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 /* asinh(x)
13 * Method :
14 * Based on
15 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
16 * we have
17 * asinh(x) := x if 1+x*x=1,
18 * := sign(x)*(log(x)+ln2)) for large |x|, else
19 * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
20 * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
21 */
22
23 #include <float.h>
24
25 #include "math.h"
26 #include "math_private.h"
27
28 static const double
29 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
30 ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
31 huge= 1.00000000000000000000e+300;
32
33 double
asinh(double x)34 asinh(double x)
35 {
36 double t,w;
37 int32_t hx,ix;
38 GET_HIGH_WORD(hx,x);
39 ix = hx&0x7fffffff;
40 if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */
41 if(ix< 0x3e300000) { /* |x|<2**-28 */
42 if(huge+x>one) return x; /* return x inexact except 0 */
43 }
44 if(ix>0x41b00000) { /* |x| > 2**28 */
45 w = log(fabs(x))+ln2;
46 } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
47 t = fabs(x);
48 w = log(2.0*t+one/(sqrt(x*x+one)+t));
49 } else { /* 2.0 > |x| > 2**-28 */
50 t = x*x;
51 w =log1p(fabs(x)+t/(one+sqrt(one+t)));
52 }
53 if(hx>0) return w; else return -w;
54 }
55
56 #if LDBL_MANT_DIG == 53
57 __weak_reference(asinh, asinhl);
58 #endif
59