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Fix relative_eq for small values #102

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Fix relative_eq for small values #102

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85342ce
Add default_relative_epsilon to RelativeEq
kitt159 Feb 21, 2026
2df1eb2
Use MIN_POSITIVE as default relative epsilon
kitt159 May 17, 2026
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9 changes: 9 additions & 0 deletions approx-derive/src/rel_diff_eq.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -232,6 +232,7 @@ impl AbsDiffEqParser {

pub fn implement_derive_rel_diff_eq(&self) -> proc_macro2::TokenStream {
let obj_name = &self.base_type.ident();
let epsilon_type = self.get_epsilon_parent_type();
let max_relative_default_value = self.get_max_relative_default_value();

let (impl_generics, ty_generics, _) = self.base_type.generics().split_for_impl();
Expand All @@ -251,6 +252,10 @@ impl AbsDiffEqParser {
impl #impl_generics #ApproxName::RelativeEq for #obj_name #ty_generics
#where_clause
{
fn default_relative_epsilon() -> Self::Epsilon {
<#epsilon_type as #ApproxName::RelativeEq>::default_relative_epsilon()
}

fn default_max_relative() -> Self::Epsilon {
#max_relative_default_value
}
Expand Down Expand Up @@ -280,6 +285,10 @@ impl AbsDiffEqParser {
impl #impl_generics #ApproxName::RelativeEq for #obj_name #ty_generics
#where_clause
{
fn default_relative_epsilon() -> Self::Epsilon {
<#epsilon_type as #ApproxName::RelativeEq>::default_relative_epsilon()
}

fn default_max_relative() -> Self::Epsilon {
#max_relative_default_value
}
Expand Down
3 changes: 1 addition & 2 deletions approx/src/abs_diff_eq.rs
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Expand Up @@ -39,8 +39,7 @@ where
/// The default tolerance to use when testing values that are close together.
///
/// This is used when no `epsilon` value is supplied to the
/// [`abs_diff_eq!`](crate::abs_diff_eq), [`relative_eq!`](crate::relative_eq),
/// or [`ulps_eq!`](crate::ulps_eq) macros.
/// [`abs_diff_eq!`](crate::abs_diff_eq), or [`ulps_eq!`](crate::ulps_eq) macros.
fn default_epsilon() -> Self::Epsilon;

/// A test for equality that uses the absolute difference to compute the approximate
Expand Down
7 changes: 6 additions & 1 deletion approx/src/lib.rs
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Expand Up @@ -113,6 +113,7 @@
//! # }
//! # }
//! # impl<T: RelativeEq> RelativeEq for Complex<T> where T::Epsilon: Copy {
//! # fn default_relative_epsilon() -> T::Epsilon { T::default_relative_epsilon() }
//! # fn default_max_relative() -> T::Epsilon { T::default_max_relative() }
//! # fn relative_eq(&self, other: &Self, epsilon: T::Epsilon, max_relative: T::Epsilon)
//! # -> bool {
Expand Down Expand Up @@ -163,6 +164,10 @@
//! impl<T: RelativeEq> RelativeEq for Complex<T> where
//! T::Epsilon: Copy,
//! {
//! fn default_relative_epsilon() -> T::Epsilon {
//! T::default_relative_epsilon()
//! }
//!
//! fn default_max_relative() -> T::Epsilon {
//! T::default_max_relative()
//! }
Expand Down Expand Up @@ -339,7 +344,7 @@ where
#[inline]
fn default() -> Relative<A, B> {
Relative {
epsilon: A::default_epsilon(),
epsilon: A::default_relative_epsilon(),
max_relative: A::default_max_relative(),
}
}
Expand Down
94 changes: 94 additions & 0 deletions approx/src/relative_eq.rs
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Expand Up @@ -37,6 +37,12 @@ pub trait RelativeEq<Rhs = Self>: AbsDiffEq<Rhs>
where
Rhs: ?Sized,
{
/// The default epsilon for testing values that are close to zero
///
/// This is used when no `epsilon` value is supplied to the
/// [`relative_eq`](crate::relative_eq) macro.
fn default_relative_epsilon() -> Self::Epsilon;

/// The default relative tolerance for testing values that are far-apart.
///
/// This is used when no `max_relative` value is supplied to the
Expand Down Expand Up @@ -67,6 +73,11 @@ where
macro_rules! impl_relative_eq {
($T:ident) => {
impl RelativeEq for $T {
#[inline]
fn default_relative_epsilon() -> $T {
$T::MIN_POSITIVE
}

#[inline]
fn default_max_relative() -> $T {
$T::EPSILON
Expand Down Expand Up @@ -117,6 +128,11 @@ impl_relative_eq!(f64);
///////////////////////////////////////////////////////////////////////////////////////////////////

impl<T: RelativeEq> RelativeEq for Option<T> {
#[inline]
fn default_relative_epsilon() -> T::Epsilon {
T::default_relative_epsilon()
}

#[inline]
fn default_max_relative() -> T::Epsilon {
T::default_max_relative()
Expand All @@ -138,6 +154,11 @@ impl<T: RelativeEq> RelativeEq for Option<T> {
}

impl<T: RelativeEq, E: RelativeEq> RelativeEq for Result<T, E> {
#[inline]
fn default_relative_epsilon() -> (T::Epsilon, E::Epsilon) {
(T::default_relative_epsilon(), E::default_relative_epsilon())
}

#[inline]
fn default_max_relative() -> (T::Epsilon, E::Epsilon) {
(T::default_max_relative(), E::default_max_relative())
Expand All @@ -159,6 +180,11 @@ impl<T: RelativeEq, E: RelativeEq> RelativeEq for Result<T, E> {
}

impl<'a, T: RelativeEq + ?Sized> RelativeEq for &'a T {
#[inline]
fn default_relative_epsilon() -> T::Epsilon {
T::default_relative_epsilon()
}

#[inline]
fn default_max_relative() -> T::Epsilon {
T::default_max_relative()
Expand All @@ -171,6 +197,11 @@ impl<'a, T: RelativeEq + ?Sized> RelativeEq for &'a T {
}

impl<'a, T: RelativeEq + ?Sized> RelativeEq for &'a mut T {
#[inline]
fn default_relative_epsilon() -> T::Epsilon {
T::default_relative_epsilon()
}

#[inline]
fn default_max_relative() -> T::Epsilon {
T::default_max_relative()
Expand All @@ -188,6 +219,11 @@ impl<'a, T: RelativeEq + ?Sized> RelativeEq for &'a mut T {
}

impl<T: RelativeEq + Copy> RelativeEq for cell::Cell<T> {
#[inline]
fn default_relative_epsilon() -> T::Epsilon {
T::default_relative_epsilon()
}

#[inline]
fn default_max_relative() -> T::Epsilon {
T::default_max_relative()
Expand All @@ -205,6 +241,11 @@ impl<T: RelativeEq + Copy> RelativeEq for cell::Cell<T> {
}

impl<T: RelativeEq + ?Sized> RelativeEq for cell::RefCell<T> {
#[inline]
fn default_relative_epsilon() -> T::Epsilon {
T::default_relative_epsilon()
}

#[inline]
fn default_max_relative() -> T::Epsilon {
T::default_max_relative()
Expand All @@ -226,6 +267,11 @@ where
A: RelativeEq<B>,
A::Epsilon: Clone,
{
#[inline]
fn default_relative_epsilon() -> A::Epsilon {
A::default_relative_epsilon()
}

#[inline]
fn default_max_relative() -> A::Epsilon {
A::default_max_relative()
Expand All @@ -246,6 +292,11 @@ where
A: RelativeEq<B>,
A::Epsilon: Clone,
{
#[inline]
fn default_relative_epsilon() -> A::Epsilon {
A::default_relative_epsilon()
}

#[inline]
fn default_max_relative() -> A::Epsilon {
A::default_max_relative()
Expand All @@ -266,6 +317,11 @@ where
A: RelativeEq<B>,
A::Epsilon: Clone,
{
#[inline]
fn default_relative_epsilon() -> A::Epsilon {
A::default_relative_epsilon()
}

#[inline]
fn default_max_relative() -> A::Epsilon {
A::default_max_relative()
Expand All @@ -284,6 +340,10 @@ where
macro_rules! impl_relative_eq {
() => {
impl RelativeEq for () {
fn default_relative_epsilon() -> Self::Epsilon {
()
}

fn default_max_relative() -> Self::Epsilon {
()
}
Expand All @@ -305,6 +365,10 @@ macro_rules! impl_relative_eq {
where
$( [<T $idx>]: RelativeEq, )+
{
fn default_relative_epsilon() -> Self::Epsilon {
($( [<T $idx>]::default_relative_epsilon(), )+)
}

fn default_max_relative() -> Self::Epsilon {
($( [<T $idx>]::default_max_relative(), )+)
}
Expand Down Expand Up @@ -348,6 +412,11 @@ impl<T: RelativeEq> RelativeEq for Complex<T>
where
T::Epsilon: Clone,
{
#[inline]
fn default_relative_epsilon() -> T::Epsilon {
T::default_relative_epsilon()
}

#[inline]
fn default_max_relative() -> T::Epsilon {
T::default_max_relative()
Expand All @@ -368,6 +437,11 @@ where
#[cfg(feature = "ordered_float")]
#[cfg_attr(docsrs, doc(cfg(feature = "ordered_float")))]
impl<T: RelativeEq + Copy> RelativeEq for NotNan<T> {
#[inline]
fn default_relative_epsilon() -> Self::Epsilon {
T::default_relative_epsilon()
}

#[inline]
fn default_max_relative() -> Self::Epsilon {
T::default_max_relative()
Expand All @@ -392,6 +466,11 @@ impl<T: RelativeEq + Copy> RelativeEq for NotNan<T> {
#[cfg(feature = "ordered_float")]
#[cfg_attr(docsrs, doc(cfg(feature = "ordered_float")))]
impl<T: RelativeEq + Float + ordered_float::FloatCore> RelativeEq<T> for NotNan<T> {
#[inline]
fn default_relative_epsilon() -> Self::Epsilon {
T::default_relative_epsilon()
}

#[inline]
fn default_max_relative() -> Self::Epsilon {
T::default_max_relative()
Expand All @@ -406,6 +485,11 @@ impl<T: RelativeEq + Float + ordered_float::FloatCore> RelativeEq<T> for NotNan<
#[cfg(feature = "ordered_float")]
#[cfg_attr(docsrs, doc(cfg(feature = "ordered_float")))]
impl<T: RelativeEq + Float + ordered_float::FloatCore> RelativeEq for OrderedFloat<T> {
#[inline]
fn default_relative_epsilon() -> Self::Epsilon {
T::default_relative_epsilon()
}

#[inline]
fn default_max_relative() -> Self::Epsilon {
T::default_max_relative()
Expand All @@ -430,6 +514,11 @@ impl<T: RelativeEq + Float + ordered_float::FloatCore> RelativeEq for OrderedFlo
#[cfg(feature = "ordered_float")]
#[cfg_attr(docsrs, doc(cfg(feature = "ordered_float")))]
impl<T: RelativeEq + Float + ordered_float::FloatCore> RelativeEq<T> for OrderedFloat<T> {
#[inline]
fn default_relative_epsilon() -> Self::Epsilon {
T::default_relative_epsilon()
}

#[inline]
fn default_max_relative() -> Self::Epsilon {
T::default_max_relative()
Expand All @@ -451,6 +540,11 @@ where
S1: BuildHasher,
S2: BuildHasher,
{
#[inline]
fn default_relative_epsilon() -> V1::Epsilon {
V1::default_relative_epsilon()
}

#[inline]
fn default_max_relative() -> V1::Epsilon {
V1::default_max_relative()
Expand Down
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