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Diffstat (limited to 'contrib/pgcrypto/imath.h')
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diff --git a/contrib/pgcrypto/imath.h b/contrib/pgcrypto/imath.h new file mode 100644 index 0000000..0e1676d --- /dev/null +++ b/contrib/pgcrypto/imath.h @@ -0,0 +1,445 @@ +/* + Name: imath.h + Purpose: Arbitrary precision integer arithmetic routines. + Author: M. J. Fromberger + + 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 <limits.h> + +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 */ + + +/* Build with words as uint64 by default. */ +#ifdef USE_32BIT_WORDS +typedef uint16 mp_digit; +typedef uint32 mp_word; +#define MP_DIGIT_MAX (PG_UINT16_MAX * 1UL) +#define MP_WORD_MAX (PG_UINT32_MAX * 1UL) +#else +typedef uint32 mp_digit; +typedef uint64 mp_word; +#define MP_DIGIT_MAX (PG_UINT32_MAX * UINT64CONST(1)) +#define MP_WORD_MAX (PG_UINT64_MAX) +#endif + +typedef struct +{ + mp_digit single; + mp_digit *digits; + mp_size alloc; + mp_size used; + mp_sign sign; +} mpz_t , + + *mp_int; + +static inline mp_digit * +MP_DIGITS(mp_int Z) +{ + return Z->digits; +} +static inline mp_size +MP_ALLOC(mp_int Z) +{ + return Z->alloc; +} +static inline mp_size +MP_USED(mp_int Z) +{ + return Z->used; +} +static inline mp_sign +MP_SIGN(mp_int Z) +{ + return 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_MAX ULONG_MAX + +#define MP_MIN_RADIX 2 +#define MP_MAX_RADIX 36 + +/** Sets the default number of digits allocated to an `mp_int` constructed by + `mp_int_init_size()` with `prec == 0`. Allocations are rounded up to + multiples of this value. `MP_DEFAULT_PREC` is the default value. Requires + `ndigits > 0`. */ +void mp_int_default_precision(mp_size ndigits); + +/** Sets the number of digits below which multiplication will use the standard + quadratic "schoolbook" multiplcation algorithm rather than Karatsuba-Ofman. + Requires `ndigits >= sizeof(mp_word)`. */ +void mp_int_multiply_threshold(mp_size ndigits); + +/** A sign indicating a (strictly) negative value. */ +extern const mp_sign MP_NEG; + +/** A sign indicating a zero or positive value. */ +extern const mp_sign MP_ZPOS; + +/** Reports whether `z` is odd, having remainder 1 when divided by 2. */ +static inline bool +mp_int_is_odd(mp_int z) +{ + return (z->digits[0] & 1) != 0; +} + +/** Reports whether `z` is even, having remainder 0 when divided by 2. */ +static inline bool +mp_int_is_even(mp_int z) +{ + return (z->digits[0] & 1) == 0; +} + +/** Initializes `z` with 1-digit precision and sets it to zero. This function + cannot fail unless `z == NULL`. */ +mp_result mp_int_init(mp_int z); + +/** Allocates a fresh zero-valued `mpz_t` on the heap, returning NULL in case + of error. The only possible error is out-of-memory. */ +mp_int mp_int_alloc(void); + +/** Initializes `z` with at least `prec` digits of storage, and sets it to + zero. If `prec` is zero, the default precision is used. In either case the + size is rounded up to the nearest multiple of the word size. */ +mp_result mp_int_init_size(mp_int z, mp_size prec); + +/** Initializes `z` to be a copy of an already-initialized value in `old`. The + new copy does not share storage with the original. */ +mp_result mp_int_init_copy(mp_int z, mp_int old); + +/** Initializes `z` to the specified signed `value` at default precision. */ +mp_result mp_int_init_value(mp_int z, mp_small value); + +/** Initializes `z` to the specified unsigned `value` at default precision. */ +mp_result mp_int_init_uvalue(mp_int z, mp_usmall uvalue); + +/** Sets `z` to the value of the specified signed `value`. */ +mp_result mp_int_set_value(mp_int z, mp_small value); + +/** Sets `z` to the value of the specified unsigned `value`. */ +mp_result mp_int_set_uvalue(mp_int z, mp_usmall uvalue); + +/** Releases the storage used by `z`. */ +void mp_int_clear(mp_int z); + +/** Releases the storage used by `z` and also `z` itself. + This should only be used for `z` allocated by `mp_int_alloc()`. */ +void mp_int_free(mp_int z); + +/** Replaces the value of `c` with a copy of the value of `a`. No new memory is + allocated unless `a` has more significant digits than `c` has allocated. */ +mp_result mp_int_copy(mp_int a, mp_int c); + +/** Swaps the values and storage between `a` and `c`. */ +void mp_int_swap(mp_int a, mp_int c); + +/** Sets `z` to zero. The allocated storage of `z` is not changed. */ +void mp_int_zero(mp_int z); + +/** Sets `c` to the absolute value of `a`. */ +mp_result mp_int_abs(mp_int a, mp_int c); + +/** Sets `c` to the additive inverse (negation) of `a`. */ +mp_result mp_int_neg(mp_int a, mp_int c); + +/** Sets `c` to the sum of `a` and `b`. */ +mp_result mp_int_add(mp_int a, mp_int b, mp_int c); + +/** Sets `c` to the sum of `a` and `value`. */ +mp_result mp_int_add_value(mp_int a, mp_small value, mp_int c); + +/** Sets `c` to the difference of `a` less `b`. */ +mp_result mp_int_sub(mp_int a, mp_int b, mp_int c); + +/** Sets `c` to the difference of `a` less `value`. */ +mp_result mp_int_sub_value(mp_int a, mp_small value, mp_int c); + +/** Sets `c` to the product of `a` and `b`. */ +mp_result mp_int_mul(mp_int a, mp_int b, mp_int c); + +/** Sets `c` to the product of `a` and `value`. */ +mp_result mp_int_mul_value(mp_int a, mp_small value, mp_int c); + +/** Sets `c` to the product of `a` and `2^p2`. Requires `p2 >= 0`. */ +mp_result mp_int_mul_pow2(mp_int a, mp_small p2, mp_int c); + +/** Sets `c` to the square of `a`. */ +mp_result mp_int_sqr(mp_int a, mp_int c); + +/** Sets `q` and `r` to the quotent and remainder of `a / b`. Division by + powers of 2 is detected and handled efficiently. The remainder is pinned + to `0 <= r < b`. + + Either of `q` or `r` may be NULL, but not both, and `q` and `r` may not + point to the same value. */ +mp_result mp_int_div(mp_int a, mp_int b, mp_int q, mp_int r); + +/** Sets `q` and `*r` to the quotent and remainder of `a / value`. Division by + powers of 2 is detected and handled efficiently. The remainder is pinned to + `0 <= *r < b`. Either of `q` or `r` may be NULL. */ +mp_result mp_int_div_value(mp_int a, mp_small value, mp_int q, mp_small *r); + +/** Sets `q` and `r` to the quotient and remainder of `a / 2^p2`. This is a + special case for division by powers of two that is more efficient than + using ordinary division. Note that `mp_int_div()` will automatically handle + this case, this function is for cases where you have only the exponent. */ +mp_result mp_int_div_pow2(mp_int a, mp_small p2, mp_int q, mp_int r); + +/** Sets `c` to the remainder of `a / m`. + The remainder is pinned to `0 <= c < m`. */ +mp_result mp_int_mod(mp_int a, mp_int m, mp_int c); + +/** Sets `c` to the value of `a` raised to the `b` power. + It returns `MP_RANGE` if `b < 0`. */ +mp_result mp_int_expt(mp_int a, mp_small b, mp_int c); + +/** Sets `c` to the value of `a` raised to the `b` power. + It returns `MP_RANGE` if `b < 0`. */ +mp_result mp_int_expt_value(mp_small a, mp_small b, mp_int c); + +/** Sets `c` to the value of `a` raised to the `b` power. + It returns `MP_RANGE`) if `b < 0`. */ +mp_result mp_int_expt_full(mp_int a, mp_int b, mp_int c); + +/** Sets `*r` to the remainder of `a / value`. + The remainder is pinned to `0 <= r < value`. */ +static inline +mp_result +mp_int_mod_value(mp_int a, mp_small value, mp_small *r) +{ + return mp_int_div_value(a, value, 0, r); +} + +/** Returns the comparator of `a` and `b`. */ +int mp_int_compare(mp_int a, mp_int b); + +/** Returns the comparator of the magnitudes of `a` and `b`, disregarding their + signs. Neither `a` nor `b` is modified by the comparison. */ +int mp_int_compare_unsigned(mp_int a, mp_int b); + +/** Returns the comparator of `z` and zero. */ +int mp_int_compare_zero(mp_int z); + +/** Returns the comparator of `z` and the signed value `v`. */ +int mp_int_compare_value(mp_int z, mp_small v); + +/** Returns the comparator of `z` and the unsigned value `uv`. */ +int mp_int_compare_uvalue(mp_int z, mp_usmall uv); + +/** Reports whether `a` is divisible by `v`. */ +bool mp_int_divisible_value(mp_int a, mp_small v); + +/** Returns `k >= 0` such that `z` is `2^k`, if such a `k` exists. If no such + `k` exists, the function returns -1. */ +int mp_int_is_pow2(mp_int z); + +/** Sets `c` to the value of `a` raised to the `b` power, reduced modulo `m`. + It returns `MP_RANGE` if `b < 0` or `MP_UNDEF` if `m == 0`. */ +mp_result mp_int_exptmod(mp_int a, mp_int b, mp_int m, mp_int c); + +/** Sets `c` to the value of `a` raised to the `value` power, modulo `m`. + It returns `MP_RANGE` if `value < 0` or `MP_UNDEF` if `m == 0`. */ +mp_result mp_int_exptmod_evalue(mp_int a, mp_small value, mp_int m, mp_int c); + +/** Sets `c` to the value of `value` raised to the `b` power, modulo `m`. + It returns `MP_RANGE` if `b < 0` or `MP_UNDEF` if `m == 0`. */ +mp_result mp_int_exptmod_bvalue(mp_small value, mp_int b, mp_int m, mp_int c); + +/** Sets `c` to the value of `a` raised to the `b` power, reduced modulo `m`, + given a precomputed reduction constant `mu` defined for Barrett's modular + reduction algorithm. + + It returns `MP_RANGE` if `b < 0` or `MP_UNDEF` if `m == 0`. */ +mp_result mp_int_exptmod_known(mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c); + +/** Sets `c` to the reduction constant for Barrett reduction by modulus `m`. + Requires that `c` and `m` point to distinct locations. */ +mp_result mp_int_redux_const(mp_int m, mp_int c); + +/** Sets `c` to the multiplicative inverse of `a` modulo `m`, if it exists. + The least non-negative representative of the congruence class is computed. + + It returns `MP_UNDEF` if the inverse does not exist, or `MP_RANGE` if `a == + 0` or `m <= 0`. */ +mp_result mp_int_invmod(mp_int a, mp_int m, mp_int c); + +/** Sets `c` to the greatest common divisor of `a` and `b`. + + It returns `MP_UNDEF` if the GCD is undefined, such as for example if `a` + and `b` are both zero. */ +mp_result mp_int_gcd(mp_int a, mp_int b, mp_int c); + +/** Sets `c` to the greatest common divisor of `a` and `b`, and sets `x` and + `y` to values satisfying Bezout's identity `gcd(a, b) = ax + by`. + + It returns `MP_UNDEF` if the GCD is undefined, such as for example if `a` + and `b` are both zero. */ +mp_result mp_int_egcd(mp_int a, mp_int b, mp_int c, mp_int x, mp_int y); + +/** Sets `c` to the least common multiple of `a` and `b`. + + It returns `MP_UNDEF` if the LCM is undefined, such as for example if `a` + and `b` are both zero. */ +mp_result mp_int_lcm(mp_int a, mp_int b, mp_int c); + +/** Sets `c` to the greatest integer not less than the `b`th root of `a`, + using Newton's root-finding algorithm. + It returns `MP_UNDEF` if `a < 0` and `b` is even. */ +mp_result mp_int_root(mp_int a, mp_small b, mp_int c); + +/** Sets `c` to the greatest integer not less than the square root of `a`. + This is a special case of `mp_int_root()`. */ +static inline +mp_result +mp_int_sqrt(mp_int a, mp_int c) +{ + return mp_int_root(a, 2, c); +} + +/** Returns `MP_OK` if `z` is representable as `mp_small`, else `MP_RANGE`. + If `out` is not NULL, `*out` is set to the value of `z` when `MP_OK`. */ +mp_result mp_int_to_int(mp_int z, mp_small *out); + +/** Returns `MP_OK` if `z` is representable as `mp_usmall`, or `MP_RANGE`. + If `out` is not NULL, `*out` is set to the value of `z` when `MP_OK`. */ +mp_result mp_int_to_uint(mp_int z, mp_usmall *out); + +/** Converts `z` to a zero-terminated string of characters in the specified + `radix`, writing at most `limit` characters to `str` including the + terminating NUL value. A leading `-` is used to indicate a negative value. + + Returns `MP_TRUNC` if `limit` was to small to write all of `z`. + Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. */ +mp_result mp_int_to_string(mp_int z, mp_size radix, char *str, int limit); + +/** Reports the minimum number of characters required to represent `z` as a + zero-terminated string in the given `radix`. + Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. */ +mp_result mp_int_string_len(mp_int z, mp_size radix); + +/** Reads a string of ASCII digits in the specified `radix` from the zero + terminated `str` provided into `z`. For values of `radix > 10`, the letters + `A`..`Z` or `a`..`z` are accepted. Letters are interpreted without respect + to case. + + Leading whitespace is ignored, and a leading `+` or `-` is interpreted as a + sign flag. Processing stops when a NUL or any other character out of range + for a digit in the given radix is encountered. + + If the whole string was consumed, `MP_OK` is returned; otherwise + `MP_TRUNC`. is returned. + + Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. */ +mp_result mp_int_read_string(mp_int z, mp_size radix, const char *str); + +/** Reads a string of ASCII digits in the specified `radix` from the zero + terminated `str` provided into `z`. For values of `radix > 10`, the letters + `A`..`Z` or `a`..`z` are accepted. Letters are interpreted without respect + to case. + + Leading whitespace is ignored, and a leading `+` or `-` is interpreted as a + sign flag. Processing stops when a NUL or any other character out of range + for a digit in the given radix is encountered. + + If the whole string was consumed, `MP_OK` is returned; otherwise + `MP_TRUNC`. is returned. If `end` is not NULL, `*end` is set to point to + the first unconsumed byte of the input string (the NUL byte if the whole + string was consumed). This emulates the behavior of the standard C + `strtol()` function. + + Requires `MP_MIN_RADIX <= radix <= MP_MAX_RADIX`. */ +mp_result mp_int_read_cstring(mp_int z, mp_size radix, const char *str, char **end); + +/** Returns the number of significant bits in `z`. */ +mp_result mp_int_count_bits(mp_int z); + +/** Converts `z` to 2's complement binary, writing at most `limit` bytes into + the given `buf`. Returns `MP_TRUNC` if the buffer limit was too small to + contain the whole value. If this occurs, the contents of buf will be + effectively garbage, as the function uses the buffer as scratch space. + + The binary representation of `z` is in base-256 with digits ordered from + most significant to least significant (network byte ordering). The + high-order bit of the first byte is set for negative values, clear for + non-negative values. + + As a result, non-negative values will be padded with a leading zero byte if + the high-order byte of the base-256 magnitude is set. This extra byte is + accounted for by the `mp_int_binary_len()` function. */ +mp_result mp_int_to_binary(mp_int z, unsigned char *buf, int limit); + +/** Reads a 2's complement binary value from `buf` into `z`, where `len` is the + length of the buffer. The contents of `buf` may be overwritten during + processing, although they will be restored when the function returns. */ +mp_result mp_int_read_binary(mp_int z, unsigned char *buf, int len); + +/** Returns the number of bytes to represent `z` in 2's complement binary. */ +mp_result mp_int_binary_len(mp_int z); + +/** Converts the magnitude of `z` to unsigned binary, writing at most `limit` + bytes into the given `buf`. The sign of `z` is ignored, but `z` is not + modified. Returns `MP_TRUNC` if the buffer limit was too small to contain + the whole value. If this occurs, the contents of `buf` will be effectively + garbage, as the function uses the buffer as scratch space during + conversion. + + The binary representation of `z` is in base-256 with digits ordered from + most significant to least significant (network byte ordering). */ +mp_result mp_int_to_unsigned(mp_int z, unsigned char *buf, int limit); + +/** Reads an unsigned binary value from `buf` into `z`, where `len` is the + length of the buffer. The contents of `buf` are not modified during + processing. */ +mp_result mp_int_read_unsigned(mp_int z, unsigned char *buf, int len); + +/** Returns the number of bytes required to represent `z` as an unsigned binary + value in base 256. */ +mp_result mp_int_unsigned_len(mp_int z); + +/** Returns a pointer to a brief, human-readable, zero-terminated string + describing `res`. The returned string is statically allocated and must not + be freed by the caller. */ +const char *mp_error_string(mp_result res); + +#endif /* end IMATH_H_ */ |