mirror of
https://github.com/vale981/arb
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80 lines
2.2 KiB
C
80 lines
2.2 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) 2013 Fredrik Johansson
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******************************************************************************/
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#include "gamma.h"
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/* evaluate sum_{k=0}^{n-1} c_{k+1} x^k
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precision estimate assumes x <= 1/2 */
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void
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gamma_taylor_eval_fmprb(fmprb_t y, const fmprb_t x, long prec)
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{
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long i, n, wp;
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fmprb_t t, u, v;
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fmpr_t z;
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n = gamma_taylor_coeffs_for_prec(prec);
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gamma_taylor_precompute(n, prec);
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fmprb_init(t);
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fmprb_init(u);
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fmprb_init(v);
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/* note: c_n is actually stored as coefficient n - 1 */
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fmprb_set(u, gamma_taylor_coeffs + n - 1);
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for (i = n - 1; i > 0; i--)
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{
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wp = prec + (gamma_taylor_bound_cached(i) - i);
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wp = FLINT_MIN(wp, prec + 10);
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wp = FLINT_MAX(wp, 10);
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if (prec > 2000)
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{
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fmprb_set_round(v, x, wp);
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fmprb_mul(u, u, v, wp);
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}
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else
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{
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fmprb_mul(u, u, x, wp);
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}
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fmprb_set_round(t, gamma_taylor_coeffs + i - 1, wp);
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fmprb_add(u, u, t, wp);
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}
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/* add error */
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fmpr_init(z);
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fmprb_get_abs_ubound_fmpr(z, x, FMPRB_RAD_PREC);
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gamma_taylor_bound_remainder(z, z, n);
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fmprb_add_error_fmpr(u, z);
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fmpr_clear(z);
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fmprb_set_round(y, u, prec);
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fmprb_clear(t);
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fmprb_clear(u);
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fmprb_clear(v);
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}
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