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/ld80/invtrig.h,v 1.2 2008/08/02 03:56:22 das Exp $
27 */
28
29 #define BIAS (LDBL_MAX_EXP - 1)
30 #define MANH_SIZE LDBL_MANH_SIZE
31
32 /* Approximation thresholds. */
33 #define ASIN_LINEAR (BIAS - 32) /* 2**-32 */
34 #define ACOS_CONST (BIAS - 65) /* 2**-65 */
35 #define ATAN_CONST (BIAS + 65) /* 2**65 */
36 #define ATAN_LINEAR (BIAS - 32) /* 2**-32 */
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 qS1 _ItL_qS1
50 #define qS2 _ItL_qS2
51 #define qS3 _ItL_qS3
52 #define qS4 _ItL_qS4
53 #define qS5 _ItL_qS5
54 #define atanhi _ItL_atanhi
55 #define atanlo _ItL_atanlo
56 #define aT _ItL_aT
57 #define pi_lo _ItL_pi_lo
58
59 #define pio2_hi atanhi[3]
60 #define pio2_lo atanlo[3]
61 #define pio4_hi atanhi[1]
62
63 #ifdef STRUCT_DECLS
64 typedef struct longdouble {
65 uint64_t mant;
66 uint16_t expsign;
67 } LONGDOUBLE;
68 #else
69 typedef long double LONGDOUBLE;
70 #endif
71
72 extern const LONGDOUBLE pS0, pS1, pS2, pS3, pS4, pS5, pS6;
73 extern const LONGDOUBLE qS1, qS2, qS3, qS4, qS5;
74 extern const LONGDOUBLE atanhi[], atanlo[], aT[];
75 extern const LONGDOUBLE pi_lo;
76
77 #ifndef STRUCT_DECLS
78
79 static inline long double
P(long double x)80 P(long double x)
81 {
82
83 return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \
84 (pS4 + x * (pS5 + x * pS6)))))));
85 }
86
87 static inline long double
Q(long double x)88 Q(long double x)
89 {
90
91 return (1.0l + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * qS5)))));
92 }
93
94 static inline long double
T_even(long double x)95 T_even(long double x)
96 {
97
98 return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \
99 (aT[8] + x * (aT[10] + x * aT[12]))))));
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])))));
108 }
109
110 #endif
111
