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 __FBSDID("$FreeBSD$");
17
18 /*
19 * See comments in e_asin.c.
20 * Converted to long double by David Schultz <das@FreeBSD.ORG>.
21 */
22
23 #include <float.h>
24
25 #include "invtrig.h"
26 #include "math.h"
27 #include "math_private.h"
28
29 static const long double
30 one = 1.00000000000000000000e+00,
31 huge = 1.000e+300;
32
33 long double
asinl(long double x)34 asinl(long double x)
35 {
36 union IEEEl2bits u;
37 long double t=0.0,w,p,q,c,r,s;
38 int16_t expsign, expt;
39 u.e = x;
40 expsign = u.xbits.expsign;
41 expt = expsign & 0x7fff;
42 if(expt >= BIAS) { /* |x|>= 1 */
43 if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0)
44 /* asin(1)=+-pi/2 with inexact */
45 return x*pio2_hi+x*pio2_lo;
46 return (x-x)/(x-x); /* asin(|x|>1) is NaN */
47 } else if (expt<BIAS-1) { /* |x|<0.5 */
48 if(expt<ASIN_LINEAR) { /* if |x| is small, asinl(x)=x */
49 if(huge+x>one) return x;/* return x with inexact if x!=0*/
50 }
51 t = x*x;
52 p = P(t);
53 q = Q(t);
54 w = p/q;
55 return x+x*w;
56 }
57 /* 1> |x|>= 0.5 */
58 w = one-fabsl(x);
59 t = w*0.5;
60 p = P(t);
61 q = Q(t);
62 s = sqrtl(t);
63 if(u.bits.manh>=THRESH) { /* if |x| is close to 1 */
64 w = p/q;
65 t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
66 } else {
67 u.e = s;
68 u.bits.manl = 0;
69 w = u.e;
70 c = (t-w*w)/(s+w);
71 r = p/q;
72 p = 2.0*s*r-(pio2_lo-2.0*c);
73 q = pio4_hi-2.0*w;
74 t = pio4_hi-(p-q);
75 }
76 if(expsign>0) return t; else return -t;
77 }
78