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 * $FreeBSD$ 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 35 36 /* Approximation thresholds. */ 37 #define ASIN_LINEAR (BIAS - 32) /* 2**-32 */ 38 #define ACOS_CONST (BIAS - 65) /* 2**-65 */ 39 #define ATAN_CONST (BIAS + 65) /* 2**65 */ 40 #define ATAN_LINEAR (BIAS - 32) /* 2**-32 */ 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 qS1 _ItL_qS1 54 #define qS2 _ItL_qS2 55 #define qS3 _ItL_qS3 56 #define qS4 _ItL_qS4 57 #define qS5 _ItL_qS5 58 #define atanhi _ItL_atanhi 59 #define atanlo _ItL_atanlo 60 #define aT _ItL_aT 61 #define pi_lo _ItL_pi_lo 62 63 #define pio2_hi atanhi[3] 64 #define pio2_lo atanlo[3] 65 #define pio4_hi atanhi[1] 66 67 #ifdef STRUCT_DECLS 68 typedef struct longdouble { 69 uint64_t mant; 70 uint16_t expsign; 71 } LONGDOUBLE; 72 #else 73 typedef long double LONGDOUBLE; 74 #endif 75 76 extern const LONGDOUBLE pS0, pS1, pS2, pS3, pS4, pS5, pS6; 77 extern const LONGDOUBLE qS1, qS2, qS3, qS4, qS5; 78 extern const LONGDOUBLE atanhi[], atanlo[], aT[]; 79 extern const LONGDOUBLE pi_lo; 80 81 #ifndef STRUCT_DECLS 82 83 static inline long double 84 P(long double x) 85 { 86 87 return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \ 88 (pS4 + x * (pS5 + x * pS6))))))); 89 } 90 91 static inline long double 92 Q(long double x) 93 { 94 95 return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * qS5))))); 96 } 97 98 static inline long double 99 T_even(long double x) 100 { 101 102 return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \ 103 (aT[8] + x * (aT[10] + x * aT[12])))))); 104 } 105 106 static inline long double 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]))))); 112 } 113 114 #endif 115