xref: /third_party/FreeBSD/lib/msun/src/e_acoshl.c (revision f9f848fa) 
1/* from: FreeBSD: head/lib/msun/src/e_acosh.c 176451 2008-02-22 02:30:36Z das */
2
3/* @(#)e_acosh.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/*
18 * See e_acosh.c for complete comments.
19 *
20 * Converted to long double by David Schultz <das@FreeBSD.ORG> and
21 * Bruce D. Evans.
22 */
23
24#include <float.h>
25#ifdef __i386__
26#include <ieeefp.h>
27#endif
28
29#include "fpmath.h"
30#include "math.h"
31#include "math_private.h"
32
33/* EXP_LARGE is the threshold above which we use acosh(x) ~= log(2x). */
34#if LDBL_MANT_DIG == 64
35#define	EXP_LARGE	34
36#elif LDBL_MANT_DIG == 113
37#define	EXP_LARGE	58
38#else
39#error "Unsupported long double format"
40#endif
41
42#if LDBL_MAX_EXP != 0x4000
43/* We also require the usual expsign encoding. */
44#error "Unsupported long double format"
45#endif
46
47#define	BIAS	(LDBL_MAX_EXP - 1)
48
49static const double
50one	= 1.0;
51
52#if LDBL_MANT_DIG == 64
53static const union IEEEl2bits
54u_ln2 =  LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L);
55#define	ln2	u_ln2.e
56#elif LDBL_MANT_DIG == 113
57static const long double
58ln2 =  6.93147180559945309417232121458176568e-1L;	/* 0x162e42fefa39ef35793c7673007e6.0p-113 */
59#else
60#error "Unsupported long double format"
61#endif
62
63long double
64acoshl(long double x)
65{
66	long double t;
67	int16_t hx;
68
69	ENTERI();
70	GET_LDBL_EXPSIGN(hx, x);
71	if (hx < 0x3fff) {		/* x < 1, or misnormal */
72	    RETURNI((x-x)/(x-x));
73	} else if (hx >= BIAS + EXP_LARGE) { /* x >= LARGE */
74	    if (hx >= 0x7fff) {		/* x is inf, NaN or misnormal */
75	        RETURNI(x+x);
76	    } else
77		RETURNI(logl(x)+ln2);	/* acosh(huge)=log(2x), or misnormal */
78	} else if (hx == 0x3fff && x == 1) {
79	    RETURNI(0.0);		/* acosh(1) = 0 */
80	} else if (hx >= 0x4000) {	/* LARGE > x >= 2, or misnormal */
81	    t=x*x;
82	    RETURNI(logl(2.0*x-one/(x+sqrtl(t-one))));
83	} else {			/* 1<x<2 */
84	    t = x-one;
85	    RETURNI(log1pl(t+sqrtl(2.0*t+t*t)));
86	}
87}
88