1 /* origin: FreeBSD /usr/src/lib/msun/src/s_asinh.c */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
10 * ====================================================
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)))
26 ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
27 huge= 1.00000000000000000000e+300;
29 double asinh(double x)
36 if (ix >= 0x7ff00000) /* x is inf or NaN */
38 if (ix < 0x3e300000) { /* |x| < 2**-28 */
39 /* return x inexact except 0 */
43 if (ix > 0x41b00000) { /* |x| > 2**28 */
44 w = log(fabs(x)) + ln2;
45 } else if (ix > 0x40000000) { /* 2**28 > |x| > 2.0 */
47 w = log(2.0*t + 1.0/(sqrt(x*x+1.0)+t));
48 } else { /* 2.0 > |x| > 2**-28 */
50 w =log1p(fabs(x) + t/(1.0+sqrt(1.0+t)));