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Diffstat (limited to 'thirdparty/includes/GSL/gsl/gsl_sf_dilog.h')
-rw-r--r-- | thirdparty/includes/GSL/gsl/gsl_sf_dilog.h | 130 |
1 files changed, 130 insertions, 0 deletions
diff --git a/thirdparty/includes/GSL/gsl/gsl_sf_dilog.h b/thirdparty/includes/GSL/gsl/gsl_sf_dilog.h new file mode 100644 index 0000000..79b2b76 --- /dev/null +++ b/thirdparty/includes/GSL/gsl/gsl_sf_dilog.h @@ -0,0 +1,130 @@ +/* specfunc/gsl_sf_dilog.h + * + * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2004 Gerard Jungman + * + * 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. + */ + +/* Author: G. Jungman */ + +#ifndef __GSL_SF_DILOG_H__ +#define __GSL_SF_DILOG_H__ + +#include <gsl/gsl_sf_result.h> + +#undef __BEGIN_DECLS +#undef __END_DECLS +#ifdef __cplusplus +# define __BEGIN_DECLS extern "C" { +# define __END_DECLS } +#else +# define __BEGIN_DECLS /* empty */ +# define __END_DECLS /* empty */ +#endif + +__BEGIN_DECLS + + +/* Real part of DiLogarithm(x), for real argument. + * In Lewin's notation, this is Li_2(x). + * + * Li_2(x) = - Re[ Integrate[ Log[1-s] / s, {s, 0, x}] ] + * + * The function in the complex plane has a branch point + * at z = 1; we place the cut in the conventional way, + * on [1, +infty). This means that the value for real x > 1 + * is a matter of definition; however, this choice does not + * affect the real part and so is not relevant to the + * interpretation of this implemented function. + */ +int gsl_sf_dilog_e(const double x, gsl_sf_result * result); +double gsl_sf_dilog(const double x); + + +/* DiLogarithm(z), for complex argument z = x + i y. + * Computes the principal branch. + * + * Recall that the branch cut is on the real axis with x > 1. + * The imaginary part of the computed value on the cut is given + * by -Pi*log(x), which is the limiting value taken approaching + * from y < 0. This is a conventional choice, though there is no + * true standardized choice. + * + * Note that there is no canonical way to lift the defining + * contour to the full Riemann surface because of the appearance + * of a "hidden branch point" at z = 0 on non-principal sheets. + * Experts will know the simple algebraic prescription for + * obtaining the sheet they want; non-experts will not want + * to know anything about it. This is why GSL chooses to compute + * only on the principal branch. + */ +int +gsl_sf_complex_dilog_xy_e( + const double x, + const double y, + gsl_sf_result * result_re, + gsl_sf_result * result_im + ); + + + +/* DiLogarithm(z), for complex argument z = r Exp[i theta]. + * Computes the principal branch, thereby assuming an + * implicit reduction of theta to the range (-2 pi, 2 pi). + * + * If theta is identically zero, the imaginary part is computed + * as if approaching from y > 0. For other values of theta no + * special consideration is given, since it is assumed that + * no other machine representations of multiples of pi will + * produce y = 0 precisely. This assumption depends on some + * subtle properties of the machine arithmetic, such as + * correct rounding and monotonicity of the underlying + * implementation of sin() and cos(). + * + * This function is ok, but the interface is confusing since + * it makes it appear that the branch structure is resolved. + * Furthermore the handling of values close to the branch + * cut is subtle. Perhap this interface should be deprecated. + */ +int +gsl_sf_complex_dilog_e( + const double r, + const double theta, + gsl_sf_result * result_re, + gsl_sf_result * result_im + ); + + + +/* Spence integral; spence(s) := Li_2(1-s) + * + * This function has a branch point at 0; we place the + * cut on (-infty,0). Because of our choice for the value + * of Li_2(z) on the cut, spence(s) is continuous as + * s approaches the cut from above. In other words, + * we define spence(x) = spence(x + i 0+). + */ +int +gsl_sf_complex_spence_xy_e( + const double x, + const double y, + gsl_sf_result * real_sp, + gsl_sf_result * imag_sp + ); + + +__END_DECLS + +#endif /* __GSL_SF_DILOG_H__ */ |