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#ifdef __i386__
32#include <ieeefp.h>
33#endif
34#include <stdint.h>
35
36#include "fpmath.h"
37#include "math.h"
38#include "math_private.h"
39
40static const union IEEEl2bits
41pi_hi_u = LD80C(0xc90fdaa200000000,   1, 3.14159265346825122833e+00L),
42pi_lo_u = LD80C(0x85a308d313198a2e, -33, 1.21542010130123852029e-10L);
43#define	pi_hi	(pi_hi_u.e)
44#define	pi_lo	(pi_lo_u.e)
45
46#include "k_cospil.h"
47#include "k_sinpil.h"
48
49volatile static const double vzero = 0;
50
51long double
52sinpil(long double x)
53{
54	long double ax, hi, lo, s;
55	uint64_t lx, m;
56	uint32_t j0;
57	uint16_t hx, ix;
58
59	EXTRACT_LDBL80_WORDS(hx, lx, x);
60	ix = hx & 0x7fff;
61	INSERT_LDBL80_WORDS(ax, ix, lx);
62
63	ENTERI();
64
65	if (ix < 0x3fff) {			/* |x| < 1 */
66		if (ix < 0x3ffd) {		/* |x| < 0.25 */
67			if (ix < 0x3fdd) {	/* |x| < 0x1p-34 */
68				if (x == 0)
69					RETURNI(x);
70				INSERT_LDBL80_WORDS(hi, hx,
71				    lx & 0xffffffff00000000ull);
72				hi *= 0x1p63L;
73				lo = x * 0x1p63L - hi;
74				s = (pi_lo + pi_hi) * lo + pi_lo * hi +
75				    pi_hi * hi;
76				RETURNI(s * 0x1p-63L);
77			}
78			s = __kernel_sinpil(ax);
79			RETURNI((hx & 0x8000) ? -s : s);
80		}
81
82		if (ix < 0x3ffe)			/* |x| < 0.5 */
83			s = __kernel_cospil(0.5 - ax);
84		else if (lx < 0xc000000000000000ull)	/* |x| < 0.75 */
85			s = __kernel_cospil(ax - 0.5);
86		else
87			s = __kernel_sinpil(1 - ax);
88		RETURNI((hx & 0x8000) ? -s : s);
89	}
90
91	if (ix < 0x403e) {			/* 1 <= |x| < 0x1p63 */
92		FFLOORL80(x, j0, ix, lx);	/* Integer part of ax. */
93		ax -= x;
94		EXTRACT_LDBL80_WORDS(ix, lx, ax);
95
96		if (ix == 0) {
97			s = 0;
98		} else {
99			if (ix < 0x3ffe) {		/* |x| < 0.5 */
100				if (ix < 0x3ffd)	/* |x| < 0.25 */
101					s = __kernel_sinpil(ax);
102				else
103					s = __kernel_cospil(0.5 - ax);
104			} else {
105							/* |x| < 0.75 */
106				if (lx < 0xc000000000000000ull)
107					s = __kernel_cospil(ax - 0.5);
108				else
109					s = __kernel_sinpil(1 - ax);
110			}
111
112			if (j0 > 40)
113				x -= 0x1p40;
114			if (j0 > 30)
115				x -= 0x1p30;
116			j0 = (uint32_t)x;
117			if (j0 & 1) s = -s;
118		}
119		RETURNI((hx & 0x8000) ? -s : s);
120	}
121
122	/* x = +-inf or nan. */
123	if (ix >= 0x7fff)
124		RETURNI(vzero / vzero);
125
126	/*
127	 * |x| >= 0x1p63 is always an integer, so return +-0.
128	 */
129	RETURNI(copysignl(0, x));
130}
131