| /* Quad-precision floating point sine on <-pi/4,pi/4>. |
| Copyright (C) 1999-2018 Free Software Foundation, Inc. |
| This file is part of the GNU C Library. |
| Based on quad-precision sine by Jakub Jelinek <jj@ultra.linux.cz> |
| |
| The GNU C Library is free software; you can redistribute it and/or |
| modify it under the terms of the GNU Lesser General Public |
| License as published by the Free Software Foundation; either |
| version 2.1 of the License, or (at your option) any later version. |
| |
| The GNU C Library 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 |
| Lesser General Public License for more details. |
| |
| You should have received a copy of the GNU Lesser General Public |
| License along with the GNU C Library; if not, see |
| <http://www.gnu.org/licenses/>. */ |
| |
| /* The polynomials have not been optimized for extended-precision and |
| may contain more terms than needed. */ |
| |
| #include <float.h> |
| #include <math.h> |
| #include <math_private.h> |
| |
| /* The polynomials have not been optimized for extended-precision and |
| may contain more terms than needed. */ |
| |
| static const long double c[] = { |
| #define ONE c[0] |
| 1.00000000000000000000000000000000000E+00L, |
| |
| /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) |
| x in <0,1/256> */ |
| #define SCOS1 c[1] |
| #define SCOS2 c[2] |
| #define SCOS3 c[3] |
| #define SCOS4 c[4] |
| #define SCOS5 c[5] |
| -5.00000000000000000000000000000000000E-01L, |
| 4.16666666666666666666666666556146073E-02L, |
| -1.38888888888888888888309442601939728E-03L, |
| 2.48015873015862382987049502531095061E-05L, |
| -2.75573112601362126593516899592158083E-07L, |
| |
| /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 ) |
| x in <0,0.1484375> */ |
| #define SIN1 c[6] |
| #define SIN2 c[7] |
| #define SIN3 c[8] |
| #define SIN4 c[9] |
| #define SIN5 c[10] |
| #define SIN6 c[11] |
| #define SIN7 c[12] |
| #define SIN8 c[13] |
| -1.66666666666666666666666666666666538e-01L, |
| 8.33333333333333333333333333307532934e-03L, |
| -1.98412698412698412698412534478712057e-04L, |
| 2.75573192239858906520896496653095890e-06L, |
| -2.50521083854417116999224301266655662e-08L, |
| 1.60590438367608957516841576404938118e-10L, |
| -7.64716343504264506714019494041582610e-13L, |
| 2.81068754939739570236322404393398135e-15L, |
| |
| /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) |
| x in <0,1/256> */ |
| #define SSIN1 c[14] |
| #define SSIN2 c[15] |
| #define SSIN3 c[16] |
| #define SSIN4 c[17] |
| #define SSIN5 c[18] |
| -1.66666666666666666666666666666666659E-01L, |
| 8.33333333333333333333333333146298442E-03L, |
| -1.98412698412698412697726277416810661E-04L, |
| 2.75573192239848624174178393552189149E-06L, |
| -2.50521016467996193495359189395805639E-08L, |
| }; |
| |
| #define SINCOSL_COS_HI 0 |
| #define SINCOSL_COS_LO 1 |
| #define SINCOSL_SIN_HI 2 |
| #define SINCOSL_SIN_LO 3 |
| extern const long double __sincosl_table[]; |
| |
| long double |
| __kernel_sinl(long double x, long double y, int iy) |
| { |
| long double absx, h, l, z, sin_l, cos_l_m1; |
| int index; |
| |
| absx = fabsl (x); |
| if (absx < 0.1484375L) |
| { |
| /* Argument is small enough to approximate it by a Chebyshev |
| polynomial of degree 17. */ |
| if (absx < 0x1p-33L) |
| { |
| math_check_force_underflow (x); |
| if (!((int)x)) return x; /* generate inexact */ |
| } |
| z = x * x; |
| return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+ |
| z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8))))))))); |
| } |
| else |
| { |
| /* So that we don't have to use too large polynomial, we find |
| l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83 |
| possible values for h. We look up cosl(h) and sinl(h) in |
| pre-computed tables, compute cosl(l) and sinl(l) using a |
| Chebyshev polynomial of degree 10(11) and compute |
| sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l). */ |
| index = (int) (128 * (absx - (0.1484375L - 1.0L / 256.0L))); |
| h = 0.1484375L + index / 128.0; |
| index *= 4; |
| if (iy) |
| l = (x < 0 ? -y : y) - (h - absx); |
| else |
| l = absx - h; |
| z = l * l; |
| sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); |
| cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5)))); |
| z = __sincosl_table [index + SINCOSL_SIN_HI] |
| + (__sincosl_table [index + SINCOSL_SIN_LO] |
| + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1) |
| + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l)); |
| return (x < 0) ? -z : z; |
| } |
| } |