approx.cppm File Reference

Compatibility bridge for IEEE approximation policies. More...

#include <concepts>
import dedekind.numbers.ieee;
import dedekind.numbers;
import dedekind.ieee.approx;
import dedekind.category;

Include dependency graph for approx.cppm:

Namespaces
namespace	dedekind::numbers

Concepts
concept	dedekind::numbers::IsIEEEPropagationOp

Typedefs
template<std::floating_point F = machine_real_scalar>
using	dedekind::numbers::Approx = dedekind::ieee::Approx<F>
template<std::floating_point F = machine_real_scalar>
using	dedekind::numbers::ReportErrorPolicy = dedekind::ieee::ReportErrorPolicy<F>
template<std::floating_point F = machine_real_scalar>
using	dedekind::numbers::IgnoreErrorPolicy = dedekind::ieee::IgnoreErrorPolicy<F>
template<std::floating_point F = machine_real_scalar>
using	dedekind::numbers::AdaptiveErrorPolicy = dedekind::ieee::AdaptiveErrorPolicy<F>

Enumerations
enum class	dedekind::numbers::NumericRegion
	Region tags for simple runtime numeric diagnostics.

Functions
template<std::floating_point F = machine_real_scalar>
constexpr NumericRegion	dedekind::numbers::classify_region (F x, F near_zero_scale=F{64}, F huge_scale=F{0.5}) noexcept
template<std::floating_point F = machine_real_scalar>
constexpr F	dedekind::numbers::roundoff_proxy (F x) noexcept
template<std::floating_point F, typename Op> requires IsIEEEPropagationOp<Op, F>
constexpr Approx< F >	dedekind::numbers::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::numbers::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::numbers::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::numbers::demo_add_ignore (const IEEE< F > &a, const IEEE< F > &b) noexcept
template<std::floating_point F = double>
constexpr Approx< F >	dedekind::numbers::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::numbers::demo_add_adaptive (const IEEE< F > &a, const IEEE< F > &b) noexcept
	Demo operation: IEEE add under adaptive policy.

Detailed Description

Compatibility bridge for IEEE approximation policies.

Copyright

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

Note

"Lorsque les valeurs successivement attribuees a une meme variable s'approchent indefiniment d'une valeur fixe, de maniere a finir par en differer aussi peu qu'on voudra, cette derniere est appelee la limite de toutes les autres." ("When the values successively assigned to the same variable approach a fixed value indefinitely, so as to differ from it by as little as one wishes, this latter is called the limit of all the others.") – Augustin-Louis Cauchy, Cours d'Analyse (1821)