1/*-
2 * Copyright (c) 2008 David Schultz <das@FreeBSD.ORG>
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, this list of conditions and the following disclaimer.
10 * 2. Redistributions in binary form must reproduce the above copyright
11 *    notice, this list of conditions and the following disclaimer in the
12 *    documentation and/or other materials provided with the distribution.
13 *
14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
15 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
16 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
17 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
18 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
19 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
20 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
21 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
22 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
23 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
24 * SUCH DAMAGE.
25 *
26 * $FreeBSD$
27 */
28
29#include <float.h>
30
31#include "fpmath.h"
32
33#define	BIAS		(LDBL_MAX_EXP - 1)
34#define	MANH_SIZE	(LDBL_MANH_SIZE + 1)
35
36/* Approximation thresholds. */
37#define	ASIN_LINEAR	(BIAS - 56)	/* 2**-56 */
38#define	ACOS_CONST	(BIAS - 113)	/* 2**-113 */
39#define	ATAN_CONST	(BIAS + 113)	/* 2**113 */
40#define	ATAN_LINEAR	(BIAS - 56)	/* 2**-56 */
41
42/* 0.95 */
43#define	THRESH	((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT)
44
45/* Constants shared by the long double inverse trig functions. */
46#define	pS0	_ItL_pS0
47#define	pS1	_ItL_pS1
48#define	pS2	_ItL_pS2
49#define	pS3	_ItL_pS3
50#define	pS4	_ItL_pS4
51#define	pS5	_ItL_pS5
52#define	pS6	_ItL_pS6
53#define	pS7	_ItL_pS7
54#define	pS8	_ItL_pS8
55#define	pS9	_ItL_pS9
56#define	qS1	_ItL_qS1
57#define	qS2	_ItL_qS2
58#define	qS3	_ItL_qS3
59#define	qS4	_ItL_qS4
60#define	qS5	_ItL_qS5
61#define	qS6	_ItL_qS6
62#define	qS7	_ItL_qS7
63#define	qS8	_ItL_qS8
64#define	qS9	_ItL_qS9
65#define	atanhi	_ItL_atanhi
66#define	atanlo	_ItL_atanlo
67#define	aT	_ItL_aT
68#define	pi_lo	_ItL_pi_lo
69
70#define	pio2_hi	atanhi[3]
71#define	pio2_lo	atanlo[3]
72#define	pio4_hi	atanhi[1]
73
74/* Constants shared by the long double inverse trig functions. */
75extern const long double pS0, pS1, pS2, pS3, pS4, pS5, pS6, pS7, pS8, pS9;
76extern const long double qS1, qS2, qS3, qS4, qS5, qS6, qS7, qS8, qS9;
77extern const long double atanhi[], atanlo[], aT[];
78extern const long double pi_lo;
79
80static inline long double
81P(long double x)
82{
83
84	return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \
85		(pS4 + x * (pS5 + x * (pS6 + x * (pS7 + x * (pS8 + x * \
86		pS9))))))))));
87}
88
89static inline long double
90Q(long double x)
91{
92
93	return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * \
94		(qS5 + x * (qS6 + x * (qS7 + x * (qS8 + x * qS9)))))))));
95}
96
97static inline long double
98T_even(long double x)
99{
100
101	return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \
102		(aT[8] + x * (aT[10] + x * (aT[12] + x * (aT[14] + x * \
103		(aT[16] + x * (aT[18] + x * (aT[20] + x * aT[22])))))))))));
104}
105
106static inline long double
107T_odd(long double x)
108{
109
110	return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \
111		(aT[9] + x * (aT[11] + x * (aT[13] + x * (aT[15] + x * \
112		(aT[17] + x * (aT[19] + x * (aT[21] + x * aT[23])))))))))));
113}
114