1 /*
2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4 *
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
8 * is preserved.
9 * ====================================================
10 */
11
12 /* __ieee754_acosh(x)
13 * Method :
14 * Based on
15 * acosh(x) = log [ x + sqrt(x*x-1) ]
16 * we have
17 * acosh(x) := log(x)+ln2, if x is large; else
18 * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
19 * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
20 *
21 * Special cases:
22 * acosh(x) is NaN with signal if x<1.
23 * acosh(NaN) is NaN without signal.
24 */
25
26 #include "math.h"
27 #include "math_private.h"
28
29 static const double
30 one = 1.0,
31 ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
32
__ieee754_acosh(double x)33 double __ieee754_acosh(double x)
34 {
35 double t;
36 int32_t hx;
37 u_int32_t lx;
38 EXTRACT_WORDS(hx,lx,x);
39 if(hx<0x3ff00000) { /* x < 1 */
40 return (x-x)/(x-x);
41 } else if(hx >=0x41b00000) { /* x > 2**28 */
42 if(hx >=0x7ff00000) { /* x is inf of NaN */
43 return x+x;
44 } else
45 return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */
46 } else if(((hx-0x3ff00000)|lx)==0) {
47 return 0.0; /* acosh(1) = 0 */
48 } else if (hx > 0x40000000) { /* 2**28 > x > 2 */
49 t=x*x;
50 return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one)));
51 } else { /* 1<x<2 */
52 t = x-one;
53 return log1p(t+sqrt(2.0*t+t*t));
54 }
55 }
56
57 /*
58 * wrapper acosh(x)
59 */
60 #ifndef _IEEE_LIBM
acosh(double x)61 double acosh(double x)
62 {
63 double z = __ieee754_acosh(x);
64 if (_LIB_VERSION == _IEEE_ || isnan(x))
65 return z;
66 if (x < 1.0)
67 return __kernel_standard(x, x, 29); /* acosh(x<1) */
68 return z;
69 }
70 #else
71 strong_alias(__ieee754_acosh, acosh)
72 #endif
73 libm_hidden_def(acosh)
74