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 __FBSDID("$FreeBSD$");
18
19 /*
20 * See e_acosh.c for complete comments.
21 *
22 * Converted to long double by David Schultz <das@FreeBSD.ORG> and
23 * Bruce D. Evans.
24 */
25
26 #include <float.h>
27 #ifdef __i386__
28 #include <ieeefp.h>
29 #endif
30
31 #include "fpmath.h"
32 #include "math.h"
33 #include "math_private.h"
34
35 /* EXP_LARGE is the threshold above which we use acosh(x) ~= log(2x). */
36 #if LDBL_MANT_DIG == 64
37 #define EXP_LARGE 34
38 #elif LDBL_MANT_DIG == 113
39 #define EXP_LARGE 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 = 1.0;
53
54 #if LDBL_MANT_DIG == 64
55 static const union IEEEl2bits
56 u_ln2 = LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L);
57 #define ln2 u_ln2.e
58 #elif LDBL_MANT_DIG == 113
59 static const long double
60 ln2 = 6.93147180559945309417232121458176568e-1L; /* 0x162e42fefa39ef35793c7673007e6.0p-113 */
61 #else
62 #error "Unsupported long double format"
63 #endif
64
65 long double
acoshl(long double x)66 acoshl(long double x)
67 {
68 long double t;
69 int16_t hx;
70
71 ENTERI();
72 GET_LDBL_EXPSIGN(hx, x);
73 if (hx < 0x3fff) { /* x < 1, or misnormal */
74 RETURNI((x-x)/(x-x));
75 } else if (hx >= BIAS + EXP_LARGE) { /* x >= LARGE */
76 if (hx >= 0x7fff) { /* x is inf, NaN or misnormal */
77 RETURNI(x+x);
78 } else
79 RETURNI(logl(x)+ln2); /* acosh(huge)=log(2x), or misnormal */
80 } else if (hx == 0x3fff && x == 1) {
81 RETURNI(0.0); /* acosh(1) = 0 */
82 } else if (hx >= 0x4000) { /* LARGE > x >= 2, or misnormal */
83 t=x*x;
84 RETURNI(logl(2.0*x-one/(x+sqrtl(t-one))));
85 } else { /* 1<x<2 */
86 t = x-one;
87 RETURNI(log1pl(t+sqrtl(2.0*t+t*t)));
88 }
89 }
90