mirror of
https://github.com/vale981/arb
synced 2025-03-05 09:21:38 -05:00
113 lines
3.3 KiB
C
113 lines
3.3 KiB
C
/*=============================================================================
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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
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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ARB is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ARB; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2014 Fredrik Johansson
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******************************************************************************/
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#include "acb_modular.h"
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static int
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good_enough(const acb_t z, const arf_t one_minus_eps, slong prec)
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{
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arf_t m;
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int res;
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if (arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), -1) > 0)
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return 0;
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if (arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), 0) >= 0)
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return 1;
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arf_init(m);
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arf_mul(m, arb_midref(acb_realref(z)), arb_midref(acb_realref(z)), prec, ARF_RND_DOWN);
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arf_addmul(m, arb_midref(acb_imagref(z)), arb_midref(acb_imagref(z)), prec, ARF_RND_DOWN);
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res = (arf_cmp(m, one_minus_eps) >= 0);
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arf_clear(m);
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return res;
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}
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void
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acb_modular_fundamental_domain_approx(acb_t w, psl2z_t g, const acb_t z,
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const arf_t one_minus_eps, slong prec)
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{
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acb_t t;
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psl2z_one(g);
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/* we must be in the upper half-plane */
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if (!acb_is_finite(z) || arf_sgn(arb_midref(acb_imagref(z))) <= 0)
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{
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acb_set(w, z);
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return;
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}
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/* too large real-value shift */
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if (arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), prec) > 0)
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{
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acb_set(w, z);
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return;
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}
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/* y >= 1: just shift x */
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if (arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), 0) >= 0)
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{
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arf_get_fmpz(&g->b, arb_midref(acb_realref(z)), ARF_RND_NEAR);
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acb_sub_fmpz(w, z, &g->b, prec);
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fmpz_neg(&g->b, &g->b);
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return;
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}
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acb_init(t);
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/* try using doubles */
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if (arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), -40) > 0 &&
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arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), 40) < 0)
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{
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double zred, zimd;
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zred = arf_get_d(arb_midref(acb_realref(z)), ARF_RND_DOWN);
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zimd = arf_get_d(arb_midref(acb_imagref(z)), ARF_RND_DOWN);
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acb_modular_fundamental_domain_approx_d(g, zred, zimd,
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arf_get_d(one_minus_eps, ARF_RND_UP));
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acb_modular_transform(t, g, z, prec);
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if (good_enough(t, one_minus_eps, prec))
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{
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acb_swap(w, t);
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acb_clear(t);
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return;
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}
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}
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/* try with full precision */
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acb_modular_fundamental_domain_approx_arf(g,
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arb_midref(acb_realref(z)), arb_midref(acb_imagref(z)),
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one_minus_eps, prec);
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acb_modular_transform(t, g, z, prec);
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acb_swap(w, t);
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acb_clear(t);
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}
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