/usr/include/flint/arith.h is in libflint-dev 2.4.4-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 | /*============================================================================
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) 2010-2012 Fredrik Johansson
******************************************************************************/
#ifndef ARITH_H
#define ARITH_H
#include <gmp.h>
#include <mpfr.h>
#include "flint.h"
#include "fmpz.h"
#include "fmpz_mat.h"
#include "fmpz_poly.h"
#include "fmpq_poly.h"
#include "fmpq.h"
#ifdef __cplusplus
extern "C" {
#endif
/* MPFR extras ***************************************************************/
void mpfr_zeta_inv_euler_product(mpfr_t res, ulong s, int char_4);
void mpfr_pi_chudnovsky(mpfr_t res, mpfr_rnd_t rnd);
/* Various arithmetic functions **********************************************/
void arith_primorial(fmpz_t res, slong n);
void _arith_harmonic_number(fmpz_t num, fmpz_t den, slong n);
void arith_harmonic_number(fmpq_t x, slong n);
void arith_ramanujan_tau(fmpz_t res, const fmpz_t n);
void arith_ramanujan_tau_series(fmpz_poly_t res, slong n);
void arith_divisors(fmpz_poly_t res, const fmpz_t n);
void arith_divisor_sigma(fmpz_t res, const fmpz_t n, ulong k);
int arith_moebius_mu(const fmpz_t n);
void arith_euler_phi(fmpz_t res, const fmpz_t n);
/* Stirling numbers **********************************************************/
void arith_stirling_number_1u(fmpz_t s, slong n, slong k);
void arith_stirling_number_1(fmpz_t s, slong n, slong k);
void arith_stirling_number_2(fmpz_t s, slong n, slong k);
void arith_stirling_number_1u_vec(fmpz * row, slong n, slong klen);
void arith_stirling_number_1_vec(fmpz * row, slong n, slong klen);
void arith_stirling_number_2_vec(fmpz * row, slong n, slong klen);
void arith_stirling_number_1u_vec_next(fmpz * row,
const fmpz * prev, slong n, slong klen);
void arith_stirling_number_1_vec_next(fmpz * row,
const fmpz * prev, slong n, slong klen);
void arith_stirling_number_2_vec_next(fmpz * row,
const fmpz * prev, slong n, slong klen);
void arith_stirling_matrix_1u(fmpz_mat_t mat);
void arith_stirling_matrix_1(fmpz_mat_t mat);
void arith_stirling_matrix_2(fmpz_mat_t mat);
/* Bell numbers **************************************************************/
#if FLINT64
#define BELL_NUMBER_TAB_SIZE 26
#else
#define BELL_NUMBER_TAB_SIZE 16
#endif
extern const mp_limb_t bell_number_tab[];
double arith_bell_number_size(ulong n);
void arith_bell_number(fmpz_t b, ulong n);
void arith_bell_number_bsplit(fmpz_t res, ulong n);
void arith_bell_number_multi_mod(fmpz_t res, ulong n);
void arith_bell_number_vec(fmpz * b, slong n);
void arith_bell_number_vec_recursive(fmpz * b, slong n);
void arith_bell_number_vec_multi_mod(fmpz * b, slong n);
mp_limb_t arith_bell_number_nmod(ulong n, nmod_t mod);
void arith_bell_number_nmod_vec(mp_ptr b, slong n, nmod_t mod);
void arith_bell_number_nmod_vec_recursive(mp_ptr b, slong n, nmod_t mod);
void arith_bell_number_nmod_vec_series(mp_ptr b, slong n, nmod_t mod);
/* Euler numbers *************************************************************/
#if FLINT64
#define SMALL_EULER_LIMIT 25
#else
#define SMALL_EULER_LIMIT 15
#endif
static const mp_limb_t euler_number_small[] = {
UWORD(1), UWORD(1), UWORD(5), UWORD(61), UWORD(1385), UWORD(50521), UWORD(2702765),
UWORD(199360981),
#if FLINT64
UWORD(19391512145), UWORD(2404879675441), UWORD(370371188237525),
UWORD(69348874393137901), UWORD(15514534163557086905)
#endif
};
double arith_euler_number_size(ulong n);
void arith_euler_number_vec(fmpz * res, slong n);
void _arith_euler_number_zeta(fmpz_t res, ulong n);
void arith_euler_number(fmpz_t res, ulong n);
void arith_euler_polynomial(fmpq_poly_t poly, ulong n);
/* Bernoulli numbers *********************************************************/
#if FLINT64
#define BERNOULLI_SMALL_NUMER_LIMIT 35
#else
#define BERNOULLI_SMALL_NUMER_LIMIT 27
#endif
static const slong _bernoulli_numer_small[] = {
WORD(1), WORD(1), WORD(-1), WORD(1), WORD(-1), WORD(5), WORD(-691), WORD(7), WORD(-3617), WORD(43867), WORD(-174611), WORD(854513),
WORD(-236364091), WORD(8553103),
#if FLINT64
WORD(-23749461029), WORD(8615841276005), WORD(-7709321041217), WORD(2577687858367)
#endif
};
void _arith_bernoulli_number(fmpz_t num, fmpz_t den, ulong n);
void arith_bernoulli_number(fmpq_t x, ulong n);
void _arith_bernoulli_number_vec(fmpz * num, fmpz * den, slong n);
void arith_bernoulli_number_vec(fmpq * num, slong n);
void arith_bernoulli_number_denom(fmpz_t den, ulong n);
double arith_bernoulli_number_size(ulong n);
void arith_bernoulli_polynomial(fmpq_poly_t poly, ulong n);
void _arith_bernoulli_number_zeta(fmpz_t num, fmpz_t den, ulong n);
void _arith_bernoulli_number_vec_multi_mod(fmpz * num, fmpz * den, slong n);
void _arith_bernoulli_number_vec_recursive(fmpz * num, fmpz * den, slong n);
void _arith_bernoulli_number_vec_zeta(fmpz * num, fmpz * den, slong n);
/* Cyclotomic polynomials ****************************************************/
void _arith_cyclotomic_polynomial(fmpz * a, ulong n, mp_ptr factors,
slong num_factors, ulong phi);
void arith_cyclotomic_polynomial(fmpz_poly_t poly, ulong n);
void _arith_cos_minpoly(fmpz * coeffs, slong d, ulong n);
void arith_cos_minpoly(fmpz_poly_t poly, ulong n);
/* Hypergeometric polynomials ************************************************/
void arith_legendre_polynomial(fmpq_poly_t poly, ulong n);
void arith_chebyshev_t_polynomial(fmpz_poly_t poly, ulong n);
void arith_chebyshev_u_polynomial(fmpz_poly_t poly, ulong n);
/* Swinnerton-Dyer polynomials ***********************************************/
void arith_swinnerton_dyer_polynomial(fmpz_poly_t poly, ulong n);
/* Landau function ***********************************************************/
void arith_landau_function_vec(fmpz * res, slong len);
/* Dedekind sums *************************************************************/
void arith_dedekind_sum_naive(fmpq_t s, const fmpz_t h, const fmpz_t k);
double arith_dedekind_sum_coprime_d(double h, double k);
void arith_dedekind_sum_coprime_large(fmpq_t s, const fmpz_t h, const fmpz_t k);
void arith_dedekind_sum_coprime(fmpq_t s, const fmpz_t h, const fmpz_t k);
void arith_dedekind_sum(fmpq_t s, const fmpz_t h, const fmpz_t k);
/* Exponential sums **********************************************************/
typedef struct
{
int n;
int prefactor;
mp_limb_t sqrt_p;
mp_limb_t sqrt_q;
mp_limb_signed_t cos_p[FLINT_BITS];
mp_limb_t cos_q[FLINT_BITS];
} trig_prod_struct;
typedef trig_prod_struct trig_prod_t[1];
static __inline__
void trig_prod_init(trig_prod_t sum)
{
sum->n = 0;
sum->prefactor = 1;
sum->sqrt_p = 1;
sum->sqrt_q = 1;
}
void arith_hrr_expsum_factored(trig_prod_t prod, mp_limb_t k, mp_limb_t n);
/* Number of partitions ******************************************************/
void arith_number_of_partitions_nmod_vec(mp_ptr res, slong len, nmod_t mod);
void arith_number_of_partitions_vec(fmpz * res, slong len);
void arith_number_of_partitions_mpfr(mpfr_t x, ulong n);
void arith_number_of_partitions(fmpz_t x, ulong n);
/* Number of sums of squares representations *********************************/
void arith_sum_of_squares(fmpz_t r, ulong k, const fmpz_t n);
void arith_sum_of_squares_vec(fmpz * r, ulong k, slong n);
#ifdef __cplusplus
}
#endif
#endif
|