath_clear(dst: &tmp); |
| 822 | } |
| 823 | |
| 824 | /* Fused multiply-subtract. |
| 825 | */ |
| 826 | inline void isl_sioimath_submul(isl_sioimath_ptr dst, isl_sioimath_src lhs, |
| 827 | isl_sioimath_src rhs) |
| 828 | { |
| 829 | isl_sioimath tmp; |
| 830 | isl_sioimath_init(dst: &tmp); |
| 831 | isl_sioimath_mul(dst: &tmp, lhs, rhs); |
| 832 | isl_sioimath_sub(dst, lhs: *dst, rhs: tmp); |
| 833 | isl_sioimath_clear(dst: &tmp); |
| 834 | } |
| 835 | |
| 836 | /* Fused multiply-add with an unsigned long. |
| 837 | */ |
| 838 | inline void isl_sioimath_submul_ui(isl_sioimath_ptr dst, isl_sioimath_src lhs, |
| 839 | unsigned long rhs) |
| 840 | { |
| 841 | isl_sioimath tmp; |
| 842 | isl_sioimath_init(dst: &tmp); |
| 843 | isl_sioimath_mul_ui(dst: &tmp, lhs, rhs); |
| 844 | isl_sioimath_sub(dst, lhs: *dst, rhs: tmp); |
| 845 | isl_sioimath_clear(dst: &tmp); |
| 846 | } |
| 847 | |
| 848 | void isl_sioimath_gcd(isl_sioimath_ptr dst, isl_sioimath_src lhs, |
| 849 | isl_sioimath_src rhs); |
| 850 | void isl_sioimath_lcm(isl_sioimath_ptr dst, isl_sioimath_src lhs, |
| 851 | isl_sioimath_src rhs); |
| 852 | |
| 853 | /* Divide lhs by rhs, rounding to zero (Truncate). |
| 854 | */ |
| 855 | inline void isl_sioimath_tdiv_q(isl_sioimath_ptr dst, isl_sioimath_src lhs, |
| 856 | isl_sioimath_src rhs) |
| 857 | { |
| 858 | isl_sioimath_scratchspace_t lhsscratch, rhsscratch; |
| 859 | int32_t lhssmall, rhssmall; |
| 860 | |
| 861 | if (isl_sioimath_decode_small(val: lhs, small: &lhssmall) && |
| 862 | isl_sioimath_decode_small(val: rhs, small: &rhssmall)) { |
| 863 | isl_sioimath_set_small(ptr: dst, val: lhssmall / rhssmall); |
| 864 | return; |
| 865 | } |
| 866 | |
| 867 | mp_int_div(a: isl_sioimath_bigarg_src(arg: lhs, scratch: &lhsscratch), |
| 868 | b: isl_sioimath_bigarg_src(arg: rhs, scratch: &rhsscratch), |
| 869 | q: isl_sioimath_reinit_big(ptr: dst), NULL); |
| 870 | isl_sioimath_try_demote(dst); |
| 871 | return; |
| 872 | } |
| 873 | |
| 874 | /* Divide lhs by an unsigned long rhs, rounding to zero (Truncate). |
| 875 | */ |
| 876 | inline void isl_sioimath_tdiv_q_ui(isl_sioimath_ptr dst, isl_sioimath_src lhs, |
| 877 | unsigned long rhs) |
| 878 | { |
| 879 | isl_sioimath_scratchspace_t lhsscratch, rhsscratch; |
| 880 | int32_t lhssmall; |
| 881 | |
| 882 | if (isl_sioimath_is_small(val: lhs) && (rhs <= (unsigned long) INT32_MAX)) { |
| 883 | lhssmall = isl_sioimath_get_small(val: lhs); |
| 884 | isl_sioimath_set_small(ptr: dst, val: lhssmall / (int32_t) rhs); |
| 885 | return; |
| 886 | } |
| 887 | |
| 888 | if (rhs <= MP_SMALL_MAX) { |
| 889 | mp_int_div_value(a: isl_sioimath_bigarg_src(arg: lhs, scratch: &lhsscratch), value: rhs, |
| 890 | q: isl_sioimath_reinit_big(ptr: dst), NULL); |
| 891 | isl_sioimath_try_demote(dst); |
| 892 | return; |
| 893 | } |
| 894 | |
| 895 | mp_int_div(a: isl_sioimath_bigarg_src(arg: lhs, scratch: &lhsscratch), |
| 896 | b: isl_sioimath_uiarg_src(arg: rhs, scratch: &rhsscratch), |
| 897 | q: isl_sioimath_reinit_big(ptr: dst), NULL); |
| 898 | isl_sioimath_try_demote(dst); |
| 899 | } |
| 900 | |
| 901 | /* Divide lhs by rhs, rounding to positive infinity (Ceil). |
| 902 | */ |
| 903 | inline void isl_sioimath_cdiv_q(isl_sioimath_ptr dst, isl_sioimath_src lhs, |
| 904 | isl_sioimath_src rhs) |
| 905 | { |
| 906 | int32_t lhssmall, rhssmall; |
| 907 | isl_sioimath_scratchspace_t lhsscratch, rhsscratch; |
| 908 | int32_t q; |
| 909 | |
| 910 | if (isl_sioimath_decode_small(val: lhs, small: &lhssmall) && |
| 911 | isl_sioimath_decode_small(val: rhs, small: &rhssmall)) { |
| 912 | if ((lhssmall >= 0) && (rhssmall >= 0)) |
| 913 | q = ((int64_t) lhssmall + (int64_t) rhssmall - 1) / |
| 914 | rhssmall; |
| 915 | else if ((lhssmall < 0) && (rhssmall < 0)) |
| 916 | q = ((int64_t) lhssmall + (int64_t) rhssmall + 1) / |
| 917 | rhssmall; |
| 918 | else |
| 919 | q = lhssmall / rhssmall; |
| 920 | isl_sioimath_set_small(ptr: dst, val: q); |
| 921 | return; |
| 922 | } |
| 923 | |
| 924 | impz_cdiv_q(q: isl_sioimath_reinit_big(ptr: dst), |
| 925 | n: isl_sioimath_bigarg_src(arg: lhs, scratch: &lhsscratch), |
| 926 | d: isl_sioimath_bigarg_src(arg: rhs, scratch: &rhsscratch)); |
| 927 | isl_sioimath_try_demote(dst); |
| 928 | } |
| 929 | |
| 930 | /* Compute the division of lhs by a rhs of type unsigned long, rounding towards |
| 931 | * positive infinity (Ceil). |
| 932 | */ |
| 933 | inline void isl_sioimath_cdiv_q_ui(isl_sioimath_ptr dst, isl_sioimath_src lhs, |
| 934 | unsigned long rhs) |
| 935 | { |
| 936 | isl_sioimath_scratchspace_t lhsscratch, rhsscratch; |
| 937 | int32_t lhssmall, q; |
| 938 | |
| 939 | if (isl_sioimath_decode_small(val: lhs, small: &lhssmall) && (rhs <= INT32_MAX)) { |
| 940 | if (lhssmall >= 0) |
| 941 | q = ((int64_t) lhssmall + ((int64_t) rhs - 1)) / |
| 942 | (int64_t) rhs; |
| 943 | else |
| 944 | q = lhssmall / (int32_t) rhs; |
| 945 | isl_sioimath_set_small(ptr: dst, val: q); |
| 946 | return; |
| 947 | } |
| 948 | |
| 949 | impz_cdiv_q(q: isl_sioimath_reinit_big(ptr: dst), |
| 950 | n: isl_sioimath_bigarg_src(arg: lhs, scratch: &lhsscratch), |
| 951 | d: isl_sioimath_uiarg_src(arg: rhs, scratch: &rhsscratch)); |
| 952 | isl_sioimath_try_demote(dst); |
| 953 | } |
| 954 | |
| 955 | /* Divide lhs by rhs, rounding to negative infinity (Floor). |
| 956 | */ |
| 957 | inline void isl_sioimath_fdiv_q(isl_sioimath_ptr dst, isl_sioimath_src lhs, |
| 958 | isl_sioimath_src rhs) |
| 959 | { |
| 960 | isl_sioimath_scratchspace_t lhsscratch, rhsscratch; |
| 961 | int32_t lhssmall, rhssmall; |
| 962 | int32_t q; |
| 963 | |
| 964 | if (isl_sioimath_decode_small(val: lhs, small: &lhssmall) && |
| 965 | isl_sioimath_decode_small(val: rhs, small: &rhssmall)) { |
| 966 | if ((lhssmall < 0) && (rhssmall >= 0)) |
| 967 | q = ((int64_t) lhssmall - ((int64_t) rhssmall - 1)) / |
| 968 | rhssmall; |
| 969 | else if ((lhssmall >= 0) && (rhssmall < 0)) |
| 970 | q = ((int64_t) lhssmall - ((int64_t) rhssmall + 1)) / |
| 971 | rhssmall; |
| 972 | else |
| 973 | q = lhssmall / rhssmall; |
| 974 | isl_sioimath_set_small(ptr: dst, val: q); |
| 975 | return; |
| 976 | } |
| 977 | |
| 978 | impz_fdiv_q(q: isl_sioimath_reinit_big(ptr: dst), |
| 979 | n: isl_sioimath_bigarg_src(arg: lhs, scratch: &lhsscratch), |
| 980 | d: isl_sioimath_bigarg_src(arg: rhs, scratch: &rhsscratch)); |
| 981 | isl_sioimath_try_demote(dst); |
| 982 | } |
| 983 | |
| 984 | /* Compute the division of lhs by a rhs of type unsigned long, rounding towards |
| 985 | * negative infinity (Floor). |
| 986 | */ |
| 987 | inline void isl_sioimath_fdiv_q_ui(isl_sioimath_ptr dst, isl_sioimath_src lhs, |
| 988 | unsigned long rhs) |
| 989 | { |
| 990 | isl_sioimath_scratchspace_t lhsscratch, rhsscratch; |
| 991 | int32_t lhssmall, q; |
| 992 | |
| 993 | if (isl_sioimath_decode_small(val: lhs, small: &lhssmall) && (rhs <= INT32_MAX)) { |
| 994 | if (lhssmall >= 0) |
| 995 | q = (uint32_t) lhssmall / rhs; |
| 996 | else |
| 997 | q = ((int64_t) lhssmall - ((int64_t) rhs - 1)) / |
| 998 | (int64_t) rhs; |
| 999 | isl_sioimath_set_small(ptr: dst, val: q); |
| 1000 | return; |
| 1001 | } |
| 1002 | |
| 1003 | impz_fdiv_q(q: isl_sioimath_reinit_big(ptr: dst), |
| 1004 | n: isl_sioimath_bigarg_src(arg: lhs, scratch: &lhsscratch), |
| 1005 | d: isl_sioimath_uiarg_src(arg: rhs, scratch: &rhsscratch)); |
| 1006 | isl_sioimath_try_demote(dst); |
| 1007 | } |
| 1008 | |
| 1009 | /* Get the remainder of: lhs divided by rhs rounded towards negative infinite |
| 1010 | * (Floor). |
| 1011 | */ |
| 1012 | inline void isl_sioimath_fdiv_r(isl_sioimath_ptr dst, isl_sioimath_src lhs, |
| 1013 | isl_sioimath_src rhs) |
| 1014 | { |
| 1015 | isl_sioimath_scratchspace_t lhsscratch, rhsscratch; |
| 1016 | int64_t lhssmall, rhssmall; |
| 1017 | int32_t r; |
| 1018 | |
| 1019 | if (isl_sioimath_is_small(val: lhs) && isl_sioimath_is_small(val: rhs)) { |
| 1020 | lhssmall = isl_sioimath_get_small(val: lhs); |
| 1021 | rhssmall = isl_sioimath_get_small(val: rhs); |
| 1022 | r = (rhssmall + lhssmall % rhssmall) % rhssmall; |
| 1023 | isl_sioimath_set_small(ptr: dst, val: r); |
| 1024 | return; |
| 1025 | } |
| 1026 | |
| 1027 | impz_fdiv_r(r: isl_sioimath_reinit_big(ptr: dst), |
| 1028 | n: isl_sioimath_bigarg_src(arg: lhs, scratch: &lhsscratch), |
| 1029 | d: isl_sioimath_bigarg_src(arg: rhs, scratch: &rhsscratch)); |
| 1030 | isl_sioimath_try_demote(dst); |
| 1031 | } |
| 1032 | |
| 1033 | void isl_sioimath_read(isl_sioimath_ptr dst, const char *str); |
| 1034 | |
| 1035 | /* Return: |
| 1036 | * +1 for a positive number |
| 1037 | * -1 for a negative number |
| 1038 | * 0 if the number is zero |
| 1039 | */ |
| 1040 | inline int isl_sioimath_sgn(isl_sioimath_src arg) |
| 1041 | { |
| 1042 | int32_t small; |
| 1043 | |
| 1044 | if (isl_sioimath_decode_small(val: arg, small: &small)) |
| 1045 | return (small > 0) - (small < 0); |
| 1046 | |
| 1047 | return mp_int_compare_zero(z: isl_sioimath_get_big(val: arg)); |
| 1048 | } |
| 1049 | |
| 1050 | /* Return: |
| 1051 | * +1 if lhs > rhs |
| 1052 | * -1 if lhs < rhs |
| 1053 | * 0 if lhs = rhs |
| 1054 | */ |
| 1055 | inline int isl_sioimath_cmp(isl_sioimath_src lhs, isl_sioimath_src rhs) |
| 1056 | { |
| 1057 | isl_sioimath_scratchspace_t lhsscratch, rhsscratch; |
| 1058 | int32_t lhssmall, rhssmall; |
| 1059 | |
| 1060 | if (isl_sioimath_decode_small(val: lhs, small: &lhssmall) && |
| 1061 | isl_sioimath_decode_small(val: rhs, small: &rhssmall)) |
| 1062 | return (lhssmall > rhssmall) - (lhssmall < rhssmall); |
| 1063 | |
| 1064 | if (isl_sioimath_decode_small(val: rhs, small: &rhssmall)) |
| 1065 | return mp_int_compare_value( |
| 1066 | z: isl_sioimath_bigarg_src(arg: lhs, scratch: &lhsscratch), v: rhssmall); |
| 1067 | |
| 1068 | if (isl_sioimath_decode_small(val: lhs, small: &lhssmall)) |
| 1069 | return -mp_int_compare_value( |
| 1070 | z: isl_sioimath_bigarg_src(arg: rhs, scratch: &rhsscratch), v: lhssmall); |
| 1071 | |
| 1072 | return mp_int_compare( |
| 1073 | a: isl_sioimath_get_big(val: lhs), b: isl_sioimath_get_big(val: rhs)); |
| 1074 | } |
| 1075 | |
| 1076 | /* As isl_sioimath_cmp, but with signed long rhs. |
| 1077 | */ |
| 1078 | inline int isl_sioimath_cmp_si(isl_sioimath_src lhs, signed long rhs) |
| 1079 | { |
| 1080 | int32_t lhssmall; |
| 1081 | |
| 1082 | if (isl_sioimath_decode_small(val: lhs, small: &lhssmall)) |
| 1083 | return (lhssmall > rhs) - (lhssmall < rhs); |
| 1084 | |
| 1085 | return mp_int_compare_value(z: isl_sioimath_get_big(val: lhs), v: rhs); |
| 1086 | } |
| 1087 | |
| 1088 | /* Return: |
| 1089 | * +1 if |lhs| > |rhs| |
| 1090 | * -1 if |lhs| < |rhs| |
| 1091 | * 0 if |lhs| = |rhs| |
| 1092 | */ |
| 1093 | inline int isl_sioimath_abs_cmp(isl_sioimath_src lhs, isl_sioimath_src rhs) |
| 1094 | { |
| 1095 | isl_sioimath_scratchspace_t lhsscratch, rhsscratch; |
| 1096 | int32_t lhssmall, rhssmall; |
| 1097 | |
| 1098 | if (isl_sioimath_decode_small(val: lhs, small: &lhssmall) && |
| 1099 | isl_sioimath_decode_small(val: rhs, small: &rhssmall)) { |
| 1100 | lhssmall = labs(x: lhssmall); |
| 1101 | rhssmall = labs(x: rhssmall); |
| 1102 | return (lhssmall > rhssmall) - (lhssmall < rhssmall); |
| 1103 | } |
| 1104 | |
| 1105 | return mp_int_compare_unsigned( |
| 1106 | a: isl_sioimath_bigarg_src(arg: lhs, scratch: &lhsscratch), |
| 1107 | b: isl_sioimath_bigarg_src(arg: rhs, scratch: &rhsscratch)); |
| 1108 | } |
| 1109 | |
| 1110 | /* Return whether lhs is divisible by rhs. |
| 1111 | * In particular, can rhs be multiplied by some integer to result in lhs? |
| 1112 | * If rhs is zero, then this means lhs has to be zero too. |
| 1113 | */ |
| 1114 | inline int isl_sioimath_is_divisible_by(isl_sioimath_src lhs, |
| 1115 | isl_sioimath_src rhs) |
| 1116 | { |
| 1117 | isl_sioimath_scratchspace_t lhsscratch, rhsscratch; |
| 1118 | int32_t lhssmall, rhssmall; |
| 1119 | mpz_t rem; |
| 1120 | int cmp; |
| 1121 | |
| 1122 | if (isl_sioimath_sgn(arg: rhs) == 0) |
| 1123 | return isl_sioimath_sgn(arg: lhs) == 0; |
| 1124 | |
| 1125 | if (isl_sioimath_decode_small(val: lhs, small: &lhssmall) && |
| 1126 | isl_sioimath_decode_small(val: rhs, small: &rhssmall)) |
| 1127 | return lhssmall % rhssmall == 0; |
| 1128 | |
| 1129 | if (isl_sioimath_decode_small(val: rhs, small: &rhssmall)) |
| 1130 | return mp_int_divisible_value( |
| 1131 | a: isl_sioimath_bigarg_src(arg: lhs, scratch: &lhsscratch), v: rhssmall); |
| 1132 | |
| 1133 | mp_int_init(z: &rem); |
| 1134 | mp_int_div(a: isl_sioimath_bigarg_src(arg: lhs, scratch: &lhsscratch), |
| 1135 | b: isl_sioimath_bigarg_src(arg: rhs, scratch: &rhsscratch), NULL, r: &rem); |
| 1136 | cmp = mp_int_compare_zero(z: &rem); |
| 1137 | mp_int_clear(z: &rem); |
| 1138 | return cmp == 0; |
| 1139 | } |
| 1140 | |
| 1141 | /* Return a hash code of an isl_sioimath. |
| 1142 | * The hash code for a number in small and big representation must be identical |
| 1143 | * on the same machine because small representation if not obligatory if fits. |
| 1144 | */ |
| 1145 | inline uint32_t isl_sioimath_hash(isl_sioimath_src arg, uint32_t hash) |
| 1146 | { |
| 1147 | int32_t small; |
| 1148 | int i; |
| 1149 | uint32_t num; |
| 1150 | mp_digit digits[(sizeof(uint32_t) + sizeof(mp_digit) - 1) / |
| 1151 | sizeof(mp_digit)]; |
| 1152 | mp_size used; |
| 1153 | const unsigned char *digitdata = (const unsigned char *) &digits; |
| 1154 | |
| 1155 | if (isl_sioimath_decode_small(val: arg, small: &small)) { |
| 1156 | if (small < 0) |
| 1157 | isl_hash_byte(hash, 0xFF); |
| 1158 | num = labs(x: small); |
| 1159 | |
| 1160 | isl_siomath_uint32_to_digits(num, digits, used: &used); |
| 1161 | for (i = 0; i < used * sizeof(mp_digit); i += 1) |
| 1162 | isl_hash_byte(hash, digitdata[i]); |
| 1163 | return hash; |
| 1164 | } |
| 1165 | |
| 1166 | return isl_imath_hash(v: isl_sioimath_get_big(val: arg), hash); |
| 1167 | } |
| 1168 | |
| 1169 | /* Return the number of digits in a number of the given base or more, i.e. the |
| 1170 | * string length without sign and null terminator. |
| 1171 | * |
| 1172 | * Current implementation for small representation returns the maximal number |
| 1173 | * of binary digits in that representation, which can be much larger than the |
| 1174 | * smallest possible solution. |
| 1175 | */ |
| 1176 | inline size_t isl_sioimath_sizeinbase(isl_sioimath_src arg, int base) |
| 1177 | { |
| 1178 | int32_t small; |
| 1179 | |
| 1180 | if (isl_sioimath_decode_small(val: arg, small: &small)) |
| 1181 | return sizeof(int32_t) * CHAR_BIT - 1; |
| 1182 | |
| 1183 | return impz_sizeinbase(op: isl_sioimath_get_big(val: arg), base); |
| 1184 | } |
| 1185 | |
| 1186 | void isl_sioimath_print(FILE *out, isl_sioimath_src i, int width); |
| 1187 | void isl_sioimath_dump(isl_sioimath_src arg); |
| 1188 | |
| 1189 | typedef isl_sioimath isl_int[1]; |
| 1190 | #define isl_int_init(i) isl_sioimath_init((i)) |
| 1191 | #define isl_int_clear(i) isl_sioimath_clear((i)) |
| 1192 | |
| 1193 | #define isl_int_set(r, i) isl_sioimath_set((r), *(i)) |
| 1194 | #define isl_int_set_si(r, i) isl_sioimath_set_si((r), i) |
| 1195 | #define isl_int_set_ui(r, i) isl_sioimath_set_ui((r), i) |
| 1196 | #define isl_int_fits_slong(r) isl_sioimath_fits_slong(*(r)) |
| 1197 | #define isl_int_get_si(r) isl_sioimath_get_si(*(r)) |
| 1198 | #define isl_int_fits_ulong(r) isl_sioimath_fits_ulong(*(r)) |
| 1199 | #define isl_int_get_ui(r) isl_sioimath_get_ui(*(r)) |
| 1200 | #define isl_int_get_d(r) isl_sioimath_get_d(*(r)) |
| 1201 | #define isl_int_get_str(r) isl_sioimath_get_str(*(r)) |
| 1202 | #define isl_int_abs(r, i) isl_sioimath_abs((r), *(i)) |
| 1203 | #define isl_int_neg(r, i) isl_sioimath_neg((r), *(i)) |
| 1204 | #define isl_int_swap(i, j) isl_sioimath_swap((i), (j)) |
| 1205 | #define isl_int_swap_or_set(i, j) isl_sioimath_swap((i), (j)) |
| 1206 | #define isl_int_add_ui(r, i, j) isl_sioimath_add_ui((r), *(i), j) |
| 1207 | #define isl_int_sub_ui(r, i, j) isl_sioimath_sub_ui((r), *(i), j) |
| 1208 | |
| 1209 | #define isl_int_add(r, i, j) isl_sioimath_add((r), *(i), *(j)) |
| 1210 | #define isl_int_sub(r, i, j) isl_sioimath_sub((r), *(i), *(j)) |
| 1211 | #define isl_int_mul(r, i, j) isl_sioimath_mul((r), *(i), *(j)) |
| 1212 | #define isl_int_mul_2exp(r, i, j) isl_sioimath_mul_2exp((r), *(i), j) |
| 1213 | #define isl_int_mul_si(r, i, j) isl_sioimath_mul_si((r), *(i), j) |
| 1214 | #define isl_int_mul_ui(r, i, j) isl_sioimath_mul_ui((r), *(i), j) |
| 1215 | #define isl_int_pow_ui(r, i, j) isl_sioimath_pow_ui((r), *(i), j) |
| 1216 | #define isl_int_addmul(r, i, j) isl_sioimath_addmul((r), *(i), *(j)) |
| 1217 | #define isl_int_addmul_ui(r, i, j) isl_sioimath_addmul_ui((r), *(i), j) |
| 1218 | #define isl_int_submul(r, i, j) isl_sioimath_submul((r), *(i), *(j)) |
| 1219 | #define isl_int_submul_ui(r, i, j) isl_sioimath_submul_ui((r), *(i), j) |
| 1220 | |
| 1221 | #define isl_int_gcd(r, i, j) isl_sioimath_gcd((r), *(i), *(j)) |
| 1222 | #define isl_int_lcm(r, i, j) isl_sioimath_lcm((r), *(i), *(j)) |
| 1223 | #define isl_int_divexact(r, i, j) isl_sioimath_tdiv_q((r), *(i), *(j)) |
| 1224 | #define isl_int_divexact_ui(r, i, j) isl_sioimath_tdiv_q_ui((r), *(i), j) |
| 1225 | #define isl_int_tdiv_q(r, i, j) isl_sioimath_tdiv_q((r), *(i), *(j)) |
| 1226 | #define isl_int_cdiv_q(r, i, j) isl_sioimath_cdiv_q((r), *(i), *(j)) |
| 1227 | #define isl_int_cdiv_q_ui(r, i, j) isl_sioimath_cdiv_q_ui((r), *(i), j) |
| 1228 | #define isl_int_fdiv_q(r, i, j) isl_sioimath_fdiv_q((r), *(i), *(j)) |
| 1229 | #define isl_int_fdiv_r(r, i, j) isl_sioimath_fdiv_r((r), *(i), *(j)) |
| 1230 | #define isl_int_fdiv_q_ui(r, i, j) isl_sioimath_fdiv_q_ui((r), *(i), j) |
| 1231 | |
| 1232 | #define isl_int_read(r, s) isl_sioimath_read((r), s) |
| 1233 | #define isl_int_sgn(i) isl_sioimath_sgn(*(i)) |
| 1234 | #define isl_int_cmp(i, j) isl_sioimath_cmp(*(i), *(j)) |
| 1235 | #define isl_int_cmp_si(i, si) isl_sioimath_cmp_si(*(i), si) |
| 1236 | #define isl_int_eq(i, j) (isl_sioimath_cmp(*(i), *(j)) == 0) |
| 1237 | #define isl_int_ne(i, j) (isl_sioimath_cmp(*(i), *(j)) != 0) |
| 1238 | #define isl_int_lt(i, j) (isl_sioimath_cmp(*(i), *(j)) < 0) |
| 1239 | #define isl_int_le(i, j) (isl_sioimath_cmp(*(i), *(j)) <= 0) |
| 1240 | #define isl_int_gt(i, j) (isl_sioimath_cmp(*(i), *(j)) > 0) |
| 1241 | #define isl_int_ge(i, j) (isl_sioimath_cmp(*(i), *(j)) >= 0) |
| 1242 | #define isl_int_abs_cmp(i, j) isl_sioimath_abs_cmp(*(i), *(j)) |
| 1243 | #define isl_int_abs_eq(i, j) (isl_sioimath_abs_cmp(*(i), *(j)) == 0) |
| 1244 | #define isl_int_abs_ne(i, j) (isl_sioimath_abs_cmp(*(i), *(j)) != 0) |
| 1245 | #define isl_int_abs_lt(i, j) (isl_sioimath_abs_cmp(*(i), *(j)) < 0) |
| 1246 | #define isl_int_abs_gt(i, j) (isl_sioimath_abs_cmp(*(i), *(j)) > 0) |
| 1247 | #define isl_int_abs_ge(i, j) (isl_sioimath_abs_cmp(*(i), *(j)) >= 0) |
| 1248 | #define isl_int_is_divisible_by(i, j) isl_sioimath_is_divisible_by(*(i), *(j)) |
| 1249 | |
| 1250 | #define isl_int_hash(v, h) isl_sioimath_hash(*(v), h) |
| 1251 | #define isl_int_free_str(s) free(s) |
| 1252 | #define isl_int_print(out, i, width) isl_sioimath_print(out, *(i), width) |
| 1253 | |
| 1254 | #endif /* ISL_INT_SIOIMATH_H */ |
| 1255 | |