1 /*- 2 * SPDX-License-Identifier: BSD-2-Clause 3 * 4 * Copyright (c) 2008 David Schultz <das (at) FreeBSD.ORG> 5 * All rights reserved. 6 * 7 * Redistribution and use in source and binary forms, with or without 8 * modification, are permitted provided that the following conditions 9 * are met: 10 * 1. Redistributions of source code must retain the above copyright 11 * notice, this list of conditions and the following disclaimer. 12 * 2. Redistributions in binary form must reproduce the above copyright 13 * notice, this list of conditions and the following disclaimer in the 14 * documentation and/or other materials provided with the distribution. 15 * 16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 17 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 18 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 19 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 20 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 21 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 22 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 23 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 24 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 25 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 26 * SUCH DAMAGE. 27 */ 28 29 #include <float.h> 30 31 32 #define BIAS (LDBL_MAX_EXP - 1) 33 #define MANH_SIZE (EXT_FRACHBITS + 1) 34 35 /* Approximation thresholds. */ 36 #define ASIN_LINEAR (BIAS - 56) /* 2**-56 */ 37 #define ACOS_CONST (BIAS - 113) /* 2**-113 */ 38 #define ATAN_CONST (BIAS + 113) /* 2**113 */ 39 #define ATAN_LINEAR (BIAS - 56) /* 2**-56 */ 40 41 /* 0.95 */ 42 #define THRESH ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT) 43 44 /* Constants shared by the long double inverse trig functions. */ 45 #define pS0 _ItL_pS0 46 #define pS1 _ItL_pS1 47 #define pS2 _ItL_pS2 48 #define pS3 _ItL_pS3 49 #define pS4 _ItL_pS4 50 #define pS5 _ItL_pS5 51 #define pS6 _ItL_pS6 52 #define pS7 _ItL_pS7 53 #define pS8 _ItL_pS8 54 #define pS9 _ItL_pS9 55 #define qS1 _ItL_qS1 56 #define qS2 _ItL_qS2 57 #define qS3 _ItL_qS3 58 #define qS4 _ItL_qS4 59 #define qS5 _ItL_qS5 60 #define qS6 _ItL_qS6 61 #define qS7 _ItL_qS7 62 #define qS8 _ItL_qS8 63 #define qS9 _ItL_qS9 64 #define atanhi _ItL_atanhi 65 #define atanlo _ItL_atanlo 66 #define aT _ItL_aT 67 #define pi_lo _ItL_pi_lo 68 69 #define pio2_hi atanhi[3] 70 #define pio2_lo atanlo[3] 71 #define pio4_hi atanhi[1] 72 73 /* Constants shared by the long double inverse trig functions. */ 74 extern const long double pS0, pS1, pS2, pS3, pS4, pS5, pS6, pS7, pS8, pS9; 75 extern const long double qS1, qS2, qS3, qS4, qS5, qS6, qS7, qS8, qS9; 76 extern const long double atanhi[], atanlo[], aT[]; 77 extern const long double pi_lo; 78 79 static inline long double 80 P(long double x) 81 { 82 83 return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \ 84 (pS4 + x * (pS5 + x * (pS6 + x * (pS7 + x * (pS8 + x * \ 85 pS9)))))))))); 86 } 87 88 static inline long double 89 Q(long double x) 90 { 91 92 return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * \ 93 (qS5 + x * (qS6 + x * (qS7 + x * (qS8 + x * qS9))))))))); 94 } 95 96 static inline long double 97 T_even(long double x) 98 { 99 100 return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \ 101 (aT[8] + x * (aT[10] + x * (aT[12] + x * (aT[14] + x * \ 102 (aT[16] + x * (aT[18] + x * (aT[20] + x * aT[22]))))))))))); 103 } 104 105 static inline long double 106 T_odd(long double x) 107 { 108 109 return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \ 110 (aT[9] + x * (aT[11] + x * (aT[13] + x * (aT[15] + x * \ 111 (aT[17] + x * (aT[19] + x * (aT[21] + x * aT[23]))))))))))); 112 } 113
Indexes created Mon Sep 22 13:09:51 GMT 2025