1 /* Quad-precision floating point sine on <-pi/4,pi/4>.
2 Copyright (C) 1999-2015 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>
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.
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.
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 <http://www.gnu.org/licenses/>. */
20 /* The polynomials have not been optimized for extended-precision and
21 may contain more terms than needed. */
25 #include <math_private.h>
27 /* The polynomials have not been optimized for extended-precision and
28 may contain more terms than needed. */
30 static const long double c
[] = {
32 1.00000000000000000000000000000000000E+00L,
34 /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
41 -5.00000000000000000000000000000000000E-01L,
42 4.16666666666666666666666666556146073E-02L,
43 -1.38888888888888888888309442601939728E-03L,
44 2.48015873015862382987049502531095061E-05L,
45 -2.75573112601362126593516899592158083E-07L,
47 /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
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,
66 /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
73 -1.66666666666666666666666666666666659E-01L,
74 8.33333333333333333333333333146298442E-03L,
75 -1.98412698412698412697726277416810661E-04L,
76 2.75573192239848624174178393552189149E-06L,
77 -2.50521016467996193495359189395805639E-08L,
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
[];
87 __kernel_sinl(long double x
, long double y
, int iy
)
89 long double absx
, h
, l
, z
, sin_l
, cos_l_m1
;
93 if (absx
< 0.1484375L)
95 /* Argument is small enough to approximate it by a Chebyshev
96 polynomial of degree 17. */
99 if (fabsl (x
) < LDBL_MIN
)
101 long double force_underflow
= x
* x
;
102 math_force_eval (force_underflow
);
104 if (!((int)x
)) return x
; /* generate inexact */
107 return x
+ (x
* (z
*(SIN1
+z
*(SIN2
+z
*(SIN3
+z
*(SIN4
+
108 z
*(SIN5
+z
*(SIN6
+z
*(SIN7
+z
*SIN8
)))))))));
112 /* So that we don't have to use too large polynomial, we find
113 l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
114 possible values for h. We look up cosl(h) and sinl(h) in
115 pre-computed tables, compute cosl(l) and sinl(l) using a
116 Chebyshev polynomial of degree 10(11) and compute
117 sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l). */
118 index
= (int) (128 * (absx
- (0.1484375L - 1.0L / 256.0L)));
119 h
= 0.1484375L + index
/ 128.0;
122 l
= (x
< 0 ? -y
: y
) - (h
- absx
);
126 sin_l
= l
*(ONE
+z
*(SSIN1
+z
*(SSIN2
+z
*(SSIN3
+z
*(SSIN4
+z
*SSIN5
)))));
127 cos_l_m1
= z
*(SCOS1
+z
*(SCOS2
+z
*(SCOS3
+z
*(SCOS4
+z
*SCOS5
))));
128 z
= __sincosl_table
[index
+ SINCOSL_SIN_HI
]
129 + (__sincosl_table
[index
+ SINCOSL_SIN_LO
]
130 + (__sincosl_table
[index
+ SINCOSL_SIN_HI
] * cos_l_m1
)
131 + (__sincosl_table
[index
+ SINCOSL_COS_HI
] * sin_l
));
132 return (x
< 0) ? -z
: z
;