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 #include <sys/cdefs.h> 15 /* 16 * See comments in e_asin.c. 17 * Converted to long double by David Schultz <das@FreeBSD.ORG>. 18 */ 19 20 #include <float.h> 21 22 #include "invtrig.h" 23 #include "math.h" 24 #include "math_private.h" 25 26 static const long double 27 one = 1.00000000000000000000e+00, 28 huge = 1.000e+300; 29 30 long double 31 asinl(long double x) 32 { 33 union IEEEl2bits u; 34 long double t=0.0,w,p,q,c,r,s; 35 int16_t expsign, expt; 36 u.e = x; 37 expsign = u.xbits.expsign; 38 expt = expsign & 0x7fff; 39 if(expt >= BIAS) { /* |x|>= 1 */ 40 if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0) 41 /* asin(1)=+-pi/2 with inexact */ 42 return x*pio2_hi+x*pio2_lo; 43 return (x-x)/(x-x); /* asin(|x|>1) is NaN */ 44 } else if (expt<BIAS-1) { /* |x|<0.5 */ 45 if(expt<ASIN_LINEAR) { /* if |x| is small, asinl(x)=x */ 46 if(huge+x>one) return x;/* return x with inexact if x!=0*/ 47 } 48 t = x*x; 49 p = P(t); 50 q = Q(t); 51 w = p/q; 52 return x+x*w; 53 } 54 /* 1> |x|>= 0.5 */ 55 w = one-fabsl(x); 56 t = w*0.5; 57 p = P(t); 58 q = Q(t); 59 s = sqrtl(t); 60 if(u.bits.manh>=THRESH) { /* if |x| is close to 1 */ 61 w = p/q; 62 t = pio2_hi-(2.0*(s+s*w)-pio2_lo); 63 } else { 64 u.e = s; 65 u.bits.manl = 0; 66 w = u.e; 67 c = (t-w*w)/(s+w); 68 r = p/q; 69 p = 2.0*s*r-(pio2_lo-2.0*c); 70 q = pio4_hi-2.0*w; 71 t = pio4_hi-(p-q); 72 } 73 if(expsign>0) return t; else return -t; 74 } 75