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
35
36/* Approximation thresholds. */
37#define	ASIN_LINEAR	(BIAS - 32)	/* 2**-32 */
38#define	ACOS_CONST	(BIAS - 65)	/* 2**-65 */
39#define	ATAN_CONST	(BIAS + 65)	/* 2**65 */
40#define	ATAN_LINEAR	(BIAS - 32)	/* 2**-32 */
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	qS1	_ItL_qS1
54#define	qS2	_ItL_qS2
55#define	qS3	_ItL_qS3
56#define	qS4	_ItL_qS4
57#define	qS5	_ItL_qS5
58#define	atanhi	_ItL_atanhi
59#define	atanlo	_ItL_atanlo
60#define	aT	_ItL_aT
61#define	pi_lo	_ItL_pi_lo
62
63#define	pio2_hi	atanhi[3]
64#define	pio2_lo	atanlo[3]
65#define	pio4_hi	atanhi[1]
66
67#ifdef STRUCT_DECLS
68typedef struct longdouble {
69	uint64_t mant;
70	uint16_t expsign;
71} LONGDOUBLE;
72#else
73typedef long double LONGDOUBLE;
74#endif
75
76extern const LONGDOUBLE pS0, pS1, pS2, pS3, pS4, pS5, pS6;
77extern const LONGDOUBLE qS1, qS2, qS3, qS4, qS5;
78extern const LONGDOUBLE atanhi[], atanlo[], aT[];
79extern const LONGDOUBLE pi_lo;
80
81#ifndef STRUCT_DECLS
82
83static inline long double
84P(long double x)
85{
86
87	return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \
88		(pS4 + x * (pS5 + x * pS6)))))));
89}
90
91static inline long double
92Q(long double x)
93{
94
95	return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * qS5)))));
96}
97
98static inline long double
99T_even(long double x)
100{
101
102	return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \
103		(aT[8] + x * (aT[10] + x * aT[12]))))));
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])))));
112}
113
114#endif
115