1/* $OpenBSD: invtrig.h,v 1.2 2016/09/12 19:47:02 guenther Exp $ */ 2/*- 3 * Copyright (c) 2008 David Schultz <das@FreeBSD.ORG> 4 * All rights reserved. 5 * 6 * Redistribution and use in source and binary forms, with or without 7 * modification, are permitted provided that the following conditions 8 * are met: 9 * 1. Redistributions of source code must retain the above copyright 10 * notice, this list of conditions and the following disclaimer. 11 * 2. Redistributions in binary form must reproduce the above copyright 12 * notice, this list of conditions and the following disclaimer in the 13 * documentation and/or other materials provided with the distribution. 14 * 15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 16 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 17 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 18 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 19 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 20 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 21 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 22 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 23 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 24 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 25 * SUCH DAMAGE. 26 * 27 * $FreeBSD: src/lib/msun/ld128/invtrig.h,v 1.1 2008/07/31 22:41:26 das Exp $ 28 */ 29 30#include <sys/types.h> 31#include <machine/ieee.h> 32#include <float.h> 33 34#define BIAS (LDBL_MAX_EXP - 1) 35#define MANH_SIZE (EXT_FRACHBITS + EXT_FRACHMBITS + 1) 36 37/* Approximation thresholds. */ 38#define ASIN_LINEAR (BIAS - 56) /* 2**-56 */ 39#define ACOS_CONST (BIAS - 113) /* 2**-113 */ 40#define ATAN_CONST (BIAS + 113) /* 2**113 */ 41#define ATAN_LINEAR (BIAS - 56) /* 2**-56 */ 42 43/* 0.95 */ 44#ifdef EXT_IMPLICIT_NBIT 45#define THRESH (0xe666666666666666ULL>>(64-(MANH_SIZE-1))) 46#else /* EXT_IMPLICIT_NBIT */ 47#define THRESH ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|0x80000000) 48#endif /* EXT_IMPLICIT_NBIT */ 49 50/* Constants shared by the long double inverse trig functions. */ 51#define pS0 _ItL_pS0 52#define pS1 _ItL_pS1 53#define pS2 _ItL_pS2 54#define pS3 _ItL_pS3 55#define pS4 _ItL_pS4 56#define pS5 _ItL_pS5 57#define pS6 _ItL_pS6 58#define pS7 _ItL_pS7 59#define pS8 _ItL_pS8 60#define pS9 _ItL_pS9 61#define qS1 _ItL_qS1 62#define qS2 _ItL_qS2 63#define qS3 _ItL_qS3 64#define qS4 _ItL_qS4 65#define qS5 _ItL_qS5 66#define qS6 _ItL_qS6 67#define qS7 _ItL_qS7 68#define qS8 _ItL_qS8 69#define qS9 _ItL_qS9 70#define atanhi _ItL_atanhi 71#define atanlo _ItL_atanlo 72#define aT _ItL_aT 73#define pi_lo _ItL_pi_lo 74 75#define pio2_hi atanhi[3] 76#define pio2_lo atanlo[3] 77#define pio4_hi atanhi[1] 78 79__BEGIN_HIDDEN_DECLS 80/* Constants shared by the long double inverse trig functions. */ 81extern const long double pS0, pS1, pS2, pS3, pS4, pS5, pS6, pS7, pS8, pS9; 82extern const long double qS1, qS2, qS3, qS4, qS5, qS6, qS7, qS8, qS9; 83extern const long double atanhi[], atanlo[], aT[]; 84extern const long double pi_lo; 85__END_HIDDEN_DECLS 86 87static inline long double 88P(long double x) 89{ 90 91 return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \ 92 (pS4 + x * (pS5 + x * (pS6 + x * (pS7 + x * (pS8 + x * \ 93 pS9)))))))))); 94} 95 96static inline long double 97Q(long double x) 98{ 99 100 return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * \ 101 (qS5 + x * (qS6 + x * (qS7 + x * (qS8 + x * qS9))))))))); 102} 103 104static inline long double 105T_even(long double x) 106{ 107 108 return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \ 109 (aT[8] + x * (aT[10] + x * (aT[12] + x * (aT[14] + x * \ 110 (aT[16] + x * (aT[18] + x * (aT[20] + x * aT[22]))))))))))); 111} 112 113static inline long double 114T_odd(long double x) 115{ 116 117 return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \ 118 (aT[9] + x * (aT[11] + x * (aT[13] + x * (aT[15] + x * \ 119 (aT[17] + x * (aT[19] + x * (aT[21] + x * aT[23]))))))))))); 120} 121