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 "math.h"
32#include "math_private.h"
33
34/*
35 * pi_hi contains the leading 56 bits of a 169 bit approximation for pi.
36 */
37static const long double
38pi_hi = 3.14159265358979322702026593105983920e+00L,
39pi_lo = 1.14423774522196636802434264184180742e-17L;
40
41static inline long double
42__kernel_tanpil(long double x)
43{
44	long double hi, lo, t;
45
46	if (x < 0.25) {
47		hi = (double)x;
48		lo = x - hi;
49		lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
50		hi *= pi_hi;
51		_2sumF(hi, lo);
52		t = __kernel_tanl(hi, lo, -1);
53	} else if (x > 0.25) {
54		x = 0.5 - x;
55		hi = (double)x;
56		lo = x - hi;
57		lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
58		hi *= pi_hi;
59		_2sumF(hi, lo);
60		t = - __kernel_tanl(hi, lo, 1);
61	} else
62		t = 1;
63
64	return (t);
65}
66
67static volatile const double vzero = 0;
68
69long double
70tanpil(long double x)
71{
72	long double ai, ar, ax, hi, lo, t;
73	double odd;
74
75	ax = fabsl(x);
76
77	if (ax < 1) {
78		if (ax < 0.5) {
79			if (ax < 0x1p-60) {
80				if (x == 0)
81					return (x);
82				hi = (double)x;
83				hi *= 0x1p113L;
84				lo = x * 0x1p113L - hi;
85				t = (pi_lo + pi_hi) * lo + pi_lo * lo +
86				    pi_hi * hi;
87				return (t * 0x1p-113L);
88			}
89			t = __kernel_tanpil(ax);
90		} else if (ax == 0.5)
91			t = 1 / vzero;
92		else
93			t = -__kernel_tanpil(1 - ax);
94		return (x < 0 ? -t : t);
95	}
96
97	if (ax < 0x1p112) {
98		/* Split ax = ai + ar with 0 <= ar < 1. */
99		FFLOORL128(ax, ai, ar);
100		odd = fmodl(ai, 2.L) == 0 ? 1 : -1;
101		if (ar < 0.5)
102			t = ar == 0 ? copysign(0., odd) : __kernel_tanpil(ar);
103		else if (ar == 0.5)
104			t = odd / vzero;
105		else
106			t = -__kernel_tanpil(1 - ar);
107		return (x < 0 ? -t : t);
108	}
109
110	/* x = +-inf or nan. */
111	if (isinf(x) || isnan(x))
112		return (vzero / vzero);
113
114	/*
115	 * For 0x1p112 <= |x| < 0x1p113 need to determine if x is an even
116	 * or odd integer to set t = +0 or -0.
117	 * For |x| >= 0x1p113, it is always an even integer, so t = 0.
118	 */
119	t = fmodl(ax,2.L) == 0  ? 0 : copysign(0., -1.);
120	return (copysignl(t, x));
121}
122