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1 
2 /* @(#)e_acosh.c 1.3 95/01/18 */
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 /* __ieee754_acosh(x)
16  * Method :
17  *	Based on
18  *		acosh(x) = log [ x + ieee_sqrt(x*x-1) ]
19  *	we have
20  *		acosh(x) := ieee_log(x)+ln2,	if x is large; else
21  *		acosh(x) := ieee_log(2x-1/(ieee_sqrt(x*x-1)+x)) if x>2; else
22  *		acosh(x) := ieee_log1p(t+ieee_sqrt(2.0*t+t*t)); where t=x-1.
23  *
24  * Special cases:
25  *	acosh(x) is NaN with signal if x<1.
26  *	acosh(NaN) is NaN without signal.
27  */
28 
29 #include "fdlibm.h"
30 
31 #ifdef __STDC__
32 static const double
33 #else
34 static double
35 #endif
36 one	= 1.0,
37 ln2	= 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
38 
39 #ifdef __STDC__
__ieee754_acosh(double x)40 	double __ieee754_acosh(double x)
41 #else
42 	double __ieee754_acosh(x)
43 	double x;
44 #endif
45 {
46 	double t;
47 	int hx;
48 	hx = __HI(x);
49 	if(hx<0x3ff00000) {		/* x < 1 */
50 	    return (x-x)/(x-x);
51 	} else if(hx >=0x41b00000) {	/* x > 2**28 */
52 	    if(hx >=0x7ff00000) {	/* x is inf of NaN */
53 	        return x+x;
54 	    } else
55 		return __ieee754_log(x)+ln2;	/* acosh(huge)=ieee_log(2x) */
56 	} else if(((hx-0x3ff00000)|__LO(x))==0) {
57 	    return 0.0;			/* acosh(1) = 0 */
58 	} else if (hx > 0x40000000) {	/* 2**28 > x > 2 */
59 	    t=x*x;
60 	    return __ieee754_log(2.0*x-one/(x+ieee_sqrt(t-one)));
61 	} else {			/* 1<x<2 */
62 	    t = x-one;
63 	    return ieee_log1p(t+ieee_sqrt(2.0*t+t*t));
64 	}
65 }
66