/* @(#)s_asinh.c 1.3 95/01/18 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunSoft, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ /* asinh(x) * Method : * Based on * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] * we have * asinh(x) := x if 1+x*x=1, * := sign(x)*(log(x)+ln2)) for large |x|, else * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) */ #include "fdlibm.h" #ifdef __STDC__ static const double #else static double #endif one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ huge= 1.00000000000000000000e+300; #ifdef __STDC__ double asinh(double x) #else double asinh(x) double x; #endif { double t,w; int hx,ix; hx = __HI(x); ix = hx&0x7fffffff; if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ if(ix< 0x3e300000) { /* |x|<2**-28 */ if(huge+x>one) return x; /* return x inexact except 0 */ } if(ix>0x41b00000) { /* |x| > 2**28 */ w = __ieee754_log(fabs(x))+ln2; } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ t = fabs(x); w = __ieee754_log(2.0*t+one/(sqrt(x*x+one)+t)); } else { /* 2.0 > |x| > 2**-28 */ t = x*x; w =log1p(fabs(x)+t/(one+sqrt(one+t))); } if(hx>0) return w; else return -w; }