arb/fmpcb_calc/cauchy_bound.c
2013-10-03 13:03:55 +02:00

86 lines
2.4 KiB
C

/*=============================================================================
This file is part of ARB.
ARB is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
ARB is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with ARB; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
=============================================================================*/
/******************************************************************************
Copyright (C) 2013 Fredrik Johansson
******************************************************************************/
#include "fmpcb_calc.h"
void
fmpcb_calc_cauchy_bound(fmprb_t bound, fmpcb_calc_func_t func, void * param,
const fmpcb_t x, const fmprb_t radius, long maxdepth, long prec)
{
long i, n, depth;
fmprb_t pi, theta, v;
fmpcb_t t, u;
fmprb_t b;
fmprb_init(pi);
fmprb_init(theta);
fmpcb_init(t);
fmpcb_init(u);
fmprb_init(v);
fmprb_init(b);
fmprb_const_pi(pi, prec);
fmprb_zero_pm_inf(b);
for (depth = 0, n = 16; depth < maxdepth; n *= 2, depth++)
{
fmprb_zero(b);
for (i = 0; i < n; i++)
{
/* theta = 2 pi ([i,i+1]/n) */
fmpr_set_si(fmprb_midref(theta), 2 * i + 1);
fmpr_set_si(fmprb_radref(theta), 2);
fmprb_div_ui(theta, theta, n, prec);
fmprb_mul(theta, theta, pi, prec);
fmprb_sin_cos(fmpcb_imagref(t), fmpcb_realref(t), theta, prec);
fmpcb_mul_fmprb(t, t, radius, prec);
fmpcb_add(t, t, x, prec);
func(u, t, param, 1, prec);
fmpcb_abs(v, u, prec);
fmprb_add(b, b, v, prec);
}
fmprb_div_ui(b, b, n, prec);
if (fmprb_is_exact(b) || fmpr_cmp(fmprb_radref(b), fmprb_midref(b)) < 0)
break;
}
fmprb_set(bound, b);
fmprb_clear(pi);
fmprb_clear(theta);
fmpcb_clear(t);
fmpcb_clear(u);
fmprb_clear(v);
fmprb_clear(b);
}