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