1181074Sdas/*- 2181074Sdas * Copyright (c) 2008 David Schultz <das@FreeBSD.ORG> 3181074Sdas * All rights reserved. 4181074Sdas * 5181074Sdas * Redistribution and use in source and binary forms, with or without 6181074Sdas * modification, are permitted provided that the following conditions 7181074Sdas * are met: 8181074Sdas * 1. Redistributions of source code must retain the above copyright 9181074Sdas * notice, this list of conditions and the following disclaimer. 10181074Sdas * 2. Redistributions in binary form must reproduce the above copyright 11181074Sdas * notice, this list of conditions and the following disclaimer in the 12181074Sdas * documentation and/or other materials provided with the distribution. 13181074Sdas * 14181074Sdas * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 15181074Sdas * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 16181074Sdas * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 17181074Sdas * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 18181074Sdas * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 19181074Sdas * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 20181074Sdas * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 21181074Sdas * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 22181074Sdas * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 23181074Sdas * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 24181074Sdas * SUCH DAMAGE. 25181074Sdas * 26181074Sdas * $FreeBSD$ 27181074Sdas */ 28181074Sdas 29181074Sdas#include <float.h> 30181074Sdas 31181074Sdas#include "fpmath.h" 32181074Sdas 33181074Sdas#define BIAS (LDBL_MAX_EXP - 1) 34181074Sdas#define MANH_SIZE LDBL_MANH_SIZE 35181074Sdas 36181074Sdas/* Approximation thresholds. */ 37181074Sdas#define ASIN_LINEAR (BIAS - 32) /* 2**-32 */ 38181074Sdas#define ACOS_CONST (BIAS - 65) /* 2**-65 */ 39181074Sdas#define ATAN_CONST (BIAS + 65) /* 2**65 */ 40181074Sdas#define ATAN_LINEAR (BIAS - 32) /* 2**-32 */ 41181074Sdas 42181074Sdas/* 0.95 */ 43181074Sdas#define THRESH ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT) 44181074Sdas 45181074Sdas/* Constants shared by the long double inverse trig functions. */ 46181074Sdas#define pS0 _ItL_pS0 47181074Sdas#define pS1 _ItL_pS1 48181074Sdas#define pS2 _ItL_pS2 49181074Sdas#define pS3 _ItL_pS3 50181074Sdas#define pS4 _ItL_pS4 51181074Sdas#define pS5 _ItL_pS5 52181074Sdas#define pS6 _ItL_pS6 53181074Sdas#define qS1 _ItL_qS1 54181074Sdas#define qS2 _ItL_qS2 55181074Sdas#define qS3 _ItL_qS3 56181074Sdas#define qS4 _ItL_qS4 57181074Sdas#define qS5 _ItL_qS5 58181074Sdas#define atanhi _ItL_atanhi 59181074Sdas#define atanlo _ItL_atanlo 60181074Sdas#define aT _ItL_aT 61181074Sdas#define pi_lo _ItL_pi_lo 62181074Sdas 63181074Sdas#define pio2_hi atanhi[3] 64181074Sdas#define pio2_lo atanlo[3] 65181074Sdas#define pio4_hi atanhi[1] 66181074Sdas 67181152Sdas#ifdef STRUCT_DECLS 68181152Sdastypedef struct longdouble { 69181152Sdas uint64_t mant; 70181152Sdas uint16_t expsign; 71181152Sdas} LONGDOUBLE; 72181152Sdas#else 73181152Sdastypedef long double LONGDOUBLE; 74181152Sdas#endif 75181074Sdas 76181152Sdasextern const LONGDOUBLE pS0, pS1, pS2, pS3, pS4, pS5, pS6; 77181152Sdasextern const LONGDOUBLE qS1, qS2, qS3, qS4, qS5; 78181152Sdasextern const LONGDOUBLE atanhi[], atanlo[], aT[]; 79181152Sdasextern const LONGDOUBLE pi_lo; 80181152Sdas 81181152Sdas#ifndef STRUCT_DECLS 82181152Sdas 83181074Sdasstatic inline long double 84181074SdasP(long double x) 85181074Sdas{ 86181074Sdas 87181074Sdas return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \ 88181074Sdas (pS4 + x * (pS5 + x * pS6))))))); 89181074Sdas} 90181074Sdas 91181074Sdasstatic inline long double 92181074SdasQ(long double x) 93181074Sdas{ 94181074Sdas 95181074Sdas return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * qS5))))); 96181074Sdas} 97181074Sdas 98181074Sdasstatic inline long double 99181074SdasT_even(long double x) 100181074Sdas{ 101181074Sdas 102181074Sdas return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \ 103181074Sdas (aT[8] + x * (aT[10] + x * aT[12])))))); 104181074Sdas} 105181074Sdas 106181074Sdasstatic inline long double 107181074SdasT_odd(long double x) 108181074Sdas{ 109181074Sdas 110181074Sdas return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \ 111181074Sdas (aT[9] + x * aT[11]))))); 112181074Sdas} 113181152Sdas 114181152Sdas#endif 115