mirror of
https://github.com/vale981/arb
synced 2025-03-06 09:51:39 -05:00
107 lines
2.9 KiB
C
107 lines
2.9 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 "elefun.h"
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#define NUM_INVERSE_FACTORIALS 256
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TLS_PREFIX fmpz inverse_factorials[NUM_INVERSE_FACTORIALS];
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TLS_PREFIX int inverse_factorials_init = 0;
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void
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compute_inverse_factorials()
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{
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int i;
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fmpz_t t;
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fmpz_init(t);
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fmpz_one(t);
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fmpz_mul_2exp(t, t, EXP_CACHE_PREC);
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for (i = 0; i < NUM_INVERSE_FACTORIALS; i++)
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{
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fmpz_init(inverse_factorials + i);
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fmpz_fac_ui(inverse_factorials + i, i);
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fmpz_tdiv_q(inverse_factorials + i, t, inverse_factorials + i);
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}
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fmpz_clear(t);
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inverse_factorials_init = 1;
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}
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void
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elefun_exp_fixed_taylor_horner_precomp(fmpz_t y, fmpz_t yerr, const fmpz_t x, long n, long prec)
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{
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if (n == 0 || prec > EXP_CACHE_PREC || n > NUM_INVERSE_FACTORIALS)
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{
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abort();
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}
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else if (n == 1) /* 1 */
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{
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fmpz_one(y);
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fmpz_mul_2exp(y, y, prec);
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fmpz_zero(yerr);
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}
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else if (n == 2) /* 1 + x */
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{
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fmpz_one(y);
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fmpz_mul_2exp(y, y, prec);
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fmpz_add(y, y, x);
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fmpz_zero(yerr);
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}
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else if (n == 3) /* 1 + x + x^2 / 2 */
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{
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fmpz_t t;
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fmpz_init(t);
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fmpz_one(y);
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fmpz_mul_2exp(y, y, prec);
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fmpz_add(y, y, x);
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fmpz_mul_tdiv_q_2exp(t, x, x, prec + 1);
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fmpz_add(y, y, t);
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fmpz_one(yerr);
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fmpz_clear(t);
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}
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else
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{
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fmpz_t t;
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long i;
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if (!inverse_factorials_init)
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compute_inverse_factorials();
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fmpz_init(t);
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fmpz_tdiv_q_2exp(y, inverse_factorials + n - 1, EXP_CACHE_PREC - prec);
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for (i = n - 2; i >= 0; i--)
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{
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fmpz_mul_tdiv_q_2exp(y, y, x, prec);
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fmpz_tdiv_q_2exp(t, inverse_factorials + i, EXP_CACHE_PREC - prec);
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fmpz_add(y, y, t);
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}
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fmpz_set_ui(yerr, 2 * n - 1);
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fmpz_clear(t);
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}
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}
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