asinh.c

/*
 *                               POK header
 * 
 * The following file is a part of the POK project. Any modification should
 * made according to the POK licence. You CANNOT use this file or a part of
 * this file is this part of a file for your own project
 *
 * For more information on the POK licence, please see our LICENCE FILE
 *
 * Please follow the coding guidelines described in doc/CODING_GUIDELINES
 *
 *                                      Copyright (c) 2007-2009 POK team 
 *
 * Created by julien on Fri Jan 30 14:41:34 2009 
 */

/* @(#)s_asinh.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, 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)))
 */

#ifdef POK_NEEDS_LIBMATH

#include <types.h>
#include <libm.h>
#include "math_private.h"

static const double
one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
huge=  1.00000000000000000000e+300;

double
asinh(double x)
{
        double t,w;
        int32_t hx,ix;
        GET_HIGH_WORD(hx,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/(__ieee754_sqrt(x*x+one)+t));
        } else {                /* 2.0 > |x| > 2**-28 */
            t = x*x;
            w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));
        }
        if(hx>0) return w; else return -w;
}

#endif