1
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunSoft, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 *
12 */
13
14 /* acosh(x)
15 * Method :
16 * Based on
17 * acosh(x) = log [ x + sqrt(x*x-1) ]
18 * we have
19 * acosh(x) := log(x)+ln2, if x is large; else
20 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
21 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
22 *
23 * Special cases:
24 * acosh(x) is NaN with signal if x<1.
25 * acosh(NaN) is NaN without signal.
26 */
27
28 #include <float.h>
29
30 #include "math.h"
31 #include "math_private.h"
32
33 static const double
34 one = 1.0,
35 ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
36
37 double
acosh(double x)38 acosh(double x)
39 {
40 double t;
41 int32_t hx;
42 u_int32_t lx;
43 EXTRACT_WORDS(hx,lx,x);
44 if(hx<0x3ff00000) { /* x < 1 */
45 return (x-x)/(x-x);
46 } else if(hx >=0x41b00000) { /* x > 2**28 */
47 if(hx >=0x7ff00000) { /* x is inf of NaN */
48 return x+x;
49 } else
50 return log(x)+ln2; /* acosh(huge)=log(2x) */
51 } else if(((hx-0x3ff00000)|lx)==0) {
52 return 0.0; /* acosh(1) = 0 */
53 } else if (hx > 0x40000000) { /* 2**28 > x > 2 */
54 t=x*x;
55 return log(2.0*x-one/(x+sqrt(t-one)));
56 } else { /* 1<x<2 */
57 t = x-one;
58 return log1p(t+sqrt(2.0*t+t*t));
59 }
60 }
61
62 #if LDBL_MANT_DIG == 53
63 __weak_reference(acosh, acoshl);
64 #endif
65