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/* sys/invhyp.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000 Brian Gough
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
#include <config.h>
#include <math.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_machine.h>
double
gsl_acosh (const double x)
{
if (x > 1.0 / GSL_SQRT_DBL_EPSILON)
{
return log (x) + M_LN2;
}
else if (x > 2)
{
return log (2 * x - 1 / (sqrt (x * x - 1) + x));
}
else if (x > 1)
{
double t = x - 1;
return log1p (t + sqrt (2 * t + t * t));
}
else if (x == 1)
{
return 0;
}
else
{
return GSL_NAN;
}
}
double
gsl_asinh (const double x)
{
double a = fabs (x);
double s = (x < 0) ? -1 : 1;
if (a > 1 / GSL_SQRT_DBL_EPSILON)
{
return s * (log (a) + M_LN2);
}
else if (a > 2)
{
return s * log (2 * a + 1 / (a + sqrt (a * a + 1)));
}
else if (a > GSL_SQRT_DBL_EPSILON)
{
double a2 = a * a;
return s * log1p (a + a2 / (1 + sqrt (1 + a2)));
}
else
{
return x;
}
}
double
gsl_atanh (const double x)
{
double a = fabs (x);
double s = (x < 0) ? -1 : 1;
if (a > 1)
{
return GSL_NAN;
}
else if (a == 1)
{
return (x < 0) ? GSL_NEGINF : GSL_POSINF;
}
else if (a >= 0.5)
{
return s * 0.5 * log1p (2 * a / (1 - a));
}
else if (a > GSL_DBL_EPSILON)
{
return s * 0.5 * log1p (2 * a + 2 * a * a / (1 - a));
}
else
{
return x;
}
}
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