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 #include <sys/cdefs.h>
15
16 #include "namespace.h"
17
18 #include <float.h>
19 #include <machine/ieee.h>
20
21 #include "math.h"
22 #include "math_private.h"
23
24 __weak_alias(asinhl, _asinhl)
25
26 #ifdef __HAVE_LONG_DOUBLE
27
28 /*
29 * See s_asinh.c for complete comments.
30 *
31 * Converted to long double by David Schultz <das@FreeBSD.ORG> and
32 * Bruce D. Evans.
33 */
34
35 /* EXP_LARGE is the threshold above which we use asinh(x) ~= log(2x). */
36 /* EXP_TINY is the threshold below which we use asinh(x) ~= x. */
37 #if LDBL_MANT_DIG == 64
38 #define EXP_LARGE 34
39 #define EXP_TINY -34
40 #elif LDBL_MANT_DIG == 113
41 #define EXP_LARGE 58
42 #define EXP_TINY -58
43 #else
44 #error "Unsupported long double format"
45 #endif
46
47 #if LDBL_MAX_EXP != 0x4000
48 /* We also require the usual expsign encoding. */
49 #error "Unsupported long double format"
50 #endif
51
52 #define BIAS (LDBL_MAX_EXP - 1)
53
54 static const double
55 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
56 huge= 1.00000000000000000000e+300;
57
58 #if LDBL_MANT_DIG == 64
59 static const union ieee_ext_u
60 u_ln2 = LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L);
61 #define ln2 u_ln2.extu_ld
62 #elif LDBL_MANT_DIG == 113
63 static const long double
64 ln2 = 6.93147180559945309417232121458176568e-1L; /* 0x162e42fefa39ef35793c7673007e6.0p-113 */
65 #else
66 #error "Unsupported long double format"
67 #endif
68
69 long double
asinhl(long double x)70 asinhl(long double x)
71 {
72 long double t, w;
73 uint16_t hx, ix;
74
75 ENTERI();
76 GET_LDBL_EXPSIGN(hx, x);
77 ix = hx & 0x7fff;
78 if (ix >= 0x7fff) RETURNI(x+x); /* x is inf, NaN or misnormal */
79 if (ix < BIAS + EXP_TINY) { /* |x| < TINY, or misnormal */
80 if (huge + x > one) RETURNI(x); /* return x inexact except 0 */
81 }
82 if (ix >= BIAS + EXP_LARGE) { /* |x| >= LARGE, or misnormal */
83 w = logl(fabsl(x))+ln2;
84 } else if (ix >= 0x4000) { /* LARGE > |x| >= 2.0, or misnormal */
85 t = fabsl(x);
86 w = logl(2.0*t+one/(sqrtl(x*x+one)+t));
87 } else { /* 2.0 > |x| >= TINY, or misnormal */
88 t = x*x;
89 w =log1pl(fabsl(x)+t/(one+sqrtl(one+t)));
90 }
91 RETURNI((hx & 0x8000) == 0 ? w : -w);
92 }
93 #else
94 long double
95 asinhl(long double x)
96 {
97 return asinh(x);
98 }
99 #endif
100