232 lines
8.7 KiB
C
232 lines
8.7 KiB
C
/*
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Name: imath.h
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Purpose: Arbitrary precision integer arithmetic routines.
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Author: M. J. Fromberger <http://spinning-yarns.org/michael/>
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Info: $Id: imath.h 635 2008-01-08 18:19:40Z sting $
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Copyright (C) 2002-2007 Michael J. Fromberger, All Rights Reserved.
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Permission is hereby granted, free of charge, to any person
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obtaining a copy of this software and associated documentation files
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(the "Software"), to deal in the Software without restriction,
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including without limitation the rights to use, copy, modify, merge,
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publish, distribute, sublicense, and/or sell copies of the Software,
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and to permit persons to whom the Software is furnished to do so,
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subject to the following conditions:
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The above copyright notice and this permission notice shall be
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included in all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
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BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
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ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
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CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.
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*/
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#ifndef IMATH_H_
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#define IMATH_H_
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#include <limits.h>
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#ifdef __cplusplus
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extern "C" {
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#endif
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typedef unsigned char mp_sign;
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typedef unsigned int mp_size;
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typedef int mp_result;
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typedef long mp_small; /* must be a signed type */
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typedef unsigned long mp_usmall; /* must be an unsigned type */
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#ifdef USE_LONG_LONG
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typedef unsigned int mp_digit;
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typedef unsigned long long mp_word;
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#else
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typedef unsigned short mp_digit;
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typedef unsigned int mp_word;
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#endif
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typedef struct mpz {
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mp_digit single;
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mp_digit *digits;
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mp_size alloc;
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mp_size used;
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mp_sign sign;
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} mpz_t, *mp_int;
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#define MP_DIGITS(Z) ((Z)->digits)
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#define MP_ALLOC(Z) ((Z)->alloc)
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#define MP_USED(Z) ((Z)->used)
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#define MP_SIGN(Z) ((Z)->sign)
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extern const mp_result MP_OK;
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extern const mp_result MP_FALSE;
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extern const mp_result MP_TRUE;
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extern const mp_result MP_MEMORY;
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extern const mp_result MP_RANGE;
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extern const mp_result MP_UNDEF;
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extern const mp_result MP_TRUNC;
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extern const mp_result MP_BADARG;
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extern const mp_result MP_MINERR;
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#define MP_DIGIT_BIT (sizeof(mp_digit) * CHAR_BIT)
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#define MP_WORD_BIT (sizeof(mp_word) * CHAR_BIT)
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#define MP_SMALL_MIN LONG_MIN
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#define MP_SMALL_MAX LONG_MAX
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#define MP_USMALL_MIN ULONG_MIN
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#define MP_USMALL_MAX ULONG_MAX
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#ifdef USE_LONG_LONG
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# ifndef ULONG_LONG_MAX
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# ifdef ULLONG_MAX
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# define ULONG_LONG_MAX ULLONG_MAX
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# else
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# error "Maximum value of unsigned long long not defined!"
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# endif
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# endif
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# define MP_DIGIT_MAX (ULONG_MAX * 1ULL)
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# define MP_WORD_MAX ULONG_LONG_MAX
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#else
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# define MP_DIGIT_MAX (USHRT_MAX * 1UL)
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# define MP_WORD_MAX (UINT_MAX * 1UL)
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#endif
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#define MP_MIN_RADIX 2
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#define MP_MAX_RADIX 36
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/* Values with fewer than this many significant digits use the
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standard multiplication algorithm; otherwise, a recursive algorithm
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is used. Choose a value to suit your platform.
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*/
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#define MP_MULT_THRESH 22
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#define MP_DEFAULT_PREC 8 /* default memory allocation, in digits */
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extern const mp_sign MP_NEG;
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extern const mp_sign MP_ZPOS;
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#define mp_int_is_odd(Z) ((Z)->digits[0] & 1)
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#define mp_int_is_even(Z) !((Z)->digits[0] & 1)
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mp_result mp_int_init(mp_int z);
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mp_int mp_int_alloc(void);
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mp_result mp_int_init_size(mp_int z, mp_size prec);
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mp_result mp_int_init_copy(mp_int z, mp_int old);
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mp_result mp_int_init_value(mp_int z, mp_small value);
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mp_result mp_int_set_value(mp_int z, mp_small value);
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void mp_int_clear(mp_int z);
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void mp_int_free(mp_int z);
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mp_result mp_int_copy(mp_int a, mp_int c); /* c = a */
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void mp_int_swap(mp_int a, mp_int c); /* swap a, c */
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void mp_int_zero(mp_int z); /* z = 0 */
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mp_result mp_int_abs(mp_int a, mp_int c); /* c = |a| */
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mp_result mp_int_neg(mp_int a, mp_int c); /* c = -a */
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mp_result mp_int_add(mp_int a, mp_int b, mp_int c); /* c = a + b */
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mp_result mp_int_add_value(mp_int a, mp_small value, mp_int c);
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mp_result mp_int_sub(mp_int a, mp_int b, mp_int c); /* c = a - b */
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mp_result mp_int_sub_value(mp_int a, mp_small value, mp_int c);
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mp_result mp_int_mul(mp_int a, mp_int b, mp_int c); /* c = a * b */
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mp_result mp_int_mul_value(mp_int a, mp_small value, mp_int c);
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mp_result mp_int_mul_pow2(mp_int a, mp_small p2, mp_int c);
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mp_result mp_int_sqr(mp_int a, mp_int c); /* c = a * a */
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mp_result mp_int_div(mp_int a, mp_int b, /* q = a / b */
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mp_int q, mp_int r); /* r = a % b */
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mp_result mp_int_div_value(mp_int a, mp_small value, /* q = a / value */
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mp_int q, mp_small *r); /* r = a % value */
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mp_result mp_int_div_pow2(mp_int a, mp_small p2, /* q = a / 2^p2 */
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mp_int q, mp_int r); /* r = q % 2^p2 */
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mp_result mp_int_mod(mp_int a, mp_int m, mp_int c); /* c = a % m */
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#define mp_int_mod_value(A, V, R) mp_int_div_value((A), (V), 0, (R))
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mp_result mp_int_expt(mp_int a, mp_small b, mp_int c); /* c = a^b */
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mp_result mp_int_expt_value(mp_small a, mp_small b, mp_int c); /* c = a^b */
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int mp_int_compare(mp_int a, mp_int b); /* a <=> b */
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int mp_int_compare_unsigned(mp_int a, mp_int b); /* |a| <=> |b| */
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int mp_int_compare_zero(mp_int z); /* a <=> 0 */
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int mp_int_compare_value(mp_int z, mp_small value); /* a <=> v */
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/* Returns true if v|a, false otherwise (including errors) */
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int mp_int_divisible_value(mp_int a, mp_small v);
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/* Returns k >= 0 such that z = 2^k, if one exists; otherwise < 0 */
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int mp_int_is_pow2(mp_int z);
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mp_result mp_int_exptmod(mp_int a, mp_int b, mp_int m,
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mp_int c); /* c = a^b (mod m) */
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mp_result mp_int_exptmod_evalue(mp_int a, mp_small value,
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mp_int m, mp_int c); /* c = a^v (mod m) */
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mp_result mp_int_exptmod_bvalue(mp_small value, mp_int b,
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mp_int m, mp_int c); /* c = v^b (mod m) */
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mp_result mp_int_exptmod_known(mp_int a, mp_int b,
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mp_int m, mp_int mu,
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mp_int c); /* c = a^b (mod m) */
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mp_result mp_int_redux_const(mp_int m, mp_int c);
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mp_result mp_int_invmod(mp_int a, mp_int m, mp_int c); /* c = 1/a (mod m) */
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mp_result mp_int_gcd(mp_int a, mp_int b, mp_int c); /* c = gcd(a, b) */
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mp_result mp_int_egcd(mp_int a, mp_int b, mp_int c, /* c = gcd(a, b) */
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mp_int x, mp_int y); /* c = ax + by */
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mp_result mp_int_lcm(mp_int a, mp_int b, mp_int c); /* c = lcm(a, b) */
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mp_result mp_int_root(mp_int a, mp_small b, mp_int c); /* c = floor(a^{1/b}) */
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#define mp_int_sqrt(a, c) mp_int_root(a, 2, c) /* c = floor(sqrt(a)) */
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/* Convert to a small int, if representable; else MP_RANGE */
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mp_result mp_int_to_int(mp_int z, mp_small *out);
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mp_result mp_int_to_uint(mp_int z, mp_usmall *out);
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/* Convert to nul-terminated string with the specified radix, writing at
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most limit characters including the nul terminator */
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mp_result mp_int_to_string(mp_int z, mp_size radix,
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char *str, int limit);
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/* Return the number of characters required to represent
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z in the given radix. May over-estimate. */
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mp_result mp_int_string_len(mp_int z, mp_size radix);
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/* Read zero-terminated string into z */
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mp_result mp_int_read_string(mp_int z, mp_size radix, const char *str);
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mp_result mp_int_read_cstring(mp_int z, mp_size radix, const char *str,
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char **end);
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/* Return the number of significant bits in z */
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mp_result mp_int_count_bits(mp_int z);
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/* Convert z to two's complement binary, writing at most limit bytes */
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mp_result mp_int_to_binary(mp_int z, unsigned char *buf, int limit);
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/* Read a two's complement binary value into z from the given buffer */
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mp_result mp_int_read_binary(mp_int z, unsigned char *buf, int len);
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/* Return the number of bytes required to represent z in binary. */
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mp_result mp_int_binary_len(mp_int z);
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/* Convert z to unsigned binary, writing at most limit bytes */
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mp_result mp_int_to_unsigned(mp_int z, unsigned char *buf, int limit);
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/* Read an unsigned binary value into z from the given buffer */
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mp_result mp_int_read_unsigned(mp_int z, unsigned char *buf, int len);
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/* Return the number of bytes required to represent z as unsigned output */
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mp_result mp_int_unsigned_len(mp_int z);
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/* Return a statically allocated string describing error code res */
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const char *mp_error_string(mp_result res);
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#if DEBUG
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void s_print(char *tag, mp_int z);
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void s_print_buf(char *tag, mp_digit *buf, mp_size num);
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#endif
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#ifdef __cplusplus
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}
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#endif
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#endif /* end IMATH_H_ */
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