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_sinpi.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 union ieee_ext_u
37*cfe182f3Schristos pi_hi_u = LD80C(0xc90fdaa200000000, 1, 3.14159265346825122833e+00L),
38*cfe182f3Schristos pi_lo_u = LD80C(0x85a308d313198a2e, -33, 1.21542010130123852029e-10L);
39*cfe182f3Schristos #define pi_hi (pi_hi_u.extu_ld)
40*cfe182f3Schristos #define pi_lo (pi_lo_u.extu_ld)
41*cfe182f3Schristos
42*cfe182f3Schristos #include "k_cospil.h"
43*cfe182f3Schristos #include "k_sinpil.h"
44*cfe182f3Schristos
45*cfe182f3Schristos static volatile const double vzero = 0;
46*cfe182f3Schristos
47*cfe182f3Schristos long double
sinpil(long double x)48*cfe182f3Schristos sinpil(long double x)
49*cfe182f3Schristos {
50*cfe182f3Schristos long double ax, hi, lo, s;
51*cfe182f3Schristos uint64_t lx;
52*cfe182f3Schristos uint32_t j0;
53*cfe182f3Schristos uint16_t hx, ix;
54*cfe182f3Schristos
55*cfe182f3Schristos EXTRACT_LDBL80_WORDS(hx, lx, x);
56*cfe182f3Schristos ix = hx & 0x7fff;
57*cfe182f3Schristos INSERT_LDBL80_WORDS(ax, ix, lx);
58*cfe182f3Schristos
59*cfe182f3Schristos ENTERI();
60*cfe182f3Schristos
61*cfe182f3Schristos if (ix < 0x3fff) { /* |x| < 1 */
62*cfe182f3Schristos if (ix < 0x3ffd) { /* |x| < 0.25 */
63*cfe182f3Schristos if (ix < 0x3fdd) { /* |x| < 0x1p-34 */
64*cfe182f3Schristos if (x == 0)
65*cfe182f3Schristos RETURNI(x);
66*cfe182f3Schristos INSERT_LDBL80_WORDS(hi, hx,
67*cfe182f3Schristos lx & 0xffffffff00000000ull);
68*cfe182f3Schristos hi *= 0x1p63L;
69*cfe182f3Schristos lo = x * 0x1p63L - hi;
70*cfe182f3Schristos s = (pi_lo + pi_hi) * lo + pi_lo * hi +
71*cfe182f3Schristos pi_hi * hi;
72*cfe182f3Schristos RETURNI(s * 0x1p-63L);
73*cfe182f3Schristos }
74*cfe182f3Schristos s = __kernel_sinpil(ax);
75*cfe182f3Schristos RETURNI((hx & 0x8000) ? -s : s);
76*cfe182f3Schristos }
77*cfe182f3Schristos
78*cfe182f3Schristos if (ix < 0x3ffe) /* |x| < 0.5 */
79*cfe182f3Schristos s = __kernel_cospil(0.5 - ax);
80*cfe182f3Schristos else if (lx < 0xc000000000000000ull) /* |x| < 0.75 */
81*cfe182f3Schristos s = __kernel_cospil(ax - 0.5);
82*cfe182f3Schristos else
83*cfe182f3Schristos s = __kernel_sinpil(1 - ax);
84*cfe182f3Schristos RETURNI((hx & 0x8000) ? -s : s);
85*cfe182f3Schristos }
86*cfe182f3Schristos
87*cfe182f3Schristos if (ix < 0x403e) { /* 1 <= |x| < 0x1p63 */
88*cfe182f3Schristos FFLOORL80(x, j0, ix, lx); /* Integer part of ax. */
89*cfe182f3Schristos ax -= x;
90*cfe182f3Schristos EXTRACT_LDBL80_WORDS(ix, lx, ax);
91*cfe182f3Schristos
92*cfe182f3Schristos if (ix == 0) {
93*cfe182f3Schristos s = 0;
94*cfe182f3Schristos } else {
95*cfe182f3Schristos if (ix < 0x3ffe) { /* |x| < 0.5 */
96*cfe182f3Schristos if (ix < 0x3ffd) /* |x| < 0.25 */
97*cfe182f3Schristos s = __kernel_sinpil(ax);
98*cfe182f3Schristos else
99*cfe182f3Schristos s = __kernel_cospil(0.5 - ax);
100*cfe182f3Schristos } else {
101*cfe182f3Schristos /* |x| < 0.75 */
102*cfe182f3Schristos if (lx < 0xc000000000000000ull)
103*cfe182f3Schristos s = __kernel_cospil(ax - 0.5);
104*cfe182f3Schristos else
105*cfe182f3Schristos s = __kernel_sinpil(1 - ax);
106*cfe182f3Schristos }
107*cfe182f3Schristos
108*cfe182f3Schristos if (j0 > 40)
109*cfe182f3Schristos x -= 0x1p40;
110*cfe182f3Schristos if (j0 > 30)
111*cfe182f3Schristos x -= 0x1p30;
112*cfe182f3Schristos j0 = (uint32_t)x;
113*cfe182f3Schristos if (j0 & 1) s = -s;
114*cfe182f3Schristos }
115*cfe182f3Schristos RETURNI((hx & 0x8000) ? -s : s);
116*cfe182f3Schristos }
117*cfe182f3Schristos
118*cfe182f3Schristos /* x = +-inf or nan. */
119*cfe182f3Schristos if (ix >= 0x7fff)
120*cfe182f3Schristos RETURNI(vzero / vzero);
121*cfe182f3Schristos
122*cfe182f3Schristos /*
123*cfe182f3Schristos * |x| >= 0x1p63 is always an integer, so return +-0.
124*cfe182f3Schristos */
125*cfe182f3Schristos RETURNI(copysignl(0, x));
126*cfe182f3Schristos }
127