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#### Mercurial (d38398e5144e)

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``````
``````/* @(#)e_acosh.c 1.3 95/01/18 */
``````/*
`````` * ====================================================
`````` * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
`````` *
`````` * Developed at SunSoft, a Sun Microsystems, Inc. business.
`````` * Permission to use, copy, modify, and distribute this
`````` * software is freely granted, provided that this notice
`````` * is preserved.
`````` * ====================================================
`````` *
`````` */
``````
``````//#include <sys/cdefs.h>
``````//__FBSDID("\$FreeBSD\$");
``````
``````/* __ieee754_acosh(x)
`````` * Method :
`````` *	Based on
`````` *		acosh(x) = log [ x + sqrt(x*x-1) ]
`````` *	we have
`````` *		acosh(x) := log(x)+ln2,	if x is large; else
`````` *		acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
`````` *		acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
`````` *
`````` * Special cases:
`````` *	acosh(x) is NaN with signal if x<1.
`````` *	acosh(NaN) is NaN without signal.
`````` */
``````
``````#include <float.h>
``````
``````#include "math_private.h"
``````
``````static const double
``````one	= 1.0,
``````ln2	= 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
``````
``````double
``````__ieee754_acosh(double x)
``````{
``````	double t;
``````	int32_t hx;
``````	u_int32_t lx;
``````	EXTRACT_WORDS(hx,lx,x);
``````	if(hx<0x3ff00000) {		/* x < 1 */
``````	    return (x-x)/(x-x);
``````	} else if(hx >=0x41b00000) {	/* x > 2**28 */
``````	    if(hx >=0x7ff00000) {	/* x is inf of NaN */
``````	        return x+x;
``````	    } else
``````		return __ieee754_log(x)+ln2;	/* acosh(huge)=log(2x) */
``````	} else if(((hx-0x3ff00000)|lx)==0) {
``````	    return 0.0;			/* acosh(1) = 0 */
``````	} else if (hx > 0x40000000) {	/* 2**28 > x > 2 */
``````	    t=x*x;
``````	    return __ieee754_log(2.0*x-one/(x+sqrt(t-one)));
``````	} else {			/* 1<x<2 */
``````	    t = x-one;
``````	    return log1p(t+sqrt(2.0*t+t*t));
``````	}
``````}
``````