1a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 2a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes/* @(#)e_asin.c 1.3 95/01/18 */ 3a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes/* FreeBSD: head/lib/msun/src/e_asin.c 176451 2008-02-22 02:30:36Z das */ 4a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes/* 5a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * ==================================================== 6a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 7a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * 8a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * Developed at SunSoft, a Sun Microsystems, Inc. business. 9a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * Permission to use, copy, modify, and distribute this 10a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * software is freely granted, provided that this notice 11a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * is preserved. 12a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * ==================================================== 13a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes */ 14a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 15a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include <sys/cdefs.h> 16a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes__FBSDID("$FreeBSD$"); 17a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 18a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes/* 19a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * See comments in e_asin.c. 20a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * Converted to long double by David Schultz <das@FreeBSD.ORG>. 21a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes */ 22a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 23a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include <float.h> 24a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 25a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include "invtrig.h" 26a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include "math.h" 27a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include "math_private.h" 28a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 29a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughesstatic const long double 30a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughesone = 1.00000000000000000000e+00, 31a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hugheshuge = 1.000e+300; 32a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 33a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hugheslong double 34a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughesasinl(long double x) 35a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes{ 36a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes union IEEEl2bits u; 37a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes long double t=0.0,w,p,q,c,r,s; 38a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes int16_t expsign, expt; 39a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes u.e = x; 40a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes expsign = u.xbits.expsign; 41a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes expt = expsign & 0x7fff; 42a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if(expt >= BIAS) { /* |x|>= 1 */ 43a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0) 44a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes /* asin(1)=+-pi/2 with inexact */ 45a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes return x*pio2_hi+x*pio2_lo; 46a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes return (x-x)/(x-x); /* asin(|x|>1) is NaN */ 47a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes } else if (expt<BIAS-1) { /* |x|<0.5 */ 48a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if(expt<ASIN_LINEAR) { /* if |x| is small, asinl(x)=x */ 49a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if(huge+x>one) return x;/* return x with inexact if x!=0*/ 50a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes } 51a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes t = x*x; 52a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes p = P(t); 53a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes q = Q(t); 54a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes w = p/q; 55a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes return x+x*w; 56a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes } 57a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes /* 1> |x|>= 0.5 */ 58a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes w = one-fabsl(x); 59a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes t = w*0.5; 60a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes p = P(t); 61a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes q = Q(t); 62a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes s = sqrtl(t); 63a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if(u.bits.manh>=THRESH) { /* if |x| is close to 1 */ 64a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes w = p/q; 65a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes t = pio2_hi-(2.0*(s+s*w)-pio2_lo); 66a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes } else { 67a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes u.e = s; 68a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes u.bits.manl = 0; 69a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes w = u.e; 70a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes c = (t-w*w)/(s+w); 71a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes r = p/q; 72a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes p = 2.0*s*r-(pio2_lo-2.0*c); 73a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes q = pio4_hi-2.0*w; 74a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes t = pio4_hi-(p-q); 75a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes } 76a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if(expsign>0) return t; else return -t; 77a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes} 78