mirror of
https://github.com/vale981/arb
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82 lines
1.9 KiB
C
82 lines
1.9 KiB
C
/*
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Copyright (C) 2015 Fredrik Johansson
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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_modular.h"
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double mag_get_log2_d_approx(const mag_t x);
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void
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acb_modular_theta_const_sum(acb_t theta2, acb_t theta3, acb_t theta4,
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const acb_t q, slong prec)
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{
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mag_t qmag, err;
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double log2q_approx;
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int is_real, is_real_or_imag;
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slong N;
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mag_init(qmag);
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mag_init(err);
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acb_get_mag(qmag, q);
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log2q_approx = mag_get_log2_d_approx(qmag);
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is_real = arb_is_zero(acb_imagref(q));
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is_real_or_imag = is_real || arb_is_zero(acb_realref(q));
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if (log2q_approx >= 0.0)
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{
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N = 1;
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mag_inf(err);
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}
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else
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{
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N = 0;
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while (0.05 * N * N < prec)
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{
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if (log2q_approx * ((N+2)*(N+2)/4) < -prec - 2)
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break;
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N++;
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}
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N = (N+2)*(N+2)/4;
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mag_geom_series(err, qmag, N);
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mag_mul_2exp_si(err, err, 1); /* each term is taken twice */
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if (mag_is_inf(err))
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N = 1;
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}
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if (N < 1800)
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acb_modular_theta_const_sum_basecase(theta2, theta3, theta4, q, N, prec);
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else
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acb_modular_theta_const_sum_rs(theta2, theta3, theta4, q, N, prec);
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if (is_real_or_imag)
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arb_add_error_mag(acb_realref(theta2), err);
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else
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acb_add_error_mag(theta2, err);
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if (is_real)
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{
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arb_add_error_mag(acb_realref(theta3), err);
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arb_add_error_mag(acb_realref(theta4), err);
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}
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else
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{
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acb_add_error_mag(theta3, err);
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acb_add_error_mag(theta4, err);
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}
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mag_clear(qmag);
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mag_clear(err);
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}
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