1 /* from: FreeBSD: head/lib/msun/src/e_atanh.c 176451 2008-02-22 02:30:36Z das */
2 
3 /* @(#)e_atanh.c 1.3 95/01/18 */
4 /*
5  * ====================================================
6  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7  *
8  * Developed at SunSoft, a Sun Microsystems, Inc. business.
9  * Permission to use, copy, modify, and distribute this
10  * software is freely granted, provided that this notice
11  * is preserved.
12  * ====================================================
13  *
14  */
15 
16 #include <sys/cdefs.h>
17 __FBSDID("$FreeBSD$");
18 
19 /*
20  * See e_atanh.c for complete comments.
21  *
22  * Converted to long double by David Schultz <das@FreeBSD.ORG> and
23  * Bruce D. Evans.
24  */
25 
26 #include <float.h>
27 #ifdef __i386__
28 #include <ieeefp.h>
29 #endif
30 
31 #include "fpmath.h"
32 #include "math.h"
33 #include "math_private.h"
34 
35 /* EXP_TINY is the threshold below which we use atanh(x) ~= x. */
36 #if LDBL_MANT_DIG == 64
37 #define	EXP_TINY	-34
38 #elif LDBL_MANT_DIG == 113
39 #define	EXP_TINY	-58
40 #else
41 #error "Unsupported long double format"
42 #endif
43 
44 #if LDBL_MAX_EXP != 0x4000
45 /* We also require the usual expsign encoding. */
46 #error "Unsupported long double format"
47 #endif
48 
49 #define	BIAS	(LDBL_MAX_EXP - 1)
50 
51 static const double one = 1.0, huge = 1e300;
52 static const double zero = 0.0;
53 
54 long double
atanhl(long double x)55 atanhl(long double x)
56 {
57 	long double t;
58 	uint16_t hx, ix;
59 
60 	ENTERI();
61 	GET_LDBL_EXPSIGN(hx, x);
62 	ix = hx & 0x7fff;
63 	if (ix >= 0x3fff)		/* |x| >= 1, or NaN or misnormal */
64 	    RETURNI(fabsl(x) == 1 ? x / zero : (x - x) / (x - x));
65 	if (ix < BIAS + EXP_TINY && (huge + x) > zero)
66 	    RETURNI(x);			/* x is tiny */
67 	SET_LDBL_EXPSIGN(x, ix);
68 	if (ix < 0x3ffe) {		/* |x| < 0.5, or misnormal */
69 	    t = x+x;
70 	    t = 0.5*log1pl(t+t*x/(one-x));
71 	} else
72 	    t = 0.5*log1pl((x+x)/(one-x));
73 	RETURNI((hx & 0x8000) == 0 ? t : -t);
74 }
75