1
2 /* @(#)e_acosh.c 1.3 95/01/18 */
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 #include <sys/cdefs.h>
16 __FBSDID("$FreeBSD$");
17
18 /* __ieee754_acosh(x)
19 * Method :
20 * Based on
21 * acosh(x) = log [ x + sqrt(x*x-1) ]
22 * we have
23 * acosh(x) := log(x)+ln2, if x is large; else
24 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
25 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
26 *
27 * Special cases:
28 * acosh(x) is NaN with signal if x<1.
29 * acosh(NaN) is NaN without signal.
30 */
31
32 #include <float.h>
33
34 #include "math.h"
35 #include "math_private.h"
36
37 static const double
38 one = 1.0,
39 ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
40
41 double
__ieee754_acosh(double x)42 __ieee754_acosh(double x)
43 {
44 double t;
45 int32_t hx;
46 u_int32_t lx;
47 EXTRACT_WORDS(hx,lx,x);
48 if(hx<0x3ff00000) { /* x < 1 */
49 return (x-x)/(x-x);
50 } else if(hx >=0x41b00000) { /* x > 2**28 */
51 if(hx >=0x7ff00000) { /* x is inf of NaN */
52 return x+x;
53 } else
54 return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */
55 } else if(((hx-0x3ff00000)|lx)==0) {
56 return 0.0; /* acosh(1) = 0 */
57 } else if (hx > 0x40000000) { /* 2**28 > x > 2 */
58 t=x*x;
59 return __ieee754_log(2.0*x-one/(x+sqrt(t-one)));
60 } else { /* 1<x<2 */
61 t = x-one;
62 return log1p(t+sqrt(2.0*t+t*t));
63 }
64 }
65
66 #if LDBL_MANT_DIG == 53
67 __weak_reference(acosh, acoshl);
68 #endif
69