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https://github.com/vale981/arb
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108 lines
2.5 KiB
C
108 lines
2.5 KiB
C
/*
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Copyright (C) 2013 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_calc.h"
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void
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acb_calc_cauchy_bound(arb_t bound, acb_calc_func_t func, void * param,
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const acb_t x, const arb_t radius, slong maxdepth, slong prec)
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{
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slong i, n, depth, wp;
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arb_t pi, theta, v, s1, c1, s2, c2, st, ct;
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acb_t t, u;
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arb_t b;
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arb_init(pi);
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arb_init(theta);
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arb_init(v);
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arb_init(s1);
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arb_init(c1);
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arb_init(s2);
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arb_init(c2);
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arb_init(st);
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arb_init(ct);
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acb_init(t);
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acb_init(u);
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arb_init(b);
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wp = prec + 20;
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arb_const_pi(pi, wp);
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arb_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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arb_zero(b);
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/* theta = 2 pi / n */
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arb_div_ui(theta, pi, n, wp);
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arb_mul_2exp_si(theta, theta, 1);
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/* sine and cosine of i*theta and (i+1)*theta */
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arb_zero(s1);
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arb_one(c1);
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arb_sin_cos(st, ct, theta, wp);
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arb_set(s2, st);
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arb_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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arb_union(acb_realref(t), c1, c2, wp);
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arb_union(acb_imagref(t), s1, s2, wp);
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acb_mul_arb(t, t, radius, wp);
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acb_add(t, t, x, prec);
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/* next angle */
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arb_mul(v, c2, ct, wp);
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arb_mul(c1, s2, st, wp);
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arb_sub(c1, v, c1, wp);
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arb_mul(v, c2, st, wp);
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arb_mul(s1, s2, ct, wp);
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arb_add(s1, v, s1, wp);
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arb_swap(c1, c2);
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arb_swap(s1, s2);
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func(u, t, param, 1, prec);
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acb_abs(v, u, prec);
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arb_add(b, b, v, prec);
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}
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arb_div_ui(b, b, n, prec);
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if (arb_is_positive(b))
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break;
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}
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arb_set(bound, b);
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arb_clear(pi);
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arb_clear(theta);
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arb_clear(v);
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acb_clear(t);
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acb_clear(u);
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arb_clear(b);
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arb_clear(s1);
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arb_clear(c1);
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arb_clear(s2);
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arb_clear(c2);
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arb_clear(st);
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arb_clear(ct);
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}
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