Integer Domain 

**** should be compatible with 5.xx function intlimit() local floor = math.floor  get highest power of 2 which Lua can still handle as integer local step = 2 while true do local nextstep = step*2 if nextstep(nextstep1) == 1 and nextstep > 0 then step = nextstep else break end end  now get the highest number which Lua can still handle as integer local limit,step = step,floor(step/2) while step > 0 do local nextlimit = limit+step if nextlimit(nextlimit1) == 1 and nextlimit > 0 then limit = nextlimit end step = floor(step/2) end return limit end
Example:
local limit = intlimit() print() print("IntegerDomain  what is the largest supported integer number?") print() **** do not rely on Lua to print "limit" properly by itself! local printablelimit = string.format("%d", limit)  fails under Lua! local printablelimit = string.format("%.16e", limit) print("supported integer range is: " .. printablelimit .. "...+" .. printablelimit)
As you can see, Lua has no problems to process large integer numbers  as long as you don't try to convert them into strings ;)
To make sure integer numbers are properly converted into string (without scientific notation), rather than using tostring(x), use format.string("%.0f",x)
Hmmm, let me think about the requirements:
Additionally, there are two other assumptions I made
Both assumptions may easily be checked explicitly (don't forget to replace "floor" by "ceil" when testing negative numbers!).
If the requirements apply, it is possible to use "successive approximation" in order to get the largest presentable integer.
As I do not mention any concrete results, I do not really assume IEEE apart from my assumptions shown above (signmagnitude coding guarantees the symmetry) and the test I've chosen:
floor(x) == x
should already be sufficient in order to test if a number is integral
x1 ~= x
has just been added in order to exclude NaN and Infinity
 I ran this algo with lua 5.1 and it did not quite worked : it gave 9007199254740994 as the max integer, but print(string.format("%0.f", intlimit()1) returns 9007199254740992 instead of 9007199254740993. I corrected three things in the code :
floor(x) == x
is useless, since you start from integers and do integer stable operation, even when going further than the max integer (floating numbers larger than what the mantis can represent are always integers)
x1 ~= x
has been replaced by x(x1) == 1
it check whether x1 is also representable (it also exclude NaN and infinity, but they are unreachable anyway)
x > 0
4xel