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 + 1) 35181074Sdas 36181074Sdas/* Approximation thresholds. */ 37181074Sdas#define ASIN_LINEAR (BIAS - 56) /* 2**-56 */ 38181074Sdas#define ACOS_CONST (BIAS - 113) /* 2**-113 */ 39181074Sdas#define ATAN_CONST (BIAS + 113) /* 2**113 */ 40181074Sdas#define ATAN_LINEAR (BIAS - 56) /* 2**-56 */ 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 pS7 _ItL_pS7 54181074Sdas#define pS8 _ItL_pS8 55181074Sdas#define pS9 _ItL_pS9 56181074Sdas#define qS1 _ItL_qS1 57181074Sdas#define qS2 _ItL_qS2 58181074Sdas#define qS3 _ItL_qS3 59181074Sdas#define qS4 _ItL_qS4 60181074Sdas#define qS5 _ItL_qS5 61181074Sdas#define qS6 _ItL_qS6 62181074Sdas#define qS7 _ItL_qS7 63181074Sdas#define qS8 _ItL_qS8 64181074Sdas#define qS9 _ItL_qS9 65181074Sdas#define atanhi _ItL_atanhi 66181074Sdas#define atanlo _ItL_atanlo 67181074Sdas#define aT _ItL_aT 68181074Sdas#define pi_lo _ItL_pi_lo 69181074Sdas 70181074Sdas#define pio2_hi atanhi[3] 71181074Sdas#define pio2_lo atanlo[3] 72181074Sdas#define pio4_hi atanhi[1] 73181074Sdas 74181074Sdas/* Constants shared by the long double inverse trig functions. */ 75181074Sdasextern const long double pS0, pS1, pS2, pS3, pS4, pS5, pS6, pS7, pS8, pS9; 76181074Sdasextern const long double qS1, qS2, qS3, qS4, qS5, qS6, qS7, qS8, qS9; 77181074Sdasextern const long double atanhi[], atanlo[], aT[]; 78181074Sdasextern const long double pi_lo; 79181074Sdas 80181074Sdasstatic inline long double 81181074SdasP(long double x) 82181074Sdas{ 83181074Sdas 84181074Sdas return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \ 85181074Sdas (pS4 + x * (pS5 + x * (pS6 + x * (pS7 + x * (pS8 + x * \ 86181074Sdas pS9)))))))))); 87181074Sdas} 88181074Sdas 89181074Sdasstatic inline long double 90181074SdasQ(long double x) 91181074Sdas{ 92181074Sdas 93181074Sdas return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * \ 94181074Sdas (qS5 + x * (qS6 + x * (qS7 + x * (qS8 + x * qS9))))))))); 95181074Sdas} 96181074Sdas 97181074Sdasstatic inline long double 98181074SdasT_even(long double x) 99181074Sdas{ 100181074Sdas 101181074Sdas return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \ 102181074Sdas (aT[8] + x * (aT[10] + x * (aT[12] + x * (aT[14] + x * \ 103181074Sdas (aT[16] + x * (aT[18] + x * (aT[20] + x * aT[22]))))))))))); 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] + x * (aT[13] + x * (aT[15] + x * \ 112181074Sdas (aT[17] + x * (aT[19] + x * (aT[21] + x * aT[23]))))))))))); 113181074Sdas} 114