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/* sys/invhyp.c
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*
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* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Brian Gough
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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#include <config.h>
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#include <math.h>
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#include <gsl/gsl_math.h>
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#include <gsl/gsl_machine.h>
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double
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gsl_acosh (const double x)
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{
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if (x > 1.0 / GSL_SQRT_DBL_EPSILON)
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{
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return log (x) + M_LN2;
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}
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else if (x > 2)
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{
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return log (2 * x - 1 / (sqrt (x * x - 1) + x));
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}
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else if (x > 1)
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{
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double t = x - 1;
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return log1p (t + sqrt (2 * t + t * t));
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}
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else if (x == 1)
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{
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return 0;
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}
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else
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{
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return GSL_NAN;
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}
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}
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double
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gsl_asinh (const double x)
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{
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double a = fabs (x);
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double s = (x < 0) ? -1 : 1;
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if (a > 1 / GSL_SQRT_DBL_EPSILON)
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{
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return s * (log (a) + M_LN2);
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}
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else if (a > 2)
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{
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return s * log (2 * a + 1 / (a + sqrt (a * a + 1)));
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}
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else if (a > GSL_SQRT_DBL_EPSILON)
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{
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double a2 = a * a;
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return s * log1p (a + a2 / (1 + sqrt (1 + a2)));
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}
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else
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{
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return x;
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}
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}
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double
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gsl_atanh (const double x)
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{
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double a = fabs (x);
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double s = (x < 0) ? -1 : 1;
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if (a > 1)
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{
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return GSL_NAN;
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}
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else if (a == 1)
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{
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return (x < 0) ? GSL_NEGINF : GSL_POSINF;
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}
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else if (a >= 0.5)
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{
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return s * 0.5 * log1p (2 * a / (1 - a));
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}
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else if (a > GSL_DBL_EPSILON)
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{
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return s * 0.5 * log1p (2 * a + 2 * a * a / (1 - a));
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}
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else
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{
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return x;
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}
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}
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