xref: /freebsd/lib/msun/ld128/s_sinpil.c (revision 783d3ff6d7fae619db8a7990b8a6387de0c677b5)
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  */
38 static const long double
39 pi_hi = 3.14159265358979322702026593105983920e+00L,
40 pi_lo = 1.14423774522196636802434264184180742e-17L;
41 
42 #include "k_cospil.h"
43 #include "k_sinpil.h"
44 
45 volatile static const double vzero = 0;
46 
47 long double
48 sinpil(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