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