1/*- 2 * SPDX-License-Identifier: BSD-2-Clause 3 * 4 * Copyright (c) 2008 David Schultz <das@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. */ 74extern const long double pS0, pS1, pS2, pS3, pS4, pS5, pS6, pS7, pS8, pS9; 75extern const long double qS1, qS2, qS3, qS4, qS5, qS6, qS7, qS8, qS9; 76extern const long double atanhi[], atanlo[], aT[]; 77extern const long double pi_lo; 78 79static inline long double 80P(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 88static inline long double 89Q(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 96static inline long double 97T_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 105static inline long double 106T_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