/*============================================================================= 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 =============================================================================*/ /****************************************************************************** Copyright (C) 2009 William Hart ******************************************************************************/ #ifndef FMPZ_H #define FMPZ_H #undef ulong #define ulong ulongxx/* interferes with system includes */ #include #include #undef ulong #include #define ulong mp_limb_t #include "flint.h" #include "nmod_vec.h" #include "fmpz-conversions.h" #ifdef __cplusplus extern "C" { #endif typedef slong fmpz; typedef fmpz fmpz_t[1]; typedef gmp_randstate_t fmpz_randstate_t; extern __mpz_struct * fmpz_arr; extern gmp_randstate_t fmpz_randstate; typedef struct { mp_ptr dinv; slong n; mp_bitcnt_t norm; } fmpz_preinvn_struct; typedef fmpz_preinvn_struct fmpz_preinvn_t[1]; /* maximum positive value a small coefficient can have */ #define COEFF_MAX ((WORD(1) << (FLINT_BITS - 2)) - WORD(1)) /* minimum negative value a small coefficient can have */ #define COEFF_MIN (-((WORD(1) << (FLINT_BITS - 2)) - WORD(1))) #define COEFF_IS_MPZ(x) (((x) >> (FLINT_BITS - 2)) == WORD(1)) /* is x a pointer not an integer */ __mpz_struct * _fmpz_new_mpz(void); void _fmpz_clear_mpz(fmpz f); void _fmpz_cleanup_mpz_content(void); void _fmpz_cleanup(void); __mpz_struct * _fmpz_promote(fmpz_t f); __mpz_struct * _fmpz_promote_val(fmpz_t f); static __inline__ void _fmpz_demote(fmpz_t f) { if (COEFF_IS_MPZ(*f)) { _fmpz_clear_mpz(*f); (*f) = WORD(0); } } void _fmpz_demote_val(fmpz_t f); void _fmpz_init_readonly_mpz(fmpz_t f, const mpz_t z); void _fmpz_clear_readonly_mpz(mpz_t); static __inline__ void fmpz_init(fmpz_t f) { (*f) = WORD(0); } void fmpz_init2(fmpz_t f, ulong limbs); static __inline__ void fmpz_init_set(fmpz_t f, const fmpz_t g) { if (!COEFF_IS_MPZ(*g)) { *f = *g; } else { __mpz_struct *ptr; ptr = _fmpz_new_mpz(); *f = PTR_TO_COEFF(ptr); mpz_set(ptr, COEFF_TO_PTR(*g)); } } static __inline__ void fmpz_init_set_ui(fmpz_t f, ulong g) { if (g <= COEFF_MAX) { *f = g; } else { __mpz_struct *ptr; ptr = _fmpz_new_mpz(); *f = PTR_TO_COEFF(ptr); flint_mpz_set_ui(ptr, g); } } static __inline__ void fmpz_clear(fmpz_t f) { _fmpz_demote(f); } void fmpz_randbits(fmpz_t f, flint_rand_t state, mp_bitcnt_t bits); void fmpz_randm(fmpz_t f, flint_rand_t state, const fmpz_t m); void fmpz_randtest(fmpz_t f, flint_rand_t state, mp_bitcnt_t bits); void fmpz_randtest_unsigned(fmpz_t f, flint_rand_t state, mp_bitcnt_t bits); void fmpz_randtest_not_zero(fmpz_t f, flint_rand_t state, mp_bitcnt_t bits); void fmpz_randtest_mod(fmpz_t f, flint_rand_t state, const fmpz_t m); void fmpz_randtest_mod_signed(fmpz_t f, flint_rand_t state, const fmpz_t m); slong fmpz_get_si(const fmpz_t f); ulong fmpz_get_ui(const fmpz_t f); static __inline__ void fmpz_set_si(fmpz_t f, slong val) { if (val < COEFF_MIN || val > COEFF_MAX) /* val is large */ { __mpz_struct *mpz_coeff = _fmpz_promote(f); flint_mpz_set_si(mpz_coeff, val); } else { _fmpz_demote(f); *f = val; /* val is small */ } } static __inline__ void fmpz_set_ui(fmpz_t f, ulong val) { if (val > COEFF_MAX) /* val is large */ { __mpz_struct *mpz_coeff = _fmpz_promote(f); flint_mpz_set_ui(mpz_coeff, val); } else { _fmpz_demote(f); *f = val; /* val is small */ } } static __inline__ void fmpz_neg_ui(fmpz_t f, ulong val) { if (val > COEFF_MAX) { __mpz_struct *mpz_coeff = _fmpz_promote(f); flint_mpz_set_ui(mpz_coeff, val); mpz_neg(mpz_coeff, mpz_coeff); } else { _fmpz_demote(f); *f = -(slong) val; } } static __inline__ void fmpz_set_uiui(fmpz_t f, mp_limb_t hi, mp_limb_t lo) { if (hi == 0) { fmpz_set_ui(f, lo); } else { __mpz_struct *z = _fmpz_promote(f); if (z->_mp_alloc < 2) mpz_realloc2(z, 2 * FLINT_BITS); z->_mp_d[0] = lo; z->_mp_d[1] = hi; z->_mp_size = 2; } } static __inline__ void fmpz_neg_uiui(fmpz_t f, mp_limb_t hi, mp_limb_t lo) { if (hi == 0) { fmpz_neg_ui(f, lo); } else { __mpz_struct *z = _fmpz_promote(f); if (z->_mp_alloc < 2) mpz_realloc2(z, 2 * FLINT_BITS); z->_mp_d[0] = lo; z->_mp_d[1] = hi; z->_mp_size = -2; } } void fmpz_get_mpz(mpz_t x, const fmpz_t f); void fmpz_set_mpz(fmpz_t f, const mpz_t x); double fmpz_get_d(const fmpz_t f); void fmpz_set_d(fmpz_t f, double c); int fmpz_set_str(fmpz_t f, const char * str, int b); void flint_mpz_init_set_readonly(mpz_t z, const fmpz_t f); void flint_mpz_clear_readonly(mpz_t z); void fmpz_init_set_readonly(fmpz_t f, const mpz_t z); void fmpz_clear_readonly(fmpz_t f); int fmpz_abs_fits_ui(const fmpz_t f); int fmpz_fits_si(const fmpz_t f); static __inline__ void fmpz_zero(fmpz_t f) { _fmpz_demote(f); (*f) = WORD(0); } static __inline__ void fmpz_one(fmpz_t f) { if (COEFF_IS_MPZ(*f)) { _fmpz_clear_mpz(*f); } *f = WORD(1); } static __inline__ int fmpz_is_zero(const fmpz_t f) { return (*f == 0); } static __inline__ int fmpz_is_one(const fmpz_t f) { return (*f == 1); } static __inline__ int fmpz_is_pm1(const fmpz_t f) { return (*f == 1 || *f == -1); } void fmpz_set(fmpz_t f, const fmpz_t g); int fmpz_equal(const fmpz_t f, const fmpz_t g); int fmpz_equal_si(const fmpz_t f, slong g); int fmpz_equal_ui(const fmpz_t f, ulong g); int fmpz_read(fmpz_t f); int fmpz_fread(FILE * file, fmpz_t f); size_t fmpz_inp_raw( fmpz_t x, FILE *fin ); int fmpz_print(const fmpz_t x); int fmpz_fprint(FILE * file, const fmpz_t x); size_t fmpz_out_raw( FILE *fout, const fmpz_t x ); size_t fmpz_sizeinbase(const fmpz_t f, int b); char * fmpz_get_str(char * str, int b, const fmpz_t f); static __inline__ void fmpz_swap(fmpz_t f, fmpz_t g) { if (f != g) /* swapping required */ { fmpz t = *f; *f = *g; *g = t; } } int fmpz_cmp(const fmpz_t f, const fmpz_t g); int fmpz_cmp_ui(const fmpz_t f, ulong g); int fmpz_cmp_si(const fmpz_t f, slong g); int fmpz_cmpabs(const fmpz_t f, const fmpz_t g); static __inline__ int fmpz_is_even(const fmpz_t f) { if (!COEFF_IS_MPZ(*f)) { return !((*f) & WORD(1)); } else { return mpz_even_p(COEFF_TO_PTR(*f)); } } static __inline__ int fmpz_is_odd(const fmpz_t f) { if (!COEFF_IS_MPZ(*f)) { return ((*f) & WORD(1)); } else { return mpz_odd_p(COEFF_TO_PTR(*f)); } } mp_size_t fmpz_size(const fmpz_t f); int fmpz_sgn(const fmpz_t f); mp_bitcnt_t fmpz_bits(const fmpz_t f); mp_bitcnt_t fmpz_val2(const fmpz_t x); static __inline__ void fmpz_neg(fmpz_t f1, const fmpz_t f2) { if (!COEFF_IS_MPZ(*f2)) /* coeff is small */ { fmpz t = -*f2; /* Need to save value in case of aliasing */ _fmpz_demote(f1); *f1 = t; } else /* coeff is large */ { /* No need to retain value in promotion, as if aliased, both already large */ __mpz_struct *mpz_ptr = _fmpz_promote(f1); mpz_neg(mpz_ptr, COEFF_TO_PTR(*f2)); } } void fmpz_abs(fmpz_t f1, const fmpz_t f2); void fmpz_add(fmpz_t f, const fmpz_t g, const fmpz_t h); void fmpz_sub(fmpz_t f, const fmpz_t g, const fmpz_t h); void fmpz_mul_ui(fmpz_t f, const fmpz_t g, ulong x); void fmpz_mul_si(fmpz_t f, const fmpz_t g, slong x); void fmpz_mul(fmpz_t f, const fmpz_t g, const fmpz_t h); void fmpz_mul_2exp(fmpz_t f, const fmpz_t g, ulong exp); void fmpz_add_ui(fmpz_t f, const fmpz_t g, ulong x); void fmpz_sub_ui(fmpz_t f, const fmpz_t g, ulong x); void fmpz_addmul_ui(fmpz_t f, const fmpz_t g, ulong x); void fmpz_submul_ui(fmpz_t f, const fmpz_t g, ulong x); void fmpz_addmul(fmpz_t f, const fmpz_t g, const fmpz_t h); void fmpz_submul(fmpz_t f, const fmpz_t g, const fmpz_t h); void fmpz_pow_ui(fmpz_t f, const fmpz_t g, ulong exp); void fmpz_powm_ui(fmpz_t f, const fmpz_t g, ulong exp, const fmpz_t m); void fmpz_powm(fmpz_t f, const fmpz_t g, const fmpz_t e, const fmpz_t m); void fmpz_setbit(fmpz_t f, ulong i); int fmpz_tstbit(const fmpz_t f, ulong i); void fmpz_clrbit(fmpz_t f, ulong i); void fmpz_complement(fmpz_t r, const fmpz_t f); void fmpz_combit(fmpz_t f, ulong i); void fmpz_and(fmpz_t r, const fmpz_t a, const fmpz_t b); void fmpz_or(fmpz_t r, const fmpz_t a, const fmpz_t b); void fmpz_xor(fmpz_t r, const fmpz_t a, const fmpz_t b); mp_bitcnt_t fmpz_popcnt(const fmpz_t c); double fmpz_dlog(const fmpz_t x); slong fmpz_flog(const fmpz_t x, const fmpz_t b); slong fmpz_flog_ui(const fmpz_t x, ulong b); slong fmpz_clog(const fmpz_t x, const fmpz_t b); slong fmpz_clog_ui(const fmpz_t x, ulong b); int fmpz_sqrtmod(fmpz_t b, const fmpz_t a, const fmpz_t p); void fmpz_sqrt(fmpz_t f, const fmpz_t g); int fmpz_is_square(const fmpz_t f); void fmpz_root(fmpz_t r, const fmpz_t f, slong n); void fmpz_sqrtrem(fmpz_t f, fmpz_t r, const fmpz_t g); ulong fmpz_fdiv_ui(const fmpz_t g, ulong h); ulong fmpz_mod_ui(fmpz_t f, const fmpz_t g, ulong h); void fmpz_mod(fmpz_t f, const fmpz_t g, const fmpz_t h); static __inline__ void fmpz_negmod(fmpz_t r, const fmpz_t a, const fmpz_t mod) { if (fmpz_is_zero(a)) fmpz_zero(r); else fmpz_sub(r, mod, a); } void fmpz_gcd(fmpz_t f, const fmpz_t g, const fmpz_t h); void fmpz_lcm(fmpz_t f, const fmpz_t g, const fmpz_t h); void fmpz_gcdinv(fmpz_t d, fmpz_t a, const fmpz_t f, const fmpz_t g); void fmpz_xgcd(fmpz_t d, fmpz_t a, fmpz_t b, const fmpz_t f, const fmpz_t g); void fmpz_xgcd_partial(fmpz_t co2, fmpz_t co1, fmpz_t r2, fmpz_t r1, const fmpz_t L); int fmpz_invmod(fmpz_t f, const fmpz_t g, const fmpz_t h); int fmpz_jacobi(const fmpz_t a, const fmpz_t p); slong _fmpz_remove(fmpz_t x, const fmpz_t f, double finv); slong fmpz_remove(fmpz_t rop, const fmpz_t op, const fmpz_t f); void fmpz_divexact(fmpz_t f, const fmpz_t g, const fmpz_t h); void fmpz_divexact_si(fmpz_t f, const fmpz_t g, slong h); void fmpz_divexact_ui(fmpz_t f, const fmpz_t g, ulong h); int fmpz_divisible(const fmpz_t f, const fmpz_t g); int fmpz_divisible_si(const fmpz_t f, slong g); void fmpz_cdiv_q(fmpz_t f, const fmpz_t g, const fmpz_t h); void fmpz_cdiv_q_si(fmpz_t f, const fmpz_t g, slong h); void fmpz_cdiv_q_ui(fmpz_t f, const fmpz_t g, ulong h); void fmpz_cdiv_q_2exp(fmpz_t f, const fmpz_t g, ulong exp); void fmpz_fdiv_qr(fmpz_t f, fmpz_t s, const fmpz_t g, const fmpz_t h); void fmpz_fdiv_qr_preinvn(fmpz_t f, fmpz_t s, const fmpz_t g, const fmpz_t h, const fmpz_preinvn_t inv); void fmpz_fdiv_q(fmpz_t f, const fmpz_t g, const fmpz_t h); void fmpz_fdiv_r(fmpz_t f, const fmpz_t g, const fmpz_t h); void fmpz_fdiv_q_ui(fmpz_t f, const fmpz_t g, ulong h); void fmpz_fdiv_q_si(fmpz_t f, const fmpz_t g, slong h); void fmpz_fdiv_q_2exp(fmpz_t f, const fmpz_t g, ulong exp); void fmpz_fdiv_r_2exp(fmpz_t f, const fmpz_t g, ulong exp); void fmpz_tdiv_q(fmpz_t f, const fmpz_t g, const fmpz_t h); void fmpz_tdiv_qr(fmpz_t f, fmpz_t s, const fmpz_t g, const fmpz_t h); void fmpz_tdiv_q_ui(fmpz_t f, const fmpz_t g, ulong h); void fmpz_tdiv_q_si(fmpz_t f, const fmpz_t g, slong h); ulong fmpz_tdiv_ui(const fmpz_t g, ulong h); void fmpz_tdiv_q_2exp(fmpz_t f, const fmpz_t g, ulong exp); void fmpz_preinvn_init(fmpz_preinvn_t inv, fmpz_t f); void fmpz_preinvn_clear(fmpz_preinvn_t inv); double fmpz_get_d_2exp(slong * exp, const fmpz_t f); static __inline__ void fmpz_mul2_uiui(fmpz_t f, const fmpz_t g, ulong h1, ulong h2) { mp_limb_t hi, lo; umul_ppmm(hi, lo, h1, h2); if (!hi) { fmpz_mul_ui(f, g, lo); } else { fmpz_mul_ui(f, g, h1); fmpz_mul_ui(f, f, h2); } } static __inline__ void fmpz_divexact2_uiui(fmpz_t f, const fmpz_t g, ulong h1, ulong h2) { mp_limb_t hi, lo; umul_ppmm(hi, lo, h1, h2); if (!hi) { fmpz_divexact_ui(f, g, lo); } else { fmpz_divexact_ui(f, g, h1); fmpz_divexact_ui(f, f, h2); } } void fmpz_mul_tdiv_q_2exp(fmpz_t f, const fmpz_t g, const fmpz_t h, ulong exp); void fmpz_mul_si_tdiv_q_2exp(fmpz_t f, const fmpz_t g, slong x, ulong exp); void fmpz_fac_ui(fmpz_t f, ulong n); void fmpz_fib_ui(fmpz_t f, ulong n); void fmpz_bin_uiui(fmpz_t res, ulong n, ulong k); void _fmpz_rfac_ui(fmpz_t r, const fmpz_t x, ulong a, ulong b); void fmpz_rfac_ui(fmpz_t r, const fmpz_t x, ulong n); void fmpz_rfac_uiui(fmpz_t r, ulong x, ulong n); int fmpz_bit_pack(mp_ptr arr, mp_bitcnt_t shift, mp_bitcnt_t bits, const fmpz_t coeff, int negate, int borrow); int fmpz_bit_unpack(fmpz_t coeff, mp_srcptr arr, mp_bitcnt_t shift, mp_bitcnt_t bits, int negate, int borrow); void fmpz_bit_unpack_unsigned(fmpz_t coeff, mp_srcptr arr, mp_bitcnt_t shift, mp_bitcnt_t bits); void _fmpz_CRT_ui_precomp(fmpz_t out, const fmpz_t r1, const fmpz_t m1, ulong r2, ulong m2, mp_limb_t m2inv, const fmpz_t m1m2, mp_limb_t c, int sign); void fmpz_CRT_ui(fmpz_t out, const fmpz_t r1, const fmpz_t m1, ulong r2, ulong m2, int sign); #define FLINT_FMPZ_LOG_MULTI_MOD_CUTOFF 2 typedef struct { const mp_limb_t * primes; slong num_primes; slong n; /* we have 2^n >= num_primes > 2^(n-1) */ fmpz ** comb; /* Array of arrays of products */ fmpz ** res; /* successive residues r_i^-1 mod r_{i+1} for pairs r_i, r_{i+1} */ nmod_t * mod; } fmpz_comb_struct; typedef struct { slong n; fmpz ** comb_temp; fmpz_t temp; fmpz_t temp2; } fmpz_comb_temp_struct; typedef fmpz_comb_struct fmpz_comb_t[1]; typedef fmpz_comb_temp_struct fmpz_comb_temp_t[1]; void fmpz_comb_temp_init(fmpz_comb_temp_t temp, const fmpz_comb_t comb); void fmpz_comb_temp_clear(fmpz_comb_temp_t temp); void fmpz_comb_init(fmpz_comb_t comb, mp_srcptr primes, slong num_primes); void fmpz_comb_clear(fmpz_comb_t comb); void fmpz_multi_mod_ui(mp_limb_t * out, const fmpz_t in, const fmpz_comb_t comb, fmpz_comb_temp_t temp); void fmpz_multi_CRT_ui(fmpz_t output, mp_srcptr residues, const fmpz_comb_t comb, fmpz_comb_temp_t temp, int sign); static __inline__ void fmpz_set_ui_smod(fmpz_t f, mp_limb_t x, mp_limb_t m) { if (x <= m / 2) fmpz_set_ui(f, x); else fmpz_set_si(f, x - m); } mp_limb_t fmpz_abs_ubound_ui_2exp(slong * exp, const fmpz_t x, int bits); mp_limb_t fmpz_abs_lbound_ui_2exp(slong * exp, const fmpz_t x, int bits); int fmpz_is_probabprime(const fmpz_t p); int fmpz_is_prime_pseudosquare(const fmpz_t n); #ifdef __cplusplus } #endif #include "fmpz_factor.h" #endif