mirror of
https://git.postgresql.org/git/postgresql.git
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This is still using the 2.0 version of pg_bsd_indent. I thought it would be good to commit this separately, so as to document the differences between 2.0 and 2.1 behavior. Discussion: https://postgr.es/m/16296.1558103386@sss.pgh.pa.us
446 lines
17 KiB
C
446 lines
17 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
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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 obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in
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all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN 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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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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/* Build with words as uint64 by default. */
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#ifdef USE_32BIT_WORDS
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typedef uint16 mp_digit;
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typedef uint32 mp_word;
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#define MP_DIGIT_MAX (PG_UINT16_MAX * 1UL)
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#define MP_WORD_MAX (PG_UINT32_MAX * 1UL)
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#else
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typedef uint32 mp_digit;
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typedef uint64 mp_word;
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#define MP_DIGIT_MAX (PG_UINT32_MAX * UINT64CONST(1))
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#define MP_WORD_MAX (PG_UINT64_MAX)
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#endif
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typedef struct
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{
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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 ,
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*mp_int;
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static inline mp_digit *
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MP_DIGITS(mp_int Z)
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{
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return Z->digits;
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}
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static inline mp_size
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MP_ALLOC(mp_int Z)
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{
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return Z->alloc;
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}
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static inline mp_size
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MP_USED(mp_int Z)
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{
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return Z->used;
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}
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static inline mp_sign
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MP_SIGN(mp_int Z)
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{
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return Z->sign;
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}
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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_MAX ULONG_MAX
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#define MP_MIN_RADIX 2
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#define MP_MAX_RADIX 36
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/** Sets the default number of digits allocated to an `mp_int` constructed by
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`mp_int_init_size()` with `prec == 0`. Allocations are rounded up to
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multiples of this value. `MP_DEFAULT_PREC` is the default value. Requires
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`ndigits > 0`. */
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void mp_int_default_precision(mp_size ndigits);
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/** Sets the number of digits below which multiplication will use the standard
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quadratic "schoolbook" multiplcation algorithm rather than Karatsuba-Ofman.
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Requires `ndigits >= sizeof(mp_word)`. */
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void mp_int_multiply_threshold(mp_size ndigits);
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/** A sign indicating a (strictly) negative value. */
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extern const mp_sign MP_NEG;
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/** A sign indicating a zero or positive value. */
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extern const mp_sign MP_ZPOS;
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/** Reports whether `z` is odd, having remainder 1 when divided by 2. */
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static inline bool
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mp_int_is_odd(mp_int z)
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{
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return (z->digits[0] & 1) != 0;
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}
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/** Reports whether `z` is even, having remainder 0 when divided by 2. */
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static inline bool
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mp_int_is_even(mp_int z)
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{
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return (z->digits[0] & 1) == 0;
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}
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/** Initializes `z` with 1-digit precision and sets it to zero. This function
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cannot fail unless `z == NULL`. */
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mp_result mp_int_init(mp_int z);
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/** Allocates a fresh zero-valued `mpz_t` on the heap, returning NULL in case
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of error. The only possible error is out-of-memory. */
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mp_int mp_int_alloc(void);
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/** Initializes `z` with at least `prec` digits of storage, and sets it to
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zero. If `prec` is zero, the default precision is used. In either case the
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size is rounded up to the nearest multiple of the word size. */
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mp_result mp_int_init_size(mp_int z, mp_size prec);
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/** Initializes `z` to be a copy of an already-initialized value in `old`. The
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new copy does not share storage with the original. */
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mp_result mp_int_init_copy(mp_int z, mp_int old);
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/** Initializes `z` to the specified signed `value` at default precision. */
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mp_result mp_int_init_value(mp_int z, mp_small value);
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/** Initializes `z` to the specified unsigned `value` at default precision. */
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mp_result mp_int_init_uvalue(mp_int z, mp_usmall uvalue);
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/** Sets `z` to the value of the specified signed `value`. */
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mp_result mp_int_set_value(mp_int z, mp_small value);
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/** Sets `z` to the value of the specified unsigned `value`. */
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mp_result mp_int_set_uvalue(mp_int z, mp_usmall uvalue);
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/** Releases the storage used by `z`. */
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void mp_int_clear(mp_int z);
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/** Releases the storage used by `z` and also `z` itself.
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This should only be used for `z` allocated by `mp_int_alloc()`. */
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void mp_int_free(mp_int z);
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/** Replaces the value of `c` with a copy of the value of `a`. No new memory is
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allocated unless `a` has more significant digits than `c` has allocated. */
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mp_result mp_int_copy(mp_int a, mp_int c);
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/** Swaps the values and storage between `a` and `c`. */
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void mp_int_swap(mp_int a, mp_int c);
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/** Sets `z` to zero. The allocated storage of `z` is not changed. */
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void mp_int_zero(mp_int z);
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/** Sets `c` to the absolute value of `a`. */
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mp_result mp_int_abs(mp_int a, mp_int c);
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/** Sets `c` to the additive inverse (negation) of `a`. */
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mp_result mp_int_neg(mp_int a, mp_int c);
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/** Sets `c` to the sum of `a` and `b`. */
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mp_result mp_int_add(mp_int a, mp_int b, mp_int c);
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/** Sets `c` to the sum of `a` and `value`. */
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mp_result mp_int_add_value(mp_int a, mp_small value, mp_int c);
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/** Sets `c` to the difference of `a` less `b`. */
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mp_result mp_int_sub(mp_int a, mp_int b, mp_int c);
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/** Sets `c` to the difference of `a` less `value`. */
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mp_result mp_int_sub_value(mp_int a, mp_small value, mp_int c);
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/** Sets `c` to the product of `a` and `b`. */
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mp_result mp_int_mul(mp_int a, mp_int b, mp_int c);
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/** Sets `c` to the product of `a` and `value`. */
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mp_result mp_int_mul_value(mp_int a, mp_small value, mp_int c);
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/** Sets `c` to the product of `a` and `2^p2`. Requires `p2 >= 0`. */
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mp_result mp_int_mul_pow2(mp_int a, mp_small p2, mp_int c);
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/** Sets `c` to the square of `a`. */
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mp_result mp_int_sqr(mp_int a, mp_int c);
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/** Sets `q` and `r` to the quotent and remainder of `a / b`. Division by
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powers of 2 is detected and handled efficiently. The remainder is pinned
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to `0 <= r < b`.
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Either of `q` or `r` may be NULL, but not both, and `q` and `r` may not
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point to the same value. */
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mp_result mp_int_div(mp_int a, mp_int b, mp_int q, mp_int r);
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/** Sets `q` and `*r` to the quotent and remainder of `a / value`. Division by
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powers of 2 is detected and handled efficiently. The remainder is pinned to
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`0 <= *r < b`. Either of `q` or `r` may be NULL. */
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mp_result mp_int_div_value(mp_int a, mp_small value, mp_int q, mp_small *r);
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/** Sets `q` and `r` to the quotient and remainder of `a / 2^p2`. This is a
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special case for division by powers of two that is more efficient than
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using ordinary division. Note that `mp_int_div()` will automatically handle
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this case, this function is for cases where you have only the exponent. */
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mp_result mp_int_div_pow2(mp_int a, mp_small p2, mp_int q, mp_int r);
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/** Sets `c` to the remainder of `a / m`.
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The remainder is pinned to `0 <= c < m`. */
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mp_result mp_int_mod(mp_int a, mp_int m, mp_int c);
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/** Sets `c` to the value of `a` raised to the `b` power.
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It returns `MP_RANGE` if `b < 0`. */
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mp_result mp_int_expt(mp_int a, mp_small b, mp_int c);
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/** Sets `c` to the value of `a` raised to the `b` power.
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It returns `MP_RANGE` if `b < 0`. */
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mp_result mp_int_expt_value(mp_small a, mp_small b, mp_int c);
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/** Sets `c` to the value of `a` raised to the `b` power.
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It returns `MP_RANGE`) if `b < 0`. */
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mp_result mp_int_expt_full(mp_int a, mp_int b, mp_int c);
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/** Sets `*r` to the remainder of `a / value`.
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The remainder is pinned to `0 <= r < value`. */
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static inline
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mp_result
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mp_int_mod_value(mp_int a, mp_small value, mp_small *r)
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{
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return mp_int_div_value(a, value, 0, r);
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}
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/** Returns the comparator of `a` and `b`. */
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int mp_int_compare(mp_int a, mp_int b);
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/** Returns the comparator of the magnitudes of `a` and `b`, disregarding their
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signs. Neither `a` nor `b` is modified by the comparison. */
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int mp_int_compare_unsigned(mp_int a, mp_int b);
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/** Returns the comparator of `z` and zero. */
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int mp_int_compare_zero(mp_int z);
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/** Returns the comparator of `z` and the signed value `v`. */
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int mp_int_compare_value(mp_int z, mp_small v);
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/** Returns the comparator of `z` and the unsigned value `uv`. */
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int mp_int_compare_uvalue(mp_int z, mp_usmall uv);
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/** Reports whether `a` is divisible by `v`. */
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bool mp_int_divisible_value(mp_int a, mp_small v);
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/** Returns `k >= 0` such that `z` is `2^k`, if such a `k` exists. If no such
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`k` exists, the function returns -1. */
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int mp_int_is_pow2(mp_int z);
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/** Sets `c` to the value of `a` raised to the `b` power, reduced modulo `m`.
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It returns `MP_RANGE` if `b < 0` or `MP_UNDEF` if `m == 0`. */
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mp_result mp_int_exptmod(mp_int a, mp_int b, mp_int m, mp_int c);
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/** Sets `c` to the value of `a` raised to the `value` power, modulo `m`.
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It returns `MP_RANGE` if `value < 0` or `MP_UNDEF` if `m == 0`. */
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mp_result mp_int_exptmod_evalue(mp_int a, mp_small value, mp_int m, mp_int c);
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/** Sets `c` to the value of `value` raised to the `b` power, modulo `m`.
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It returns `MP_RANGE` if `b < 0` or `MP_UNDEF` if `m == 0`. */
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mp_result mp_int_exptmod_bvalue(mp_small value, mp_int b, mp_int m, mp_int c);
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/** Sets `c` to the value of `a` raised to the `b` power, reduced modulo `m`,
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given a precomputed reduction constant `mu` defined for Barrett's modular
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reduction algorithm.
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It returns `MP_RANGE` if `b < 0` or `MP_UNDEF` if `m == 0`. */
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mp_result mp_int_exptmod_known(mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c);
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/** Sets `c` to the reduction constant for Barrett reduction by modulus `m`.
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Requires that `c` and `m` point to distinct locations. */
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mp_result mp_int_redux_const(mp_int m, mp_int c);
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/** Sets `c` to the multiplicative inverse of `a` modulo `m`, if it exists.
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The least non-negative representative of the congruence class is computed.
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It returns `MP_UNDEF` if the inverse does not exist, or `MP_RANGE` if `a ==
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0` or `m <= 0`. */
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mp_result mp_int_invmod(mp_int a, mp_int m, mp_int c);
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/** Sets `c` to the greatest common divisor of `a` and `b`.
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It returns `MP_UNDEF` if the GCD is undefined, such as for example if `a`
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and `b` are both zero. */
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mp_result mp_int_gcd(mp_int a, mp_int b, mp_int c);
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/** Sets `c` to the greatest common divisor of `a` and `b`, and sets `x` and
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`y` to values satisfying Bezout's identity `gcd(a, b) = ax + by`.
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It returns `MP_UNDEF` if the GCD is undefined, such as for example if `a`
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and `b` are both zero. */
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mp_result mp_int_egcd(mp_int a, mp_int b, mp_int c, mp_int x, mp_int y);
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/** Sets `c` to the least common multiple of `a` and `b`.
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It returns `MP_UNDEF` if the LCM is undefined, such as for example if `a`
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and `b` are both zero. */
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mp_result mp_int_lcm(mp_int a, mp_int b, mp_int c);
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/** Sets `c` to the greatest integer not less than the `b`th root of `a`,
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using Newton's root-finding algorithm.
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It returns `MP_UNDEF` if `a < 0` and `b` is even. */
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mp_result mp_int_root(mp_int a, mp_small b, mp_int c);
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/** Sets `c` to the greatest integer not less than the square root of `a`.
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This is a special case of `mp_int_root()`. */
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static inline
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mp_result
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mp_int_sqrt(mp_int a, mp_int c)
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{
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return mp_int_root(a, 2, c);
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}
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/** Returns `MP_OK` if `z` is representable as `mp_small`, else `MP_RANGE`.
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If `out` is not NULL, `*out` is set to the value of `z` when `MP_OK`. */
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mp_result mp_int_to_int(mp_int z, mp_small *out);
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/** Returns `MP_OK` if `z` is representable as `mp_usmall`, or `MP_RANGE`.
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If `out` is not NULL, `*out` is set to the value of `z` when `MP_OK`. */
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mp_result mp_int_to_uint(mp_int z, mp_usmall *out);
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/** Converts `z` to a zero-terminated string of characters in the specified
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`radix`, writing at most `limit` characters to `str` including the
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terminating NUL value. A leading `-` is used to indicate a negative value.
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Returns `MP_TRUNC` if `limit` was to small to write all of `z`.
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Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. */
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mp_result mp_int_to_string(mp_int z, mp_size radix, char *str, int limit);
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/** Reports the minimum number of characters required to represent `z` as a
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zero-terminated string in the given `radix`.
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Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. */
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mp_result mp_int_string_len(mp_int z, mp_size radix);
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/** Reads a string of ASCII digits in the specified `radix` from the zero
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terminated `str` provided into `z`. For values of `radix > 10`, the letters
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`A`..`Z` or `a`..`z` are accepted. Letters are interpreted without respect
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to case.
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Leading whitespace is ignored, and a leading `+` or `-` is interpreted as a
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sign flag. Processing stops when a NUL or any other character out of range
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for a digit in the given radix is encountered.
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If the whole string was consumed, `MP_OK` is returned; otherwise
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`MP_TRUNC`. is returned.
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Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. */
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mp_result mp_int_read_string(mp_int z, mp_size radix, const char *str);
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/** Reads a string of ASCII digits in the specified `radix` from the zero
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terminated `str` provided into `z`. For values of `radix > 10`, the letters
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`A`..`Z` or `a`..`z` are accepted. Letters are interpreted without respect
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to case.
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Leading whitespace is ignored, and a leading `+` or `-` is interpreted as a
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sign flag. Processing stops when a NUL or any other character out of range
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for a digit in the given radix is encountered.
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If the whole string was consumed, `MP_OK` is returned; otherwise
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`MP_TRUNC`. is returned. If `end` is not NULL, `*end` is set to point to
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the first unconsumed byte of the input string (the NUL byte if the whole
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string was consumed). This emulates the behavior of the standard C
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`strtol()` function.
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Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. */
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mp_result mp_int_read_cstring(mp_int z, mp_size radix, const char *str, char **end);
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/** Returns the number of significant bits in `z`. */
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mp_result mp_int_count_bits(mp_int z);
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/** Converts `z` to 2's complement binary, writing at most `limit` bytes into
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the given `buf`. Returns `MP_TRUNC` if the buffer limit was too small to
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contain the whole value. If this occurs, the contents of buf will be
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effectively garbage, as the function uses the buffer as scratch space.
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The binary representation of `z` is in base-256 with digits ordered from
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most significant to least significant (network byte ordering). The
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high-order bit of the first byte is set for negative values, clear for
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non-negative values.
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As a result, non-negative values will be padded with a leading zero byte if
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the high-order byte of the base-256 magnitude is set. This extra byte is
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accounted for by the `mp_int_binary_len()` function. */
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mp_result mp_int_to_binary(mp_int z, unsigned char *buf, int limit);
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/** Reads a 2's complement binary value from `buf` into `z`, where `len` is the
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length of the buffer. The contents of `buf` may be overwritten during
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processing, although they will be restored when the function returns. */
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mp_result mp_int_read_binary(mp_int z, unsigned char *buf, int len);
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/** Returns the number of bytes to represent `z` in 2's complement binary. */
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mp_result mp_int_binary_len(mp_int z);
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/** Converts the magnitude of `z` to unsigned binary, writing at most `limit`
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|
bytes into the given `buf`. The sign of `z` is ignored, but `z` is not
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modified. Returns `MP_TRUNC` if the buffer limit was too small to contain
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the whole value. If this occurs, the contents of `buf` will be effectively
|
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garbage, as the function uses the buffer as scratch space during
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conversion.
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The binary representation of `z` is in base-256 with digits ordered from
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most significant to least significant (network byte ordering). */
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mp_result mp_int_to_unsigned(mp_int z, unsigned char *buf, int limit);
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/** Reads an unsigned binary value from `buf` into `z`, where `len` is the
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|
length of the buffer. The contents of `buf` are not modified during
|
|
processing. */
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|
mp_result mp_int_read_unsigned(mp_int z, unsigned char *buf, int len);
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/** Returns the number of bytes required to represent `z` as an unsigned binary
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|
value in base 256. */
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|
mp_result mp_int_unsigned_len(mp_int z);
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|
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/** Returns a pointer to a brief, human-readable, zero-terminated string
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|
describing `res`. The returned string is statically allocated and must not
|
|
be freed by the caller. */
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|
const char *mp_error_string(mp_result res);
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#endif /* end IMATH_H_ */
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