mirror of
https://github.com/vale981/arb
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124 lines
3.1 KiB
C
124 lines
3.1 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.h"
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#include "gamma.h"
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/* corrects branch cut of sum_{k=0}^{r-1} log(z+k), given the
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logarithm of the product */
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void
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_fmpcb_log_rising_correct_branch(fmpcb_t t,
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const fmpcb_t t_wrong, const fmpcb_t z, ulong r, long prec)
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{
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fmpcb_t f;
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fmprb_t pi, u, v;
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fmpz_t pi_mult;
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long i, argprec;
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fmpcb_init(f);
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fmprb_init(u);
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fmprb_init(pi);
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fmprb_init(v);
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fmpz_init(pi_mult);
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argprec = FLINT_MIN(prec, 40);
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fmprb_zero(u);
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for (i = 0; i < r; i++)
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{
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fmpcb_add_ui(f, z, i, argprec);
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fmpcb_arg(v, f, argprec);
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fmprb_add(u, u, v, argprec);
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}
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if (argprec == prec)
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{
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fmprb_set(fmpcb_imagref(t), u);
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}
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else
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{
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fmprb_sub(v, u, fmpcb_imagref(t), argprec);
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fmprb_const_pi(pi, argprec);
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fmprb_div(v, v, pi, argprec);
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if (fmprb_get_unique_fmpz(pi_mult, v))
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{
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fmprb_const_pi(v, prec);
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fmprb_mul_fmpz(v, v, pi_mult, prec);
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fmprb_add(fmpcb_imagref(t), fmpcb_imagref(t), v, prec);
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}
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else
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{
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fmprb_zero(u);
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for (i = 0; i < r; i++)
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{
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fmpcb_add_ui(f, z, i, prec);
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fmpcb_arg(v, f, prec);
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fmprb_add(u, u, v, prec);
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}
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fmprb_set(fmpcb_imagref(t), u);
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}
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}
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fmpcb_clear(f);
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fmprb_clear(u);
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fmprb_clear(v);
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fmprb_clear(pi);
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fmpz_clear(pi_mult);
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}
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void
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fmpcb_lgamma(fmpcb_t y, const fmpcb_t x, long prec)
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{
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int reflect;
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long r, n, wp;
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fmpcb_t t, u;
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wp = prec + FLINT_BIT_COUNT(prec);
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gamma_stirling_choose_param_fmpcb(&reflect, &r, &n, x, 0, 0, wp);
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/* log(gamma(x)) = log(gamma(x+r)) - log(rf(x,r)) */
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fmpcb_init(t);
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fmpcb_init(u);
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fmpcb_add_ui(t, x, r, wp);
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gamma_stirling_eval_fmpcb(u, t, n, 0, wp);
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gamma_rising_fmpcb_ui_bsplit(t, x, r, prec);
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fmpcb_log(t, t, prec);
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_fmpcb_log_rising_correct_branch(t, t, x, r, wp);
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fmpcb_sub(y, u, t, prec);
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fmpcb_clear(t);
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fmpcb_clear(u);
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}
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