1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
|
/*-
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
* Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
* k_sinl.c and k_cosl.c merged by Steven G. Kargl
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
#if LDBL_MANT_DIG == 64 /* ld80 version of k_sincosl.c. */
#if defined(__amd64__) || defined(__i386__)
/* Long double constants are slow on these arches, and broken on i386. */
static const volatile double
C1hi = 0.041666666666666664, /* 0x15555555555555.0p-57 */
C1lo = 2.2598839032744733e-18, /* 0x14d80000000000.0p-111 */
S1hi = -0.16666666666666666, /* -0x15555555555555.0p-55 */
S1lo = -9.2563760475949941e-18; /* -0x15580000000000.0p-109 */
#define S1 ((long double)S1hi + S1lo)
#define C1 ((long double)C1hi + C1lo)
#else
static const long double
C1 = 0.0416666666666666666136L, /* 0xaaaaaaaaaaaaaa9b.0p-68 */
S1 = -0.166666666666666666671L; /* -0xaaaaaaaaaaaaaaab.0p-66 */
#endif
static const double
C2 = -0.0013888888888888874, /* -0x16c16c16c16c10.0p-62 */
C3 = 0.000024801587301571716, /* 0x1a01a01a018e22.0p-68 */
C4 = -0.00000027557319215507120, /* -0x127e4fb7602f22.0p-74 */
C5 = 0.0000000020876754400407278, /* 0x11eed8caaeccf1.0p-81 */
C6 = -1.1470297442401303e-11, /* -0x19393412bd1529.0p-89 */
C7 = 4.7383039476436467e-14, /* 0x1aac9d9af5c43e.0p-97 */
S2 = 0.0083333333333333332, /* 0x11111111111111.0p-59 */
S3 = -0.00019841269841269427, /* -0x1a01a01a019f81.0p-65 */
S4 = 0.0000027557319223597490, /* 0x171de3a55560f7.0p-71 */
S5 = -0.000000025052108218074604, /* -0x1ae64564f16cad.0p-78 */
S6 = 1.6059006598854211e-10, /* 0x161242b90243b5.0p-85 */
S7 = -7.6429779983024564e-13, /* -0x1ae42ebd1b2e00.0p-93 */
S8 = 2.6174587166648325e-15; /* 0x179372ea0b3f64.0p-101 */
static inline void
__kernel_sincosl(long double x, long double y, int iy, long double *sn,
long double *cs)
{
long double hz, r, v, w, z;
z = x * x;
v = z * x;
/*
* XXX Replace Horner scheme with an algorithm suitable for CPUs
* with more complex pipelines.
*/
r = S2 + z * (S3 + z * (S4 + z * (S5 + z * (S6 + z * (S7 + z * S8)))));
if (iy == 0)
*sn = x + v * (S1 + z * r);
else
*sn = x - ((z * (y / 2 - v * r) - y) - v * S1);
hz = z / 2;
w = 1 - hz;
r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * (C6 +
z * C7))))));
*cs = w + (((1 - w) - hz) + (z * r - x * y));
}
#elif LDBL_MANT_DIG == 113 /* ld128 version of k_sincosl.c. */
static const long double
S1 = -0.16666666666666666666666666666666666606732416116558L,
S2 = 0.0083333333333333333333333333333331135404851288270047L,
S3 = -0.00019841269841269841269841269839935785325638310428717L,
S4 = 0.27557319223985890652557316053039946268333231205686e-5L,
S5 = -0.25052108385441718775048214826384312253862930064745e-7L,
S6 = 0.16059043836821614596571832194524392581082444805729e-9L,
S7 = -0.76471637318198151807063387954939213287488216303768e-12L,
S8 = 0.28114572543451292625024967174638477283187397621303e-14L;
static const double
S9 = -0.82206352458348947812512122163446202498005154296863e-17,
S10 = 0.19572940011906109418080609928334380560135358385256e-19,
S11 = -0.38680813379701966970673724299207480965452616911420e-22,
S12 = 0.64038150078671872796678569586315881020659912139412e-25;
static const long double
C1 = 4.16666666666666666666666666666666667e-02L,
C2 = -1.38888888888888888888888888888888834e-03L,
C3 = 2.48015873015873015873015873015446795e-05L,
C4 = -2.75573192239858906525573190949988493e-07L,
C5 = 2.08767569878680989792098886701451072e-09L,
C6 = -1.14707455977297247136657111139971865e-11L,
C7 = 4.77947733238738518870113294139830239e-14L,
C8 = -1.56192069685858079920640872925306403e-16L,
C9 = 4.11031762320473354032038893429515732e-19L,
C10= -8.89679121027589608738005163931958096e-22L,
C11= 1.61171797801314301767074036661901531e-24L,
C12= -2.46748624357670948912574279501044295e-27L;
static inline void
__kernel_sincosl(long double x, long double y, int iy, long double *sn,
long double *cs)
{
long double hz, r, v, w, z;
z = x * x;
v = z * x;
/*
* XXX Replace Horner scheme with an algorithm suitable for CPUs
* with more complex pipelines.
*/
r = S2 + z * (S3 + z * (S4 + z * (S5 + z * (S6 + z * (S7 + z * (S8 +
z * (S9 + z * (S10 + z * (S11 + z * S12)))))))));
if (iy == 0)
*sn = x + v * (S1 + z * r);
else
*sn = x - ((z * (y / 2 - v * r) - y) - v * S1);
hz = z / 2;
w = 1 - hz;
r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * (C6 +
z * (C7 + z * (C8 + z * (C9 + z * (C10 + z * (C11+z*C12)))))))))));
*cs = w + (((1 - w) - hz) + (z * r - x * y));
}
#else
#error "Unsupported long double format"
#endif
|
