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