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- /* sys/invhyp.c
- *
- * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 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 3 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 "gsl__config.h"
- #include <math.h>
- #include "gsl_math.h"
- #include "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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