My Integer Doesn't fit

I was playing on my computer and accidentally tried this expression to see what the computer would output:

julia> 9007199254740992.0 + 1.0 == 9007199254740992.0

The REPL output was:

julia> 9007199254740992.0 + 1.0 == 9007199254740992.0
true

This is obviously incorrect mathematically. However, this arbitrary number is the maximum integer that a 64-bit float can store. In Julia, this number can be found using the maxintfloat function with the Float64 type:

julia> maxintfloat(Float64) + 1 == maxintfloat(Float64)
true

Interestingly enough, adding two “fixes” the comparison:

julia> maxintfloat(Float64) + 2 == maxintfloat(Float64)
false

Other float types also have their own largest integer values that they can represent:

julia> maxintfloat(Float64)
9.007199254740992e15

julia> maxintfloat(Float32)
1.6777216f7

julia> maxintfloat(BigFloat)
1.15792089237316195423570985008687907853269984665640564039457584007913129639936e+77

I guess the takeaway is that using something like Float32 for variables that store amounts of money is not advisable, as you run the risk of losing valuable information for large amounts. Float64 might suffice, but it also has its limitations. On the other hand, integer types can store much larger integer values:

julia> typemax(Int64)
9223372036854775807

julia> typemax(Int32)
2147483647

The maximum value for a 64-bit integer is three orders of magnitude larger than its float counterpart:

julia> typemax(Int64) / maxintfloat(Float64)
1024.0

julia> typemax(Int32) / maxintfloat(Float32)
128.0f0