1181074Sdas 2181074Sdas/* @(#)e_asin.c 1.3 95/01/18 */ 3181074Sdas/* FreeBSD: head/lib/msun/src/e_asin.c 176451 2008-02-22 02:30:36Z das */ 4181074Sdas/* 5181074Sdas * ==================================================== 6181074Sdas * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7181074Sdas * 8181074Sdas * Developed at SunSoft, a Sun Microsystems, Inc. business. 9181074Sdas * Permission to use, copy, modify, and distribute this 10181074Sdas * software is freely granted, provided that this notice 11181074Sdas * is preserved. 12181074Sdas * ==================================================== 13181074Sdas */ 14181074Sdas 15181074Sdas#include <sys/cdefs.h> 16181074Sdas__FBSDID("$FreeBSD$"); 17181074Sdas 18181074Sdas/* 19181074Sdas * See comments in e_asin.c. 20181074Sdas * Converted to long double by David Schultz <das@FreeBSD.ORG>. 21181074Sdas */ 22181074Sdas 23181074Sdas#include <float.h> 24181074Sdas 25181074Sdas#include "invtrig.h" 26181074Sdas#include "math.h" 27181074Sdas#include "math_private.h" 28181074Sdas 29181074Sdasstatic const long double 30181074Sdasone = 1.00000000000000000000e+00, 31181074Sdashuge = 1.000e+300; 32181074Sdas 33181074Sdaslong double 34181074Sdasasinl(long double x) 35181074Sdas{ 36181074Sdas union IEEEl2bits u; 37181074Sdas long double t=0.0,w,p,q,c,r,s; 38181074Sdas int16_t expsign, expt; 39181074Sdas u.e = x; 40181074Sdas expsign = u.xbits.expsign; 41181074Sdas expt = expsign & 0x7fff; 42181074Sdas if(expt >= BIAS) { /* |x|>= 1 */ 43181074Sdas if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0) 44181074Sdas /* asin(1)=+-pi/2 with inexact */ 45181074Sdas return x*pio2_hi+x*pio2_lo; 46181074Sdas return (x-x)/(x-x); /* asin(|x|>1) is NaN */ 47181074Sdas } else if (expt<BIAS-1) { /* |x|<0.5 */ 48181074Sdas if(expt<ASIN_LINEAR) { /* if |x| is small, asinl(x)=x */ 49181074Sdas if(huge+x>one) return x;/* return x with inexact if x!=0*/ 50181258Sdas } 51181258Sdas t = x*x; 52181258Sdas p = P(t); 53181258Sdas q = Q(t); 54181258Sdas w = p/q; 55181258Sdas return x+x*w; 56181074Sdas } 57181074Sdas /* 1> |x|>= 0.5 */ 58181074Sdas w = one-fabsl(x); 59181074Sdas t = w*0.5; 60181074Sdas p = P(t); 61181074Sdas q = Q(t); 62181074Sdas s = sqrtl(t); 63181074Sdas if(u.bits.manh>=THRESH) { /* if |x| is close to 1 */ 64181074Sdas w = p/q; 65181074Sdas t = pio2_hi-(2.0*(s+s*w)-pio2_lo); 66181074Sdas } else { 67181074Sdas u.e = s; 68181074Sdas u.bits.manl = 0; 69181074Sdas w = u.e; 70181074Sdas c = (t-w*w)/(s+w); 71181074Sdas r = p/q; 72181074Sdas p = 2.0*s*r-(pio2_lo-2.0*c); 73181074Sdas q = pio4_hi-2.0*w; 74181074Sdas t = pio4_hi-(p-q); 75181074Sdas } 76181074Sdas if(expsign>0) return t; else return -t; 77181074Sdas} 78