1 /* @(#)s_asinh.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 #include <sys/cdefs.h>
14 __FBSDID("$FreeBSD$");
15
16 /* asinh(x)
17 * Method :
18 * Based on
19 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
20 * we have
21 * asinh(x) := x if 1+x*x=1,
22 * := sign(x)*(log(x)+ln2)) for large |x|, else
23 * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
24 * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
25 */
26
27 #include <float.h>
28
29 #include "math.h"
30 #include "math_private.h"
31
32 static const double
33 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
34 ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
35 huge= 1.00000000000000000000e+300;
36
37 double
asinh(double x)38 asinh(double x)
39 {
40 double t,w;
41 int32_t hx,ix;
42 GET_HIGH_WORD(hx,x);
43 ix = hx&0x7fffffff;
44 if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */
45 if(ix< 0x3e300000) { /* |x|<2**-28 */
46 if(huge+x>one) return x; /* return x inexact except 0 */
47 }
48 if(ix>0x41b00000) { /* |x| > 2**28 */
49 w = __ieee754_log(fabs(x))+ln2;
50 } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
51 t = fabs(x);
52 w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t));
53 } else { /* 2.0 > |x| > 2**-28 */
54 t = x*x;
55 w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));
56 }
57 if(hx>0) return w; else return -w;
58 }
59
60 #if LDBL_MANT_DIG == 53
61 __weak_reference(asinh, asinhl);
62 #endif
63