/// @file grotto/piecewise.hpp
/// @brief Horner evaluation of a cubic and a bound-selected piece.
/// @details `eval_horner` evaluates one polynomial. `piecewise_eval` selects
///          the piece whose upper bound is the first entry of `bounds`
///          strictly greater than `x`.
/// @author Ryan Henry <ryan.henry@ucalgary.ca>
/// @copyright Copyright (c) 2019-2026 Ryan Henry and [others](@ref authors)
/// @license Released under a GNU General Public v2.0 (GPLv2) license;
///          see [LICENSE.md](@ref license) for details.

#ifndef LIBDPF_INCLUDE_GROTTO_PIECEWISE_HPP__
#define LIBDPF_INCLUDE_GROTTO_PIECEWISE_HPP__

#include <array>
#include <iterator>
#include <algorithm>

#include "hedley/hedley.h"

namespace grotto
{

namespace polynomials
{

/// @name Polynomial shapes
/// @brief Coefficient arrays, constant term in element 0. Degree is `size - 1`.
/// @{
template <typename T> using poly_constant  = std::array<T, 1>;
template <typename T> using poly_linear    = std::array<T, 2>;
template <typename T> using poly_quadratic = std::array<T, 3>;
template <typename T> using poly_cubic     = std::array<T, 4>;
/// @}

/// @brief Horner evaluation. The four overloads are degrees 0 through 3.
/// @tparam T coefficient type
/// @param f coefficients, constant term in `f[0]`
/// @param x the evaluation point
/// @return the polynomial value
/// @see grotto::piecewise_eval
/// \complexity Unrolled: 0, 1, 2, or 3 multiplies. `Θ(1)` time and extra space.
template <typename T>
HEDLEY_PURE
HEDLEY_NO_THROW
constexpr auto eval_horner(const poly_constant<T> & f, T x) noexcept { return f[0]; }
/// @brief Degree-1 Horner. Constant term in `f[0]`.
/// @see grotto::eval_horner
/// \complexity One multiply-add. `Θ(1)`.
template <typename T>
HEDLEY_PURE
HEDLEY_NO_THROW
constexpr auto eval_horner(const poly_linear<T> & f, T x) noexcept { return f[1] * x + f[0]; }
/// @brief Degree-2 Horner. Constant term in `f[0]`.
/// @see grotto::eval_horner
/// \complexity Two multiply-adds. `Θ(1)`.
template <typename T>
HEDLEY_PURE
HEDLEY_NO_THROW
constexpr auto eval_horner(const poly_quadratic<T> & f, T x) noexcept { return (f[2] * x + f[1]) * x + f[0]; }
/// @brief Degree-3 Horner. Constant term in `f[0]`.
/// @see grotto::eval_horner
/// \complexity Three multiply-adds. `Θ(1)`.
template <typename T>
HEDLEY_PURE
HEDLEY_NO_THROW
constexpr auto eval_horner(const poly_cubic<T> & f, T x) noexcept { return ((f[3] * x + f[2]) * x + f[1]) * x + f[0]; }

/// @brief Select the piece whose upper bound is the first entry of `bounds` strictly greater than `x`, then Horner-evaluate it.
/// @tparam T coefficient and bound type
/// @tparam D coefficients per piece
/// @tparam N1 number of pieces
/// @tparam N2 number of bounds
/// @param polys one coefficient array per piece, constant term first
/// @param bounds upper bounds of the pieces
/// @param x the query
/// @return `eval_horner` of the selected piece
/// @see grotto::eval_horner
/// \complexity `upper_bound` on `bounds` (`Θ(log N2)`), then one `eval_horner` (`Θ(1)`, `D` is 1..4). Extra space `Θ(1)`.
template <typename T, std::size_t D, std::size_t N1, std::size_t N2>
HEDLEY_PURE
HEDLEY_NO_THROW
auto piecewise_eval(const std::array<std::array<T, D>, N1> & polys, const std::array<T, N2> & bounds, T x) noexcept
{
    auto it = std::upper_bound(std::cbegin(bounds), std::cend(bounds), x,
        [](const T & lhs, const T & rhs){ return lhs < rhs; });
    auto i = std::distance(std::cbegin(bounds), it);
    return eval_horner(polys[i], x);
}

}  // namespace polynomials

}  // namespace grotto

#endif  // LIBDPF_INCLUDE_GROTTO_PIECEWISE_HPP__