xref: /minix3/lib/libm/src/e_acosh.c (revision 2fe8fb192fe7e8720e3e7a77f928da545e872a6a)
1*2fe8fb19SBen Gras /* @(#)e_acosh.c 5.1 93/09/24 */
2*2fe8fb19SBen Gras /*
3*2fe8fb19SBen Gras  * ====================================================
4*2fe8fb19SBen Gras  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5*2fe8fb19SBen Gras  *
6*2fe8fb19SBen Gras  * Developed at SunPro, a Sun Microsystems, Inc. business.
7*2fe8fb19SBen Gras  * Permission to use, copy, modify, and distribute this
8*2fe8fb19SBen Gras  * software is freely granted, provided that this notice
9*2fe8fb19SBen Gras  * is preserved.
10*2fe8fb19SBen Gras  * ====================================================
11*2fe8fb19SBen Gras  */
12*2fe8fb19SBen Gras 
13*2fe8fb19SBen Gras #include <sys/cdefs.h>
14*2fe8fb19SBen Gras #if defined(LIBM_SCCS) && !defined(lint)
15*2fe8fb19SBen Gras __RCSID("$NetBSD: e_acosh.c,v 1.12 2002/05/26 22:01:48 wiz Exp $");
16*2fe8fb19SBen Gras #endif
17*2fe8fb19SBen Gras 
18*2fe8fb19SBen Gras /* __ieee754_acosh(x)
19*2fe8fb19SBen Gras  * Method :
20*2fe8fb19SBen Gras  *	Based on
21*2fe8fb19SBen Gras  *		acosh(x) = log [ x + sqrt(x*x-1) ]
22*2fe8fb19SBen Gras  *	we have
23*2fe8fb19SBen Gras  *		acosh(x) := log(x)+ln2,	if x is large; else
24*2fe8fb19SBen Gras  *		acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
25*2fe8fb19SBen Gras  *		acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
26*2fe8fb19SBen Gras  *
27*2fe8fb19SBen Gras  * Special cases:
28*2fe8fb19SBen Gras  *	acosh(x) is NaN with signal if x<1.
29*2fe8fb19SBen Gras  *	acosh(NaN) is NaN without signal.
30*2fe8fb19SBen Gras  */
31*2fe8fb19SBen Gras 
32*2fe8fb19SBen Gras #include "math.h"
33*2fe8fb19SBen Gras #include "math_private.h"
34*2fe8fb19SBen Gras 
35*2fe8fb19SBen Gras static const double
36*2fe8fb19SBen Gras one	= 1.0,
37*2fe8fb19SBen Gras ln2	= 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */
38*2fe8fb19SBen Gras 
39*2fe8fb19SBen Gras double
__ieee754_acosh(double x)40*2fe8fb19SBen Gras __ieee754_acosh(double x)
41*2fe8fb19SBen Gras {
42*2fe8fb19SBen Gras 	double t;
43*2fe8fb19SBen Gras 	int32_t hx;
44*2fe8fb19SBen Gras 	u_int32_t lx;
45*2fe8fb19SBen Gras 	EXTRACT_WORDS(hx,lx,x);
46*2fe8fb19SBen Gras 	if(hx<0x3ff00000) {		/* x < 1 */
47*2fe8fb19SBen Gras 	    return (x-x)/(x-x);
48*2fe8fb19SBen Gras 	} else if(hx >=0x41b00000) {	/* x > 2**28 */
49*2fe8fb19SBen Gras 	    if(hx >=0x7ff00000) {	/* x is inf of NaN */
50*2fe8fb19SBen Gras 	        return x+x;
51*2fe8fb19SBen Gras 	    } else
52*2fe8fb19SBen Gras 		return __ieee754_log(x)+ln2;	/* acosh(huge)=log(2x) */
53*2fe8fb19SBen Gras 	} else if(((hx-0x3ff00000)|lx)==0) {
54*2fe8fb19SBen Gras 	    return 0.0;			/* acosh(1) = 0 */
55*2fe8fb19SBen Gras 	} else if (hx > 0x40000000) {	/* 2**28 > x > 2 */
56*2fe8fb19SBen Gras 	    t=x*x;
57*2fe8fb19SBen Gras 	    return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one)));
58*2fe8fb19SBen Gras 	} else {			/* 1<x<2 */
59*2fe8fb19SBen Gras 	    t = x-one;
60*2fe8fb19SBen Gras 	    return log1p(t+sqrt(2.0*t+t*t));
61*2fe8fb19SBen Gras 	}
62*2fe8fb19SBen Gras }
63