mirror of
https://github.com/vale981/arb
synced 2025-03-06 01:41:39 -05:00
122 lines
3.3 KiB
C
122 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) 2013 Fredrik Johansson
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******************************************************************************/
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#include "fmpcb_calc.h"
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void
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fmpcb_calc_cauchy_bound(fmprb_t bound, fmpcb_calc_func_t func, void * param,
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const fmpcb_t x, const fmprb_t radius, long maxdepth, long prec)
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{
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long i, n, depth, wp;
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fmprb_t pi, theta, v, s1, c1, s2, c2, st, ct;
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fmpcb_t t, u;
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fmprb_t b;
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fmprb_init(pi);
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fmprb_init(theta);
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fmprb_init(v);
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fmprb_init(s1);
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fmprb_init(c1);
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fmprb_init(s2);
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fmprb_init(c2);
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fmprb_init(st);
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fmprb_init(ct);
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fmpcb_init(t);
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fmpcb_init(u);
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fmprb_init(b);
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wp = prec + 20;
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fmprb_const_pi(pi, wp);
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fmprb_zero_pm_inf(b);
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for (depth = 0, n = 16; depth < maxdepth; n *= 2, depth++)
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{
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fmprb_zero(b);
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/* theta = 2 pi / n */
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fmprb_div_ui(theta, pi, n, wp);
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fmprb_mul_2exp_si(theta, theta, 1);
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/* sine and cosine of i*theta and (i+1)*theta */
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fmprb_zero(s1);
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fmprb_one(c1);
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fmprb_sin_cos(st, ct, theta, wp);
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fmprb_set(s2, st);
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fmprb_set(c2, ct);
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for (i = 0; i < n; i++)
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{
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/* sine and cosine of 2 pi ([i,i+1]/n) */
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/* since we use power of two subdivision points, the
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sine and cosine are monotone on each subinterval */
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fmprb_union(fmpcb_realref(t), c1, c2, wp);
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fmprb_union(fmpcb_imagref(t), s1, s2, wp);
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fmpcb_mul_fmprb(t, t, radius, wp);
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fmpcb_add(t, t, x, prec);
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/* next angle */
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fmprb_mul(v, c2, ct, wp);
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fmprb_mul(c1, s2, st, wp);
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fmprb_sub(c1, v, c1, wp);
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fmprb_mul(v, c2, st, wp);
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fmprb_mul(s1, s2, ct, wp);
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fmprb_add(s1, v, s1, wp);
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fmprb_swap(c1, c2);
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fmprb_swap(s1, s2);
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func(u, t, param, 1, prec);
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fmpcb_abs(v, u, prec);
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fmprb_add(b, b, v, prec);
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}
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fmprb_div_ui(b, b, n, prec);
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if (fmprb_is_exact(b) || fmpr_cmp(fmprb_radref(b), fmprb_midref(b)) < 0)
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break;
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}
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fmprb_set(bound, b);
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fmprb_clear(pi);
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fmprb_clear(theta);
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fmprb_clear(v);
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fmpcb_clear(t);
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fmpcb_clear(u);
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fmprb_clear(b);
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fmprb_clear(s1);
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fmprb_clear(c1);
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fmprb_clear(s2);
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fmprb_clear(c2);
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fmprb_clear(st);
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fmprb_clear(ct);
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}
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