mirror of
https://github.com/vale981/arb
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64 lines
1.5 KiB
C
64 lines
1.5 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_elliptic.h"
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#include "acb_modular.h"
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void
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acb_elliptic_p(acb_t r, const acb_t z, const acb_t tau, slong prec)
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{
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acb_struct t0[4], tz[4];
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acb_t t;
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int i, real;
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real = acb_is_real(z) && arb_is_int_2exp_si(acb_realref(tau), -1) &&
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arb_is_positive(acb_imagref(tau));
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acb_init(t);
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for (i = 0; i < 4; i++)
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{
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acb_init(t0 + i);
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acb_init(tz + i);
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}
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acb_modular_theta(tz + 0, tz + 1, tz + 2, tz + 3, z, tau, prec);
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acb_zero(t);
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acb_modular_theta(t0 + 0, t0 + 1, t0 + 2, t0 + 3, t, tau, prec);
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acb_mul(t, t0 + 1, t0 + 2, prec);
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acb_mul(t, t, tz + 3, prec);
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acb_div(t, t, tz + 0, prec);
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acb_mul(t, t, t, prec);
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acb_pow_ui(t0 + 1, t0 + 1, 4, prec);
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acb_pow_ui(t0 + 2, t0 + 2, 4, prec);
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acb_add(r, t0 + 1, t0 + 2, prec);
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acb_div_ui(r, r, 3, prec);
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acb_sub(r, t, r, prec);
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acb_const_pi(t, prec);
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acb_mul(t, t, t, prec);
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acb_mul(r, r, t, prec);
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if (real)
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arb_zero(acb_imagref(r));
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acb_clear(t);
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for (i = 0; i < 4; i++)
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{
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acb_clear(t0 + i);
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acb_clear(tz + i);
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}
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}
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