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 __FBSDID("$FreeBSD$");
18 
19 /*
20  * See e_acosh.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_LARGE is the threshold above which we use acosh(x) ~= log(2x). */
36 #if LDBL_MANT_DIG == 64
37 #define	EXP_LARGE	34
38 #elif LDBL_MANT_DIG == 113
39 #define	EXP_LARGE	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
52 one	= 1.0;
53 
54 #if LDBL_MANT_DIG == 64
55 static const union IEEEl2bits
56 u_ln2 =  LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L);
57 #define	ln2	u_ln2.e
58 #elif LDBL_MANT_DIG == 113
59 static const long double
60 ln2 =  6.93147180559945309417232121458176568e-1L;	/* 0x162e42fefa39ef35793c7673007e6.0p-113 */
61 #else
62 #error "Unsupported long double format"
63 #endif
64 
65 long double
acoshl(long double x)66 acoshl(long double x)
67 {
68 	long double t;
69 	int16_t hx;
70 
71 	ENTERI();
72 	GET_LDBL_EXPSIGN(hx, x);
73 	if (hx < 0x3fff) {		/* x < 1, or misnormal */
74 	    RETURNI((x-x)/(x-x));
75 	} else if (hx >= BIAS + EXP_LARGE) { /* x >= LARGE */
76 	    if (hx >= 0x7fff) {		/* x is inf, NaN or misnormal */
77 	        RETURNI(x+x);
78 	    } else
79 		RETURNI(logl(x)+ln2);	/* acosh(huge)=log(2x), or misnormal */
80 	} else if (hx == 0x3fff && x == 1) {
81 	    RETURNI(0.0);		/* acosh(1) = 0 */
82 	} else if (hx >= 0x4000) {	/* LARGE > x >= 2, or misnormal */
83 	    t=x*x;
84 	    RETURNI(logl(2.0*x-one/(x+sqrtl(t-one))));
85 	} else {			/* 1<x<2 */
86 	    t = x-one;
87 	    RETURNI(log1pl(t+sqrtl(2.0*t+t*t)));
88 	}
89 }
90