mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
124 lines
2.6 KiB
C
124 lines
2.6 KiB
C
/*
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Copyright (C) 2019 D.H.J Polymath
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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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#include "acb_dirichlet.h"
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#include "arb_hypgeom.h"
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/* Increase precision adaptively. */
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static void
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_gamma_upper_workaround(arb_t res, const arb_t s, const arb_t z,
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int regularized, slong prec)
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{
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if (!arb_is_finite(s) || !arb_is_finite(z))
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{
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arb_indeterminate(res);
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}
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else
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{
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arb_t x;
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slong i;
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arb_init(x);
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for (i = 0; i < 5; i++)
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{
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arb_hypgeom_gamma_upper(x, s, z, regularized, prec << i);
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if (arb_rel_accuracy_bits(x) > 1)
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{
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break;
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}
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}
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arb_swap(res, x);
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arb_clear(x);
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}
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}
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/* Lemma A5 requires B > h*sqrt(k) */
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static int
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_platt_lemma_A5_constraint(slong B, const arb_t h, slong k, slong prec)
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{
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int result;
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arb_t lhs, rhs;
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arb_init(rhs);
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arb_init(lhs);
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arb_set_si(lhs, B);
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arb_sqrt_ui(rhs, (ulong) k, prec);
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arb_mul(rhs, rhs, h, prec);
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result = arb_gt(lhs, rhs);
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arb_clear(rhs);
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arb_clear(lhs);
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return result;
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}
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void
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acb_dirichlet_platt_lemma_A5(arb_t out, slong B, const arb_t h,
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slong k, slong prec)
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{
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arb_t a, b;
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arb_t x1, x2, x3, x4, x5, x6;
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if (!_platt_lemma_A5_constraint(B, h, k, prec))
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{
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arb_zero_pm_inf(out);
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return;
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}
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arb_init(a);
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arb_init(b);
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arb_init(x1);
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arb_init(x2);
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arb_init(x3);
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arb_init(x4);
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arb_init(x5);
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arb_init(x6);
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arb_const_pi(x1, prec);
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arb_mul_si(x1, x1, B, prec);
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arb_pow_ui(x1, x1, (ulong) k, prec);
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arb_mul_2exp_si(x1, x1, 3);
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arb_set_si(a, B);
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arb_div(a, a, h, prec);
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arb_sqr(a, a, prec);
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arb_mul_2exp_si(a, a, -3);
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arb_neg(x2, a);
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arb_exp(x2, x2, prec);
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arb_set_si(x3, 3*k - 1);
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arb_mul_2exp_si(x3, x3, -1);
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arb_set_ui(x4, 2);
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arb_pow(x4, x4, x3, prec);
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arb_set_si(b, k+1);
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arb_div_si(x5, h, B, prec);
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arb_pow_ui(x5, x5, (ulong) (k+1), prec);
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arb_mul_2exp_si(x6, b, -1);
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_gamma_upper_workaround(x6, x6, a, 0, prec);
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arb_mul(out, x4, x5, prec);
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arb_mul(out, out, x6, prec);
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arb_add(out, out, x2, prec);
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arb_mul(out, out, x1, prec);
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arb_clear(a);
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arb_clear(b);
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arb_clear(x1);
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arb_clear(x2);
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arb_clear(x3);
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arb_clear(x4);
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arb_clear(x5);
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arb_clear(x6);
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}
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