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 + 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 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 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 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 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