1 /* @(#)s_asinh.c 5.1 93/09/24 */
2 /* $FreeBSD: head/lib/msun/src/s_asinh.c 251599 2013-06-10 06:04:58Z das $ */
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 * Developed at SunPro, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
11 * ====================================================
17 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
19 * asinh(x) := x if 1+x*x=1,
20 * := sign(x)*(log(x)+ln2)) for large |x|, else
21 * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
22 * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
28 #include "math_private.h"
31 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
32 ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
33 huge= 1.00000000000000000000e+300;
42 if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */
43 if(ix< 0x3e300000) { /* |x|<2**-28 */
44 if(huge+x>one) return x; /* return x inexact except 0 */
46 if(ix>0x41b00000) { /* |x| > 2**28 */
47 w = __ieee754_log(fabs(x))+ln2;
48 } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
50 w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t));
51 } else { /* 2.0 > |x| > 2**-28 */
53 w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));
55 if(hx>0) return w; else return -w;
58 #if LDBL_MANT_DIG == 53
59 __weak_reference(asinh, asinhl);