Inconsistent behavior around tolerances in isequal and isless

[hyrodium]

Examples of inconsistent behaviors

I am trying to remove method isless(::Point, ::Point) as discussed in #300 (comment), and I found some inconsistent behavior in isequal and isless.

julia> using Luxor

julia> p1 = Point(1, 1)
Point(1.0, 1.0)

julia> p2 = Point(1, 2)
Point(1.0, 2.0)

julia> p3 = Point(0.99999999, 3)
Point(0.99999999, 3.0)

julia> p1 < p2 < p3 < p1, p1 < p1  # does not satisfy transitive relation
(true, false)

julia> p4 = Point(1.000000001, 3)
Point(1.000000001, 3.0)

julia> p5 = Point(1.000000008, 3)
Point(1.000000008, 3.0)

julia> p6 = Point(1.000000015, 3)
Point(1.000000015, 3.0)

julia> p4 == p5 == p6, p4 == p6  # does not satisfy transitive relation
(true, false)

Proposal on removing the tolerances

I think removing these tolerances would be better for the following points.

Specialized unique method can be removed.

This is related to the following TODO comment.

Luxor.jl/src/point.jl

Lines 160 to 172 in 6c271e9

	# a unique that works better on points?
	# I think this uses ==
	# TODO perhaps unique(x -> round(x, sigdigits=13), myarray) ?
	# "any implementation of unique with a tolerance will have some odd behaviors" Steven GJohnson
	function Base.unique(pts::Array{Point,1})
	apts = Point[]
	for pt in pts
	if pt ∉ apts
	push!(apts, pt)
	end
	end
	return apts
	end

Base.hash will be consistent.

The Base.hash should be consistent with Base.isequal. Currently, isequal(x::Point, y::Point) does not imply hash(x)==hash(y).

julia> isequal(p4, p5)
true

julia> hash(p4) == hash(p5)
false

https://github.com/JuliaLang/julia/blob/396abe4fdc8615e162462910bfc16729be7c95ed/base/hashing.jl#L5-L9

[cormullion]

For 4.0 or a future version?

[hyrodium]

Removing the tolerances would be a breaking change, so I think this is for 4.0. (Or, remove the tolerances on v5 release?)

[cormullion]

Cool. I want to release v4.0 on Monday (choosing a day at random 😂), so I’m happy to merge PRs if the tests pass. Otherwise issues can be addressed for the following release cycle.

[hyrodium]

Thank you for notifying the release schedule!

[cormullion]

Well it's not so much a schedule :) - but it's probably a good idea to make a release fairly soon.