mirror of
https://github.com/vale981/arb
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290 lines
7.4 KiB
C
290 lines
7.4 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, 2013 Fredrik Johansson
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******************************************************************************/
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#include "fmprb.h"
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#define MAGLIM(prec) FLINT_MAX(65536, (4*prec))
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static long
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_fmpr_sin(fmpr_t y, const fmpr_t x, long prec, fmpr_rnd_t rnd)
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{
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long r;
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CALL_MPFR_FUNC(r, mpfr_sin, y, x, prec, rnd);
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return r;
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}
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static long
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_fmpr_cos(fmpr_t y, const fmpr_t x, long prec, fmpr_rnd_t rnd)
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{
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long r;
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CALL_MPFR_FUNC(r, mpfr_cos, y, x, prec, rnd);
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return r;
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}
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static void
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_fmpr_sin_cos(long * r1, long * r2, fmpr_t s, fmpr_t c, const fmpr_t x, long prec, fmpr_rnd_t rnd)
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{
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CALL_MPFR_FUNC_2X1(*r1, *r2, mpfr_sin_cos, s, c, x, prec, rnd);
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}
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void
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fmprb_sin_fmpr(fmprb_t s, const fmpr_t x, long prec, long maglim)
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{
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if (fmpr_is_special(x))
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{
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if (fmpr_is_zero(x))
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{
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fmprb_zero(s);
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}
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else if (fmpr_is_nan(x))
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{
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fmpr_nan(fmprb_midref(s));
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fmpr_pos_inf(fmprb_radref(s));
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}
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else
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{
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fmpr_zero(fmprb_midref(s));
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fmpr_one(fmprb_radref(s));
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}
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}
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else
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{
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long r;
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fmpz_t mag;
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fmpz_init(mag);
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/* 2^(mag-1) <= |x| < 2^mag */
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fmpr_abs_bound_lt_2exp_fmpz(mag, x);
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/* sin x = x + eps, |eps| < x^3 */
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if (fmpz_cmp_si(mag, -(prec/3) - 2) < 0)
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{
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fmpz_mul_ui(mag, mag, 3);
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fmprb_set_fmpr(s, x);
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fmprb_set_round(s, s, prec);
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fmprb_add_error_2exp_fmpz(s, mag);
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}
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/* huge */
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else if (fmpz_cmp_si(mag, maglim) > 0)
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{
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fmpr_zero(fmprb_midref(s));
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fmpr_one(fmprb_radref(s));
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}
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else
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{
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r = _fmpr_sin(fmprb_midref(s), x, prec, FMPR_RND_DOWN);
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fmpr_set_error_result(fmprb_radref(s), fmprb_midref(s), r);
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}
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fmpz_clear(mag);
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}
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}
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void
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fmprb_cos_fmpr(fmprb_t c, const fmpr_t x, long prec, long maglim)
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{
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if (fmpr_is_special(x))
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{
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if (fmpr_is_zero(x))
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{
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fmprb_one(c);
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}
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else if (fmpr_is_nan(x))
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{
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fmpr_nan(fmprb_midref(c));
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fmpr_pos_inf(fmprb_radref(c));
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}
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else
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{
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fmpr_zero(fmprb_midref(c));
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fmpr_one(fmprb_radref(c));
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}
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}
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else
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{
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long r;
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fmpz_t mag;
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fmpz_init(mag);
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/* 2^(mag-1) <= |x| < 2^mag */
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fmpr_abs_bound_lt_2exp_fmpz(mag, x);
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/* cos x = 1 - eps, |eps| < x^2 */
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if (fmpz_cmp_si(mag, -(prec/2) - 2) < 0)
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{
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fmpz_mul_ui(mag, mag, 2);
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fmprb_one(c);
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fmprb_add_error_2exp_fmpz(c, mag);
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}
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/* huge */
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else if (fmpz_cmp_si(mag, maglim) > 0)
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{
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fmpr_zero(fmprb_midref(c));
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fmpr_one(fmprb_radref(c));
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}
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else
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{
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r = _fmpr_cos(fmprb_midref(c), x, prec, FMPR_RND_DOWN);
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fmpr_set_error_result(fmprb_radref(c), fmprb_midref(c), r);
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}
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fmpz_clear(mag);
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}
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}
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void
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fmprb_sin_cos_fmpr(fmprb_t s, fmprb_t c, const fmpr_t x, long prec, long maglim)
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{
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if (fmpr_is_special(x))
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{
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if (fmpr_is_zero(x))
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{
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fmprb_zero(s);
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fmprb_one(c);
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}
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else if (fmpr_is_nan(x))
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{
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fmpr_nan(fmprb_midref(s));
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fmpr_pos_inf(fmprb_radref(s));
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fmprb_set(c, s);
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}
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else
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{
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fmpr_zero(fmprb_midref(s));
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fmpr_one(fmprb_radref(s));
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fmprb_set(c, s);
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}
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}
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else
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{
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long r1, r2;
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fmpz_t mag;
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fmpz_init(mag);
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/* 2^(mag-1) <= |x| < 2^mag */
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fmpr_abs_bound_lt_2exp_fmpz(mag, x);
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/* sin x = x + eps, |eps| < x^3 */
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/* cos x = 1 - eps, |eps| < x^2 */
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if (fmpz_cmp_si(mag, -(prec/2) - 2) < 0)
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{
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fmpz_mul_ui(mag, mag, 3);
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fmprb_set_fmpr(s, x);
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fmprb_set_round(s, s, prec);
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fmprb_add_error_2exp_fmpz(s, mag);
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fmpz_divexact_ui(mag, mag, 3);
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fmpz_mul_ui(mag, mag, 2);
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fmprb_one(c);
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fmprb_add_error_2exp_fmpz(c, mag);
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}
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/* huge */
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else if (fmpz_cmp_si(mag, maglim) > 0)
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{
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fmpr_zero(fmprb_midref(s));
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fmpr_one(fmprb_radref(s));
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fmprb_set(c, s);
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}
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else
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{
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_fmpr_sin_cos(&r1, &r2, fmprb_midref(s), fmprb_midref(c), x, prec, FMPR_RND_DOWN);
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fmpr_set_error_result(fmprb_radref(s), fmprb_midref(s), r1);
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fmpr_set_error_result(fmprb_radref(c), fmprb_midref(c), r2);
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}
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fmpz_clear(mag);
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}
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}
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void
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fmprb_sin(fmprb_t s, const fmprb_t x, long prec)
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{
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if (fmprb_is_exact(x))
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{
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fmprb_sin_fmpr(s, fmprb_midref(x), prec, MAGLIM(prec));
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}
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else
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{
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fmpr_t t;
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fmpr_init(t);
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if (fmpr_cmpabs_2exp_si(fmprb_radref(x), 1) > 0)
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fmpr_set_si_2exp_si(t, 1, 1);
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else
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fmpr_set(t, fmprb_radref(x));
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fmprb_sin_fmpr(s, fmprb_midref(x), prec, MAGLIM(prec));
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fmpr_add(fmprb_radref(s), fmprb_radref(s), t, FMPRB_RAD_PREC, FMPR_RND_UP);
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fmpr_clear(t);
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}
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fmprb_adjust(s);
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}
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void
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fmprb_cos(fmprb_t c, const fmprb_t x, long prec)
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{
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if (fmprb_is_exact(x))
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{
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fmprb_cos_fmpr(c, fmprb_midref(x), prec, MAGLIM(prec));
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}
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else
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{
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fmpr_t t;
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fmpr_init(t);
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if (fmpr_cmpabs_2exp_si(fmprb_radref(x), 1) > 0)
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fmpr_set_si_2exp_si(t, 1, 1);
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else
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fmpr_set(t, fmprb_radref(x));
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fmprb_cos_fmpr(c, fmprb_midref(x), prec, MAGLIM(prec));
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fmpr_add(fmprb_radref(c), fmprb_radref(c), t, FMPRB_RAD_PREC, FMPR_RND_UP);
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fmpr_clear(t);
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}
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fmprb_adjust(c);
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}
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void
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fmprb_sin_cos(fmprb_t s, fmprb_t c, const fmprb_t x, long prec)
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{
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if (fmprb_is_exact(x))
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{
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fmprb_sin_cos_fmpr(s, c, fmprb_midref(x), prec, MAGLIM(prec));
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}
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else
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{
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fmpr_t t;
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fmpr_init(t);
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if (fmpr_cmpabs_2exp_si(fmprb_radref(x), 1) > 0)
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fmpr_set_si_2exp_si(t, 1, 1);
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else
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fmpr_set(t, fmprb_radref(x));
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fmprb_sin_cos_fmpr(s, c, fmprb_midref(x), prec, MAGLIM(prec));
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fmpr_add(fmprb_radref(s), fmprb_radref(s), t, FMPRB_RAD_PREC, FMPR_RND_UP);
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fmpr_add(fmprb_radref(c), fmprb_radref(c), t, FMPRB_RAD_PREC, FMPR_RND_UP);
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fmpr_clear(t);
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}
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fmprb_adjust(s);
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fmprb_adjust(c);
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}
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