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 |
73 |
|
|
typedef struct longdouble { |
74 |
|
|
uint64_t mant; |
75 |
|
|
uint16_t expsign; |
76 |
|
|
} LONGDOUBLE; |
77 |
|
|
#else |
78 |
|
|
typedef long double LONGDOUBLE; |
79 |
|
|
#endif |
80 |
|
|
|
81 |
|
|
__BEGIN_HIDDEN_DECLS |
82 |
|
|
extern const LONGDOUBLE pS0, pS1, pS2, pS3, pS4, pS5, pS6; |
83 |
|
|
extern const LONGDOUBLE qS1, qS2, qS3, qS4, qS5; |
84 |
|
|
extern const LONGDOUBLE atanhi[], atanlo[], aT[]; |
85 |
|
|
extern const LONGDOUBLE pi_lo; |
86 |
|
|
__END_HIDDEN_DECLS |
87 |
|
|
|
88 |
|
|
#ifndef STRUCT_DECLS |
89 |
|
|
|
90 |
|
|
static inline long double |
91 |
|
|
P(long double x) |
92 |
|
|
{ |
93 |
|
|
|
94 |
|
|
return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \ |
95 |
|
|
(pS4 + x * (pS5 + x * pS6))))))); |
96 |
|
|
} |
97 |
|
|
|
98 |
|
|
static inline long double |
99 |
|
|
Q(long double x) |
100 |
|
|
{ |
101 |
|
|
|
102 |
|
|
return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * qS5))))); |
103 |
|
|
} |
104 |
|
|
|
105 |
|
|
static inline long double |
106 |
|
|
T_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 |
|
|
|
113 |
|
|
static inline long double |
114 |
|
|
T_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 |