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
53static const double
54one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
55huge=  1.00000000000000000000e+300;
56
57#if LDBL_MANT_DIG == 64
58static const union IEEEl2bits
59u_ln2 =  LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L);
60#define	ln2	u_ln2.e
61#elif LDBL_MANT_DIG == 113
62static const long double
63ln2 =  6.93147180559945309417232121458176568e-1L;	/* 0x162e42fefa39ef35793c7673007e6.0p-113 */
64#else
65#error "Unsupported long double format"
66#endif
67
68long double
69asinhl(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