1/*-
2 * Copyright (c) 2017-2023 Steven G. Kargl
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 * 1. Redistributions of source code must retain the above copyright
9 *    notice unmodified, this list of conditions, and the following
10 *    disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright
12 *    notice, this list of conditions and the following disclaimer in the
13 *    documentation and/or other materials provided with the distribution.
14 *
15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
16 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
17 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
18 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
19 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
20 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
21 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
22 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
23 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
24 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
25 */
26
27/*
28 * See ../src/s_sinpi.c for implementation details.
29 */
30
31#include "fpmath.h"
32#include "math.h"
33#include "math_private.h"
34
35/*
36 * pi_hi contains the leading 56 bits of a 169 bit approximation for pi.
37 */
38static const long double
39pi_hi = 3.14159265358979322702026593105983920e+00L,
40pi_lo = 1.14423774522196636802434264184180742e-17L;
41
42#include "k_cospil.h"
43#include "k_sinpil.h"
44
45volatile static const double vzero = 0;
46
47long double
48sinpil(long double x)
49{
50	long double ai, ar, ax, hi, lo, s, xhi, xlo;
51
52	ax = fabsl(x);
53
54	if (ax < 1) {
55		if (ax < 0.25) {
56			if (ax < 0x1p-60) {
57				if (x == 0)
58					return (x);
59				hi = (double)x;
60				hi *= 0x1p113L;
61				lo = x * 0x1p113L - hi;
62				s = (pi_lo + pi_hi) * lo + pi_lo * lo +
63				    pi_hi * hi;
64				return (s * 0x1p-113L);
65			}
66
67			s = __kernel_sinpil(ax);
68			return (x < 0 ? -s : s);
69		}
70
71		if (ax < 0.5)
72			s = __kernel_cospil(0.5 - ax);
73		else if (ax < 0.75)
74			s = __kernel_cospil(ax - 0.5);
75		else
76			s = __kernel_sinpil(1 - ax);
77		return (x < 0 ? -s : s);
78	}
79
80	if (ax < 0x1p112) {
81		/* Split ax = ai + ar with 0 <= ar < 1. */
82		FFLOORL128(ax, ai, ar);
83
84		if (ar == 0) {
85			s = 0;
86		} else {
87			if (ar < 0.5) {
88				if (ar <= 0.25)
89					s = __kernel_sinpil(ar);
90				else
91					s = __kernel_cospil(0.5 - ar);
92			} else {
93				if (ar < 0.75)
94					s = __kernel_cospil(ar - 0.5);
95				else
96					s = __kernel_sinpil(1 - ar);
97			}
98
99			s = fmodl(ai, 2.L) == 0 ? s : -s;
100		}
101		return (x < 0 ? -s : s);
102	}
103
104	if (isinf(x) || isnan(x))
105		return (vzero / vzero);
106
107	/*
108	 * |x| >= 0x1p112 is always an integer, so return +-0.
109	 */
110	return (copysignl(0, x));
111}
112