1 /* $OpenBSD: invtrig.h,v 1.1 2008/12/09 20:00:35 martynas 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 extern const LONGDOUBLE pS0, pS1, pS2, pS3, pS4, pS5, pS6;
82 extern const LONGDOUBLE qS1, qS2, qS3, qS4, qS5;
83 extern const LONGDOUBLE atanhi[], atanlo[], aT[];
84 extern const LONGDOUBLE pi_lo;
85
86 #ifndef STRUCT_DECLS
87
88 static inline long double
P(long double x)89 P(long double x)
90 {
91
92 return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \
93 (pS4 + x * (pS5 + x * pS6)))))));
94 }
95
96 static inline long double
Q(long double x)97 Q(long double x)
98 {
99
100 return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * qS5)))));
101 }
102
103 static inline long double
T_even(long double x)104 T_even(long double x)
105 {
106
107 return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \
108 (aT[8] + x * (aT[10] + x * aT[12]))))));
109 }
110
111 static inline long double
T_odd(long double x)112 T_odd(long double x)
113 {
114
115 return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \
116 (aT[9] + x * aT[11])))));
117 }
118
119 #endif
120