k_sincosl.h revision 324006 
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__FBSDID("$FreeBSD: stable/11/lib/msun/src/k_sincosl.h 324006 2017-09-26 09:01:56Z dim $");
17
18#if LDBL_MANT_DIG == 64		/* ld80 version of k_sincosl.c. */
19
20#if defined(__amd64__) || defined(__i386__)
21/* Long double constants are slow on these arches, and broken on i386. */
22static const volatile double
23C1hi = 0.041666666666666664,		/*  0x15555555555555.0p-57 */
24C1lo = 2.2598839032744733e-18,		/*  0x14d80000000000.0p-111 */
25S1hi = -0.16666666666666666,		/* -0x15555555555555.0p-55 */
26S1lo = -9.2563760475949941e-18;		/* -0x15580000000000.0p-109 */
27#define	S1	((long double)S1hi + S1lo)
28#define	C1	((long double)C1hi + C1lo)
29#else
30static const long double
31C1 =  0.0416666666666666666136L;	/*  0xaaaaaaaaaaaaaa9b.0p-68 */
32S1 = -0.166666666666666666671L,		/* -0xaaaaaaaaaaaaaaab.0p-66 */
33#endif
34
35static const double
36C2 = -0.0013888888888888874,		/* -0x16c16c16c16c10.0p-62 */
37C3 =  0.000024801587301571716,		/*  0x1a01a01a018e22.0p-68 */
38C4 = -0.00000027557319215507120,	/* -0x127e4fb7602f22.0p-74 */
39C5 =  0.0000000020876754400407278,	/*  0x11eed8caaeccf1.0p-81 */
40C6 = -1.1470297442401303e-11,		/* -0x19393412bd1529.0p-89 */
41C7 =  4.7383039476436467e-14,		/*  0x1aac9d9af5c43e.0p-97 */
42S2 =  0.0083333333333333332,		/*  0x11111111111111.0p-59 */
43S3 = -0.00019841269841269427,		/* -0x1a01a01a019f81.0p-65 */
44S4 =  0.0000027557319223597490,		/*  0x171de3a55560f7.0p-71 */
45S5 = -0.000000025052108218074604,	/* -0x1ae64564f16cad.0p-78 */
46S6 =  1.6059006598854211e-10,		/*  0x161242b90243b5.0p-85 */
47S7 = -7.6429779983024564e-13,		/* -0x1ae42ebd1b2e00.0p-93 */
48S8 =  2.6174587166648325e-15;		/*  0x179372ea0b3f64.0p-101 */
49
50static inline void
51__kernel_sincosl(long double x, long double y, int iy, long double *sn,
52    long double *cs)
53{
54	long double hz, r, v, w, z;
55
56	z = x * x;
57	v = z * x;
58	/*
59	 * XXX Replace Horner scheme with an algorithm suitable for CPUs
60	 * with more complex pipelines.
61	 */
62	r = S2 + z * (S3 + z * (S4 + z * (S5 + z * (S6 + z * (S7 + z * S8)))));
63
64	if (iy == 0)
65		*sn = x + v * (S1 + z * r);
66	else
67		*sn = x - ((z * (y / 2 - v * r) - y) - v * S1);
68
69	hz = z / 2;
70	w = 1 - hz;
71	r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * (C6 +
72	    z * C7))))));
73	*cs = w + (((1 - w) - hz) + (z * r - x * y));
74}
75
76#elif LDBL_MANT_DIG == 113	/* ld128 version of k_sincosl.c. */
77
78static const long double
79C1 =  0.04166666666666666666666666666666658424671L,
80C2 = -0.001388888888888888888888888888863490893732L,
81C3 =  0.00002480158730158730158730158600795304914210L,
82C4 = -0.2755731922398589065255474947078934284324e-6L,
83C5 =  0.2087675698786809897659225313136400793948e-8L,
84C6 = -0.1147074559772972315817149986812031204775e-10L,
85C7 =  0.4779477332386808976875457937252120293400e-13L,
86S1 = -0.16666666666666666666666666666666666606732416116558L,
87S2 =  0.0083333333333333333333333333333331135404851288270047L,
88S3 = -0.00019841269841269841269841269839935785325638310428717L,
89S4 =  0.27557319223985890652557316053039946268333231205686e-5L,
90S5 = -0.25052108385441718775048214826384312253862930064745e-7L,
91S6 =  0.16059043836821614596571832194524392581082444805729e-9L,
92S7 = -0.76471637318198151807063387954939213287488216303768e-12L,
93S8 =  0.28114572543451292625024967174638477283187397621303e-14L;
94
95static const double
96C8  = -0.1561920696721507929516718307820958119868e-15,
97C9  =  0.4110317413744594971475941557607804508039e-18,
98C10 = -0.8896592467191938803288521958313920156409e-21,
99C11 =  0.1601061435794535138244346256065192782581e-23,
100S9  = -0.82206352458348947812512122163446202498005154296863e-17,
101S10 =  0.19572940011906109418080609928334380560135358385256e-19,
102S11 = -0.38680813379701966970673724299207480965452616911420e-22,
103S12 =  0.64038150078671872796678569586315881020659912139412e-25;
104
105static inline void
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		*cs = 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))))))))));
129
130	*cs =  w + (((1 - w) - hz) + (z * r - x * y));
131}
132#else
133#error "Unsupported long double format"
134#endif
135