xref: /freebsd/lib/msun/src/s_asinh.c (revision 06c3fb2749bda94cb5201f81ffdb8fa6c3161b2e)
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 #include <sys/cdefs.h>
13 /* asinh(x)
14  * Method :
15  *	Based on
16  *		asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
17  *	we have
18  *	asinh(x) := x  if  1+x*x=1,
19  *		 := sign(x)*(log(x)+ln2)) for large |x|, else
20  *		 := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
21  *		 := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
22  */
23 
24 #include <float.h>
25 
26 #include "math.h"
27 #include "math_private.h"
28 
29 static const double
30 one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
31 ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
32 huge=  1.00000000000000000000e+300;
33 
34 double
35 asinh(double x)
36 {
37 	double t,w;
38 	int32_t hx,ix;
39 	GET_HIGH_WORD(hx,x);
40 	ix = hx&0x7fffffff;
41 	if(ix>=0x7ff00000) return x+x;	/* x is inf or NaN */
42 	if(ix< 0x3e300000) {	/* |x|<2**-28 */
43 	    if(huge+x>one) return x;	/* return x inexact except 0 */
44 	}
45 	if(ix>0x41b00000) {	/* |x| > 2**28 */
46 	    w = log(fabs(x))+ln2;
47 	} else if (ix>0x40000000) {	/* 2**28 > |x| > 2.0 */
48 	    t = fabs(x);
49 	    w = log(2.0*t+one/(sqrt(x*x+one)+t));
50 	} else {		/* 2.0 > |x| > 2**-28 */
51 	    t = x*x;
52 	    w =log1p(fabs(x)+t/(one+sqrt(one+t)));
53 	}
54 	if(hx>0) return w; else return -w;
55 }
56 
57 #if LDBL_MANT_DIG == 53
58 __weak_reference(asinh, asinhl);
59 #endif
60