Ryan Henry
0d22946a0e
Ship the TLS mesh, composer, Beaver/Yao/leaf MPC, prep/online paths, apps, and docs so the tree is pushable before elevating share_expr, security_mode, and prep resume. Co-authored-by: Cursor <cursoragent@cursor.com>
94 lines
3.5 KiB
C++
94 lines
3.5 KiB
C++
/// @file grotto/piecewise.hpp
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/// @brief Horner evaluation of a cubic and a bound-selected piece.
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/// @details `eval_horner` evaluates one polynomial. `piecewise_eval` selects
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/// the piece whose upper bound is the first entry of `bounds`
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/// strictly greater than `x`.
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/// @author Ryan Henry <ryan.henry@ucalgary.ca>
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/// @copyright Copyright (c) 2019-2026 Ryan Henry and [others](@ref authors)
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/// @license Released under a GNU General Public v2.0 (GPLv2) license;
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/// see [LICENSE.md](@ref license) for details.
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#ifndef LIBDPF_INCLUDE_GROTTO_PIECEWISE_HPP__
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#define LIBDPF_INCLUDE_GROTTO_PIECEWISE_HPP__
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#include <array>
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#include <iterator>
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#include <algorithm>
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#include "hedley/hedley.h"
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namespace grotto
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{
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namespace polynomials
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{
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/// @name Polynomial shapes
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/// @brief Coefficient arrays, constant term in element 0. Degree is `size - 1`.
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/// @{
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template <typename T> using poly_constant = std::array<T, 1>;
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template <typename T> using poly_linear = std::array<T, 2>;
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template <typename T> using poly_quadratic = std::array<T, 3>;
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template <typename T> using poly_cubic = std::array<T, 4>;
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/// @}
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/// @brief Horner evaluation. The four overloads are degrees 0 through 3.
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/// @tparam T coefficient type
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/// @param f coefficients, constant term in `f[0]`
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/// @param x the evaluation point
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/// @return the polynomial value
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/// @see grotto::piecewise_eval
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/// \complexity Unrolled: 0, 1, 2, or 3 multiplies. `Θ(1)` time and extra space.
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template <typename T>
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HEDLEY_PURE
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HEDLEY_NO_THROW
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constexpr auto eval_horner(const poly_constant<T> & f, T x) noexcept { return f[0]; }
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/// @brief Degree-1 Horner. Constant term in `f[0]`.
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/// @see grotto::eval_horner
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/// \complexity One multiply-add. `Θ(1)`.
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template <typename T>
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HEDLEY_PURE
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HEDLEY_NO_THROW
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constexpr auto eval_horner(const poly_linear<T> & f, T x) noexcept { return f[1] * x + f[0]; }
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/// @brief Degree-2 Horner. Constant term in `f[0]`.
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/// @see grotto::eval_horner
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/// \complexity Two multiply-adds. `Θ(1)`.
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template <typename T>
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HEDLEY_PURE
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HEDLEY_NO_THROW
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constexpr auto eval_horner(const poly_quadratic<T> & f, T x) noexcept { return (f[2] * x + f[1]) * x + f[0]; }
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/// @brief Degree-3 Horner. Constant term in `f[0]`.
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/// @see grotto::eval_horner
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/// \complexity Three multiply-adds. `Θ(1)`.
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template <typename T>
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HEDLEY_PURE
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HEDLEY_NO_THROW
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constexpr auto eval_horner(const poly_cubic<T> & f, T x) noexcept { return ((f[3] * x + f[2]) * x + f[1]) * x + f[0]; }
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/// @brief Select the piece whose upper bound is the first entry of `bounds` strictly greater than `x`, then Horner-evaluate it.
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/// @tparam T coefficient and bound type
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/// @tparam D coefficients per piece
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/// @tparam N1 number of pieces
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/// @tparam N2 number of bounds
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/// @param polys one coefficient array per piece, constant term first
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/// @param bounds upper bounds of the pieces
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/// @param x the query
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/// @return `eval_horner` of the selected piece
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/// @see grotto::eval_horner
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/// \complexity `upper_bound` on `bounds` (`Θ(log N2)`), then one `eval_horner` (`Θ(1)`, `D` is 1..4). Extra space `Θ(1)`.
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template <typename T, std::size_t D, std::size_t N1, std::size_t N2>
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HEDLEY_PURE
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HEDLEY_NO_THROW
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auto piecewise_eval(const std::array<std::array<T, D>, N1> & polys, const std::array<T, N2> & bounds, T x) noexcept
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{
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auto it = std::upper_bound(std::cbegin(bounds), std::cend(bounds), x,
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[](const T & lhs, const T & rhs){ return lhs < rhs; });
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auto i = std::distance(std::cbegin(bounds), it);
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return eval_horner(polys[i], x);
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}
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} // namespace polynomials
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} // namespace grotto
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#endif // LIBDPF_INCLUDE_GROTTO_PIECEWISE_HPP__
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