* of special functions or implement the interface to the bignum package. */
/*
- * GiNaC Copyright (C) 1999-2019 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2023 Johannes Gutenberg University Mainz, Germany
*
* 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
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
-#ifdef HAVE_CONFIG_H
-#include "config.h"
-#endif
-
#include "numeric.h"
#include "ex.h"
#include "operators.h"
/**
* @brief Check if CLN integer can be converted into int
*
- * @sa http://www.ginac.de/pipermail/cln-list/2006-October/000248.html
+ * @sa https://www.ginac.de/pipermail/cln-list/2006-October/000248.html
*/
template<>
inline bool coerce<int, cln::cl_I>(int& dst, const cln::cl_I& arg)
/** The Binomial coefficients. It computes the binomial coefficients. For
* integer n and k and positive n this is the number of ways of choosing k
- * objects from n distinct objects. If n is negative, the formula
- * binomial(n,k) == (-1)^k*binomial(k-n-1,k) is used to compute the result. */
+ * objects from n distinct objects. If n is a negative integer, the formula
+ * binomial(n,k) == (-1)^k*binomial(k-n-1,k) (if k>=0)
+ * binomial(n,k) == (-1)^(n-k)*binomial(-k-1,n-k) (otherwise)
+ * is used to compute the result. */
const numeric binomial(const numeric &n, const numeric &k)
{
if (n.is_integer() && k.is_integer()) {
else
return *_num0_p;
} else {
- return _num_1_p->power(k)*binomial(k-n-(*_num1_p),k);
+ if (k.is_nonneg_integer())
+ return _num_1_p->power(k)*binomial(k-n-(*_num1_p), k);
+ else
+ return _num_1_p->power(n-k)*binomial(-k-(*_num1_p), n-k);
}
}