1 /* Quad-precision floating point sine on <-pi/4,pi/4>.
2 Copyright (C) 1999-2023 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4
5 The GNU C Library is free software; you can redistribute it and/or
6 modify it under the terms of the GNU Lesser General Public
7 License as published by the Free Software Foundation; either
8 version 2.1 of the License, or (at your option) any later version.
9
10 The GNU C Library is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 Lesser General Public License for more details.
14
15 You should have received a copy of the GNU Lesser General Public
16 License along with the GNU C Library; if not, see
17 <https://www.gnu.org/licenses/>. */
18
19 /* The polynomials have not been optimized for extended-precision and
20 may contain more terms than needed. */
21
22 #include <float.h>
23 #include <math.h>
24 #include <math_private.h>
25 #include <math-underflow.h>
26
27 /* The polynomials have not been optimized for extended-precision and
28 may contain more terms than needed. */
29
30 static const long double c[] = {
31 #define ONE c[0]
32 1.00000000000000000000000000000000000E+00L,
33
34 /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
35 x in <0,1/256> */
36 #define SCOS1 c[1]
37 #define SCOS2 c[2]
38 #define SCOS3 c[3]
39 #define SCOS4 c[4]
40 #define SCOS5 c[5]
41 -5.00000000000000000000000000000000000E-01L,
42 4.16666666666666666666666666556146073E-02L,
43 -1.38888888888888888888309442601939728E-03L,
44 2.48015873015862382987049502531095061E-05L,
45 -2.75573112601362126593516899592158083E-07L,
46
47 /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
48 x in <0,0.1484375> */
49 #define SIN1 c[6]
50 #define SIN2 c[7]
51 #define SIN3 c[8]
52 #define SIN4 c[9]
53 #define SIN5 c[10]
54 #define SIN6 c[11]
55 #define SIN7 c[12]
56 #define SIN8 c[13]
57 -1.66666666666666666666666666666666538e-01L,
58 8.33333333333333333333333333307532934e-03L,
59 -1.98412698412698412698412534478712057e-04L,
60 2.75573192239858906520896496653095890e-06L,
61 -2.50521083854417116999224301266655662e-08L,
62 1.60590438367608957516841576404938118e-10L,
63 -7.64716343504264506714019494041582610e-13L,
64 2.81068754939739570236322404393398135e-15L,
65
66 /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
67 x in <0,1/256> */
68 #define SSIN1 c[14]
69 #define SSIN2 c[15]
70 #define SSIN3 c[16]
71 #define SSIN4 c[17]
72 #define SSIN5 c[18]
73 -1.66666666666666666666666666666666659E-01L,
74 8.33333333333333333333333333146298442E-03L,
75 -1.98412698412698412697726277416810661E-04L,
76 2.75573192239848624174178393552189149E-06L,
77 -2.50521016467996193495359189395805639E-08L,
78 };
79
80 #define SINCOSL_COS_HI 0
81 #define SINCOSL_COS_LO 1
82 #define SINCOSL_SIN_HI 2
83 #define SINCOSL_SIN_LO 3
84 extern const long double __sincosl_table[];
85
86 long double
87 __kernel_sinl(long double x, long double y, int iy)
88 {
89 long double absx, h, l, z, sin_l, cos_l_m1;
90 int index;
91
92 absx = fabsl (x);
93 if (absx < 0.1484375L)
94 {
95 /* Argument is small enough to approximate it by a Chebyshev
96 polynomial of degree 17. */
97 if (absx < 0x1p-33L)
98 {
99 math_check_force_underflow (x);
100 if (!((int)x)) return x; /* generate inexact */
101 }
102 z = x * x;
103 return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
104 z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
105 }
106 else
107 {
108 /* So that we don't have to use too large polynomial, we find
109 l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
110 possible values for h. We look up cosl(h) and sinl(h) in
111 pre-computed tables, compute cosl(l) and sinl(l) using a
112 Chebyshev polynomial of degree 10(11) and compute
113 sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l). */
114 index = (int) (128 * (absx - (0.1484375L - 1.0L / 256.0L)));
115 h = 0.1484375L + index / 128.0;
116 index *= 4;
117 if (iy)
118 l = (x < 0 ? -y : y) - (h - absx);
119 else
120 l = absx - h;
121 z = l * l;
122 sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
123 cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
124 z = __sincosl_table [index + SINCOSL_SIN_HI]
125 + (__sincosl_table [index + SINCOSL_SIN_LO]
126 + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1)
127 + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l));
128 return (x < 0) ? -z : z;
129 }
130 }