#pragma once
// Copyright (c) 2024-2026 Tarik Moussa.
// SPDX-License-Identifier: MIT

// gauss_legendre.hpp
//
// 10-point Gauss-Legendre quadrature nodes and weights on [-1,1].
//
// Previously duplicated verbatim in:
//   euclidean_functional.hpp, spherical_functional.hpp,
//   inversive_distance_functional.hpp  (MINOR-3 fix)
//
// Usage (integration over [0,1] via change of variables t=(1+s)/2, w=w_GL/2):
//
//   const auto* s = conformallab::gl10_nodes();
//   const auto* w = conformallab::gl10_weights();
//   for (int k = 0; k < 10; ++k) {
//       double t  = (1.0 + s[k]) * 0.5;
//       double wt = w[k] * 0.5;
//       E += wt * dot(G(t*x), x);
//   }

namespace conformallab {

/// 10-point Gauss-Legendre nodes on [−1, 1].
inline const double* gl10_nodes() noexcept {
    static constexpr double s[10] = {
        -0.9739065285171717,  -0.8650633666889845,
        -0.6794095682990244,  -0.4333953941292472,
        -0.1488743389816312,   0.1488743389816312,
         0.4333953941292472,   0.6794095682990244,
         0.8650633666889845,   0.9739065285171717
    };
    return s;
}

/// 10-point Gauss-Legendre weights on [−1, 1].
inline const double* gl10_weights() noexcept {
    static constexpr double w[10] = {
        0.0666713443086881,  0.1494513491505806,
        0.2190863625159820,  0.2692667193099963,
        0.2955242247147529,  0.2955242247147529,
        0.2692667193099963,  0.2190863625159820,
        0.1494513491505806,  0.0666713443086881
    };
    return w;
}

} // namespace conformallab