Ratios

This package provides types similar to Julia's Rational type, which make some sacrifices but have better computational performance at the risk of greater risk of overflow.

Currently the only type provided is SimpleRatio(num, den) for two integers num and den.

Demo:

julia> x, y, z = SimpleRatio(1, 8), SimpleRatio(1, 4), SimpleRatio(2, 8)
(SimpleRatio{Int}(1, 8), SimpleRatio{Int}(1, 4), SimpleRatio{Int}(2, 8))

julia> x+y
SimpleRatio{Int}(12, 32)

julia> x+z
SimpleRatio{Int}(3, 8)

y and z both represent the rational number 1//4, but when performing arithmetic with x z is preferred because it has the same denominator and is less likely to overflow.

To detect overflow, SaferIntegers.jl is recommended:

julia> using Ratios, SaferIntegers

julia> x, y = SimpleRatio{SafeInt8}(1, 20), SimpleRatio{SafeInt8}(1, 21)
(SimpleRatio{SafeInt8}(1, 20), SimpleRatio{SafeInt8}(1, 21))

julia> x + y
ERROR: OverflowError: 20 * 21 overflowed for type Int8
Stacktrace:
[...]

FastRationals is another package with safety and performance characteristics that lies somewhere between SimpleRatio and Rational:

julia> @btime x + y setup=((x, y) = (SimpleRatio(rand(-20:20), rand(2:20)), SimpleRatio(rand(-20:20), rand(2:20))));
  1.969 ns (0 allocations: 0 bytes)

julia> @btime x + y setup=((x, y) = (FastRational(rand(-20:20), rand(2:20)), FastRational(rand(-20:20), rand(2:20))));
  3.192 ns (0 allocations: 0 bytes)

julia> @btime x + y setup=((x, y) = (Rational(rand(-20:20), rand(2:20)), Rational(rand(-20:20), rand(2:20))));
  23.065 ns (0 allocations: 0 bytes)