1 /* from: FreeBSD: head/lib/msun/src/e_acosh.c 176451 2008-02-22 02:30:36Z das */
2 
3 /* @(#)s_asinh.c 5.1 93/09/24 */
4 /*
5  * ====================================================
6  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7  *
8  * Developed at SunPro, 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 #include <sys/cdefs.h>
16 __FBSDID("$FreeBSD$");
17 
18 /*
19  * See s_asinh.c for complete comments.
20  *
21  * Converted to long double by David Schultz <das@FreeBSD.ORG> and
22  * Bruce D. Evans.
23  */
24 
25 #include <float.h>
26 #ifdef __i386__
27 #include <ieeefp.h>
28 #endif
29 
30 #include "fpmath.h"
31 #include "math.h"
32 #include "math_private.h"
33 
34 /* EXP_LARGE is the threshold above which we use asinh(x) ~= log(2x). */
35 /* EXP_TINY is the threshold below which we use asinh(x) ~= x. */
36 #if LDBL_MANT_DIG == 64
37 #define	EXP_LARGE	34
38 #define	EXP_TINY	-34
39 #elif LDBL_MANT_DIG == 113
40 #define	EXP_LARGE	58
41 #define	EXP_TINY	-58
42 #else
43 #error "Unsupported long double format"
44 #endif
45 
46 #if LDBL_MAX_EXP != 0x4000
47 /* We also require the usual expsign encoding. */
48 #error "Unsupported long double format"
49 #endif
50 
51 #define	BIAS	(LDBL_MAX_EXP - 1)
52 
53 static const double
54 one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
55 huge=  1.00000000000000000000e+300;
56 
57 #if LDBL_MANT_DIG == 64
58 static const union IEEEl2bits
59 u_ln2 =  LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L);
60 #define	ln2	u_ln2.e
61 #elif LDBL_MANT_DIG == 113
62 static const long double
63 ln2 =  6.93147180559945309417232121458176568e-1L;	/* 0x162e42fefa39ef35793c7673007e6.0p-113 */
64 #else
65 #error "Unsupported long double format"
66 #endif
67 
68 long double
asinhl(long double x)69 asinhl(long double x)
70 {
71 	long double t, w;
72 	uint16_t hx, ix;
73 
74 	ENTERI();
75 	GET_LDBL_EXPSIGN(hx, x);
76 	ix = hx & 0x7fff;
77 	if (ix >= 0x7fff) RETURNI(x+x);	/* x is inf, NaN or misnormal */
78 	if (ix < BIAS + EXP_TINY) {	/* |x| < TINY, or misnormal */
79 	    if (huge + x > one) RETURNI(x);	/* return x inexact except 0 */
80 	}
81 	if (ix >= BIAS + EXP_LARGE) {	/* |x| >= LARGE, or misnormal */
82 	    w = logl(fabsl(x))+ln2;
83 	} else if (ix >= 0x4000) {	/* LARGE > |x| >= 2.0, or misnormal */
84 	    t = fabsl(x);
85 	    w = logl(2.0*t+one/(sqrtl(x*x+one)+t));
86 	} else {		/* 2.0 > |x| >= TINY, or misnormal */
87 	    t = x*x;
88 	    w =log1pl(fabsl(x)+t/(one+sqrtl(one+t)));
89 	}
90 	RETURNI((hx & 0x8000) == 0 ? w : -w);
91 }
92