2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
9 * ====================================================
15 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
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)))
24 #include "math_private.h"
27 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
28 ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
29 huge= 1.00000000000000000000e+300;
31 double asinh(double x)
37 if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */
38 if(ix< 0x3e300000) { /* |x|<2**-28 */
39 if(huge+x>one) return x; /* return x inexact except 0 */
41 if(ix>0x41b00000) { /* |x| > 2**28 */
42 w = __ieee754_log(fabs(x))+ln2;
43 } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
45 w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t));
46 } else { /* 2.0 > |x| > 2**-28 */
48 w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));
50 if(hx>0) return w; else return -w;
52 libm_hidden_def(asinh)