min does not return the minimum with respect to isless when values tie #868

min is documented to "return the minimum of the arguments, with respect to isless", but for a Dual that ties in value it returns whichever argument comes first:

julia> using ForwardDiff

julia> x = ForwardDiff.Dual(48.0, 1.0);

julia> isless(48.0, x)
true

julia> min(x, 48.0)
Dual{Nothing}(48.0,1.0)

julia> min(48.0, x)
Dual{Nothing}(48.0,0.0)

Since #695, isless breaks a value tie on the partials, so 48.0 is the smaller argument here, but min(x, 48.0) returns x. min picks its argument by value only, so on a tie the result depends on argument order rather than on isless.

I ran into this through differentiating Interpolations.jl, whose linear extrapolation clamps with min and then bounds-checks the result with <=, so it throws a BoundsError under --check-bounds=yes when differentiating exactly at the last knot.

ForwardDiff 1.4.6, Julia 1.12.7.