xref: /freebsd/lib/msun/src/s_asinhl.c (revision 7899f917b1c0ea178f1d2be0cfb452086d079d23)
1 /* from: FreeBSD: head/lib/msun/src/e_acosh.c 176451 2008-02-22 02:30:36Z das */
2 
3 /*
4  * ====================================================
5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6  *
7  * Developed at SunPro, a Sun Microsystems, Inc. business.
8  * Permission to use, copy, modify, and distribute this
9  * software is freely granted, provided that this notice
10  * is preserved.
11  * ====================================================
12  */
13 
14 /*
15  * See s_asinh.c for complete comments.
16  *
17  * Converted to long double by David Schultz <das@FreeBSD.ORG> and
18  * Bruce D. Evans.
19  */
20 
21 #include <float.h>
22 #ifdef __i386__
23 #include <ieeefp.h>
24 #endif
25 
26 #include "fpmath.h"
27 #include "math.h"
28 #include "math_private.h"
29 
30 /* EXP_LARGE is the threshold above which we use asinh(x) ~= log(2x). */
31 /* EXP_TINY is the threshold below which we use asinh(x) ~= x. */
32 #if LDBL_MANT_DIG == 64
33 #define	EXP_LARGE	34
34 #define	EXP_TINY	-34
35 #elif LDBL_MANT_DIG == 113
36 #define	EXP_LARGE	58
37 #define	EXP_TINY	-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 
49 static const double
50 one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
51 huge=  1.00000000000000000000e+300;
52 
53 #if LDBL_MANT_DIG == 64
54 static const union IEEEl2bits
55 u_ln2 =  LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L);
56 #define	ln2	u_ln2.e
57 #elif LDBL_MANT_DIG == 113
58 static const long double
59 ln2 =  6.93147180559945309417232121458176568e-1L;	/* 0x162e42fefa39ef35793c7673007e6.0p-113 */
60 #else
61 #error "Unsupported long double format"
62 #endif
63 
64 long double
65 asinhl(long double x)
66 {
67 	long double t, w;
68 	uint16_t hx, ix;
69 
70 	ENTERI();
71 	GET_LDBL_EXPSIGN(hx, x);
72 	ix = hx & 0x7fff;
73 	if (ix >= 0x7fff) RETURNI(x+x);	/* x is inf, NaN or misnormal */
74 	if (ix < BIAS + EXP_TINY) {	/* |x| < TINY, or misnormal */
75 	    if (huge + x > one) RETURNI(x);	/* return x inexact except 0 */
76 	}
77 	if (ix >= BIAS + EXP_LARGE) {	/* |x| >= LARGE, or misnormal */
78 	    w = logl(fabsl(x))+ln2;
79 	} else if (ix >= 0x4000) {	/* LARGE > |x| >= 2.0, or misnormal */
80 	    t = fabsl(x);
81 	    w = logl(2.0*t+one/(sqrtl(x*x+one)+t));
82 	} else {		/* 2.0 > |x| >= TINY, or misnormal */
83 	    t = x*x;
84 	    w =log1pl(fabsl(x)+t/(one+sqrtl(one+t)));
85 	}
86 	RETURNI((hx & 0x8000) == 0 ? w : -w);
87 }
88