1/*	$OpenBSD: invtrig.h,v 1.2 2016/09/12 19:47:03 guenther Exp $	*/
2/*-
3 * Copyright (c) 2008 David Schultz <das@FreeBSD.ORG>
4 * All rights reserved.
5 *
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
8 * are met:
9 * 1. Redistributions of source code must retain the above copyright
10 *    notice, this list of conditions and the following 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 AND CONTRIBUTORS ``AS IS'' AND
16 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
17 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
18 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
19 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
20 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
21 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
22 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
23 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
24 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
25 * SUCH DAMAGE.
26 *
27 * $FreeBSD: src/lib/msun/ld80/invtrig.h,v 1.2 2008/08/02 03:56:22 das Exp $
28 */
29
30#include <sys/types.h>
31#include <machine/ieee.h>
32#include <float.h>
33
34#define	BIAS		(LDBL_MAX_EXP - 1)
35#define	MANH_SIZE	EXT_FRACHBITS
36
37/* Approximation thresholds. */
38#define	ASIN_LINEAR	(BIAS - 32)	/* 2**-32 */
39#define	ACOS_CONST	(BIAS - 65)	/* 2**-65 */
40#define	ATAN_CONST	(BIAS + 65)	/* 2**65 */
41#define	ATAN_LINEAR	(BIAS - 32)	/* 2**-32 */
42
43/* 0.95 */
44#ifdef EXT_IMPLICIT_NBIT
45#define	THRESH	(0xe666666666666666ULL>>(64-(MANH_SIZE-1)))
46#else /* EXT_IMPLICIT_NBIT */
47#define	THRESH	((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|0x80000000)
48#endif /* EXT_IMPLICIT_NBIT */
49
50/* Constants shared by the long double inverse trig functions. */
51#define	pS0	_ItL_pS0
52#define	pS1	_ItL_pS1
53#define	pS2	_ItL_pS2
54#define	pS3	_ItL_pS3
55#define	pS4	_ItL_pS4
56#define	pS5	_ItL_pS5
57#define	pS6	_ItL_pS6
58#define	qS1	_ItL_qS1
59#define	qS2	_ItL_qS2
60#define	qS3	_ItL_qS3
61#define	qS4	_ItL_qS4
62#define	qS5	_ItL_qS5
63#define	atanhi	_ItL_atanhi
64#define	atanlo	_ItL_atanlo
65#define	aT	_ItL_aT
66#define	pi_lo	_ItL_pi_lo
67
68#define	pio2_hi	atanhi[3]
69#define	pio2_lo	atanlo[3]
70#define	pio4_hi	atanhi[1]
71
72#ifdef STRUCT_DECLS
73typedef struct longdouble {
74	uint64_t mant;
75	uint16_t expsign;
76} LONGDOUBLE;
77#else
78typedef long double LONGDOUBLE;
79#endif
80
81__BEGIN_HIDDEN_DECLS
82extern const LONGDOUBLE pS0, pS1, pS2, pS3, pS4, pS5, pS6;
83extern const LONGDOUBLE qS1, qS2, qS3, qS4, qS5;
84extern const LONGDOUBLE atanhi[], atanlo[], aT[];
85extern const LONGDOUBLE pi_lo;
86__END_HIDDEN_DECLS
87
88#ifndef STRUCT_DECLS
89
90static inline long double
91P(long double x)
92{
93
94	return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \
95		(pS4 + x * (pS5 + x * pS6)))))));
96}
97
98static inline long double
99Q(long double x)
100{
101
102	return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * qS5)))));
103}
104
105static inline long double
106T_even(long double x)
107{
108
109	return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \
110		(aT[8] + x * (aT[10] + x * aT[12]))))));
111}
112
113static inline long double
114T_odd(long double x)
115{
116
117	return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \
118		(aT[9] + x * aT[11])))));
119}
120
121#endif
122