approx.cppm File Reference

Approximation policies for the IEEE effect context. More...

#include <cmath>
#include <concepts>
#include <limits>
#include <utility>
import dedekind.ieee;
import dedekind.category;

Include dependency graph for approx.cppm:

Classes
struct	dedekind::ieee::Approx< F >
	Approximation envelope for an IEEE value. More...
struct	dedekind::ieee::ReportErrorPolicy< F >
	Report policy: keep value and attach an error envelope. More...
struct	dedekind::ieee::IgnoreErrorPolicy< F >
	Ignore policy: run fast lane and drop all diagnostics. More...
struct	dedekind::ieee::AdaptiveErrorPolicy< F >
	Adaptive policy: respond to risky regions via ternary status. More...

Concepts
concept	dedekind::ieee::IsIEEEPropagationOp
	Category-grounded contract for propagation operation tokens.

Enumerations
enum class	dedekind::ieee::NumericRegion { Regular , NearZero , Huge , NonFinite }
	Region tags for simple runtime numeric diagnostics.

Functions
template<std::floating_point F = double>
constexpr NumericRegion	dedekind::ieee::classify_region (F x, F near_zero_scale=F{64}, F huge_scale=F{0.5}) noexcept
	Classify a scalar into a numeric region.
template<std::floating_point F = double>
constexpr F	dedekind::ieee::roundoff_proxy (F x) noexcept
	Conservative local rounding proxy: eps*|x|.
template<std::floating_point F, typename Op> requires IsIEEEPropagationOp<Op, F>
constexpr Approx< F >	dedekind::ieee::propagate (const Approx< F > &a, const Approx< F > &b, const Op &op={}) noexcept
	Propagate approximation error through a binary IEEE operation.
template<std::floating_point F = double>
constexpr Approx< F >	dedekind::ieee::demo_propagate_add (const Approx< F > &a, const Approx< F > &b) noexcept
	Demo: propagate error through IEEE addition.
template<std::floating_point F = double>
constexpr Approx< F >	dedekind::ieee::demo_propagate_mul (const Approx< F > &a, const Approx< F > &b) noexcept
	Demo: propagate error through IEEE multiplication.
template<std::floating_point F = double>
constexpr IEEE< F >	dedekind::ieee::demo_add_ignore (const IEEE< F > &a, const IEEE< F > &b) noexcept
template<std::floating_point F = double>
constexpr Approx< F >	dedekind::ieee::demo_add_report (const IEEE< F > &a, const IEEE< F > &b) noexcept
	Demo operation: IEEE add under report policy.
template<std::floating_point F = double>
constexpr TernaryResult< Approx< F > >	dedekind::ieee::demo_add_adaptive (const IEEE< F > &a, const IEEE< F > &b) noexcept
	Demo operation: IEEE add under adaptive policy.

Detailed Description

Approximation policies for the IEEE effect context.

Copyright

2026 The Dedekind Authors Licensed under the Apache License, Version 2.0.

Note

"Begin with the simplest examples." – David Hilbert, quoted in Hilbert-Courant (1984)