invtrig.h revision 181152
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: head/lib/msun/ld80/invtrig.h 181152 2008-08-02 03:56:22Z das $ 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 35 36/* Approximation thresholds. */ 37#define ASIN_LINEAR (BIAS - 32) /* 2**-32 */ 38#define ACOS_CONST (BIAS - 65) /* 2**-65 */ 39#define ATAN_CONST (BIAS + 65) /* 2**65 */ 40#define ATAN_LINEAR (BIAS - 32) /* 2**-32 */ 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 qS1 _ItL_qS1 54#define qS2 _ItL_qS2 55#define qS3 _ItL_qS3 56#define qS4 _ItL_qS4 57#define qS5 _ItL_qS5 58#define atanhi _ItL_atanhi 59#define atanlo _ItL_atanlo 60#define aT _ItL_aT 61#define pi_lo _ItL_pi_lo 62 63#define pio2_hi atanhi[3] 64#define pio2_lo atanlo[3] 65#define pio4_hi atanhi[1] 66 67#ifdef STRUCT_DECLS 68typedef struct longdouble { 69 uint64_t mant; 70 uint16_t expsign; 71} LONGDOUBLE; 72#else 73typedef long double LONGDOUBLE; 74#endif 75 76extern const LONGDOUBLE pS0, pS1, pS2, pS3, pS4, pS5, pS6; 77extern const LONGDOUBLE qS1, qS2, qS3, qS4, qS5; 78extern const LONGDOUBLE atanhi[], atanlo[], aT[]; 79extern const LONGDOUBLE pi_lo; 80 81#ifndef STRUCT_DECLS 82 83static inline long double 84P(long double x) 85{ 86 87 return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \ 88 (pS4 + x * (pS5 + x * pS6))))))); 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 * qS5))))); 96} 97 98static inline long double 99T_even(long double x) 100{ 101 102 return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \ 103 (aT[8] + x * (aT[10] + x * aT[12])))))); 104} 105 106static inline long double 107T_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]))))); 112} 113 114#endif 115