1 /* $OpenBSD: invtrig.h,v 1.2 2016/09/12 19:47:02 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/ld128/invtrig.h,v 1.1 2008/07/31 22:41:26 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 + EXT_FRACHMBITS + 1)
36
37 /* Approximation thresholds. */
38 #define ASIN_LINEAR (BIAS - 56) /* 2**-56 */
39 #define ACOS_CONST (BIAS - 113) /* 2**-113 */
40 #define ATAN_CONST (BIAS + 113) /* 2**113 */
41 #define ATAN_LINEAR (BIAS - 56) /* 2**-56 */
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 pS7 _ItL_pS7
59 #define pS8 _ItL_pS8
60 #define pS9 _ItL_pS9
61 #define qS1 _ItL_qS1
62 #define qS2 _ItL_qS2
63 #define qS3 _ItL_qS3
64 #define qS4 _ItL_qS4
65 #define qS5 _ItL_qS5
66 #define qS6 _ItL_qS6
67 #define qS7 _ItL_qS7
68 #define qS8 _ItL_qS8
69 #define qS9 _ItL_qS9
70 #define atanhi _ItL_atanhi
71 #define atanlo _ItL_atanlo
72 #define aT _ItL_aT
73 #define pi_lo _ItL_pi_lo
74
75 #define pio2_hi atanhi[3]
76 #define pio2_lo atanlo[3]
77 #define pio4_hi atanhi[1]
78
79 __BEGIN_HIDDEN_DECLS
80 /* Constants shared by the long double inverse trig functions. */
81 extern const long double pS0, pS1, pS2, pS3, pS4, pS5, pS6, pS7, pS8, pS9;
82 extern const long double qS1, qS2, qS3, qS4, qS5, qS6, qS7, qS8, qS9;
83 extern const long double atanhi[], atanlo[], aT[];
84 extern const long double pi_lo;
85 __END_HIDDEN_DECLS
86
87 static inline long double
P(long double x)88 P(long double x)
89 {
90
91 return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \
92 (pS4 + x * (pS5 + x * (pS6 + x * (pS7 + x * (pS8 + x * \
93 pS9))))))))));
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 * \
101 (qS5 + x * (qS6 + x * (qS7 + x * (qS8 + x * qS9)))))))));
102 }
103
104 static inline long double
T_even(long double x)105 T_even(long double x)
106 {
107
108 return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \
109 (aT[8] + x * (aT[10] + x * (aT[12] + x * (aT[14] + x * \
110 (aT[16] + x * (aT[18] + x * (aT[20] + x * aT[22])))))))))));
111 }
112
113 static inline long double
T_odd(long double x)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] + x * (aT[13] + x * (aT[15] + x * \
119 (aT[17] + x * (aT[19] + x * (aT[21] + x * aT[23])))))))))));
120 }
121