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 <stdint.h>
32
33#include "math.h"
34#include "math_private.h"
35
36static const double
37pi_hi =  3.1415926814079285e+00,	/* 0x400921fb 0x58000000 */
38pi_lo = -2.7818135228334233e-08;	/* 0xbe5dde97 0x3dcb3b3a */
39
40static inline long double
41__kernel_tanpil(long double x)
42{
43	long double hi, lo, t;
44
45	if (x < 0.25) {
46		hi = (float)x;
47		lo = x - hi;
48		lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
49		hi *= pi_hi;
50		_2sumF(hi, lo);
51		t = __kernel_tanl(hi, lo, -1);
52	} else if (x > 0.25) {
53		x = 0.5 - x;
54		hi = (float)x;
55		lo = x - hi;
56		lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
57		hi *= pi_hi;
58		_2sumF(hi, lo);
59		t = - __kernel_tanl(hi, lo, 1);
60	} else
61		t = 1;
62
63	return (t);
64}
65
66static volatile const double vzero = 0;
67
68long double
69tanpil(long double x)
70{
71	long double ax, hi, lo, odd, t;
72	uint64_t lx;
73	uint32_t j0;
74	uint16_t hx, ix;
75
76	EXTRACT_LDBL80_WORDS(hx, lx, x);
77	ix = hx & 0x7fff;
78	INSERT_LDBL80_WORDS(ax, ix, lx);
79
80	ENTERI();
81
82	if (ix < 0x3fff) {			/* |x| < 1 */
83		if (ix < 0x3ffe) {		/* |x| < 0.5 */
84			if (ix < 0x3fdd) {	/* |x| < 0x1p-34 */
85				if (x == 0)
86					RETURNI(x);
87				INSERT_LDBL80_WORDS(hi, hx,
88				    lx & 0xffffffff00000000ull);
89				hi *= 0x1p63L;
90				lo = x * 0x1p63L - hi;
91				t = (pi_lo + pi_hi) * lo + pi_lo * hi +
92				    pi_hi * hi;
93				RETURNI(t * 0x1p-63L);
94			}
95			t = __kernel_tanpil(ax);
96		} else if (ax == 0.5)
97			t = 1 / vzero;
98		else
99			t = -__kernel_tanpil(1 - ax);
100		RETURNI((hx & 0x8000) ? -t : t);
101	}
102
103	if (ix < 0x403e) {			/* 1 <= |x| < 0x1p63 */
104		FFLOORL80(x, j0, ix, lx);	/* Integer part of ax. */
105		odd = (uint64_t)x & 1 ? -1 : 1;
106		ax -= x;
107		EXTRACT_LDBL80_WORDS(ix, lx, ax);
108
109		if (ix < 0x3ffe)		/* |x| < 0.5 */
110			t = ix == 0 ? copysignl(0, odd) : __kernel_tanpil(ax);
111		else if (ax == 0.5L)
112			t = odd / vzero;
113		else
114			t = -__kernel_tanpil(1 - ax);
115		RETURNI((hx & 0x8000) ? -t : t);
116	}
117
118	/* x = +-inf or nan. */
119	if (ix >= 0x7fff)
120		RETURNI(vzero / vzero);
121
122	/*
123	 * For 0x1p63 <= |x| < 0x1p64 need to determine if x is an even
124	 * or odd integer to set t = +0 or -0.
125	 * For |x| >= 0x1p64, it is always an even integer, so t = 0.
126	 */
127	t = ix >= 0x403f ? 0 : (copysignl(0, (lx & 1) ? -1 : 1));
128	RETURNI((hx & 0x8000) ? -t : t);
129}
130