1/* Quad-precision floating point sine on <-pi/4,pi/4>.
2 Copyright (C) 1999-2020 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4 Based on quad-precision sine by Jakub Jelinek <jj@ultra.linux.cz>
5
6 The GNU C Library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Lesser General Public
8 License as published by the Free Software Foundation; either
9 version 2.1 of the License, or (at your option) any later version.
10
11 The GNU C Library is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
15
16 You should have received a copy of the GNU Lesser General Public
17 License along with the GNU C Library; if not, see
18 <https://www.gnu.org/licenses/>. */
19
20/* The polynomials have not been optimized for extended-precision and
21 may contain more terms than needed. */
22
23#include <float.h>
24#include <math.h>
25#include <math_private.h>
26#include <math-underflow.h>
27
28/* The polynomials have not been optimized for extended-precision and
29 may contain more terms than needed. */
30
31static const long double c[] = {
32#define ONE c[0]
33 1.00000000000000000000000000000000000E+00L,
34
35/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
36 x in <0,1/256> */
37#define SCOS1 c[1]
38#define SCOS2 c[2]
39#define SCOS3 c[3]
40#define SCOS4 c[4]
41#define SCOS5 c[5]
42-5.00000000000000000000000000000000000E-01L,
43 4.16666666666666666666666666556146073E-02L,
44-1.38888888888888888888309442601939728E-03L,
45 2.48015873015862382987049502531095061E-05L,
46-2.75573112601362126593516899592158083E-07L,
47
48/* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
49 x in <0,0.1484375> */
50#define SIN1 c[6]
51#define SIN2 c[7]
52#define SIN3 c[8]
53#define SIN4 c[9]
54#define SIN5 c[10]
55#define SIN6 c[11]
56#define SIN7 c[12]
57#define SIN8 c[13]
58-1.66666666666666666666666666666666538e-01L,
59 8.33333333333333333333333333307532934e-03L,
60-1.98412698412698412698412534478712057e-04L,
61 2.75573192239858906520896496653095890e-06L,
62-2.50521083854417116999224301266655662e-08L,
63 1.60590438367608957516841576404938118e-10L,
64-7.64716343504264506714019494041582610e-13L,
65 2.81068754939739570236322404393398135e-15L,
66
67/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
68 x in <0,1/256> */
69#define SSIN1 c[14]
70#define SSIN2 c[15]
71#define SSIN3 c[16]
72#define SSIN4 c[17]
73#define SSIN5 c[18]
74-1.66666666666666666666666666666666659E-01L,
75 8.33333333333333333333333333146298442E-03L,
76-1.98412698412698412697726277416810661E-04L,
77 2.75573192239848624174178393552189149E-06L,
78-2.50521016467996193495359189395805639E-08L,
79};
80
81#define SINCOSL_COS_HI 0
82#define SINCOSL_COS_LO 1
83#define SINCOSL_SIN_HI 2
84#define SINCOSL_SIN_LO 3
85extern const long double __sincosl_table[];
86
87long double
88__kernel_sinl(long double x, long double y, int iy)
89{
90 long double absx, h, l, z, sin_l, cos_l_m1;
91 int index;
92
93 absx = fabsl (x);
94 if (absx < 0.1484375L)
95 {
96 /* Argument is small enough to approximate it by a Chebyshev
97 polynomial of degree 17. */
98 if (absx < 0x1p-33L)
99 {
100 math_check_force_underflow (x);
101 if (!((int)x)) return x; /* generate inexact */
102 }
103 z = x * x;
104 return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
105 z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
106 }
107 else
108 {
109 /* So that we don't have to use too large polynomial, we find
110 l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
111 possible values for h. We look up cosl(h) and sinl(h) in
112 pre-computed tables, compute cosl(l) and sinl(l) using a
113 Chebyshev polynomial of degree 10(11) and compute
114 sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l). */
115 index = (int) (128 * (absx - (0.1484375L - 1.0L / 256.0L)));
116 h = 0.1484375L + index / 128.0;
117 index *= 4;
118 if (iy)
119 l = (x < 0 ? -y : y) - (h - absx);
120 else
121 l = absx - h;
122 z = l * l;
123 sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
124 cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
125 z = __sincosl_table [index + SINCOSL_SIN_HI]
126 + (__sincosl_table [index + SINCOSL_SIN_LO]
127 + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1)
128 + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l));
129 return (x < 0) ? -z : z;
130 }
131}
132