1 /*-
2 * Copyright (c) 2008 David Schultz <das@FreeBSD.ORG>
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 * 1. Redistributions of source code must retain the above copyright
9 * notice, this list of conditions and the following disclaimer.
10 * 2. Redistributions in binary form must reproduce the above copyright
11 * notice, this list of conditions and the following disclaimer in the
12 * documentation and/or other materials provided with the distribution.
13 *
14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
15 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
16 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
17 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
18 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
19 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
20 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
21 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
22 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
23 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
24 * SUCH DAMAGE.
25 *
26 * $FreeBSD: src/lib/msun/ld128/invtrig.h,v 1.1 2008/07/31 22:41:26 das Exp $
27 */
28
29 #include <float.h>
30
31 #include "fpmath.h"
32
33 #define BIAS (LDBL_MAX_EXP - 1)
34 #define MANH_SIZE (LDBL_MANH_SIZE + 1)
35
36 /* Approximation thresholds. */
37 #define ASIN_LINEAR (BIAS - 56) /* 2**-56 */
38 #define ACOS_CONST (BIAS - 113) /* 2**-113 */
39 #define ATAN_CONST (BIAS + 113) /* 2**113 */
40 #define ATAN_LINEAR (BIAS - 56) /* 2**-56 */
41
42 /* 0.95 */
43 #define THRESH ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT)
44
45 /* Constants shared by the long double inverse trig functions. */
46 #define pS0 _ItL_pS0
47 #define pS1 _ItL_pS1
48 #define pS2 _ItL_pS2
49 #define pS3 _ItL_pS3
50 #define pS4 _ItL_pS4
51 #define pS5 _ItL_pS5
52 #define pS6 _ItL_pS6
53 #define pS7 _ItL_pS7
54 #define pS8 _ItL_pS8
55 #define pS9 _ItL_pS9
56 #define qS1 _ItL_qS1
57 #define qS2 _ItL_qS2
58 #define qS3 _ItL_qS3
59 #define qS4 _ItL_qS4
60 #define qS5 _ItL_qS5
61 #define qS6 _ItL_qS6
62 #define qS7 _ItL_qS7
63 #define qS8 _ItL_qS8
64 #define qS9 _ItL_qS9
65 #define atanhi _ItL_atanhi
66 #define atanlo _ItL_atanlo
67 #define aT _ItL_aT
68 #define pi_lo _ItL_pi_lo
69
70 #define pio2_hi atanhi[3]
71 #define pio2_lo atanlo[3]
72 #define pio4_hi atanhi[1]
73
74 /* Constants shared by the long double inverse trig functions. */
75 extern const long double pS0, pS1, pS2, pS3, pS4, pS5, pS6, pS7, pS8, pS9;
76 extern const long double qS1, qS2, qS3, qS4, qS5, qS6, qS7, qS8, qS9;
77 extern const long double atanhi[], atanlo[], aT[];
78 extern const long double pi_lo;
79
80 static inline long double
P(long double x)81 P(long double x)
82 {
83
84 return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \
85 (pS4 + x * (pS5 + x * (pS6 + x * (pS7 + x * (pS8 + x * \
86 pS9))))))))));
87 }
88
89 static inline long double
Q(long double x)90 Q(long double x)
91 {
92
93 return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * \
94 (qS5 + x * (qS6 + x * (qS7 + x * (qS8 + x * qS9)))))))));
95 }
96
97 static inline long double
T_even(long double x)98 T_even(long double x)
99 {
100
101 return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \
102 (aT[8] + x * (aT[10] + x * (aT[12] + x * (aT[14] + x * \
103 (aT[16] + x * (aT[18] + x * (aT[20] + x * aT[22])))))))))));
104 }
105
106 static inline long double
T_odd(long double x)107 T_odd(long double x)
108 {
109
110 return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \
111 (aT[9] + x * (aT[11] + x * (aT[13] + x * (aT[15] + x * \
112 (aT[17] + x * (aT[19] + x * (aT[21] + x * aT[23])))))))))));
113 }
114