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