1/*-
2 * SPDX-License-Identifier: BSD-2-Clause
3 *
4 * Copyright (c) 2008 David Schultz <das@FreeBSD.ORG>
5 * All rights reserved.
6 *
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
9 * are met:
10 * 1. Redistributions of source code must retain the above copyright
11 *    notice, this list of conditions and the following disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 *    notice, this list of conditions and the following disclaimer in the
14 *    documentation and/or other materials provided with the distribution.
15 *
16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
17 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
18 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
19 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
20 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
21 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
22 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
23 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
24 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
25 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
26 * SUCH DAMAGE.
27 */
28
29#include <float.h>
30
31
32#define	BIAS		(LDBL_MAX_EXP - 1)
33#define	MANH_SIZE	(EXT_FRACHBITS + 1)
34
35/* Approximation thresholds. */
36#define	ASIN_LINEAR	(BIAS - 56)	/* 2**-56 */
37#define	ACOS_CONST	(BIAS - 113)	/* 2**-113 */
38#define	ATAN_CONST	(BIAS + 113)	/* 2**113 */
39#define	ATAN_LINEAR	(BIAS - 56)	/* 2**-56 */
40
41/* 0.95 */
42#define	THRESH	((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT)
43
44/* Constants shared by the long double inverse trig functions. */
45#define	pS0	_ItL_pS0
46#define	pS1	_ItL_pS1
47#define	pS2	_ItL_pS2
48#define	pS3	_ItL_pS3
49#define	pS4	_ItL_pS4
50#define	pS5	_ItL_pS5
51#define	pS6	_ItL_pS6
52#define	pS7	_ItL_pS7
53#define	pS8	_ItL_pS8
54#define	pS9	_ItL_pS9
55#define	qS1	_ItL_qS1
56#define	qS2	_ItL_qS2
57#define	qS3	_ItL_qS3
58#define	qS4	_ItL_qS4
59#define	qS5	_ItL_qS5
60#define	qS6	_ItL_qS6
61#define	qS7	_ItL_qS7
62#define	qS8	_ItL_qS8
63#define	qS9	_ItL_qS9
64#define	atanhi	_ItL_atanhi
65#define	atanlo	_ItL_atanlo
66#define	aT	_ItL_aT
67#define	pi_lo	_ItL_pi_lo
68
69#define	pio2_hi	atanhi[3]
70#define	pio2_lo	atanlo[3]
71#define	pio4_hi	atanhi[1]
72
73/* Constants shared by the long double inverse trig functions. */
74extern const long double pS0, pS1, pS2, pS3, pS4, pS5, pS6, pS7, pS8, pS9;
75extern const long double qS1, qS2, qS3, qS4, qS5, qS6, qS7, qS8, qS9;
76extern const long double atanhi[], atanlo[], aT[];
77extern const long double pi_lo;
78
79static inline long double
80P(long double x)
81{
82
83	return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \
84		(pS4 + x * (pS5 + x * (pS6 + x * (pS7 + x * (pS8 + x * \
85		pS9))))))))));
86}
87
88static inline long double
89Q(long double x)
90{
91
92	return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * \
93		(qS5 + x * (qS6 + x * (qS7 + x * (qS8 + x * qS9)))))))));
94}
95
96static inline long double
97T_even(long double x)
98{
99
100	return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \
101		(aT[8] + x * (aT[10] + x * (aT[12] + x * (aT[14] + x * \
102		(aT[16] + x * (aT[18] + x * (aT[20] + x * aT[22])))))))))));
103}
104
105static inline long double
106T_odd(long double x)
107{
108
109	return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \
110		(aT[9] + x * (aT[11] + x * (aT[13] + x * (aT[15] + x * \
111		(aT[17] + x * (aT[19] + x * (aT[21] + x * aT[23])))))))))));
112}
113