Add norm kwarg to isapprox (#35883)

Fixes #13132

NEWS.md

@@ -38,6 +38,7 @@ New library features
 Standard library changes
 ------------------------
 * The `nextprod` function now accepts tuples and other array types for its first argument ([#35791]).
+* The function `isapprox(x,y)` now accepts the `norm` keyword argument also for numeric (i.e., non-array) arguments `x` and `y` ([#35883]).
 
 #### LinearAlgebra
 

base/floatfuncs.jl

@@ -223,7 +223,7 @@ end
 
 # isapprox: approximate equality of numbers
 """
-    isapprox(x, y; rtol::Real=atol>0 ? 0 : √eps, atol::Real=0, nans::Bool=false, norm::Function)
+    isapprox(x, y; atol::Real=0, rtol::Real=atol>0 ? 0 : √eps, nans::Bool=false[, norm::Function])
 
 Inexact equality comparison: `true` if `norm(x-y) <= max(atol, rtol*max(norm(x), norm(y)))`. The
 default `atol` is zero and the default `rtol` depends on the types of `x` and `y`. The keyword
@@ -234,10 +234,9 @@ the square root of [`eps`](@ref) of the type of `x` or `y`, whichever is bigger
 This corresponds to requiring equality of about half of the significand digits. Otherwise,
 e.g. for integer arguments or if an `atol > 0` is supplied, `rtol` defaults to zero.
 
-`x` and `y` may also be arrays of numbers, in which case `norm` defaults to the usual
-`norm` function in LinearAlgebra, but
-may be changed by passing a `norm::Function` keyword argument. (For numbers, `norm` is the
-same thing as `abs`.) When `x` and `y` are arrays, if `norm(x-y)` is not finite (i.e. `±Inf`
+The `norm` keyword defaults to `abs` for numeric `(x,y)` and to `LinearAlgebra.norm` for
+arrays (where an alternative `norm` choice is sometimes useful).
+When `x` and `y` are arrays, if `norm(x-y)` is not finite (i.e. `±Inf`
 or `NaN`), the comparison falls back to checking whether all elements of `x` and `y` are
 approximately equal component-wise.
 
@@ -273,8 +272,10 @@ julia> isapprox(1e-10, 0, atol=1e-8)
 true
 ```
 """
-function isapprox(x::Number, y::Number; atol::Real=0, rtol::Real=rtoldefault(x,y,atol), nans::Bool=false)
-    x == y || (isfinite(x) && isfinite(y) && abs(x-y) <= max(atol, rtol*max(abs(x), abs(y)))) || (nans && isnan(x) && isnan(y))
+function isapprox(x::Number, y::Number;
+                  atol::Real=0, rtol::Real=rtoldefault(x,y,atol),
+                  nans::Bool=false, norm::Function=abs)
+    x == y || (isfinite(x) && isfinite(y) && norm(x-y) <= max(atol, rtol*max(norm(x), norm(y)))) || (nans && isnan(x) && isnan(y))
 end
 
 """

test/math.jl

@@ -670,10 +670,16 @@ end
     @test exp10(Float16(1.0)) === Float16(exp10(1.0))
 end
 
-# #22742: updated isapprox semantics
-@test !isapprox(1.0, 1.0+1e-12, atol=1e-14)
-@test isapprox(1.0, 1.0+0.5*sqrt(eps(1.0)))
-@test !isapprox(1.0, 1.0+1.5*sqrt(eps(1.0)), atol=sqrt(eps(1.0)))
+@testset "isapprox" begin
+  # #22742: updated isapprox semantics
+  @test !isapprox(1.0, 1.0+1e-12, atol=1e-14)
+  @test isapprox(1.0, 1.0+0.5*sqrt(eps(1.0)))
+  @test !isapprox(1.0, 1.0+1.5*sqrt(eps(1.0)), atol=sqrt(eps(1.0)))
+
+  # #13132: Use of `norm` kwarg for scalar arguments
+  @test isapprox(1, 1+1.0e-12, norm=abs)
+  @test !isapprox(1, 1+1.0e-12, norm=x->1)
+end
 
 # test AbstractFloat fallback pr22716
 struct Float22716{T<:AbstractFloat} <: AbstractFloat