mirror of
https://github.com/vale981/arb
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116 lines
3.2 KiB
C
116 lines
3.2 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) 2012 Fredrik Johansson
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******************************************************************************/
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#include <math.h>
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#include "gamma.h"
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#include "bernoulli.h"
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void
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gamma_stirling_eval_fmprb(fmprb_t s, const fmprb_t z, long nterms, int digamma, long prec)
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{
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fmprb_t b, t, logz, zinv, zinv2;
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fmpr_t err;
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long k, term_prec;
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double z_mag, term_mag;
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fmprb_init(b);
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fmprb_init(t);
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fmprb_init(logz);
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fmprb_init(zinv);
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fmprb_init(zinv2);
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fmprb_log(logz, z, prec);
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fmprb_inv(zinv, z, prec);
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nterms = FLINT_MAX(nterms, 1);
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fmprb_zero(s);
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if (nterms > 1)
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{
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fmprb_mul(zinv2, zinv, zinv, prec);
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z_mag = fmpr_get_d(fmprb_midref(logz), FMPR_RND_UP) * 1.44269504088896;
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for (k = nterms - 1; k >= 1; k--)
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{
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term_mag = bernoulli_bound_2exp_si(2 * k);
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term_mag -= (2 * k - 1) * z_mag;
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term_prec = prec + term_mag;
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term_prec = FLINT_MIN(term_prec, prec);
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term_prec = FLINT_MAX(term_prec, 10);
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if (prec > 2000)
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{
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fmprb_set_round(t, zinv2, term_prec);
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fmprb_mul(s, s, t, term_prec);
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}
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else
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fmprb_mul(s, s, zinv2, term_prec);
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gamma_stirling_coeff(b, k, digamma, term_prec);
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fmprb_add(s, s, b, term_prec);
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}
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if (digamma)
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fmprb_mul(s, s, zinv2, prec);
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else
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fmprb_mul(s, s, zinv, prec);
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}
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/* remainder bound */
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fmpr_init(err);
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gamma_stirling_bound_fmprb(err, z, digamma ? 1 : 0, 1, nterms);
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fmprb_add_error_fmpr(s, err);
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fmpr_clear(err);
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if (digamma)
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{
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fmprb_neg(s, s);
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fmprb_mul_2exp_si(zinv, zinv, -1);
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fmprb_sub(s, s, zinv, prec);
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fmprb_add(s, s, logz, prec);
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}
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else
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{
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/* (z-0.5)*log(z) - z + log(2*pi)/2 */
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fmprb_one(t);
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fmprb_mul_2exp_si(t, t, -1);
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fmprb_sub(t, z, t, prec);
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fmprb_mul(t, logz, t, prec);
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fmprb_add(s, s, t, prec);
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fmprb_sub(s, s, z, prec);
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fmprb_const_log_sqrt2pi(t, prec);
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fmprb_add(s, s, t, prec);
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}
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fmprb_clear(t);
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fmprb_clear(b);
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fmprb_clear(zinv);
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fmprb_clear(zinv2);
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fmprb_clear(logz);
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}
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