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 0
17 __FBSDID("$FreeBSD: head/lib/msun/src/k_sincosl.h 354520 2019-11-07 23:57:48Z lwhsu $");
18 #endif
19 #if defined(LIBM_SCCS) && !defined(lint)
20 __RCSID("$NetBSD: k_sincosl.h,v 1.2 2022/08/29 01:48:34 riastradh Exp $");
21 #endif
22
23 #if LDBL_MANT_DIG == 64 /* ld80 version of k_sincosl.c. */
24
25 #if defined(__amd64__) || defined(__i386__)
26 /* Long double constants are slow on these arches, and broken on i386. */
27 static const volatile double
28 C1hi = 0.041666666666666664, /* 0x15555555555555.0p-57 */
29 C1lo = 2.2598839032744733e-18, /* 0x14d80000000000.0p-111 */
30 S1hi = -0.16666666666666666, /* -0x15555555555555.0p-55 */
31 S1lo = -9.2563760475949941e-18; /* -0x15580000000000.0p-109 */
32 #define S1 ((long double)S1hi + S1lo)
33 #define C1 ((long double)C1hi + C1lo)
34 #else
35 static const long double
36 C1 = 0.0416666666666666666136L, /* 0xaaaaaaaaaaaaaa9b.0p-68 */
37 S1 = -0.166666666666666666671L; /* -0xaaaaaaaaaaaaaaab.0p-66 */
38 #endif
39
40 static const double
41 C2 = -0.0013888888888888874, /* -0x16c16c16c16c10.0p-62 */
42 C3 = 0.000024801587301571716, /* 0x1a01a01a018e22.0p-68 */
43 C4 = -0.00000027557319215507120, /* -0x127e4fb7602f22.0p-74 */
44 C5 = 0.0000000020876754400407278, /* 0x11eed8caaeccf1.0p-81 */
45 C6 = -1.1470297442401303e-11, /* -0x19393412bd1529.0p-89 */
46 C7 = 4.7383039476436467e-14, /* 0x1aac9d9af5c43e.0p-97 */
47 S2 = 0.0083333333333333332, /* 0x11111111111111.0p-59 */
48 S3 = -0.00019841269841269427, /* -0x1a01a01a019f81.0p-65 */
49 S4 = 0.0000027557319223597490, /* 0x171de3a55560f7.0p-71 */
50 S5 = -0.000000025052108218074604, /* -0x1ae64564f16cad.0p-78 */
51 S6 = 1.6059006598854211e-10, /* 0x161242b90243b5.0p-85 */
52 S7 = -7.6429779983024564e-13, /* -0x1ae42ebd1b2e00.0p-93 */
53 S8 = 2.6174587166648325e-15; /* 0x179372ea0b3f64.0p-101 */
54
55 static inline void
__kernel_sincosl(long double x,long double y,int iy,long double * sn,long double * cs)56 __kernel_sincosl(long double x, long double y, int iy, long double *sn,
57 long double *cs)
58 {
59 long double hz, r, v, w, z;
60
61 z = x * x;
62 v = z * x;
63 /*
64 * XXX Replace Horner scheme with an algorithm suitable for CPUs
65 * with more complex pipelines.
66 */
67 r = S2 + z * (S3 + z * (S4 + z * (S5 + z * (S6 + z * (S7 + z * S8)))));
68
69 if (iy == 0)
70 *sn = x + v * (S1 + z * r);
71 else
72 *sn = x - ((z * (y / 2 - v * r) - y) - v * S1);
73
74 hz = z / 2;
75 w = 1 - hz;
76 r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * (C6 +
77 z * C7))))));
78 *cs = w + (((1 - w) - hz) + (z * r - x * y));
79 }
80
81 #elif LDBL_MANT_DIG == 113 /* ld128 version of k_sincosl.c. */
82
83 static const long double
84 C1 = 0.04166666666666666666666666666666658424671L,
85 C2 = -0.001388888888888888888888888888863490893732L,
86 C3 = 0.00002480158730158730158730158600795304914210L,
87 C4 = -0.2755731922398589065255474947078934284324e-6L,
88 C5 = 0.2087675698786809897659225313136400793948e-8L,
89 C6 = -0.1147074559772972315817149986812031204775e-10L,
90 C7 = 0.4779477332386808976875457937252120293400e-13L,
91 S1 = -0.16666666666666666666666666666666666606732416116558L,
92 S2 = 0.0083333333333333333333333333333331135404851288270047L,
93 S3 = -0.00019841269841269841269841269839935785325638310428717L,
94 S4 = 0.27557319223985890652557316053039946268333231205686e-5L,
95 S5 = -0.25052108385441718775048214826384312253862930064745e-7L,
96 S6 = 0.16059043836821614596571832194524392581082444805729e-9L,
97 S7 = -0.76471637318198151807063387954939213287488216303768e-12L,
98 S8 = 0.28114572543451292625024967174638477283187397621303e-14L;
99
100 static const double
101 C8 = -0.1561920696721507929516718307820958119868e-15,
102 C9 = 0.4110317413744594971475941557607804508039e-18,
103 C10 = -0.8896592467191938803288521958313920156409e-21,
104 C11 = 0.1601061435794535138244346256065192782581e-23,
105 S9 = -0.82206352458348947812512122163446202498005154296863e-17,
106 S10 = 0.19572940011906109418080609928334380560135358385256e-19,
107 S11 = -0.38680813379701966970673724299207480965452616911420e-22,
108 S12 = 0.64038150078671872796678569586315881020659912139412e-25;
109
110 static inline void
__kernel_sincosl(long double x,long double y,int iy,long double * sn,long double * cs)111 __kernel_sincosl(long double x, long double y, int iy, long double *sn,
112 long double *cs)
113 {
114 long double hz, r, v, w, z;
115
116 z = x * x;
117 v = z * x;
118 /*
119 * XXX Replace Horner scheme with an algorithm suitable for CPUs
120 * with more complex pipelines.
121 */
122 r = S2 + z * (S3 + z * (S4 + z * (S5 + z * (S6 + z * (S7 + z * (S8 +
123 z * (S9 + z * (S10 + z * (S11 + z * S12)))))))));
124
125 if (iy == 0)
126 *sn = x + v * (S1 + z * r);
127 else
128 *sn = x - ((z * (y / 2 - v * r) - y) - v * S1);
129
130 hz = z / 2;
131 w = 1 - hz;
132 r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * (C6 +
133 z * (C7 + z * (C8 + z * (C9 + z * (C10 + z * C11))))))))));
134
135 *cs = w + (((1 - w) - hz) + (z * r - x * y));
136 }
137 #else
138 #error "Unsupported long double format"
139 #endif
140