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      1 /* @(#)e_acosh.c 5.1 93/09/24 */
      2 /*
      3  * ====================================================
      4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
      5  *
      6  * Developed at SunPro, a Sun Microsystems, Inc. business.
      7  * Permission to use, copy, modify, and distribute this
      8  * software is freely granted, provided that this notice
      9  * is preserved.
     10  * ====================================================
     11  */
     12 
     13 #include <sys/cdefs.h>
     14 #if defined(LIBM_SCCS) && !defined(lint)
     15 __RCSID("$NetBSD: e_acosh.c,v 1.12 2002/05/26 22:01:48 wiz Exp $");
     16 #endif
     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 "math.h"
     33 #include "math_private.h"
     34 
     35 static const double
     36 one	= 1.0,
     37 ln2	= 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
     38 
     39 double
     40 __ieee754_acosh(double x)
     41 {
     42 	double t;
     43 	int32_t hx;
     44 	u_int32_t lx;
     45 	EXTRACT_WORDS(hx,lx,x);
     46 	if(hx<0x3ff00000) {		/* x < 1 */
     47 	    return (x-x)/(x-x);
     48 	} else if(hx >=0x41b00000) {	/* x > 2**28 */
     49 	    if(hx >=0x7ff00000) {	/* x is inf of NaN */
     50 	        return x+x;
     51 	    } else
     52 		return __ieee754_log(x)+ln2;	/* acosh(huge)=log(2x) */
     53 	} else if(((hx-0x3ff00000)|lx)==0) {
     54 	    return 0.0;			/* acosh(1) = 0 */
     55 	} else if (hx > 0x40000000) {	/* 2**28 > x > 2 */
     56 	    t=x*x;
     57 	    return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one)));
     58 	} else {			/* 1<x<2 */
     59 	    t = x-one;
     60 	    return log1p(t+sqrt(2.0*t+t*t));
     61 	}
     62 }
     63