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https://github.com/vale981/arb
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first versions of fmprb_[sin|cos|sin_cos]_pi_fmpq
This commit is contained in:
Fredrik Johansson
parent
6702c756a4
commit
493ec76e0e
6 changed files with 551 additions and 0 deletions
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@ -480,6 +480,24 @@ Elementary functions
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Sets `s = \sin \pi x`, `c = \cos \pi x`.
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.. function:: void fmprb_sin_pi_fmpq(fmprb_t s, const fmpq_t x, long prec)
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.. function:: void fmprb_cos_pi_fmpq(fmprb_t c, const fmpq_t x, long prec)
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.. function:: void fmprb_sin_cos_pi_fmpq(fmprb_t s, fmprb_t c, const fmpq_t x, long prec)
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Sets `s = \sin \pi x`, `c = \cos \pi x` where `x` is a rational
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number (whose numerator and denominator are assumed to be reduced).
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We first use trigonometric symmetries to reduce the argument to the
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octant `[0, 1/4]`. If the reduced argument is one of
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`0, 1/4, 1/6, 1/8, 1/5, 1/10`, we use an explicit algebraic
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formula. Otherwise
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we multiply by a numerical approximation of `\pi`
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and evaluate the trigonometric function the usual way.
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Since the argument has been reduced to the first octant, this
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gives full accuracy even if the original argument is close to
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some root other the origin.
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.. function:: void fmprb_atan(fmprb_t z, const fmprb_t x, long prec)
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Sets `z = \tan^{-1} x`. Letting `d = \max(0, |m| - r)`,
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4
fmprb.h
4
fmprb.h
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@ -275,6 +275,10 @@ void fmprb_sin_pi(fmprb_t s, const fmprb_t x, long prec);
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void fmprb_cos_pi(fmprb_t c, const fmprb_t x, long prec);
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void fmprb_sin_cos_pi(fmprb_t s, fmprb_t c, const fmprb_t x, long prec);
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void fmprb_sin_cos_pi_fmpq(fmprb_t s, fmprb_t c, const fmpq_t x, long prec);
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void fmprb_sin_pi_fmpq(fmprb_t s, const fmpq_t x, long prec);
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void fmprb_cos_pi_fmpq(fmprb_t c, const fmpq_t x, long prec);
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void fmprb_sinh(fmprb_t z, const fmprb_t x, long prec);
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void fmprb_cosh(fmprb_t z, const fmprb_t x, long prec);
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void fmprb_sinh_cosh(fmprb_t s, fmprb_t c, const fmprb_t x, long prec);
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289
fmprb/sin_cos_pi_fmpq.c
Normal file
289
fmprb/sin_cos_pi_fmpq.c
Normal file
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@ -0,0 +1,289 @@
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/*=============================================================================
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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 "fmprb.h"
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/* evaluates sin(pi v/w), cos(pi v/w) assuming
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(for best performance and accuracy)
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v, w reduced and 0 <= v/w <= 1/4. */
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void
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_fmprb_sin_cos_pi_fmpq_oct(fmprb_t s, fmprb_t c,
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const fmpz_t v, const fmpz_t w, long prec)
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{
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if (*v == 0)
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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 (*v == 1 && *w == 4)
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{
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fmprb_sqrt_ui(s, 2, prec);
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fmprb_mul_2exp_si(s, s, -1);
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fmprb_set(c, s);
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}
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else if (*v == 1 && *w == 6)
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{
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fmprb_one(s);
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fmprb_mul_2exp_si(s, s, -1);
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fmprb_sqrt_ui(c, 3, prec);
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fmprb_mul_2exp_si(c, c, -1);
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}
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else if (*v == 1 && *w == 8)
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{
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fmprb_sqrt_ui(s, 2, prec);
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fmprb_add_ui(c, s, 2, prec);
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fmprb_sqrt(c, c, prec);
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fmprb_mul_2exp_si(c, c, -1);
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fmprb_sub_ui(s, s, 2, prec);
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fmprb_neg(s, s);
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fmprb_sqrt(s, s, prec);
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fmprb_mul_2exp_si(s, s, -1);
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}
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else if (*v == 1 && *w == 5)
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{
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fmprb_sqrt_ui(s, 5, prec);
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fmprb_add_ui(c, s, 1, prec);
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fmprb_mul_2exp_si(c, c, -2);
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fmprb_sub_ui(s, s, 5, prec);
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fmprb_neg(s, s);
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fmprb_mul_2exp_si(s, s, -3);
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fmprb_sqrt(s, s, prec);
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}
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else if (*v == 1 && *w == 10)
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{
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fmprb_sqrt_ui(c, 5, prec);
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fmprb_sub_ui(s, c, 1, prec);
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fmprb_mul_2exp_si(s, s, -2);
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fmprb_add_ui(c, c, 5, prec);
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fmprb_mul_2exp_si(c, c, -3);
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fmprb_sqrt(c, c, prec);
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}
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else
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{
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fmprb_const_pi(s, prec);
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fmprb_mul_fmpz(s, s, v, prec);
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fmprb_div_fmpz(s, s, w, prec);
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fmprb_sin_cos(s, c, s, prec);
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}
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}
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void
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_fmprb_sin_pi_fmpq_oct(fmprb_t s, const fmpz_t v, const fmpz_t w, long prec)
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{
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if (*v == 0)
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{
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fmprb_zero(s);
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}
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else if (*v == 1 && *w == 4)
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{
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fmprb_sqrt_ui(s, 2, prec);
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fmprb_mul_2exp_si(s, s, -1);
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}
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else if (*v == 1 && *w == 6)
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{
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fmprb_one(s);
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fmprb_mul_2exp_si(s, s, -1);
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}
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else if (*v == 1 && *w == 8)
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{
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fmprb_sqrt_ui(s, 2, prec);
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fmprb_sub_ui(s, s, 2, prec);
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fmprb_neg(s, s);
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fmprb_sqrt(s, s, prec);
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fmprb_mul_2exp_si(s, s, -1);
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}
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else if (*v == 1 && *w == 5)
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{
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fmprb_sqrt_ui(s, 5, prec);
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fmprb_sub_ui(s, s, 5, prec);
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fmprb_neg(s, s);
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fmprb_mul_2exp_si(s, s, -3);
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fmprb_sqrt(s, s, prec);
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}
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else if (*v == 1 && *w == 10)
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{
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fmprb_sqrt_ui(s, 5, prec);
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fmprb_sub_ui(s, s, 1, prec);
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fmprb_mul_2exp_si(s, s, -2);
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}
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else
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{
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fmprb_const_pi(s, prec);
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fmprb_mul_fmpz(s, s, v, prec);
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fmprb_div_fmpz(s, s, w, prec);
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fmprb_sin(s, s, prec);
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}
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}
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void
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_fmprb_cos_pi_fmpq_oct(fmprb_t c, const fmpz_t v, const fmpz_t w, long prec)
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{
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if (*v == 0)
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{
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fmprb_one(c);
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}
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else if (*v == 1 && *w == 4)
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{
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fmprb_sqrt_ui(c, 2, prec);
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fmprb_mul_2exp_si(c, c, -1);
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}
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else if (*v == 1 && *w == 6)
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{
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fmprb_sqrt_ui(c, 3, prec);
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fmprb_mul_2exp_si(c, c, -1);
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}
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else if (*v == 1 && *w == 8)
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{
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fmprb_sqrt_ui(c, 2, prec);
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fmprb_add_ui(c, c, 2, prec);
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fmprb_sqrt(c, c, prec);
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fmprb_mul_2exp_si(c, c, -1);
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}
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else if (*v == 1 && *w == 5)
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{
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fmprb_sqrt_ui(c, 5, prec);
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fmprb_add_ui(c, c, 1, prec);
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fmprb_mul_2exp_si(c, c, -2);
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}
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else if (*v == 1 && *w == 10)
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{
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fmprb_sqrt_ui(c, 5, prec);
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fmprb_add_ui(c, c, 5, prec);
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fmprb_mul_2exp_si(c, c, -3);
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fmprb_sqrt(c, c, prec);
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}
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else
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{
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fmprb_const_pi(c, prec);
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fmprb_mul_fmpz(c, c, v, prec);
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fmprb_div_fmpz(c, c, w, prec);
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fmprb_cos(c, c, prec);
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}
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}
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unsigned int
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reduce_octant(fmpz_t v, fmpz_t w, const fmpq_t x)
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{
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const fmpz * p = fmpq_numref(x);
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const fmpz * q = fmpq_denref(x);
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fmpz_t u;
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unsigned int octant;
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mp_bitcnt_t vval, wval;
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fmpz_init(u);
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fmpz_mul_2exp(w, p, 2);
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fmpz_fdiv_qr(w, v, w, q);
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octant = fmpz_fdiv_ui(w, 8);
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fmpz_mul_2exp(w, q, 2);
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if (octant % 2 != 0)
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fmpz_sub(v, q, v);
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vval = fmpz_val2(v);
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wval = fmpz_val2(w);
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vval = FLINT_MIN(vval, wval);
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if (vval != 0)
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{
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fmpz_tdiv_q_2exp(v, v, vval);
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fmpz_tdiv_q_2exp(w, w, vval);
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}
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fmpz_clear(u);
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return octant;
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}
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void
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fmprb_sin_cos_pi_fmpq(fmprb_t s, fmprb_t c, const fmpq_t x, long prec)
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{
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fmpz_t v, w;
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unsigned int octant;
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fmpz_init(v);
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fmpz_init(w);
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octant = reduce_octant(v, w, x);
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if ((octant + 1) % 4 < 2)
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_fmprb_sin_cos_pi_fmpq_oct(s, c, v, w, prec);
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else
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_fmprb_sin_cos_pi_fmpq_oct(c, s, v, w, prec);
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if ((octant + 6) % 8 < 4) fmprb_neg(c, c);
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if (octant >= 4) fmprb_neg(s, s);
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fmpz_clear(v);
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fmpz_clear(w);
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}
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void
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fmprb_sin_pi_fmpq(fmprb_t s, const fmpq_t x, long prec)
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{
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fmpz_t v, w;
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unsigned int octant;
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fmpz_init(v);
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fmpz_init(w);
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octant = reduce_octant(v, w, x);
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if ((octant + 1) % 4 < 2)
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_fmprb_sin_pi_fmpq_oct(s, v, w, prec);
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else
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_fmprb_cos_pi_fmpq_oct(s, v, w, prec);
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if (octant >= 4)
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fmprb_neg(s, s);
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fmpz_clear(v);
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fmpz_clear(w);
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}
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void
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fmprb_cos_pi_fmpq(fmprb_t c, const fmpq_t x, long prec)
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{
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fmpz_t v, w;
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unsigned int octant;
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fmpz_init(v);
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fmpz_init(w);
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octant = reduce_octant(v, w, x);
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if ((octant + 1) % 4 < 2)
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_fmprb_cos_pi_fmpq_oct(c, v, w, prec);
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else
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_fmprb_sin_pi_fmpq_oct(c, v, w, prec);
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if ((octant + 6) % 8 < 4)
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fmprb_neg(c, c);
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fmpz_clear(v);
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fmpz_clear(w);
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}
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78
fmprb/test/t-cos_pi_fmpq.c
Normal file
78
fmprb/test/t-cos_pi_fmpq.c
Normal file
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@ -0,0 +1,78 @@
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/*=============================================================================
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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
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
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ARB is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with ARB; if not, write to the Free Software
|
||||
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 "fmprb.h"
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int main()
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{
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long iter;
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flint_rand_t state;
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printf("cos_pi_fmpq....");
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fflush(stdout);
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flint_randinit(state);
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for (iter = 0; iter < 10000; iter++)
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{
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fmprb_t c1, c2;
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fmpq_t x;
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long prec;
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prec = 2 + n_randint(state, 1000);
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fmprb_init(c1);
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fmprb_init(c2);
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fmpq_init(x);
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fmpq_randtest(x, state, 1 + n_randint(state, 200));
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fmprb_cos_pi_fmpq(c1, x, prec);
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fmprb_const_pi(c2, prec);
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fmprb_mul_fmpz(c2, c2, fmpq_numref(x), prec);
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fmprb_div_fmpz(c2, c2, fmpq_denref(x), prec);
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fmprb_cos(c2, c2, prec);
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if (!fmprb_overlaps(c1, c2))
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{
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printf("FAIL: overlap\n\n");
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printf("x = "); fmpq_print(x); printf("\n\n");
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printf("c1 = "); fmprb_printd(c1, 15); printf("\n\n");
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printf("c2 = "); fmprb_printd(c2, 15); printf("\n\n");
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abort();
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}
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fmprb_clear(c1);
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fmprb_clear(c2);
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fmpq_clear(x);
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}
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flint_randclear(state);
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_fmpz_cleanup();
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printf("PASS\n");
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return EXIT_SUCCESS;
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}
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84
fmprb/test/t-sin_cos_pi_fmpq.c
Normal file
84
fmprb/test/t-sin_cos_pi_fmpq.c
Normal file
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@ -0,0 +1,84 @@
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/*=============================================================================
|
||||
|
||||
This file is part of ARB.
|
||||
|
||||
ARB is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
ARB is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with ARB; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
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Copyright (C) 2013 Fredrik Johansson
|
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|
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******************************************************************************/
|
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#include "fmprb.h"
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int main()
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{
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long iter;
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flint_rand_t state;
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printf("sin_cos_pi_fmpq....");
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fflush(stdout);
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flint_randinit(state);
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for (iter = 0; iter < 10000; iter++)
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{
|
||||
fmprb_t s1, c1, s2, c2;
|
||||
fmpq_t x;
|
||||
long prec;
|
||||
|
||||
prec = 2 + n_randint(state, 1000);
|
||||
|
||||
fmprb_init(s1);
|
||||
fmprb_init(c1);
|
||||
fmprb_init(s2);
|
||||
fmprb_init(c2);
|
||||
fmpq_init(x);
|
||||
|
||||
fmpq_randtest(x, state, 1 + n_randint(state, 200));
|
||||
|
||||
fmprb_sin_cos_pi_fmpq(s1, c1, x, prec);
|
||||
|
||||
fmprb_const_pi(s2, prec);
|
||||
fmprb_mul_fmpz(s2, s2, fmpq_numref(x), prec);
|
||||
fmprb_div_fmpz(s2, s2, fmpq_denref(x), prec);
|
||||
fmprb_sin_cos(s2, c2, s2, prec);
|
||||
|
||||
if (!fmprb_overlaps(s1, s2) || !fmprb_overlaps(c1, c2))
|
||||
{
|
||||
printf("FAIL: overlap\n\n");
|
||||
printf("x = "); fmpq_print(x); printf("\n\n");
|
||||
printf("s1 = "); fmprb_printd(s1, 15); printf("\n\n");
|
||||
printf("c1 = "); fmprb_printd(c1, 15); printf("\n\n");
|
||||
printf("s2 = "); fmprb_printd(s2, 15); printf("\n\n");
|
||||
printf("c2 = "); fmprb_printd(c2, 15); printf("\n\n");
|
||||
abort();
|
||||
}
|
||||
|
||||
fmprb_clear(s1);
|
||||
fmprb_clear(c1);
|
||||
fmprb_clear(s2);
|
||||
fmprb_clear(c2);
|
||||
fmpq_clear(x);
|
||||
}
|
||||
|
||||
flint_randclear(state);
|
||||
_fmpz_cleanup();
|
||||
printf("PASS\n");
|
||||
return EXIT_SUCCESS;
|
||||
}
|
||||
|
||||
78
fmprb/test/t-sin_pi_fmpq.c
Normal file
78
fmprb/test/t-sin_pi_fmpq.c
Normal file
|
|
@ -0,0 +1,78 @@
|
|||
/*=============================================================================
|
||||
|
||||
This file is part of ARB.
|
||||
|
||||
ARB is free software; you can redistribute it and/or modify
|
||||
it under the terms of the GNU General Public License as published by
|
||||
the Free Software Foundation; either version 2 of the License, or
|
||||
(at your option) any later version.
|
||||
|
||||
ARB is distributed in the hope that it will be useful,
|
||||
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
||||
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
||||
GNU General Public License for more details.
|
||||
|
||||
You should have received a copy of the GNU General Public License
|
||||
along with ARB; if not, write to the Free Software
|
||||
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
||||
|
||||
=============================================================================*/
|
||||
/******************************************************************************
|
||||
|
||||
Copyright (C) 2013 Fredrik Johansson
|
||||
|
||||
******************************************************************************/
|
||||
|
||||
#include "fmprb.h"
|
||||
|
||||
int main()
|
||||
{
|
||||
long iter;
|
||||
flint_rand_t state;
|
||||
|
||||
printf("sin_pi_fmpq....");
|
||||
fflush(stdout);
|
||||
|
||||
flint_randinit(state);
|
||||
|
||||
for (iter = 0; iter < 10000; iter++)
|
||||
{
|
||||
fmprb_t s1, s2;
|
||||
fmpq_t x;
|
||||
long prec;
|
||||
|
||||
prec = 2 + n_randint(state, 1000);
|
||||
|
||||
fmprb_init(s1);
|
||||
fmprb_init(s2);
|
||||
fmpq_init(x);
|
||||
|
||||
fmpq_randtest(x, state, 1 + n_randint(state, 200));
|
||||
|
||||
fmprb_sin_pi_fmpq(s1, x, prec);
|
||||
|
||||
fmprb_const_pi(s2, prec);
|
||||
fmprb_mul_fmpz(s2, s2, fmpq_numref(x), prec);
|
||||
fmprb_div_fmpz(s2, s2, fmpq_denref(x), prec);
|
||||
fmprb_sin(s2, s2, prec);
|
||||
|
||||
if (!fmprb_overlaps(s1, s2))
|
||||
{
|
||||
printf("FAIL: overlap\n\n");
|
||||
printf("x = "); fmpq_print(x); printf("\n\n");
|
||||
printf("s1 = "); fmprb_printd(s1, 15); printf("\n\n");
|
||||
printf("s2 = "); fmprb_printd(s2, 15); printf("\n\n");
|
||||
abort();
|
||||
}
|
||||
|
||||
fmprb_clear(s1);
|
||||
fmprb_clear(s2);
|
||||
fmpq_clear(x);
|
||||
}
|
||||
|
||||
flint_randclear(state);
|
||||
_fmpz_cleanup();
|
||||
printf("PASS\n");
|
||||
return EXIT_SUCCESS;
|
||||
}
|
||||
|
||||
Loading…
Add table
Reference in a new issue