From 4abc6fe2fd96c8b6b9c63ba4bb78705efcf4210c Mon Sep 17 00:00:00 2001
From: Jishnu Bhattacharya <jishnub.github@gmail.com>
Date: Wed, 4 Jun 2025 13:55:53 +0530
Subject: [PATCH 1/6] Iterator norm in `isapprox` for `Array`s

---
 src/generic.jl  | 8 +++++++-
 test/generic.jl | 7 +++++++
 2 files changed, 14 insertions(+), 1 deletion(-)

diff --git a/src/generic.jl b/src/generic.jl
index c8336f87..ef4b89f1 100644
--- a/src/generic.jl
+++ b/src/generic.jl
@@ -2004,7 +2004,7 @@ function isapprox(x::AbstractArray, y::AbstractArray;
     atol::Real=0,
     rtol::Real=Base.rtoldefault(promote_leaf_eltypes(x),promote_leaf_eltypes(y),atol),
     nans::Bool=false, norm::Function=norm)
-    d = norm(x - y)
+    d = norm_x_minus_y(x, y)
     if isfinite(d)
         return iszero(rtol) ? d <= atol : d <= max(atol, rtol*max(norm(x), norm(y)))
     else
@@ -2014,6 +2014,12 @@ function isapprox(x::AbstractArray, y::AbstractArray;
     end
 end
 
+norm_x_minus_y(x, y) = norm(x - y)
+function norm_x_minus_y(x::Array, y::Array)
+    Base.promote_shape(size(x), size(y)) # ensure same size
+    norm(Iterators.map(splat(-), zip(x,y)))
+end
+
 """
     normalize!(a::AbstractArray, p::Real=2)
 
diff --git a/test/generic.jl b/test/generic.jl
index 4fd48a6f..1983166b 100644
--- a/test/generic.jl
+++ b/test/generic.jl
@@ -938,4 +938,11 @@ end
     @test B == A2
 end
 
+@testset "isapprox alloc" begin
+    A = rand(3,3)
+    isapprox(A, A)
+    n = @allocated isapprox(A, A)
+    @test n == 0
+end
+
 end # module TestGeneric

From abfb65d471ceb42654affd46ba063cb691b29e2d Mon Sep 17 00:00:00 2001
From: Jishnu Bhattacharya <jishnub.github@gmail.com>
Date: Wed, 4 Jun 2025 15:40:48 +0530
Subject: [PATCH 2/6] Handle empty arrays

---
 src/generic.jl  | 7 ++++++-
 test/generic.jl | 3 ++-
 2 files changed, 8 insertions(+), 2 deletions(-)

diff --git a/src/generic.jl b/src/generic.jl
index ef4b89f1..55a328eb 100644
--- a/src/generic.jl
+++ b/src/generic.jl
@@ -2004,7 +2004,12 @@ function isapprox(x::AbstractArray, y::AbstractArray;
     atol::Real=0,
     rtol::Real=Base.rtoldefault(promote_leaf_eltypes(x),promote_leaf_eltypes(y),atol),
     nans::Bool=false, norm::Function=norm)
-    d = norm_x_minus_y(x, y)
+    d = if isempty(x) && isempty(y)
+        Base.promote_shape(size(x), size(y)) # ensure same size
+        norm(zero(eltype(x)) - zero(eltype(y)))
+    else
+        norm_x_minus_y(x, y)
+    end
     if isfinite(d)
         return iszero(rtol) ? d <= atol : d <= max(atol, rtol*max(norm(x), norm(y)))
     else
diff --git a/test/generic.jl b/test/generic.jl
index 1983166b..576781cc 100644
--- a/test/generic.jl
+++ b/test/generic.jl
@@ -938,11 +938,12 @@ end
     @test B == A2
 end
 
-@testset "isapprox alloc" begin
+@testset "isapprox for Arrays" begin
     A = rand(3,3)
     isapprox(A, A)
     n = @allocated isapprox(A, A)
     @test n == 0
+    @test Int[] ≈ Int[]
 end
 
 end # module TestGeneric

From 4906add57fc76b752235259f8fb3bc84819a508f Mon Sep 17 00:00:00 2001
From: Jishnu Bhattacharya <jishnub.github@gmail.com>
Date: Fri, 13 Jun 2025 20:33:15 +0530
Subject: [PATCH 3/6] Specialize for strided contiguous `SubArray`s

---
 src/generic.jl | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/src/generic.jl b/src/generic.jl
index 55a328eb..83185926 100644
--- a/src/generic.jl
+++ b/src/generic.jl
@@ -2004,8 +2004,8 @@ function isapprox(x::AbstractArray, y::AbstractArray;
     atol::Real=0,
     rtol::Real=Base.rtoldefault(promote_leaf_eltypes(x),promote_leaf_eltypes(y),atol),
     nans::Bool=false, norm::Function=norm)
+    Base.promote_shape(size(x), size(y)) # ensure compatible size
     d = if isempty(x) && isempty(y)
-        Base.promote_shape(size(x), size(y)) # ensure same size
         norm(zero(eltype(x)) - zero(eltype(y)))
     else
         norm_x_minus_y(x, y)
@@ -2020,8 +2020,8 @@ function isapprox(x::AbstractArray, y::AbstractArray;
 end
 
 norm_x_minus_y(x, y) = norm(x - y)
-function norm_x_minus_y(x::Array, y::Array)
-    Base.promote_shape(size(x), size(y)) # ensure same size
+const ArrayOrFastContiguousSubArrayStrided = Union{Array, FastContiguousSubArrayStrided}
+function norm_x_minus_y(x::ArrayOrFastContiguousSubArrayStrided, y::ArrayOrFastContiguousSubArrayStrided)
     norm(Iterators.map(splat(-), zip(x,y)))
 end
 

From 2a7518ea93b457d3b4d40988c19e17f5446ec3af Mon Sep 17 00:00:00 2001
From: Jishnu Bhattacharya <jishnub.github@gmail.com>
Date: Fri, 20 Jun 2025 15:59:40 +0530
Subject: [PATCH 4/6] Limit to Array views

---
 src/generic.jl | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/src/generic.jl b/src/generic.jl
index 83185926..c0090c10 100644
--- a/src/generic.jl
+++ b/src/generic.jl
@@ -2020,8 +2020,9 @@ function isapprox(x::AbstractArray, y::AbstractArray;
 end
 
 norm_x_minus_y(x, y) = norm(x - y)
-const ArrayOrFastContiguousSubArrayStrided = Union{Array, FastContiguousSubArrayStrided}
-function norm_x_minus_y(x::ArrayOrFastContiguousSubArrayStrided, y::ArrayOrFastContiguousSubArrayStrided)
+FastContiguousArrayView{T,N,P<:Array,I<:Tuple{AbstractUnitRange, Vararg{Any}}} = Base.SubArray{T,N,P,I,true}
+const ArrayOrFastContiguousArrayView = Union{Array, FastContiguousArrayView}
+function norm_x_minus_y(x::ArrayOrFastContiguousArrayView, y::ArrayOrFastContiguousArrayView)
     norm(Iterators.map(splat(-), zip(x,y)))
 end
 

From 35c5dd3353f7681233334c7c8dce537cb4a39fdd Mon Sep 17 00:00:00 2001
From: Jishnu Bhattacharya <jishnub.github@gmail.com>
Date: Fri, 20 Jun 2025 16:02:34 +0530
Subject: [PATCH 5/6] Remove initial call before `@allocated` test

---
 test/generic.jl | 1 -
 1 file changed, 1 deletion(-)

diff --git a/test/generic.jl b/test/generic.jl
index 576781cc..c6037315 100644
--- a/test/generic.jl
+++ b/test/generic.jl
@@ -940,7 +940,6 @@ end
 
 @testset "isapprox for Arrays" begin
     A = rand(3,3)
-    isapprox(A, A)
     n = @allocated isapprox(A, A)
     @test n == 0
     @test Int[] ≈ Int[]

From ef309a63aa372de06c228352900a826f8e792c92 Mon Sep 17 00:00:00 2001
From: Jishnu Bhattacharya <jishnub.github@gmail.com>
Date: Wed, 2 Jul 2025 03:02:12 +0530
Subject: [PATCH 6/6] Move checks to within `norm_x_minus_y` method for
 `Array`s

---
 src/generic.jl | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/src/generic.jl b/src/generic.jl
index c0090c10..85e029c7 100644
--- a/src/generic.jl
+++ b/src/generic.jl
@@ -2004,12 +2004,7 @@ function isapprox(x::AbstractArray, y::AbstractArray;
     atol::Real=0,
     rtol::Real=Base.rtoldefault(promote_leaf_eltypes(x),promote_leaf_eltypes(y),atol),
     nans::Bool=false, norm::Function=norm)
-    Base.promote_shape(size(x), size(y)) # ensure compatible size
-    d = if isempty(x) && isempty(y)
-        norm(zero(eltype(x)) - zero(eltype(y)))
-    else
-        norm_x_minus_y(x, y)
-    end
+    d = norm_x_minus_y(x, y)
     if isfinite(d)
         return iszero(rtol) ? d <= atol : d <= max(atol, rtol*max(norm(x), norm(y)))
     else
@@ -2023,7 +2018,12 @@ norm_x_minus_y(x, y) = norm(x - y)
 FastContiguousArrayView{T,N,P<:Array,I<:Tuple{AbstractUnitRange, Vararg{Any}}} = Base.SubArray{T,N,P,I,true}
 const ArrayOrFastContiguousArrayView = Union{Array, FastContiguousArrayView}
 function norm_x_minus_y(x::ArrayOrFastContiguousArrayView, y::ArrayOrFastContiguousArrayView)
-    norm(Iterators.map(splat(-), zip(x,y)))
+    Base.promote_shape(size(x), size(y)) # ensure compatible size
+    if isempty(x) && isempty(y)
+        norm(zero(eltype(x)) - zero(eltype(y)))
+    else
+        norm(Iterators.map(splat(-), zip(x,y)))
+    end
 end
 
 """