1 /* @(#)e_acosh.c 5.1 93/09/24 */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, 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 /* acosh(x)
14 * Method :
15 * Based on
16 * acosh(x) = log [ x + sqrt(x*x-1) ]
17 * we have
18 * acosh(x) := log(x)+ln2, if x is large; else
19 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
20 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
21 *
22 * Special cases:
23 * acosh(x) is NaN with signal if x<1.
24 * acosh(NaN) is NaN without signal.
25 */
26
27 #include <float.h>
28 #include <math.h>
29
30 #include "math_private.h"
31
32 static const double
33 one = 1.0,
34 ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
35
36 double
acosh(double x)37 acosh(double x)
38 {
39 double t;
40 int32_t hx;
41 u_int32_t lx;
42 EXTRACT_WORDS(hx,lx,x);
43 if(hx<0x3ff00000) { /* x < 1 */
44 return (x-x)/(x-x);
45 } else if(hx >=0x41b00000) { /* x > 2**28 */
46 if(hx >=0x7ff00000) { /* x is inf of NaN */
47 return x+x;
48 } else
49 return log(x)+ln2; /* acosh(huge)=log(2x) */
50 } else if(((hx-0x3ff00000)|lx)==0) {
51 return 0.0; /* acosh(1) = 0 */
52 } else if (hx > 0x40000000) { /* 2**28 > x > 2 */
53 t=x*x;
54 return log(2.0*x-one/(x+sqrt(t-one)));
55 } else { /* 1<x<2 */
56 t = x-one;
57 return log1p(t+sqrt(2.0*t+t*t));
58 }
59 }
60
61 #if LDBL_MANT_DIG == DBL_MANT_DIG
62 __strong_alias(acoshl, acosh);
63 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
64