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