1*cfe182f3Schristos /*-
2*cfe182f3Schristos * Copyright (c) 2017-2023 Steven G. Kargl
3*cfe182f3Schristos * All rights reserved.
4*cfe182f3Schristos *
5*cfe182f3Schristos * Redistribution and use in source and binary forms, with or without
6*cfe182f3Schristos * modification, are permitted provided that the following conditions
7*cfe182f3Schristos * are met:
8*cfe182f3Schristos * 1. Redistributions of source code must retain the above copyright
9*cfe182f3Schristos * notice unmodified, this list of conditions, and the following
10*cfe182f3Schristos * disclaimer.
11*cfe182f3Schristos * 2. Redistributions in binary form must reproduce the above copyright
12*cfe182f3Schristos * notice, this list of conditions and the following disclaimer in the
13*cfe182f3Schristos * documentation and/or other materials provided with the distribution.
14*cfe182f3Schristos *
15*cfe182f3Schristos * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
16*cfe182f3Schristos * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
17*cfe182f3Schristos * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
18*cfe182f3Schristos * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
19*cfe182f3Schristos * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
20*cfe182f3Schristos * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
21*cfe182f3Schristos * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
22*cfe182f3Schristos * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
23*cfe182f3Schristos * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
24*cfe182f3Schristos * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
25*cfe182f3Schristos */
26*cfe182f3Schristos
27*cfe182f3Schristos /*
28*cfe182f3Schristos * See ../src/s_cospi.c for implementation details.
29*cfe182f3Schristos */
30*cfe182f3Schristos
31*cfe182f3Schristos #include "math.h"
32*cfe182f3Schristos #include "math_private.h"
33*cfe182f3Schristos
34*cfe182f3Schristos /*
35*cfe182f3Schristos * pi_hi contains the leading 56 bits of a 169 bit approximation for pi.
36*cfe182f3Schristos */
37*cfe182f3Schristos static const long double
38*cfe182f3Schristos pi_hi = 3.14159265358979322702026593105983920e+00L,
39*cfe182f3Schristos pi_lo = 1.14423774522196636802434264184180742e-17L;
40*cfe182f3Schristos
41*cfe182f3Schristos #include "k_cospil.h"
42*cfe182f3Schristos #include "k_sinpil.h"
43*cfe182f3Schristos
44*cfe182f3Schristos static volatile const double vzero = 0;
45*cfe182f3Schristos
46*cfe182f3Schristos long double
cospil(long double x)47*cfe182f3Schristos cospil(long double x)
48*cfe182f3Schristos {
49*cfe182f3Schristos long double ai, ar, ax, c;
50*cfe182f3Schristos
51*cfe182f3Schristos ax = fabsl(x);
52*cfe182f3Schristos
53*cfe182f3Schristos if (ax <= 1) {
54*cfe182f3Schristos if (ax < 0.25) {
55*cfe182f3Schristos if (ax < 0x1p-60) {
56*cfe182f3Schristos if ((int)x == 0)
57*cfe182f3Schristos return (1);
58*cfe182f3Schristos }
59*cfe182f3Schristos return (__kernel_cospil(ax));
60*cfe182f3Schristos }
61*cfe182f3Schristos
62*cfe182f3Schristos if (ax < 0.5)
63*cfe182f3Schristos c = __kernel_sinpil(0.5 - ax);
64*cfe182f3Schristos else if (ax < 0.75) {
65*cfe182f3Schristos if (ax == 0.5)
66*cfe182f3Schristos return (0);
67*cfe182f3Schristos c = -__kernel_sinpil(ax - 0.5);
68*cfe182f3Schristos } else
69*cfe182f3Schristos c = -__kernel_cospil(1 - ax);
70*cfe182f3Schristos return (c);
71*cfe182f3Schristos }
72*cfe182f3Schristos
73*cfe182f3Schristos if (ax < 0x1p112) {
74*cfe182f3Schristos /* Split ax = ai + ar with 0 <= ar < 1. */
75*cfe182f3Schristos FFLOORL128(ax, ai, ar);
76*cfe182f3Schristos
77*cfe182f3Schristos if (ar < 0.5) {
78*cfe182f3Schristos if (ar < 0.25)
79*cfe182f3Schristos c = ar == 0 ? 1 : __kernel_cospil(ar);
80*cfe182f3Schristos else
81*cfe182f3Schristos c = __kernel_sinpil(0.5 - ar);
82*cfe182f3Schristos } else {
83*cfe182f3Schristos if (ar < 0.75) {
84*cfe182f3Schristos if (ar == 0.5)
85*cfe182f3Schristos return (0);
86*cfe182f3Schristos c = -__kernel_sinpil(ar - 0.5);
87*cfe182f3Schristos } else
88*cfe182f3Schristos c = -__kernel_cospil(1 - ar);
89*cfe182f3Schristos }
90*cfe182f3Schristos return (fmodl(ai, 2.L) == 0 ? c : -c);
91*cfe182f3Schristos }
92*cfe182f3Schristos
93*cfe182f3Schristos if (isinf(x) || isnan(x))
94*cfe182f3Schristos return (vzero / vzero);
95*cfe182f3Schristos
96*cfe182f3Schristos /*
97*cfe182f3Schristos * For |x| >= 0x1p113, it is always an even integer, so return 1.
98*cfe182f3Schristos */
99*cfe182f3Schristos if (ax >= 0x1p113)
100*cfe182f3Schristos return (1);
101*cfe182f3Schristos /*
102*cfe182f3Schristos * For 0x1p112 <= |x| < 0x1p113 need to determine if x is an even
103*cfe182f3Schristos * or odd integer to return 1 or -1.
104*cfe182f3Schristos */
105*cfe182f3Schristos
106*cfe182f3Schristos return (fmodl(ax, 2.L) == 0 ? 1 : -1);
107*cfe182f3Schristos }
108