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__
32static const double
33#else
34static double
35#endif
36one	= 1.0,
37ln2	= 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
38
39#ifdef __STDC__
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