refactor IncompleteGamma class
Varun Agrawal
parent
d0b3f1dd25
commit
8201c77b30
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@ -103,154 +103,147 @@ static const long double gauss_legendre_50_weights[50] = {
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namespace internal {
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/// 50 point Gauss-Legendre quadrature
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template <typename T>
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constexpr T incomplete_gamma_quad_inp_vals(const T lb, const T ub,
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const int counter) noexcept {
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return (ub - lb) * gauss_legendre_50_points[counter] / T(2) +
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(ub + lb) / T(2);
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}
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class IncompleteGamma {
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/// 50 point Gauss-Legendre quadrature
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static constexpr T quadrature_inp_vals(const T lb, const T ub,
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const int counter) noexcept {
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return (ub - lb) * gauss_legendre_50_points[counter] / T(2) +
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(ub + lb) / T(2);
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}
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template <typename T>
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constexpr T incomplete_gamma_quad_weight_vals(const T lb, const T ub,
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const int counter) noexcept {
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return (ub - lb) * gauss_legendre_50_weights[counter] / T(2);
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}
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static constexpr T quadrature_weight_vals(const T lb, const T ub,
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const int counter) noexcept {
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return (ub - lb) * gauss_legendre_50_weights[counter] / T(2);
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}
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template <typename T>
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constexpr T incomplete_gamma_quad_fn(const T x, const T a,
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const T lg_term) noexcept {
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return exp(-x + (a - T(1)) * log(x) - lg_term);
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}
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static constexpr T quadrature_fn(const T x, const T a,
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const T lg_term) noexcept {
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return exp(-x + (a - T(1)) * log(x) - lg_term);
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}
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template <typename T>
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constexpr T incomplete_gamma_quad_recur(const T lb, const T ub, const T a,
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const T lg_term,
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const int counter) noexcept {
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return (counter < 49 ? // if
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incomplete_gamma_quad_fn(
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incomplete_gamma_quad_inp_vals(lb, ub, counter), a, lg_term) *
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incomplete_gamma_quad_weight_vals(lb, ub, counter) +
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incomplete_gamma_quad_recur(lb, ub, a, lg_term, counter + 1)
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:
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// else
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incomplete_gamma_quad_fn(
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incomplete_gamma_quad_inp_vals(lb, ub, counter), a, lg_term) *
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incomplete_gamma_quad_weight_vals(lb, ub, counter));
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}
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static constexpr T quadrature_recur(const T lb, const T ub, const T a,
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const T lg_term,
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const int counter) noexcept {
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if (counter < 49) {
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return quadrature_fn(quadrature_inp_vals(lb, ub, counter), a, lg_term) *
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quadrature_weight_vals(lb, ub, counter) +
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quadrature_recur(lb, ub, a, lg_term, counter + 1);
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} else {
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return quadrature_fn(quadrature_inp_vals(lb, ub, counter), a, lg_term) *
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quadrature_weight_vals(lb, ub, counter);
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}
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}
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template <typename T>
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constexpr T incomplete_gamma_quad_lb(const T a, const T z) noexcept {
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// break integration into ranges
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return (a > T(1000) ? std::max(T(0), std::min(z, a) - 11 * sqrt(a))
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: a > T(800) ? std::max(T(0), std::min(z, a) - 11 * sqrt(a))
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: a > T(500) ? std::max(T(0), std::min(z, a) - 10 * sqrt(a))
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: a > T(300) ? std::max(T(0), std::min(z, a) - 10 * sqrt(a))
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: a > T(100) ? std::max(T(0), std::min(z, a) - 9 * sqrt(a))
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: a > T(90) ? std::max(T(0), std::min(z, a) - 9 * sqrt(a))
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: a > T(70) ? std::max(T(0), std::min(z, a) - 8 * sqrt(a))
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: a > T(50) ? std::max(T(0), std::min(z, a) - 7 * sqrt(a))
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: a > T(40) ? std::max(T(0), std::min(z, a) - 6 * sqrt(a))
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: a > T(30) ? std::max(T(0), std::min(z, a) - 5 * sqrt(a))
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: std::max(T(0), std::min(z, a) - 4 * sqrt(a)));
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}
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static constexpr T quadrature_lb(const T a, const T z) noexcept {
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// break integration into ranges
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return a > T(1000) ? std::max(T(0), std::min(z, a) - 11 * sqrt(a))
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: a > T(800) ? std::max(T(0), std::min(z, a) - 11 * sqrt(a))
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: a > T(500) ? std::max(T(0), std::min(z, a) - 10 * sqrt(a))
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: a > T(300) ? std::max(T(0), std::min(z, a) - 10 * sqrt(a))
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: a > T(100) ? std::max(T(0), std::min(z, a) - 9 * sqrt(a))
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: a > T(90) ? std::max(T(0), std::min(z, a) - 9 * sqrt(a))
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: a > T(70) ? std::max(T(0), std::min(z, a) - 8 * sqrt(a))
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: a > T(50) ? std::max(T(0), std::min(z, a) - 7 * sqrt(a))
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: a > T(40) ? std::max(T(0), std::min(z, a) - 6 * sqrt(a))
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: a > T(30) ? std::max(T(0), std::min(z, a) - 5 * sqrt(a))
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: std::max(T(0), std::min(z, a) - 4 * sqrt(a));
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}
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template <typename T>
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constexpr T incomplete_gamma_quad_ub(const T a, const T z) noexcept {
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return (a > T(1000) ? std::min(z, a + 10 * sqrt(a))
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: a > T(800) ? std::min(z, a + 10 * sqrt(a))
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: a > T(500) ? std::min(z, a + 9 * sqrt(a))
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: a > T(300) ? std::min(z, a + 9 * sqrt(a))
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: a > T(100) ? std::min(z, a + 8 * sqrt(a))
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: a > T(90) ? std::min(z, a + 8 * sqrt(a))
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: a > T(70) ? std::min(z, a + 7 * sqrt(a))
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: a > T(50) ? std::min(z, a + 6 * sqrt(a))
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: std::min(z, a + 5 * sqrt(a)));
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}
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static constexpr T quadrature_ub(const T a, const T z) noexcept {
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return a > T(1000) ? std::min(z, a + 10 * sqrt(a))
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: a > T(800) ? std::min(z, a + 10 * sqrt(a))
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: a > T(500) ? std::min(z, a + 9 * sqrt(a))
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: a > T(300) ? std::min(z, a + 9 * sqrt(a))
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: a > T(100) ? std::min(z, a + 8 * sqrt(a))
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: a > T(90) ? std::min(z, a + 8 * sqrt(a))
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: a > T(70) ? std::min(z, a + 7 * sqrt(a))
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: a > T(50) ? std::min(z, a + 6 * sqrt(a))
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: std::min(z, a + 5 * sqrt(a));
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}
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template <typename T>
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constexpr T incomplete_gamma_quad(const T a, const T z) noexcept {
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return incomplete_gamma_quad_recur(incomplete_gamma_quad_lb(a, z),
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incomplete_gamma_quad_ub(a, z), a,
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lgamma(a), 0);
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}
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static constexpr T quadrature(const T a, const T z) noexcept {
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return quadrature_recur(quadrature_lb(a, z), quadrature_ub(a, z), a,
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lgamma(a), 0);
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}
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// reverse cf expansion
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// see: https://functions.wolfram.com/GammaBetaErf/Gamma2/10/0003/
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// reverse cf expansion
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// see: https://functions.wolfram.com/GammaBetaErf/Gamma2/10/0003/
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static constexpr T cf_2_recur(const T a, const T z,
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const int depth) noexcept {
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if (depth < 100) {
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return (1 + (depth - 1) * 2 - a + z) +
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depth * (a - depth) / cf_2_recur(a, z, depth + 1);
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} else {
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return 1 + (depth - 1) * 2 - a + z;
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}
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}
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template <typename T>
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constexpr T incomplete_gamma_cf_2_recur(const T a, const T z,
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const int depth) noexcept {
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return (depth < 100 ? (1 + (depth - 1) * 2 - a + z) +
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depth * (a - depth) /
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incomplete_gamma_cf_2_recur(a, z, depth + 1)
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: (1 + (depth - 1) * 2 - a + z));
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}
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/**
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* @brief Lower (regularized) incomplete gamma function
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*
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* @param a
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* @param z
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* @return constexpr T
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*/
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static constexpr T cf_2(const T a, const T z) noexcept {
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return T(1.0) - exp(a * log(z) - z - lgamma(a)) / cf_2_recur(a, z, 1);
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}
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template <typename T>
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constexpr T incomplete_gamma_cf_2(
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const T a,
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const T z) noexcept { // lower (regularized) incomplete gamma function
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return (T(1.0) - exp(a * log(z) - z - lgamma(a)) /
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incomplete_gamma_cf_2_recur(a, z, 1));
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}
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// continued fraction expansion
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// see: http://functions.wolfram.com/GammaBetaErf/Gamma2/10/0009/
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static constexpr T cf_1_coef(const T a, const T z, const int depth) noexcept {
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return (is_odd(depth) ? -(a - 1 + T(depth + 1) / T(2)) * z
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: T(depth) / T(2) * z);
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}
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// cf expansion
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// see: http://functions.wolfram.com/GammaBetaErf/Gamma2/10/0009/
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static constexpr T cf_1_recur(const T a, const T z,
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const int depth) noexcept {
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if (depth < 55) {
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return (a + depth - 1) +
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cf_1_coef(a, z, depth) / cf_1_recur(a, z, depth + 1);
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} else {
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return (a + depth - 1);
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}
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}
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template <typename T>
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constexpr T incomplete_gamma_cf_1_coef(const T a, const T z,
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const int depth) noexcept {
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return (is_odd(depth) ? -(a - 1 + T(depth + 1) / T(2)) * z
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: T(depth) / T(2) * z);
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}
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/**
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* @brief Lower (regularized) incomplete gamma function
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*
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* @param a
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* @param z
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* @return constexpr T
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*/
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static constexpr T cf_1(const T a, const T z) noexcept {
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return exp(a * log(z) - z - lgamma(a)) / cf_1_recur(a, z, 1);
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}
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template <typename T>
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constexpr T incomplete_gamma_cf_1_recur(const T a, const T z,
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const int depth) noexcept {
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return (depth < 55 ? // if
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(a + depth - 1) + incomplete_gamma_cf_1_coef(a, z, depth) /
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incomplete_gamma_cf_1_recur(a, z, depth + 1)
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:
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// else
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(a + depth - 1));
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}
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template <typename T>
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constexpr T incomplete_gamma_cf_1(
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const T a,
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const T z) noexcept { // lower (regularized) incomplete gamma function
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return (exp(a * log(z) - z - lgamma(a)) /
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incomplete_gamma_cf_1_recur(a, z, 1));
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}
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//
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template <typename T>
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constexpr T incomplete_gamma_check(const T a, const T z) noexcept {
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return ( // NaN check
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(is_nan(a) || is_nan(z)) ? LIM<T>::quiet_NaN() :
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//
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a < T(0) ? LIM<T>::quiet_NaN()
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:
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//
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LIM<T>::min() > z ? T(0)
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:
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//
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LIM<T>::min() > a ? T(1)
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:
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// cf or quadrature
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(a < T(10)) && (z - a < T(10)) ? incomplete_gamma_cf_1(a, z)
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: (a < T(10)) || (z / a > T(3)) ? incomplete_gamma_cf_2(a, z)
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:
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// else
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incomplete_gamma_quad(a, z));
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}
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template <typename T1, typename T2, typename TC = common_return_t<T1, T2>>
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constexpr TC incomplete_gamma_type_check(const T1 a, const T2 p) noexcept {
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return incomplete_gamma_check(static_cast<TC>(a), static_cast<TC>(p));
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}
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public:
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/**
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* @brief Compute the CDF for the Gamma distribution.
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*
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* @param a
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* @param z
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* @return constexpr T
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*/
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static constexpr T compute(const T a, const T z) noexcept {
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if (is_nan(a) || is_nan(z)) { // NaN check
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return LIM<T>::quiet_NaN();
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} else if (a < T(0)) {
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return LIM<T>::quiet_NaN();
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} else if (LIM<T>::min() > z) {
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return T(0);
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} else if (LIM<T>::min() > a) {
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return T(1);
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} else if (a < T(10) && z - a < T(10)) {
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return cf_1(a, z);
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} else if (a < T(10) || z / a > T(3)) {
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return cf_2(a, z);
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} else {
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return quadrature(a, z);
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}
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}
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};
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} // namespace internal
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@ -274,7 +267,9 @@ constexpr TC incomplete_gamma_type_check(const T1 a, const T2 p) noexcept {
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template <typename T1, typename T2>
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constexpr common_return_t<T1, T2> incomplete_gamma(const T1 a,
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const T2 x) noexcept {
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return internal::incomplete_gamma_type_check(a, x);
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using TC = common_return_t<T1, T2>;
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return internal::IncompleteGamma<TC>::compute(static_cast<TC>(a),
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static_cast<TC>(x));
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}
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namespace internal {
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