isapprox now tests max(atol,rtol*...) rather than atol+rtol*...

NEWS.md

@@ -132,6 +132,9 @@ Library improvements
   * `@test isequal(x, y)` and `@test isapprox(x, y)` now prints an evaluated expression when
     the test fails ([#22296]).
 
+  * `isapprox(x,y)` now tests `norm(x-y) <= max(atol, rtol*max(norm(x), norm(y)))`
+    rather than `norm(x-y) <= atol + ...`.
+
   * Uses of `Val{c}` in `Base` has been replaced with `Val{c}()`, which is now easily
     accessible via the `@pure` constructor `Val(c)`. Functions are defined as
     `f(::Val{c}) = ...` and called by `f(Val(c))`. Notable affected functions include:

base/floatfuncs.jl

@@ -203,7 +203,7 @@ end
 """
     isapprox(x, y; rtol::Real=sqrt(eps), atol::Real=0, nans::Bool=false, norm::Function)
 
-Inexact equality comparison: `true` if `norm(x-y) <= atol + rtol*max(norm(x), norm(y))`. The
+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
 argument `nans` determines whether or not NaN values are considered equal (defaults to false).
 
@@ -233,7 +233,7 @@ true
 ```
 """
 function isapprox(x::Number, y::Number; rtol::Real=rtoldefault(x,y), atol::Real=0, nans::Bool=false)
-    x == y || (isfinite(x) && isfinite(y) && abs(x-y) <= atol + rtol*max(abs(x), abs(y))) || (nans && isnan(x) && isnan(y))
+    x == y || (isfinite(x) && isfinite(y) && abs(x-y) <= max(atol, rtol*max(abs(x), abs(y)))) || (nans && isnan(x) && isnan(y))
 end
 
 const ≈ = isapprox

base/linalg/generic.jl

@@ -1299,7 +1299,7 @@ function isapprox(x::AbstractArray, y::AbstractArray;
     atol::Real=0, nans::Bool=false, norm::Function=vecnorm)
     d = norm(x - y)
     if isfinite(d)
-        return d <= atol + rtol*max(norm(x), norm(y))
+        return d <= max(atol, rtol*max(norm(x), norm(y)))
     else
         # Fall back to a component-wise approximate comparison
         return all(ab -> isapprox(ab[1], ab[2]; rtol=rtol, atol=atol, nans=nans), zip(x, y))