xref: /freebsd/lib/msun/src/e_acosh.c (revision 6fd05b64b5b65dd4ba9b86482a0634a5f0b96c29)
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 #ifndef lint
14 static char rcsid[] = "$FreeBSD$";
15 #endif
16 
17 /* __ieee754_acosh(x)
18  * Method :
19  *	Based on
20  *		acosh(x) = log [ x + sqrt(x*x-1) ]
21  *	we have
22  *		acosh(x) := log(x)+ln2,	if x is large; else
23  *		acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
24  *		acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
25  *
26  * Special cases:
27  *	acosh(x) is NaN with signal if x<1.
28  *	acosh(NaN) is NaN without signal.
29  */
30 
31 #include "math.h"
32 #include "math_private.h"
33 
34 static const double
35 one	= 1.0,
36 ln2	= 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
37 
38 double
39 __ieee754_acosh(double x)
40 {
41 	double t;
42 	int32_t hx;
43 	u_int32_t lx;
44 	EXTRACT_WORDS(hx,lx,x);
45 	if(hx<0x3ff00000) {		/* x < 1 */
46 	    return (x-x)/(x-x);
47 	} else if(hx >=0x41b00000) {	/* x > 2**28 */
48 	    if(hx >=0x7ff00000) {	/* x is inf of NaN */
49 	        return x+x;
50 	    } else
51 		return __ieee754_log(x)+ln2;	/* acosh(huge)=log(2x) */
52 	} else if(((hx-0x3ff00000)|lx)==0) {
53 	    return 0.0;			/* acosh(1) = 0 */
54 	} else if (hx > 0x40000000) {	/* 2**28 > x > 2 */
55 	    t=x*x;
56 	    return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one)));
57 	} else {			/* 1<x<2 */
58 	    t = x-one;
59 	    return log1p(t+__ieee754_sqrt(2.0*t+t*t));
60 	}
61 }
62