Fix integer overflow in isapprox (#50730)

Ensure that `isapprox` gives correct results when comparing an integer
with another integer or with a float. For comparison between integers,
the fix only works when keeping default values for `rtol` and `norm`,
and with `atol < 1`.

It is not possible to handle the (atypical) case where `norm !== abs`,
but that's OK since the user is responsible for providing a safe
function.

It would be possible to handle the case where `rtol > 0` or `atol >= 1`,
but with complex code which would check for overflow and handle all
possible corner cases; it would work only for types defined in Base and
would not be extensible by packages. So I'm not sure that's worth it. At
least with PR fixes the most common case.

Fixes #50380.

base/floatfuncs.jl

@@ -239,7 +239,20 @@ true
 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))
+    x′, y′ = promote(x, y) # to avoid integer overflow
+    x == y ||
+        (isfinite(x) && isfinite(y) && norm(x-y) <= max(atol, rtol*max(norm(x′), norm(y′)))) ||
+         (nans && isnan(x) && isnan(y))
+end
+
+function isapprox(x::Integer, y::Integer;
+                  atol::Real=0, rtol::Real=rtoldefault(x,y,atol),
+                  nans::Bool=false, norm::Function=abs)
+    if norm === abs && atol < 1 && rtol == 0
+        return x == y
+    else
+        return norm(x - y) <= max(atol, rtol*max(norm(x), norm(y)))
+    end
 end
 
 """

test/floatfuncs.jl

@@ -209,3 +209,47 @@ end
     struct CustomNumber <: Number end
     @test !isnan(CustomNumber())
 end
+
+@testset "isapprox and integer overflow" begin
+    for T in (Int8, Int16, Int32)
+        T === Int && continue
+        @test !isapprox(typemin(T), T(0))
+        @test !isapprox(typemin(T), unsigned(T)(0))
+        @test !isapprox(typemin(T), 0)
+        @test !isapprox(typemin(T), T(0), atol=0.99)
+        @test !isapprox(typemin(T), unsigned(T)(0), atol=0.99)
+        @test !isapprox(typemin(T), 0, atol=0.99)
+        @test_broken !isapprox(typemin(T), T(0), atol=1)
+        @test_broken !isapprox(typemin(T), unsigned(T)(0), atol=1)
+        @test !isapprox(typemin(T), 0, atol=1)
+
+        @test !isapprox(typemin(T)+T(10), T(10))
+        @test !isapprox(typemin(T)+T(10), unsigned(T)(10))
+        @test !isapprox(typemin(T)+T(10), 10)
+        @test !isapprox(typemin(T)+T(10), T(10), atol=0.99)
+        @test !isapprox(typemin(T)+T(10), unsigned(T)(10), atol=0.99)
+        @test !isapprox(typemin(T)+T(10), 10, atol=0.99)
+        @test_broken !isapprox(typemin(T)+T(10), T(10), atol=1)
+        @test !isapprox(typemin(T)+T(10), unsigned(T)(10), atol=1)
+        @test !isapprox(typemin(T)+T(10), 10, atol=1)
+
+        @test isapprox(typemin(T), 0.0, rtol=1)
+    end
+    for T in (Int, Int64, Int128)
+        @test !isapprox(typemin(T), T(0))
+        @test !isapprox(typemin(T), unsigned(T)(0))
+        @test !isapprox(typemin(T), T(0), atol=0.99)
+        @test !isapprox(typemin(T), unsigned(T)(0), atol=0.99)
+        @test_broken !isapprox(typemin(T), T(0), atol=1)
+        @test_broken !isapprox(typemin(T), unsigned(T)(0), atol=1)
+
+        @test !isapprox(typemin(T)+T(10), T(10))
+        @test !isapprox(typemin(T)+T(10), unsigned(T)(10))
+        @test !isapprox(typemin(T)+T(10), T(10), atol=0.99)
+        @test !isapprox(typemin(T)+T(10), unsigned(T)(10), atol=0.99)
+        @test_broken !isapprox(typemin(T)+T(10), T(10), atol=1)
+        @test !isapprox(typemin(T)+T(10), unsigned(T)(10), atol=1)
+
+        @test isapprox(typemin(T), 0.0, rtol=1)
+    end
+end