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_tanpi.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 static inline long double
__kernel_tanpil(long double x)43 __kernel_tanpil(long double x)
44 {
45 long double hi, lo, t;
46
47 if (x < 0.25) {
48 hi = (double)x;
49 lo = x - hi;
50 lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
51 hi *= pi_hi;
52 _2sumF(hi, lo);
53 t = __kernel_tanl(hi, lo, -1);
54 } else if (x > 0.25) {
55 x = 0.5 - x;
56 hi = (double)x;
57 lo = x - hi;
58 lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
59 hi *= pi_hi;
60 _2sumF(hi, lo);
61 t = - __kernel_tanl(hi, lo, 1);
62 } else
63 t = 1;
64
65 return (t);
66 }
67
68 volatile static const double vzero = 0;
69
70 long double
tanpil(long double x)71 tanpil(long double x)
72 {
73 long double ai, ar, ax, hi, lo, t;
74 double odd;
75
76 ax = fabsl(x);
77
78 if (ax < 1) {
79 if (ax < 0.5) {
80 if (ax < 0x1p-60) {
81 if (x == 0)
82 return (x);
83 hi = (double)x;
84 hi *= 0x1p113L;
85 lo = x * 0x1p113L - hi;
86 t = (pi_lo + pi_hi) * lo + pi_lo * lo +
87 pi_hi * hi;
88 return (t * 0x1p-113L);
89 }
90 t = __kernel_tanpil(ax);
91 } else if (ax == 0.5)
92 t = 1 / vzero;
93 else
94 t = -__kernel_tanpil(1 - ax);
95 return (x < 0 ? -t : t);
96 }
97
98 if (ax < 0x1p112) {
99 /* Split ax = ai + ar with 0 <= ar < 1. */
100 FFLOORL128(ax, ai, ar);
101 odd = fmodl(ai, 2.L) == 0 ? 1 : -1;
102 if (ar < 0.5)
103 t = ar == 0 ? copysign(0., odd) : __kernel_tanpil(ar);
104 else if (ar == 0.5)
105 t = odd / vzero;
106 else
107 t = -__kernel_tanpil(1 - ar);
108 return (x < 0 ? -t : t);
109 }
110
111 /* x = +-inf or nan. */
112 if (isinf(x) || isnan(x))
113 return (vzero / vzero);
114
115 /*
116 * For 0x1p112 <= |x| < 0x1p113 need to determine if x is an even
117 * or odd integer to set t = +0 or -0.
118 * For |x| >= 0x1p113, it is always an even integer, so t = 0.
119 */
120 t = fmodl(ax,2.L) == 0 ? 0 : copysign(0., -1.);
121 return (copysignl(t, x));
122 }
123