| /* 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; |
| } |
| } |