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 SunSoft, 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 /*
16 * See e_acosh.c for complete comments.
17 *
18 * Converted to long double by David Schultz <das@FreeBSD.ORG> and
19 * Bruce D. Evans.
20 */
21
22 #include <float.h>
23 #ifdef __i386__
24 #include <ieeefp.h>
25 #endif
26
27 #include "fpmath.h"
28 #include "math.h"
29 #include "math_private.h"
30
31 /* EXP_LARGE is the threshold above which we use acosh(x) ~= log(2x). */
32 #if LDBL_MANT_DIG == 64
33 #define EXP_LARGE 34
34 #elif LDBL_MANT_DIG == 113
35 #define EXP_LARGE 58
36 #else
37 #error "Unsupported long double format"
38 #endif
39
40 #if LDBL_MAX_EXP != 0x4000
41 /* We also require the usual expsign encoding. */
42 #error "Unsupported long double format"
43 #endif
44
45 #define BIAS (LDBL_MAX_EXP - 1)
46
47 static const double
48 one = 1.0;
49
50 #if LDBL_MANT_DIG == 64
51 static const union IEEEl2bits
52 u_ln2 = LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L);
53 #define ln2 u_ln2.e
54 #elif LDBL_MANT_DIG == 113
55 static const long double
56 ln2 = 6.93147180559945309417232121458176568e-1L; /* 0x162e42fefa39ef35793c7673007e6.0p-113 */
57 #else
58 #error "Unsupported long double format"
59 #endif
60
61 long double
acoshl(long double x)62 acoshl(long double x)
63 {
64 long double t;
65 int16_t hx;
66
67 ENTERI();
68 GET_LDBL_EXPSIGN(hx, x);
69 if (hx < 0x3fff) { /* x < 1, or misnormal */
70 RETURNI((x-x)/(x-x));
71 } else if (hx >= BIAS + EXP_LARGE) { /* x >= LARGE */
72 if (hx >= 0x7fff) { /* x is inf, NaN or misnormal */
73 RETURNI(x+x);
74 } else
75 RETURNI(logl(x)+ln2); /* acosh(huge)=log(2x), or misnormal */
76 } else if (hx == 0x3fff && x == 1) {
77 RETURNI(0.0); /* acosh(1) = 0 */
78 } else if (hx >= 0x4000) { /* LARGE > x >= 2, or misnormal */
79 t=x*x;
80 RETURNI(logl(2.0*x-one/(x+sqrtl(t-one))));
81 } else { /* 1<x<2 */
82 t = x-one;
83 RETURNI(log1pl(t+sqrtl(2.0*t+t*t)));
84 }
85 }
86