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 <stdint.h>
32*cfe182f3Schristos
33*cfe182f3Schristos #include "math.h"
34*cfe182f3Schristos #include "math_private.h"
35*cfe182f3Schristos
36*cfe182f3Schristos static const double
37*cfe182f3Schristos pi_hi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */
38*cfe182f3Schristos pi_lo =-2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */
39*cfe182f3Schristos
40*cfe182f3Schristos #include "k_cospil.h"
41*cfe182f3Schristos #include "k_sinpil.h"
42*cfe182f3Schristos
43*cfe182f3Schristos static volatile const double vzero = 0;
44*cfe182f3Schristos
45*cfe182f3Schristos long double
cospil(long double x)46*cfe182f3Schristos cospil(long double x)
47*cfe182f3Schristos {
48*cfe182f3Schristos long double ax, c;
49*cfe182f3Schristos uint64_t lx;
50*cfe182f3Schristos uint32_t j0;
51*cfe182f3Schristos uint16_t hx, ix;
52*cfe182f3Schristos
53*cfe182f3Schristos EXTRACT_LDBL80_WORDS(hx, lx, x);
54*cfe182f3Schristos ix = hx & 0x7fff;
55*cfe182f3Schristos INSERT_LDBL80_WORDS(ax, ix, lx);
56*cfe182f3Schristos
57*cfe182f3Schristos ENTERI();
58*cfe182f3Schristos
59*cfe182f3Schristos if (ix < 0x3fff) { /* |x| < 1 */
60*cfe182f3Schristos if (ix < 0x3ffd) { /* |x| < 0.25 */
61*cfe182f3Schristos if (ix < 0x3fdd) { /* |x| < 0x1p-34 */
62*cfe182f3Schristos if ((int)x == 0)
63*cfe182f3Schristos RETURNI(1);
64*cfe182f3Schristos }
65*cfe182f3Schristos RETURNI(__kernel_cospil(ax));
66*cfe182f3Schristos }
67*cfe182f3Schristos
68*cfe182f3Schristos if (ix < 0x3ffe) /* |x| < 0.5 */
69*cfe182f3Schristos c = __kernel_sinpil(0.5 - ax);
70*cfe182f3Schristos else if (lx < 0xc000000000000000ull) { /* |x| < 0.75 */
71*cfe182f3Schristos if (ax == 0.5)
72*cfe182f3Schristos RETURNI(0);
73*cfe182f3Schristos c = -__kernel_sinpil(ax - 0.5);
74*cfe182f3Schristos } else
75*cfe182f3Schristos c = -__kernel_cospil(1 - ax);
76*cfe182f3Schristos RETURNI(c);
77*cfe182f3Schristos }
78*cfe182f3Schristos
79*cfe182f3Schristos if (ix < 0x403e) { /* 1 <= |x| < 0x1p63 */
80*cfe182f3Schristos FFLOORL80(x, j0, ix, lx); /* Integer part of ax. */
81*cfe182f3Schristos ax -= x;
82*cfe182f3Schristos EXTRACT_LDBL80_WORDS(ix, lx, ax);
83*cfe182f3Schristos
84*cfe182f3Schristos if (ix < 0x3ffe) { /* |x| < 0.5 */
85*cfe182f3Schristos if (ix < 0x3ffd) /* |x| < 0.25 */
86*cfe182f3Schristos c = ix == 0 ? 1 : __kernel_cospil(ax);
87*cfe182f3Schristos else
88*cfe182f3Schristos c = __kernel_sinpil(0.5 - ax);
89*cfe182f3Schristos
90*cfe182f3Schristos } else {
91*cfe182f3Schristos if (lx < 0xc000000000000000ull) { /* |x| < 0.75 */
92*cfe182f3Schristos if (ax == 0.5)
93*cfe182f3Schristos RETURNI(0);
94*cfe182f3Schristos c = -__kernel_sinpil(ax - 0.5);
95*cfe182f3Schristos } else
96*cfe182f3Schristos c = -__kernel_cospil(1 - ax);
97*cfe182f3Schristos }
98*cfe182f3Schristos
99*cfe182f3Schristos if (j0 > 40)
100*cfe182f3Schristos x -= 0x1p40;
101*cfe182f3Schristos if (j0 > 30)
102*cfe182f3Schristos x -= 0x1p30;
103*cfe182f3Schristos j0 = (uint32_t)x;
104*cfe182f3Schristos
105*cfe182f3Schristos RETURNI(j0 & 1 ? -c : c);
106*cfe182f3Schristos }
107*cfe182f3Schristos
108*cfe182f3Schristos if (ix >= 0x7fff)
109*cfe182f3Schristos RETURNI(vzero / vzero);
110*cfe182f3Schristos
111*cfe182f3Schristos /*
112*cfe182f3Schristos * For 0x1p63 <= |x| < 0x1p64 need to determine if x is an even
113*cfe182f3Schristos * or odd integer to return t = +1 or -1.
114*cfe182f3Schristos * For |x| >= 0x1p64, it is always an even integer, so t = 1.
115*cfe182f3Schristos */
116*cfe182f3Schristos RETURNI(ix >= 0x403f ? 1 : ((lx & 1) ? -1 : 1));
117*cfe182f3Schristos }
118