1 /* from: FreeBSD: head/lib/msun/src/e_acosh.c 176451 2008-02-22 02:30:36Z das */
2
3 /* @(#)e_acosh.c 1.3 95/01/18 */
4 /*
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 *
8 * Developed at SunSoft, 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
16 #include <sys/cdefs.h>
17 /*
18 * See e_acosh.c for complete comments.
19 *
20 * Converted to long double by David Schultz <das@FreeBSD.ORG> and
21 * Bruce D. Evans.
22 */
23
24 #include <float.h>
25 #ifdef __i386__
26 #include <ieeefp.h>
27 #endif
28
29 #include "fpmath.h"
30 #include "math.h"
31 #include "math_private.h"
32
33 /* EXP_LARGE is the threshold above which we use acosh(x) ~= log(2x). */
34 #if LDBL_MANT_DIG == 64
35 #define EXP_LARGE 34
36 #elif LDBL_MANT_DIG == 113
37 #define EXP_LARGE 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 = 1.0;
51
52 #if LDBL_MANT_DIG == 64
53 static const union IEEEl2bits
54 u_ln2 = LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L);
55 #define ln2 u_ln2.e
56 #elif LDBL_MANT_DIG == 113
57 static const long double
58 ln2 = 6.93147180559945309417232121458176568e-1L; /* 0x162e42fefa39ef35793c7673007e6.0p-113 */
59 #else
60 #error "Unsupported long double format"
61 #endif
62
63 long double
acoshl(long double x)64 acoshl(long double x)
65 {
66 long double t;
67 int16_t hx;
68
69 ENTERI();
70 GET_LDBL_EXPSIGN(hx, x);
71 if (hx < 0x3fff) { /* x < 1, or misnormal */
72 RETURNI((x-x)/(x-x));
73 } else if (hx >= BIAS + EXP_LARGE) { /* x >= LARGE */
74 if (hx >= 0x7fff) { /* x is inf, NaN or misnormal */
75 RETURNI(x+x);
76 } else
77 RETURNI(logl(x)+ln2); /* acosh(huge)=log(2x), or misnormal */
78 } else if (hx == 0x3fff && x == 1) {
79 RETURNI(0.0); /* acosh(1) = 0 */
80 } else if (hx >= 0x4000) { /* LARGE > x >= 2, or misnormal */
81 t=x*x;
82 RETURNI(logl(2.0*x-one/(x+sqrtl(t-one))));
83 } else { /* 1<x<2 */
84 t = x-one;
85 RETURNI(log1pl(t+sqrtl(2.0*t+t*t)));
86 }
87 }
88