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#include <sys/cdefs.h>
16__FBSDID("$FreeBSD$");
17
18/* __ieee754_acosh(x)
19 * Method :
20 *	Based on
21 *		acosh(x) = log [ x + sqrt(x*x-1) ]
22 *	we have
23 *		acosh(x) := log(x)+ln2,	if x is large; else
24 *		acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
25 *		acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
26 *
27 * Special cases:
28 *	acosh(x) is NaN with signal if x<1.
29 *	acosh(NaN) is NaN without signal.
30 */
31
32#include <float.h>
33
34#include "math.h"
35#include "math_private.h"
36
37static const double
38one	= 1.0,
39ln2	= 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
40
41double
42__ieee754_acosh(double x)
43{
44	double t;
45	int32_t hx;
46	u_int32_t lx;
47	EXTRACT_WORDS(hx,lx,x);
48	if(hx<0x3ff00000) {		/* x < 1 */
49	    return (x-x)/(x-x);
50	} else if(hx >=0x41b00000) {	/* x > 2**28 */
51	    if(hx >=0x7ff00000) {	/* x is inf of NaN */
52	        return x+x;
53	    } else
54		return __ieee754_log(x)+ln2;	/* acosh(huge)=log(2x) */
55	} else if(((hx-0x3ff00000)|lx)==0) {
56	    return 0.0;			/* acosh(1) = 0 */
57	} else if (hx > 0x40000000) {	/* 2**28 > x > 2 */
58	    t=x*x;
59	    return __ieee754_log(2.0*x-one/(x+sqrt(t-one)));
60	} else {			/* 1<x<2 */
61	    t = x-one;
62	    return log1p(t+sqrt(2.0*t+t*t));
63	}
64}
65
66#if LDBL_MANT_DIG == 53
67__weak_reference(acosh, acoshl);
68#endif
69