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