mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
204 lines
10 KiB
C
204 lines
10 KiB
C
/*
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Copyright (C) 2015 Jonathan Bober
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Copyright (C) 2016 Fredrik Johansson
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Copyright (C) 2016 Pascal Molin
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This file is part of Arb.
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Arb is free software: you can redistribute it and/or modify it under
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the terms of the GNU Lesser General Public License (LGPL) as published
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by the Free Software Foundation; either version 2.1 of the License, or
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(at your option) any later version. See <http://www.gnu.org/licenses/>.
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*/
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#ifndef ACB_DIRICHLET_H
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#define ACB_DIRICHLET_H
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#ifdef ACB_DIRICHLET_INLINES_C
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#define ACB_DIRICHLET_INLINE
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#else
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#define ACB_DIRICHLET_INLINE static __inline__
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#endif
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#include "acb.h"
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#include "acb_poly.h"
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#include "dirichlet.h"
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#ifdef __cplusplus
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extern "C" {
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#endif
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void acb_dirichlet_powsum_term(acb_ptr res, arb_t log_prev, ulong * prev,
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const acb_t s, ulong k, int integer, int critical_line, slong len, slong prec);
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void acb_dirichlet_powsum_sieved(acb_ptr z, const acb_t s, ulong n, slong len, slong prec);
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void acb_dirichlet_powsum_smooth(acb_ptr z, const acb_t s, ulong n, slong len, slong prec);
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void acb_dirichlet_zeta_bound(mag_t res, const acb_t s);
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void acb_dirichlet_zeta_rs_f_coeffs(acb_ptr c, const arb_t p, slong N, slong prec);
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void acb_dirichlet_zeta_rs_d_coeffs(arb_ptr d, const arb_t sigma, slong k, slong prec);
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void acb_dirichlet_zeta_rs_bound(mag_t err, const acb_t s, slong K);
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void acb_dirichlet_zeta_rs_r(acb_t res, const acb_t s, slong K, slong prec);
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void acb_dirichlet_zeta_rs(acb_t res, const acb_t s, slong K, slong prec);
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void acb_dirichlet_zeta(acb_t res, const acb_t s, slong prec);
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void acb_dirichlet_zeta_jet_rs(acb_ptr res, const acb_t s, slong len, slong prec);
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void acb_dirichlet_zeta_jet(acb_t res, const acb_t s, int deflate, slong len, slong prec);
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void acb_dirichlet_hurwitz(acb_t res, const acb_t s, const acb_t a, slong prec);
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void acb_dirichlet_stieltjes(acb_t res, const fmpz_t n, const acb_t a, slong prec);
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typedef struct
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{
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acb_struct s;
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mag_struct err;
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acb_ptr coeffs;
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int deflate;
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slong A;
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slong N;
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slong K;
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}
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acb_dirichlet_hurwitz_precomp_struct;
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typedef acb_dirichlet_hurwitz_precomp_struct acb_dirichlet_hurwitz_precomp_t[1];
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void acb_dirichlet_hurwitz_precomp_init(acb_dirichlet_hurwitz_precomp_t pre, const acb_t s, int deflate, slong A, slong K, slong N, slong prec);
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void acb_dirichlet_hurwitz_precomp_init_num(acb_dirichlet_hurwitz_precomp_t pre, const acb_t s, int deflate, double num_eval, slong prec);
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void acb_dirichlet_hurwitz_precomp_clear(acb_dirichlet_hurwitz_precomp_t pre);
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void acb_dirichlet_hurwitz_precomp_bound(mag_t res, const acb_t s, slong A, slong K, slong N);
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void acb_dirichlet_hurwitz_precomp_eval(acb_t res, const acb_dirichlet_hurwitz_precomp_t pre, ulong p, ulong q, slong prec);
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void acb_dirichlet_hurwitz_precomp_choose_param(ulong * A, ulong * K, ulong * N, const acb_t s, double num_eval, slong prec);
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void _acb_dirichlet_euler_product_real_ui(arb_t res, ulong s,
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const signed char * chi, int mod, int reciprocal, slong prec);
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void acb_dirichlet_eta(acb_t res, const acb_t s, slong prec);
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void acb_dirichlet_xi(acb_t res, const acb_t s, slong prec);
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void acb_dirichlet_pairing(acb_t res, const dirichlet_group_t G, ulong m, ulong n, slong prec);
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void acb_dirichlet_pairing_char(acb_t res, const dirichlet_group_t G, const dirichlet_char_t a, const dirichlet_char_t b, slong prec);
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/* precompute roots of unity */
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typedef struct
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{
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ulong order;
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ulong reduced_order;
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acb_t z;
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slong size;
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slong depth;
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acb_ptr * Z;
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int use_pow;
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}
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acb_dirichlet_roots_struct;
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typedef acb_dirichlet_roots_struct acb_dirichlet_roots_t[1];
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void acb_dirichlet_roots_init(acb_dirichlet_roots_t t, ulong order, slong num, slong prec);
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void acb_dirichlet_roots_clear(acb_dirichlet_roots_t t);
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void acb_dirichlet_root(acb_t z, const acb_dirichlet_roots_t t, ulong n, slong prec);
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void acb_dirichlet_chi(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, ulong n, slong prec);
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void acb_dirichlet_chi_vec(acb_ptr v, const dirichlet_group_t G, const dirichlet_char_t chi, slong nv, slong prec);
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void acb_dirichlet_arb_quadratic_powers(arb_ptr v, slong nv, const arb_t x, slong prec);
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void acb_dirichlet_qseries_arb(acb_t res, acb_srcptr a, const arb_t x, slong len, slong prec);
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void acb_dirichlet_qseries_arb_powers_naive(acb_t res, const arb_t x, int parity, const ulong *a, const acb_dirichlet_roots_t z, slong len, slong prec);
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void acb_dirichlet_qseries_arb_powers_smallorder(acb_t res, const arb_t x, int parity, const ulong *a, const acb_dirichlet_roots_t z, slong len, slong prec);
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ulong acb_dirichlet_theta_length_d(ulong q, double x, slong prec);
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ulong acb_dirichlet_theta_length(ulong q, const arb_t x, slong prec);
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void mag_tail_kexpk2_arb(mag_t res, const arb_t a, ulong n);
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void _acb_dirichlet_theta_argument_at_arb(arb_t xt, ulong q, const arb_t t, slong prec);
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void acb_dirichlet_theta_arb(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, const arb_t t, slong prec);
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void acb_dirichlet_ui_theta_arb(acb_t res, const dirichlet_group_t G, ulong a, const arb_t t, slong prec);
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void acb_dirichlet_gauss_sum_naive(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec);
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void acb_dirichlet_gauss_sum_factor(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec);
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void acb_dirichlet_gauss_sum_order2(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec);
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void acb_dirichlet_gauss_sum_theta(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec);
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void acb_dirichlet_gauss_sum(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec);
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void acb_dirichlet_root_number_theta(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec);
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void acb_dirichlet_root_number(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec);
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void acb_dirichlet_si_poly_evaluate(acb_t res, slong * v, slong len, const acb_t z, slong prec);
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void acb_dirichlet_jacobi_sum_naive(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi1, const dirichlet_char_t chi2, slong prec);
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ulong jacobi_one_prime(ulong p, ulong e, ulong pe, ulong cond);
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void acb_dirichlet_jacobi_sum_factor(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi1, const dirichlet_char_t chi2, slong prec);
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void acb_dirichlet_jacobi_sum_gauss(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi1, const dirichlet_char_t chi2, slong prec);
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void acb_dirichlet_jacobi_sum(acb_t res, const dirichlet_group_t G, const dirichlet_char_t chi1, const dirichlet_char_t chi2, slong prec);
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void acb_dirichlet_jacobi_sum_ui(acb_t res, const dirichlet_group_t G, ulong a, ulong b, slong prec);
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void acb_dirichlet_l_euler_product(acb_t res, const acb_t s, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec);
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void acb_dirichlet_l_hurwitz(acb_t res, const acb_t s, const acb_dirichlet_hurwitz_precomp_t precomp,
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const dirichlet_group_t G, const dirichlet_char_t chi, slong prec);
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void acb_dirichlet_l(acb_t res, const acb_t s, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec);
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void acb_dirichlet_l_vec_hurwitz(acb_ptr res, const acb_t s, const acb_dirichlet_hurwitz_precomp_t precomp, const dirichlet_group_t G, slong prec);
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void acb_dirichlet_l_jet(acb_ptr res, const acb_t s, const dirichlet_group_t G, const dirichlet_char_t chi, int deflate, slong len, slong prec);
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void _acb_dirichlet_l_series(acb_ptr res, acb_srcptr s, slong slen,
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const dirichlet_group_t G, const dirichlet_char_t chi,
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int deflate, slong len, slong prec);
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void acb_dirichlet_l_series(acb_poly_t res, const acb_poly_t s,
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const dirichlet_group_t G, const dirichlet_char_t chi,
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int deflate, slong len, slong prec);
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void acb_dirichlet_hardy_theta(acb_ptr res, const acb_t t,
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const dirichlet_group_t G, const dirichlet_char_t chi,
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slong len, slong prec);
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void acb_dirichlet_hardy_z(acb_ptr res, const acb_t t,
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const dirichlet_group_t G, const dirichlet_char_t chi,
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slong len, slong prec);
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void _acb_dirichlet_hardy_theta_series(acb_ptr res, acb_srcptr s, slong slen, const dirichlet_group_t G, const dirichlet_char_t chi, slong len, slong prec);
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void acb_dirichlet_hardy_theta_series(acb_poly_t res, const acb_poly_t s, const dirichlet_group_t G, const dirichlet_char_t chi, slong len, slong prec);
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void _acb_dirichlet_hardy_z_series(acb_ptr res, acb_srcptr s, slong slen, const dirichlet_group_t G, const dirichlet_char_t chi, slong len, slong prec);
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void acb_dirichlet_hardy_z_series(acb_poly_t res, const acb_poly_t s, const dirichlet_group_t G, const dirichlet_char_t chi, slong len, slong prec);
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void acb_dirichlet_gram_point(arb_t res, const fmpz_t n, const dirichlet_group_t G, const dirichlet_char_t chi, slong prec);
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void acb_dirichlet_backlund_s_bound(mag_t res, const arb_t t);
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ulong acb_dirichlet_turing_method_bound(const fmpz_t p);
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int _acb_dirichlet_definite_hardy_z(arb_t res, const arf_t t, slong *pprec);
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void _acb_dirichlet_isolate_gram_hardy_z_zero(arf_t a, arf_t b, const fmpz_t n);
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void _acb_dirichlet_isolate_rosser_hardy_z_zero(arf_t a, arf_t b, const fmpz_t n);
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void _acb_dirichlet_isolate_turing_hardy_z_zero(arf_t a, arf_t b, const fmpz_t n);
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void acb_dirichlet_isolate_hardy_z_zero(arf_t a, arf_t b, const fmpz_t n);
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void _acb_dirichlet_refine_hardy_z_zero(arb_t res, const arf_t a, const arf_t b, slong prec);
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void acb_dirichlet_hardy_z_zero(arb_t res, const fmpz_t n, slong prec);
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void acb_dirichlet_hardy_z_zeros(arb_ptr res, const fmpz_t n, slong len, slong prec);
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void acb_dirichlet_zeta_zero(acb_t res, const fmpz_t n, slong prec);
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void acb_dirichlet_zeta_zeros(acb_ptr res, const fmpz_t n, slong len, slong prec);
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void _acb_dirichlet_exact_zeta_nzeros(fmpz_t res, const arf_t t);
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void acb_dirichlet_zeta_nzeros(arb_t res, const arb_t t, slong prec);
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void acb_dirichlet_backlund_s(arb_t res, const arb_t t, slong prec);
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/* Discrete Fourier Transform */
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void acb_dirichlet_dft_index(acb_ptr w, acb_srcptr v, const dirichlet_group_t G, slong prec);
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void acb_dirichlet_dft(acb_ptr w, acb_srcptr v, const dirichlet_group_t G, slong prec);
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/* utils */
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ACB_DIRICHLET_INLINE void
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acb_vec_printd(acb_srcptr vec, slong len, slong digits)
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{
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slong i;
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for (i = 0; i < len; i++)
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acb_printd(vec + i, digits), flint_printf("\n");
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}
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#ifdef __cplusplus
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}
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#endif
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#endif
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