invtrig.h revision 330897 
1/*-
2 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
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 * $FreeBSD: stable/11/lib/msun/ld80/invtrig.h 330897 2018-03-14 03:19:51Z eadler $
29 */
30
31#include <float.h>
32
33#include "fpmath.h"
34
35#define	BIAS		(LDBL_MAX_EXP - 1)
36#define	MANH_SIZE	LDBL_MANH_SIZE
37
38/* Approximation thresholds. */
39#define	ASIN_LINEAR	(BIAS - 32)	/* 2**-32 */
40#define	ACOS_CONST	(BIAS - 65)	/* 2**-65 */
41#define	ATAN_CONST	(BIAS + 65)	/* 2**65 */
42#define	ATAN_LINEAR	(BIAS - 32)	/* 2**-32 */
43
44/* 0.95 */
45#define	THRESH	((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT)
46
47/* Constants shared by the long double inverse trig functions. */
48#define	pS0	_ItL_pS0
49#define	pS1	_ItL_pS1
50#define	pS2	_ItL_pS2
51#define	pS3	_ItL_pS3
52#define	pS4	_ItL_pS4
53#define	pS5	_ItL_pS5
54#define	pS6	_ItL_pS6
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	atanhi	_ItL_atanhi
61#define	atanlo	_ItL_atanlo
62#define	aT	_ItL_aT
63#define	pi_lo	_ItL_pi_lo
64
65#define	pio2_hi	atanhi[3]
66#define	pio2_lo	atanlo[3]
67#define	pio4_hi	atanhi[1]
68
69#ifdef STRUCT_DECLS
70typedef struct longdouble {
71	uint64_t mant;
72	uint16_t expsign;
73} LONGDOUBLE;
74#else
75typedef long double LONGDOUBLE;
76#endif
77
78extern const LONGDOUBLE pS0, pS1, pS2, pS3, pS4, pS5, pS6;
79extern const LONGDOUBLE qS1, qS2, qS3, qS4, qS5;
80extern const LONGDOUBLE atanhi[], atanlo[], aT[];
81extern const LONGDOUBLE pi_lo;
82
83#ifndef STRUCT_DECLS
84
85static inline long double
86P(long double x)
87{
88
89	return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \
90		(pS4 + x * (pS5 + x * pS6)))))));
91}
92
93static inline long double
94Q(long double x)
95{
96
97	return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * qS5)))));
98}
99
100static inline long double
101T_even(long double x)
102{
103
104	return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \
105		(aT[8] + x * (aT[10] + x * aT[12]))))));
106}
107
108static inline long double
109T_odd(long double x)
110{
111
112	return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \
113		(aT[9] + x * aT[11])))));
114}
115
116#endif
117