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/* Translated from Cython into C++ by SciPy developers in 2024.
*
* Original authors: Pauli Virtanen, Eric Moore
*/
// Binomial coefficient
#pragma once
#include "config.h"
#include "cephes/beta.h"
#include "cephes/gamma.h"
namespace xsf {
XSF_HOST_DEVICE inline double binom(double n, double k) {
double kx, nx, num, den, dk, sgn;
if (n < 0) {
nx = std::floor(n);
if (n == nx) {
// Undefined
return std::numeric_limits<double>::quiet_NaN();
}
}
kx = std::floor(k);
if (k == kx && (std::abs(n) > 1E-8 || n == 0)) {
/* Integer case: use multiplication formula for less rounding
* error for cases where the result is an integer.
*
* This cannot be used for small nonzero n due to loss of
* precision. */
nx = std::floor(n);
if (nx == n && kx > nx / 2 && nx > 0) {
// Reduce kx by symmetry
kx = nx - kx;
}
if (kx >= 0 && kx < 20) {
num = 1.0;
den = 1.0;
for (int i = 1; i < 1 + static_cast<int>(kx); i++) {
num *= i + n - kx;
den *= i;
if (std::abs(num) > 1E50) {
num /= den;
den = 1.0;
}
}
return num / den;
}
}
// general case
if (n >= 1E10 * k and k > 0) {
// avoid under/overflows intermediate results
return std::exp(-cephes::lbeta(1 + n - k, 1 + k) - std::log(n + 1));
}
if (k > 1E8 * std::abs(n)) {
// avoid loss of precision
num = cephes::Gamma(1 + n) / std::abs(k) + cephes::Gamma(1 + n) * n / (2 * k * k); // + ...
num /= M_PI * std::pow(std::abs(k), n);
if (k > 0) {
kx = std::floor(k);
if (static_cast<int>(kx) == kx) {
dk = k - kx;
sgn = (static_cast<int>(kx) % 2 == 0) ? 1 : -1;
} else {
dk = k;
sgn = 1;
}
return num * std::sin((dk - n) * M_PI) * sgn;
}
kx = std::floor(k);
if (static_cast<int>(kx) == kx) {
return 0;
}
return num * std::sin(k * M_PI);
}
return 1 / (n + 1) / cephes::beta(1 + n - k, 1 + k);
}
XSF_HOST_DEVICE inline float binom(float n, float k) {
return binom(static_cast<double>(n), static_cast<double>(k));
}
} // namespace xsf
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