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https://github.com/vale981/arb
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69 lines
1.8 KiB
C
69 lines
1.8 KiB
C
/*
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Copyright (C) 2014 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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void
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acb_modular_lambda(acb_t r, const acb_t tau, slong prec)
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{
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psl2z_t g;
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arf_t one_minus_eps;
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acb_t tau_prime, q;
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acb_struct thetas[4];
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int R[4], S[4], C;
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int Rsum, qpower;
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psl2z_init(g);
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arf_init(one_minus_eps);
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acb_init(tau_prime);
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acb_init(q);
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acb_init(thetas + 0);
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acb_init(thetas + 1);
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acb_init(thetas + 2);
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acb_init(thetas + 3);
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arf_set_ui_2exp_si(one_minus_eps, 63, -6);
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acb_modular_fundamental_domain_approx(tau_prime, g, tau,
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one_minus_eps, prec);
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acb_modular_theta_transform(R, S, &C, g);
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acb_exp_pi_i(q, tau_prime, prec);
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acb_modular_theta_const_sum(thetas + 1, thetas + 2, thetas + 3, q, prec);
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acb_zero(thetas + 0);
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/* divide the transformation factors */
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Rsum = 4 * (R[1] - R[2]);
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/* possible factor [q^(+/- 1/4)]^4 needed for theta_1^4 or theta_2^4 */
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qpower = (S[1] == 0 || S[1] == 1) - (S[2] == 0 || S[2] == 1);
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acb_div(r, thetas + S[1], thetas + S[2], prec);
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acb_mul(r, r, r, prec);
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acb_mul(r, r, r, prec);
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if ((Rsum & 7) == 4)
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acb_neg(r, r);
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if (qpower == 1)
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acb_mul(r, r, q, prec);
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else if (qpower == -1)
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acb_div(r, r, q, prec);
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psl2z_clear(g);
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arf_clear(one_minus_eps);
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acb_clear(tau_prime);
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acb_clear(q);
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acb_clear(thetas + 0);
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acb_clear(thetas + 1);
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acb_clear(thetas + 2);
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acb_clear(thetas + 3);
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}
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