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 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 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 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 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