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 #define BIAS (LDBL_MAX_EXP - 1)
30 #define MANH_SIZE (LDBL_MANH_SIZE + 1)
31
32 /* Approximation thresholds. */
33 #define ASIN_LINEAR (BIAS - 56) /* 2**-56 */
34 #define ACOS_CONST (BIAS - 113) /* 2**-113 */
35 #define ATAN_CONST (BIAS + 113) /* 2**113 */
36 #define ATAN_LINEAR (BIAS - 56) /* 2**-56 */
37
38 /* 0.95 */
39 #define THRESH ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT)
40
41 /* Constants shared by the long double inverse trig functions. */
42 #define pS0 _ItL_pS0
43 #define pS1 _ItL_pS1
44 #define pS2 _ItL_pS2
45 #define pS3 _ItL_pS3
46 #define pS4 _ItL_pS4
47 #define pS5 _ItL_pS5
48 #define pS6 _ItL_pS6
49 #define pS7 _ItL_pS7
50 #define pS8 _ItL_pS8
51 #define pS9 _ItL_pS9
52 #define qS1 _ItL_qS1
53 #define qS2 _ItL_qS2
54 #define qS3 _ItL_qS3
55 #define qS4 _ItL_qS4
56 #define qS5 _ItL_qS5
57 #define qS6 _ItL_qS6
58 #define qS7 _ItL_qS7
59 #define qS8 _ItL_qS8
60 #define qS9 _ItL_qS9
61 #define atanhi _ItL_atanhi
62 #define atanlo _ItL_atanlo
63 #define aT _ItL_aT
64 #define pi_lo _ItL_pi_lo
65
66 #define pio2_hi atanhi[3]
67 #define pio2_lo atanlo[3]
68 #define pio4_hi atanhi[1]
69
70 /* Constants shared by the long double inverse trig functions. */
71 extern const long double pS0, pS1, pS2, pS3, pS4, pS5, pS6, pS7, pS8, pS9;
72 extern const long double qS1, qS2, qS3, qS4, qS5, qS6, qS7, qS8, qS9;
73 extern const long double atanhi[], atanlo[], aT[];
74 extern const long double pi_lo;
75
76 static inline long double
P(long double x)77 P(long double x)
78 {
79
80 return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \
81 (pS4 + x * (pS5 + x * (pS6 + x * (pS7 + x * (pS8 + x * \
82 pS9))))))))));
83 }
84
85 static inline long double
Q(long double x)86 Q(long double x)
87 {
88
89 return (1.0L + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * \
90 (qS5 + x * (qS6 + x * (qS7 + x * (qS8 + x * qS9)))))))));
91 }
92
93 static inline long double
T_even(long double x)94 T_even(long double x)
95 {
96
97 return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \
98 (aT[8] + x * (aT[10] + x * (aT[12] + x * (aT[14] + x * \
99 (aT[16] + x * (aT[18] + x * (aT[20] + x * aT[22])))))))))));
100 }
101
102 static inline long double
T_odd(long double x)103 T_odd(long double x)
104 {
105
106 return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \
107 (aT[9] + x * (aT[11] + x * (aT[13] + x * (aT[15] + x * \
108 (aT[17] + x * (aT[19] + x * (aT[21] + x * aT[23])))))))))));
109 }
110
