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/* See LICENSE file for copyright and license details. */
/* Warning: libzahl is not thread-safe. */
/* Caution: Do not use libzahl for cryptographic applications, use a specialised library. */
#ifndef ZAHL_H
#define ZAHL_H 1
#include <stddef.h>
#include <setjmp.h>
#include <stdint.h>
#include <limits.h>
#ifndef ZAHL_INLINE
# if defined(__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
# define ZAHL_INLINE static inline
# else
# define ZAHL_INLINE static
# endif
#endif
/* You should pretend like this typedef does not exist. */
typedef uint64_t zahl_char_t;
/* This structure should be considered opaque. */
typedef struct {
int sign;
#if INT_MAX != LONG_MAX
int padding__;
#endif
size_t used;
size_t alloced;
zahl_char_t *chars;
} z_t[1];
enum zprimality {
NONPRIME = 0, /* The number is definitely composite. */
PROBABLY_PRIME, /* The number is probably prime. */
PRIME /* The number is definitely prime. */
};
enum zranddev {
FAST_RANDOM = 0, /* Random numbers are generated directly from /dev/urandom. */
SECURE_RANDOM /* Random numbers are generated directly from /dev/random. */
};
enum zranddist {
QUASIUNIFORM = 0, /* Almost uniformly random, per the usual recommendation. */
UNIFORM /* Actually uniformly random. */
};
enum zerror {
ZERROR_ERRNO_SET = 0, /* Please refer to errno. */
ZERROR_0_POW_0, /* Indeterminate form: 0:th power of 0. (Translatable to EDOM.) */
ZERROR_0_DIV_0, /* Indeterminate form: 0 divided by 0. (Translatable to EDOM.) */
ZERROR_DIV_0, /* Undefined result: Division by 0. (Translatable to EDOM.) */
ZERROR_NEGATIVE /* Argument must be non-negative. (Translatable to EDOM or EINVAL.) */
};
/* The parameters in the functions below are numbers a, b, c, ... */
/* Library initialisation and destruction. */
void zsetup(jmp_buf); /* Prepare libzahl for use. */
void zunsetup(void); /* Free resources used by libzahl */
/* Memory functions. */
ZAHL_INLINE void zinit(z_t); /* Prepare a for use. */
ZAHL_INLINE void zswap(z_t, z_t); /* (a, b) := (b, a) */
void zfree(z_t); /* Free resources in a. */
size_t zsave(z_t, void *); /* Store a into b (if !!b), and return number of written bytes. */
size_t zload(z_t, const void *); /* Restore a from b, and return number of read bytes. */
/* Assignment functions. */
void zset(z_t, z_t); /* a := b */
void zsetu(z_t, uint64_t); /* a := b */
ZAHL_INLINE void zseti(z_t, int64_t); /* a := b */
/* Comparison functions. */
int zcmp(z_t, z_t); /* signum (a - b) */
int zcmpu(z_t, uint64_t); /* signum (a - b) */
int zcmpi(z_t, int64_t); /* signum (a - b) */
int zcmpmag(z_t, z_t); /* signum (|a| - |b|) */
/* Arithmetic functions. */
ZAHL_INLINE void zabs(z_t, z_t); /* a := |b| */
ZAHL_INLINE void zneg(z_t, z_t); /* a := -b */
void zadd(z_t, z_t, z_t); /* a := b + c */
void zsub(z_t, z_t, z_t); /* a := b - c */
void zmul(z_t, z_t, z_t); /* a := b * c */
void zmodmul(z_t, z_t, z_t, z_t); /* a := (b * c) % d */
void zdiv(z_t, z_t, z_t); /* a := b / c */
void zdivmod(z_t, z_t, z_t, z_t); /* a := c / d, b = c % d */
void zmod(z_t, z_t, z_t); /* a := b % c */
void zsqr(z_t, z_t); /* a := b² */
void zmodsqr(z_t, z_t, z_t); /* a := b² % c */
void zpow(z_t, z_t, z_t); /* a := b ↑ c */
void zmodpow(z_t, z_t, z_t, z_t); /* a := (b ↑ c) % d */
void zpowu(z_t, z_t, unsigned long long int);
void zmodpowu(z_t, z_t, unsigned long long int, z_t);
/* These are used internally and may be removed in a future version. */
void zadd_unsigned(z_t, z_t, z_t); /* a := |b| + |c| */
void zsub_unsigned(z_t, z_t, z_t); /* a := |b| - |c| */
/* Bitwise operations. */
void zand(z_t, z_t, z_t); /* a := b & c */
void zor(z_t, z_t, z_t); /* a := b | c */
void zxor(z_t, z_t, z_t); /* a := b ^ c */
void znot(z_t, z_t); /* a := ~b */
void zlsh(z_t, z_t, size_t); /* a := b << c */
void zrsh(z_t, z_t, size_t); /* a := b >> c */
void ztrunc(z_t, z_t, size_t); /* a := b & ((1 << c) - 1) */
int zbtest(z_t, size_t); /* (a >> b) & 1 */
void zsplit(z_t, z_t, z_t, size_t); /* a := c >> d, b := c - (a << d) */
ZAHL_INLINE size_t zlsb(z_t); /* Index of first set bit, SIZE_MAX if none are set. */
ZAHL_INLINE size_t zbits(z_t); /* ⌊log₂ |a|⌋ + 1, 1 if a = 0 */
/* If d > 0: a := b | (1 << c), if d = 0: a := b & ~(1 << c), if d < 0: a := b ^ (1 << c) */
void zbset(z_t, z_t, size_t, int);
/* Number theory. */
ZAHL_INLINE int zeven(z_t); /* Is a even? */
ZAHL_INLINE int zodd(z_t); /* Is a odd? */
ZAHL_INLINE int zeven_nonzero(z_t); /* Is a even? Assumes a ≠ 0. */
ZAHL_INLINE int zodd_nonzero(z_t); /* Is a odd? Assumes a ≠ 0. */
ZAHL_INLINE int zzero(z_t); /* Is a zero? */
ZAHL_INLINE int zsignum(z_t); /* a/|a|, 0 if a is zero. */
void zgcd(z_t, z_t, z_t); /* a := gcd(b, c) */
/* NONPRIME if b ∉ ℙ, PROBABLY_PRIME, if b ∈ ℙ with (1 − 4↑−c) certainty, 2 if PRIME ∈ ℙ.
* If NONPRIME is returned the witness of b's compositeness is stored in a. */
enum zprimality zptest(z_t, z_t, int);
/* Random number generation. */
/* Pick a randomly from [0, d] ∩ ℤ. */
void zrand(z_t, enum zranddev, enum zranddist, z_t);
/* String conversion. */
char *zstr(z_t, char *); /* Write a in decimal onto b. */
int zsets(z_t, const char *); /* a := b */
/* Length of a in radix b. */
size_t zstr_length(z_t, unsigned long long int);
/* Error handling functions. */
enum zerror zerror(const char **); /* Return the current error code, and unless !a, a description in *a. */
void zperror(const char *); /* Identical to perror(3p) except it supports libzahl errors. */
/* ------------------------------- Implementations of inline functions. ------------------------------- */
#if defined(__GNUC__) || defined(__clang__)
# define ZAHL_UNLIKELY(expr) __builtin_expect(!!(expr), 0)
# define ZAHL_LIKELY(expr) __builtin_expect(!!(expr), 1)
#else
# define ZAHL_UNLIKELY(expr) (expr)
# define ZAHL_LIKELY(expr) (expr)
#endif
ZAHL_INLINE void zinit(z_t a) { a->alloced = 0; a->chars = 0; }
ZAHL_INLINE int zeven(z_t a) { return !a->sign || !(a->chars[0] & 1); }
ZAHL_INLINE int zodd(z_t a) { return a->sign && (a->chars[0] & 1); }
ZAHL_INLINE int zeven_nonzero(z_t a) { return !(a->chars[0] & 1); }
ZAHL_INLINE int zodd_nonzero(z_t a) { return (a->chars[0] & 1); }
ZAHL_INLINE int zzero(z_t a) { return !a->sign; }
ZAHL_INLINE int zsignum(z_t a) { return a->sign; }
ZAHL_INLINE void zabs(z_t a, z_t b) { if (a != b) zset(a, b); a->sign = !!a->sign; }
ZAHL_INLINE void zneg(z_t a, z_t b) { if (a != b) zset(a, b); a->sign = -a->sign; }
ZAHL_INLINE void
zswap(z_t a, z_t b)
{
z_t t;
t->sign = a->sign;
a->sign = b->sign;
b->sign = t->sign;
t->used = b->used;
b->used = a->used;
a->used = t->used;
t->alloced = a->alloced;
a->alloced = b->alloced;
b->alloced = t->alloced;
t->chars = b->chars;
b->chars = a->chars;
a->chars = t->chars;
}
ZAHL_INLINE void
zseti(z_t a, int64_t b)
{
if (ZAHL_UNLIKELY(b >= 0)) {
zsetu(a, (uint64_t)b);
} else {
zsetu(a, (uint64_t)-b);
a->sign = -1;
}
}
ZAHL_INLINE size_t
zlsb(z_t a)
{
#if defined(__GNUC__) || defined(__clang__)
size_t i = 0;
if (ZAHL_UNLIKELY(zzero(a)))
return SIZE_MAX;
for (; !a->chars[i]; i++);
i *= 8 * sizeof(zahl_char_t);
i += (size_t)__builtin_ctzll(a->chars[i]);
return i;
#else
size_t i = 0;
zahl_char_t x;
if (ZAHL_UNLIKELY(zzero(a)))
return SIZE_MAX;
for (; !a->chars[i]; i++);
i *= 8 * sizeof(zahl_char_t);
x = ~(a->chars[i]);
for (; x & 1; x >>= 1, i++);
return i;
#endif
}
ZAHL_INLINE size_t
zbits(z_t a)
{
#if defined(__GNUC__) || defined(__clang__)
size_t rc;
if (ZAHL_UNLIKELY(zzero(a)))
return 1;
while (!a->chars[a->used - 1]) a->used--; /* TODO should not be necessary */
rc = a->used * 8 * sizeof(zahl_char_t);
rc -= (size_t)__builtin_clzll(a->chars[a->used - 1]);
return rc;
#else
size_t rc;
zahl_char_t x;
if (ZAHL_UNLIKELY(zzero(a)))
return 1;
while (!a->chars[a->used - 1]) a->used--; /* TODO should not be necessary */
x = a->chars[a->used - 1];
rc = (a->used - 1) * 8 * sizeof(zahl_char_t);
for (; x; x >>= 1, rc++);
return rc;
#endif
}
#endif
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