invtrig.h revision 330897
1/*- 2 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD 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 * $FreeBSD: stable/11/lib/msun/ld128/invtrig.h 330897 2018-03-14 03:19:51Z eadler $ 29 */ 30 31#include <float.h> 32 33#include "fpmath.h" 34 35#define BIAS (LDBL_MAX_EXP - 1) 36#define MANH_SIZE (LDBL_MANH_SIZE + 1) 37 38/* Approximation thresholds. */ 39#define ASIN_LINEAR (BIAS - 56) /* 2**-56 */ 40#define ACOS_CONST (BIAS - 113) /* 2**-113 */ 41#define ATAN_CONST (BIAS + 113) /* 2**113 */ 42#define ATAN_LINEAR (BIAS - 56) /* 2**-56 */ 43 44/* 0.95 */ 45#define THRESH ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT) 46 47/* Constants shared by the long double inverse trig functions. */ 48#define pS0 _ItL_pS0 49#define pS1 _ItL_pS1 50#define pS2 _ItL_pS2 51#define pS3 _ItL_pS3 52#define pS4 _ItL_pS4 53#define pS5 _ItL_pS5 54#define pS6 _ItL_pS6 55#define pS7 _ItL_pS7 56#define pS8 _ItL_pS8 57#define pS9 _ItL_pS9 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 qS6 _ItL_qS6 64#define qS7 _ItL_qS7 65#define qS8 _ItL_qS8 66#define qS9 _ItL_qS9 67#define atanhi _ItL_atanhi 68#define atanlo _ItL_atanlo 69#define aT _ItL_aT 70#define pi_lo _ItL_pi_lo 71 72#define pio2_hi atanhi[3] 73#define pio2_lo atanlo[3] 74#define pio4_hi atanhi[1] 75 76/* Constants shared by the long double inverse trig functions. */ 77extern const long double pS0, pS1, pS2, pS3, pS4, pS5, pS6, pS7, pS8, pS9; 78extern const long double qS1, qS2, qS3, qS4, qS5, qS6, qS7, qS8, qS9; 79extern const long double atanhi[], atanlo[], aT[]; 80extern const long double pi_lo; 81 82static inline long double 83P(long double x) 84{ 85 86 return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \ 87 (pS4 + x * (pS5 + x * (pS6 + x * (pS7 + x * (pS8 + x * \ 88 pS9)))))))))); 89} 90 91static inline long double 92Q(long double x) 93{ 94 95 return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * \ 96 (qS5 + x * (qS6 + x * (qS7 + x * (qS8 + x * qS9))))))))); 97} 98 99static inline long double 100T_even(long double x) 101{ 102 103 return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \ 104 (aT[8] + x * (aT[10] + x * (aT[12] + x * (aT[14] + x * \ 105 (aT[16] + x * (aT[18] + x * (aT[20] + x * aT[22]))))))))))); 106} 107 108static inline long double 109T_odd(long double x) 110{ 111 112 return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \ 113 (aT[9] + x * (aT[11] + x * (aT[13] + x * (aT[15] + x * \ 114 (aT[17] + x * (aT[19] + x * (aT[21] + x * aT[23]))))))))))); 115} 116