xref: /third_party/FreeBSD/lib/msun/src/s_asinhl.c (revision f9f848fa) 
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/*
17 * See s_asinh.c for complete comments.
18 *
19 * Converted to long double by David Schultz <das@FreeBSD.ORG> and
20 * Bruce D. Evans.
21 */
22
23#include <float.h>
24#ifdef __i386__
25#include <ieeefp.h>
26#endif
27
28#include "fpmath.h"
29#include "math.h"
30#include "math_private.h"
31
32/* EXP_LARGE is the threshold above which we use asinh(x) ~= log(2x). */
33/* EXP_TINY is the threshold below which we use asinh(x) ~= x. */
34#if LDBL_MANT_DIG == 64
35#define	EXP_LARGE	34
36#define	EXP_TINY	-34
37#elif LDBL_MANT_DIG == 113
38#define	EXP_LARGE	58
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
51static const double
52one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
53huge=  1.00000000000000000000e+300;
54
55#if LDBL_MANT_DIG == 64
56static const union IEEEl2bits
57u_ln2 =  LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L);
58#define	ln2	u_ln2.e
59#elif LDBL_MANT_DIG == 113
60static const long double
61ln2 =  6.93147180559945309417232121458176568e-1L;	/* 0x162e42fefa39ef35793c7673007e6.0p-113 */
62#else
63#error "Unsupported long double format"
64#endif
65
66long double
67asinhl(long double x)
68{
69	long double t, w;
70	uint16_t hx, ix;
71
72	ENTERI();
73	GET_LDBL_EXPSIGN(hx, x);
74	ix = hx & 0x7fff;
75	if (ix >= 0x7fff) RETURNI(x+x);	/* x is inf, NaN or misnormal */
76	if (ix < BIAS + EXP_TINY) {	/* |x| < TINY, or misnormal */
77	    if (huge + x > one) RETURNI(x);	/* return x inexact except 0 */
78	}
79	if (ix >= BIAS + EXP_LARGE) {	/* |x| >= LARGE, or misnormal */
80	    w = logl(fabsl(x))+ln2;
81	} else if (ix >= 0x4000) {	/* LARGE > |x| >= 2.0, or misnormal */
82	    t = fabsl(x);
83	    w = logl(2.0*t+one/(sqrtl(x*x+one)+t));
84	} else {		/* 2.0 > |x| >= TINY, or misnormal */
85	    t = x*x;
86	    w =log1pl(fabsl(x)+t/(one+sqrtl(one+t)));
87	}
88	RETURNI((hx & 0x8000) == 0 ? w : -w);
89}
90