DiFipp/include/math_utils.h

// Copyright (c) 2019, Vincent SAMY
// All rights reserved.

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// modification, are permitted provided that the following conditions are met:

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#pragma once
#include <type_traits>

namespace difi {

// https://stackoverflow.com/questions/44718971/calculate-binomial-coffeficient-very-reliably
template <typename T>
constexpr T Binomial(size_t n, size_t k)
{
    if (k > n)
        return T(0);
    else if (k == 0 || k == n)
        return T(1);
    else if (k == 1 || k == n - 1)
        return T(n);
    else if (2 * k < n)
        return Binomial<T>(n - 1, k - 1) * n / k;
    else
        return Binomial<T>(n - 1, k) * n / (n - k);
}

template <typename T>
constexpr T pow(T n, T k)
{
    static_assert(std::is_integral_v<T>, "For integral values only, eitherwise, use std::pow");
    if (n == 0)
        return (k == 0) ? 1 : 0;
    else if (k == 0)
        return T(1);
    else
        return n * pow(n, k - 1);
}

} // namespace difi