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long_extras.h
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/*============================================================================
This file is part of FLINT.
FLINT is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
FLINT is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
===============================================================================*/
/******************************************************************************
long_extras.h
Header file for long_extras.c.
(C) 2006, 2007, 2008 William Hart
Copyright (C) 2008, Peter Shrimpton
Some of the macros in this file were borrowed from GMP, (C) Free Software Foundation
******************************************************************************/
#ifndef LONGEXTRAS_H
#define LONGEXTRAS_H
#ifdef __cplusplus
extern "C" {
#endif
#include <math.h>
#include "longlong_wrapper.h"
#include "longlong.h"
#include "flint.h"
//======================================================================================
//
// The code in this section is borrowed from the GMP library v 4.2.1
// See gmp-impl.h, (C) Free Software Foundation
//
//======================================================================================
#define invert_limb(invxl, xl) \
do { \
mp_limb_t dummy; \
udiv_qrnnd (invxl, dummy, ~(xl), ~(0L), xl); \
} while (0)
#define LIMB_HIGHBIT_TO_MASK(n) \
(((mp_limb_signed_t) -1 >> 1) < 0 \
? (mp_limb_signed_t) (n) >> (FLINT_BITS - 1) \
: (n) & (1L<<(FLINT_BITS-1)) ? (~ (mp_limb_t) 0L) : (0L))
#define udiv_qrnnd_preinv(q, r, nh, nl, d, di) \
do { \
mp_limb_t _n2, _n10, _nmask, _nadj, _q1; \
mp_limb_t _xh, _xl; \
_n2 = (nh); \
_n10 = (nl); \
_nmask = LIMB_HIGHBIT_TO_MASK (_n10); \
_nadj = _n10 + (_nmask & (d)); \
umul_ppmm (_xh, _xl, di, _n2 - _nmask); \
add_ssaaaa (_xh, _xl, _xh, _xl, _n2, _nadj); \
_q1 = ~_xh; \
umul_ppmm (_xh, _xl, _q1, d); \
add_ssaaaa (_xh, _xl, _xh, _xl, nh, nl); \
_xh -= (d); /* xh = 0 or -1 */ \
(r) = _xl + ((d) & _xh); \
(q) = _xh - _q1; \
} while (0)
//=====================================================================================
typedef struct factor_s
{
int num;
unsigned long p[15];
unsigned long exp[15];
} factor_t;
typedef struct pair_s
{
ulong x, y;
} pair_t;
#define pre_inv_t double
#define pre_inv2_t double
#define pre_inv_ll_t double
unsigned long z_randint(unsigned long limit);
unsigned long z_randbits(unsigned long bits);
unsigned long z_randprime(unsigned long bits, int proved);
double z_precompute_inverse(unsigned long n);
double z_precompute_inverse2(unsigned long n);
double z_ll_precompute_inverse(unsigned long n);
#if FLINT_BITS == 64
uint32_t z_precompute_inverse32(unsigned long n);
uint32_t z_mod32_precomp(unsigned long n64, uint32_t d, uint32_t di);
unsigned long z_mulmod32_precomp(unsigned long a, unsigned long b,
unsigned long n, uint32_t ninv);
#endif
static inline
unsigned long z_addmod(unsigned long a, unsigned long b, unsigned long p)
{
unsigned long neg1 = p - a;
if (neg1 > b)
return a + b;
else
return b - neg1;
}
static inline
unsigned long z_submod(unsigned long a, unsigned long b, unsigned long p)
{
if (a < b)
return p + a - b;
else
return a - b;
}
static inline
unsigned long z_negmod(unsigned long a, unsigned long p)
{
if (a)
return p - a;
else
return 0;
}
unsigned long z_mod_precomp(unsigned long a, unsigned long n, double ninv);
unsigned long z_div_64_precomp(unsigned long a, unsigned long n, double ninv);
unsigned long z_mod_64_precomp(unsigned long a, unsigned long n, double ninv);
unsigned long z_ll_mod_precomp(unsigned long a_hi, unsigned long a_lo,
unsigned long n, double ninv);
unsigned long z_mulmod_precomp(unsigned long a, unsigned long b,
unsigned long n, double ninv);
unsigned long z_mulmod_64_precomp(unsigned long a, unsigned long b, unsigned long n,
double ninv);
unsigned long z_powmod(unsigned long a, long exp, unsigned long n);
unsigned long z_powmod_64(unsigned long a, long exp, unsigned long n);
unsigned long z_powmod_precomp(unsigned long a, long exp,
unsigned long n, double ninv);
unsigned long z_powmod_64_precomp(unsigned long a, long exp,
unsigned long n, double ninv);
#if FLINT_BITS == 64
#define z_div2_precomp z_div_64_precomp
#define z_mod2_precomp z_mod_64_precomp
#define z_mulmod2_precomp z_mulmod_64_precomp
#define z_powmod2 z_powmod_64
#define z_powmod2_precomp z_powmod_64_precomp
#else
#define z_div2_precomp z_div_64_precomp
#define z_mod2_precomp z_mod_precomp
#define z_mulmod2_precomp z_mulmod_precomp
#define z_powmod2 z_powmod
#define z_powmod2_precomp z_powmod_precomp
#endif
int z_legendre_precomp(unsigned long a, unsigned long p, double pinv);
int z_jacobi(long x, unsigned long y);
int z_ispseudoprime_fermat(unsigned long const n, unsigned long const i);
int z_isprobab_prime(unsigned long n);
int z_isprobab_prime_precomp(unsigned long n, double ninv);
int z_isprime(unsigned long n);
int z_isprime_precomp(unsigned long n, double ninv);
int z_miller_rabin_precomp(unsigned long n, double ninv, unsigned long reps);
unsigned long z_nextprime(unsigned long n, int proved);
int z_isprime_pocklington(unsigned long const n, unsigned long const iterations);
int z_isprime_nm1(unsigned long const n, unsigned long const iterations);
int z_ispseudoprime_lucas_ab(ulong n, int a, int b);
int z_ispseudoprime_lucas(ulong n);
int z_ispseudoprime_fibonacci_precomp(unsigned long n, pre_inv2_t inv);
int z_isprobab_prime_BPSW(unsigned long n);
unsigned long z_pow(unsigned long a, unsigned long exp);
unsigned long z_sqrtmod(unsigned long a, unsigned long p);
unsigned long z_cuberootmod(unsigned long * cuberoot1,
unsigned long a, unsigned long p);
unsigned long z_invert(unsigned long a, unsigned long p);
long z_gcd_invert(long* a, long x, long y);
long z_xgcd(long* a, long* b, long x, long y);
unsigned long z_gcd(long x, long y);
unsigned long z_intsqrt(unsigned long r);
unsigned long z_intcuberoot(unsigned long n);
static inline int z_issquare2(unsigned long x, unsigned long *s)
{
static int mod64[64] = {1,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0};
static int mod65[65] = {1,1,0,0,1,0,0,0,0,1,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,1,0,0,0,0,1,0,0,1};
static int mod_ui[63] = {1,1,0,0,1,0,0,1,0,1,0,0,0,0,1,0,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,1,1,1,0,0,0,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,1,0,1,0,0,0,0};
if (!mod64[x%64]) return 0;
if (!mod_ui[x%63]) return 0;
if (!mod65[x%65]) return 0;
*s = (unsigned long) sqrt((double)x);
return (x == (*s)*(*s));
}
static inline int z_issquare(unsigned long x)
{
unsigned long s;
return z_issquare2(x,&s);
}
unsigned long z_CRT(unsigned long x1, unsigned long n1,
unsigned long x2, unsigned long n2);
int z_issquarefree(unsigned long n, int proved);
int z_remove_precomp(unsigned long * n, unsigned long p, double pinv);
int z_remove(unsigned long * n, unsigned long p);
unsigned long z_factor_trial(factor_t * factors, unsigned long n);
unsigned long z_factor_SQUFOF(unsigned long n);
unsigned long z_factor_tinyQS(unsigned long n);
unsigned long z_factor_HOLF(unsigned long n, unsigned long iterations);
void z_factor(factor_t * factors, unsigned long n, int proved);
unsigned long z_factor_partial(factor_t * factors, unsigned long n, unsigned long limit, int proved);
unsigned long z_primitive_root(unsigned long p);
unsigned long z_primitive_root_precomp(unsigned long p, double p_inv);
void z_remove_power(factor_t *factors, unsigned long n, unsigned int power, int proved);
unsigned long z_factor_235power(unsigned long n, unsigned long *exp);
unsigned long z_intcuberoot(unsigned long n);
unsigned long z_intfifthroot(unsigned long n);
unsigned long z_factor_HOLF(unsigned long n, unsigned long iters);
unsigned long z_factor_trial_extended(unsigned long n);
void z_compute_extended_primes();
static inline void z_initialize_extended_primes();
void insert_factorpower(factor_t * factors, unsigned long p, unsigned long e);
#ifdef __cplusplus
}
#endif
#endif