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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 #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 
     37 static const double
     38 one	= 1.0,
     39 ln2	= 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
     40 
     41 double
     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