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