Module:math/compare

local math_module = "Module:math"

local function is_NaN(...)
	is_NaN = require(math_module).is_NaN
	return is_NaN(...)
end

local function sign(...)
	sign = require(math_module).sign
	return sign(...)
end

--[==[
A comparison function for numbers, which returns {true} if {a} sorts before {b}, or otherwise {false}; it can be used as the sort function with {table.sort}.

This function is roughly equivalent to the {<} operator, but contains the following special considerations in accordance with the {{w|IEEE 754}} standard:
* {{w|NaN}} is sorted as though it has a larger absolute value than infinity ({-NaN < -Inf}; {+Inf < +NaN}).
* {{w|Signed zero}} is acknowledged, with {-0 < +0}.]==]
return function(a, b)
	-- <, > and == canot return true if either `a` or `b` are NaN.
	if a < b then
		return true
	-- Use > then == instead of >=, so that the ±0 check is only done when `a`
	-- and `b` are equal.
	elseif a > b then
		return false
	elseif a == b then
		-- 1/(+0) is Inf; 1/(-0) is -Inf.
		return a == 0 and b == 0 and 1 / a < 1 / b or false
	-- One or both must be NaN, and NaN is the only number that returns false
	-- to a self-equality check, so if `a` == `a` then `b` is NaN (and vice-
	-- versa). -NaN sorts before everything and +NaN after everything, so the
	-- sign determines the result.
	elseif not is_NaN(a) then -- `b` is NaN
		return sign(b) == 1
	elseif not is_NaN(b) then -- `a` is NaN
		return sign(a) == -1
	end
	-- If both are NaN, only return true if `a` is -NaN and `b` is +NaN.
	return sign(a) < sign(b)
end