// Copyright (C) 2026 Kiyotsugu Arai
// SPDX-License-Identifier: LGPL-3.0-or-later

// RationalConstants.hpp
// Rational-valued constants: Bernoulli numbers, Stirling coefficients
//

#ifndef SANGI_RATIONAL_CONSTANTS_HPP
#define SANGI_RATIONAL_CONSTANTS_HPP

#include <math/core/mp/Rational/RationalBase.hpp>

namespace sangi {

    /**
     * @brief Compute the Bernoulli number B(n)
     *
     * Standard recurrence: B(n) = -1/(n+1) * sum C(n+1,k) * B(k).
     * B(0) = 1, B(1) = -1/2, B(odd > 1) = 0.
     * Previously computed values are kept in a static cache (thread-safe).
     *
     * @param n index of the Bernoulli number (n >= 0)
     * @return B(n) as a Rational
     */
    [[nodiscard]] Rational bernoulli(int n);

    /**
     * @brief Compute the Stirling coefficient c[k]
     *
     * Coefficient in Stirling's approximation
     *   n! ~ sqrt(2*pi*n) * (n/e)^n * (1 + c[1]/n + c[2]/n^2 + ...).
     * c[0] = 1. Computed via a recurrence involving Bernoulli numbers.
     * Previously computed values are kept in a static cache (thread-safe).
     *
     * Sources:
     *   "Concerning Two Series for the Gamma Function" p618
     *   "A New Derivation of Stirling's Approximation to n!" p828
     *
     * @param k coefficient index (k >= 0)
     * @return c[k] as a Rational
     */
    [[nodiscard]] Rational stirlingCoefficient(int k);

} // namespace sangi

#endif // SANGI_RATIONAL_CONSTANTS_HPP