| /* |
| Name: imath.h |
| Purpose: Arbitrary precision integer arithmetic routines. |
| Author: M. J. Fromberger <http://spinning-yarns.org/michael/> |
| |
| Copyright (C) 2002-2007 Michael J. Fromberger, All Rights Reserved. |
| |
| Permission is hereby granted, free of charge, to any person obtaining a copy |
| of this software and associated documentation files (the "Software"), to deal |
| in the Software without restriction, including without limitation the rights |
| to use, copy, modify, merge, publish, distribute, sublicense, and/or sell |
| copies of the Software, and to permit persons to whom the Software is |
| furnished to do so, subject to the following conditions: |
| |
| The above copyright notice and this permission notice shall be included in |
| all copies or substantial portions of the Software. |
| |
| THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
| IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
| FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
| AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
| LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
| OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE |
| SOFTWARE. |
| */ |
| |
| #ifndef IMATH_H_ |
| #define IMATH_H_ |
| |
| #include <stdint.h> |
| #include <limits.h> |
| |
| #ifdef __cplusplus |
| extern "C" { |
| #endif |
| |
| typedef unsigned char mp_sign; |
| typedef unsigned int mp_size; |
| typedef int mp_result; |
| typedef long mp_small; /* must be a signed type */ |
| typedef unsigned long mp_usmall; /* must be an unsigned type */ |
| |
| /* Force building with uint64_t so that the library builds consistently |
| * whether we build from the makefile or by embedding imath in another project. |
| */ |
| #undef USE_64BIT_WORDS |
| #define USE_64BIT_WORDS |
| #ifdef USE_64BIT_WORDS |
| typedef uint32_t mp_digit; |
| typedef uint64_t mp_word; |
| #else |
| typedef uint16_t mp_digit; |
| typedef uint32_t mp_word; |
| #endif |
| |
| typedef struct mpz { |
| mp_digit single; |
| mp_digit *digits; |
| mp_size alloc; |
| mp_size used; |
| mp_sign sign; |
| } mpz_t, *mp_int; |
| |
| #define MP_DIGITS(Z) ((Z)->digits) |
| #define MP_ALLOC(Z) ((Z)->alloc) |
| #define MP_USED(Z) ((Z)->used) |
| #define MP_SIGN(Z) ((Z)->sign) |
| |
| extern const mp_result MP_OK; |
| extern const mp_result MP_FALSE; |
| extern const mp_result MP_TRUE; |
| extern const mp_result MP_MEMORY; |
| extern const mp_result MP_RANGE; |
| extern const mp_result MP_UNDEF; |
| extern const mp_result MP_TRUNC; |
| extern const mp_result MP_BADARG; |
| extern const mp_result MP_MINERR; |
| |
| #define MP_DIGIT_BIT (sizeof(mp_digit) * CHAR_BIT) |
| #define MP_WORD_BIT (sizeof(mp_word) * CHAR_BIT) |
| #define MP_SMALL_MIN LONG_MIN |
| #define MP_SMALL_MAX LONG_MAX |
| #define MP_USMALL_MIN ULONG_MIN |
| #define MP_USMALL_MAX ULONG_MAX |
| |
| #ifdef USE_64BIT_WORDS |
| # define MP_DIGIT_MAX (UINT32_MAX * UINT64_C(1)) |
| # define MP_WORD_MAX (UINT64_MAX) |
| #else |
| # define MP_DIGIT_MAX (UINT16_MAX * 1UL) |
| # define MP_WORD_MAX (UINT32_MAX * 1UL) |
| #endif |
| |
| #define MP_MIN_RADIX 2 |
| #define MP_MAX_RADIX 36 |
| |
| /* Values with fewer than this many significant digits use the standard |
| multiplication algorithm; otherwise, a recursive algorithm is used. |
| Choose a value to suit your platform. |
| */ |
| #define MP_MULT_THRESH 22 |
| |
| #define MP_DEFAULT_PREC 8 /* default memory allocation, in digits */ |
| |
| extern const mp_sign MP_NEG; |
| extern const mp_sign MP_ZPOS; |
| |
| #define mp_int_is_odd(Z) ((Z)->digits[0] & 1) |
| #define mp_int_is_even(Z) !((Z)->digits[0] & 1) |
| |
| mp_result mp_int_init(mp_int z); |
| mp_int mp_int_alloc(void); |
| mp_result mp_int_init_size(mp_int z, mp_size prec); |
| mp_result mp_int_init_copy(mp_int z, mp_int old); |
| mp_result mp_int_init_value(mp_int z, mp_small value); |
| mp_result mp_int_init_uvalue(mp_int z, mp_usmall uvalue); |
| mp_result mp_int_set_value(mp_int z, mp_small value); |
| mp_result mp_int_set_uvalue(mp_int z, mp_usmall uvalue); |
| void mp_int_clear(mp_int z); |
| void mp_int_free(mp_int z); |
| |
| mp_result mp_int_copy(mp_int a, mp_int c); /* c = a */ |
| void mp_int_swap(mp_int a, mp_int c); /* swap a, c */ |
| void mp_int_zero(mp_int z); /* z = 0 */ |
| mp_result mp_int_abs(mp_int a, mp_int c); /* c = |a| */ |
| mp_result mp_int_neg(mp_int a, mp_int c); /* c = -a */ |
| mp_result mp_int_add(mp_int a, mp_int b, mp_int c); /* c = a + b */ |
| mp_result mp_int_add_value(mp_int a, mp_small value, mp_int c); |
| mp_result mp_int_sub(mp_int a, mp_int b, mp_int c); /* c = a - b */ |
| mp_result mp_int_sub_value(mp_int a, mp_small value, mp_int c); |
| mp_result mp_int_mul(mp_int a, mp_int b, mp_int c); /* c = a * b */ |
| mp_result mp_int_mul_value(mp_int a, mp_small value, mp_int c); |
| mp_result mp_int_mul_pow2(mp_int a, mp_small p2, mp_int c); |
| mp_result mp_int_sqr(mp_int a, mp_int c); /* c = a * a */ |
| mp_result mp_int_div(mp_int a, mp_int b, /* q = a / b */ |
| mp_int q, mp_int r); /* r = a % b */ |
| mp_result mp_int_div_value(mp_int a, mp_small value, /* q = a / value */ |
| mp_int q, mp_small *r); /* r = a % value */ |
| mp_result mp_int_div_pow2(mp_int a, mp_small p2, /* q = a / 2^p2 */ |
| mp_int q, mp_int r); /* r = q % 2^p2 */ |
| mp_result mp_int_mod(mp_int a, mp_int m, mp_int c); /* c = a % m */ |
| #define mp_int_mod_value(A, V, R) mp_int_div_value((A), (V), 0, (R)) |
| mp_result mp_int_expt(mp_int a, mp_small b, mp_int c); /* c = a^b */ |
| mp_result mp_int_expt_value(mp_small a, mp_small b, mp_int c); /* c = a^b */ |
| mp_result mp_int_expt_full(mp_int a, mp_int b, mp_int c); /* c = a^b */ |
| |
| int mp_int_compare(mp_int a, mp_int b); /* a <=> b */ |
| int mp_int_compare_unsigned(mp_int a, mp_int b); /* |a| <=> |b| */ |
| int mp_int_compare_zero(mp_int z); /* a <=> 0 */ |
| int mp_int_compare_value(mp_int z, mp_small v); /* a <=> v */ |
| int mp_int_compare_uvalue(mp_int z, mp_usmall uv); /* a <=> uv */ |
| |
| /* Returns true if v|a, false otherwise (including errors) */ |
| int mp_int_divisible_value(mp_int a, mp_small v); |
| |
| /* Returns k >= 0 such that z = 2^k, if one exists; otherwise < 0 */ |
| int mp_int_is_pow2(mp_int z); |
| |
| mp_result mp_int_exptmod(mp_int a, mp_int b, mp_int m, |
| mp_int c); /* c = a^b (mod m) */ |
| mp_result mp_int_exptmod_evalue(mp_int a, mp_small value, |
| mp_int m, mp_int c); /* c = a^v (mod m) */ |
| mp_result mp_int_exptmod_bvalue(mp_small value, mp_int b, |
| mp_int m, mp_int c); /* c = v^b (mod m) */ |
| mp_result mp_int_exptmod_known(mp_int a, mp_int b, |
| mp_int m, mp_int mu, |
| mp_int c); /* c = a^b (mod m) */ |
| mp_result mp_int_redux_const(mp_int m, mp_int c); |
| |
| mp_result mp_int_invmod(mp_int a, mp_int m, mp_int c); /* c = 1/a (mod m) */ |
| |
| mp_result mp_int_gcd(mp_int a, mp_int b, mp_int c); /* c = gcd(a, b) */ |
| |
| mp_result mp_int_egcd(mp_int a, mp_int b, mp_int c, /* c = gcd(a, b) */ |
| mp_int x, mp_int y); /* c = ax + by */ |
| |
| mp_result mp_int_lcm(mp_int a, mp_int b, mp_int c); /* c = lcm(a, b) */ |
| |
| mp_result mp_int_root(mp_int a, mp_small b, mp_int c); /* c = floor(a^{1/b}) */ |
| #define mp_int_sqrt(a, c) mp_int_root(a, 2, c) /* c = floor(sqrt(a)) */ |
| |
| /* Convert to a small int, if representable; else MP_RANGE */ |
| mp_result mp_int_to_int(mp_int z, mp_small *out); |
| mp_result mp_int_to_uint(mp_int z, mp_usmall *out); |
| |
| /* Convert to nul-terminated string with the specified radix, writing at |
| most limit characters including the nul terminator */ |
| mp_result mp_int_to_string(mp_int z, mp_size radix, |
| char *str, int limit); |
| |
| /* Return the number of characters required to represent |
| z in the given radix. May over-estimate. */ |
| mp_result mp_int_string_len(mp_int z, mp_size radix); |
| |
| /* Read zero-terminated string into z */ |
| mp_result mp_int_read_string(mp_int z, mp_size radix, const char *str); |
| mp_result mp_int_read_cstring(mp_int z, mp_size radix, const char *str, |
| char **end); |
| |
| /* Return the number of significant bits in z */ |
| mp_result mp_int_count_bits(mp_int z); |
| |
| /* Convert z to two's complement binary, writing at most limit bytes */ |
| mp_result mp_int_to_binary(mp_int z, unsigned char *buf, int limit); |
| |
| /* Read a two's complement binary value into z from the given buffer */ |
| mp_result mp_int_read_binary(mp_int z, unsigned char *buf, int len); |
| |
| /* Return the number of bytes required to represent z in binary. */ |
| mp_result mp_int_binary_len(mp_int z); |
| |
| /* Convert z to unsigned binary, writing at most limit bytes */ |
| mp_result mp_int_to_unsigned(mp_int z, unsigned char *buf, int limit); |
| |
| /* Read an unsigned binary value into z from the given buffer */ |
| mp_result mp_int_read_unsigned(mp_int z, unsigned char *buf, int len); |
| |
| /* Return the number of bytes required to represent z as unsigned output */ |
| mp_result mp_int_unsigned_len(mp_int z); |
| |
| /* Return a statically allocated string describing error code res */ |
| const char *mp_error_string(mp_result res); |
| |
| #if DEBUG |
| void s_print(char *tag, mp_int z); |
| void s_print_buf(char *tag, mp_digit *buf, mp_size num); |
| #endif |
| |
| #ifdef __cplusplus |
| } |
| #endif |
| #endif /* end IMATH_H_ */ |