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> @benchmark x + y setup=((x, y) = (SimpleRatio(rand(-20:20), rand(2:20)), SimpleRatio(rand(-20:20), rand(2:20))))
BenchmarkTools.Trial: 10000 samples with 1000 evaluations.
 Range (min … max):  1.727 ns … 28.575 ns  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     1.739 ns              ┊ GC (median):    0.00%
 Time  (mean ± σ):   1.753 ns ±  0.445 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

            ▂ ▃ ▃ ▃ ▄ ▆ ▇ █ ▆ ▅  ▅ ▇ ▄ ▁
  ▂▁▂▁▃▁▅▁█▁█▁█▁█▁█▁█▁█▁█▁█▁█▁█▁▁█▁█▁█▁█▁▆▁▃▁▃▁▃▁▃▁▃▁▃▁▃▁▃▁▂ ▄
  1.73 ns        Histogram: frequency by time        1.76 ns <

 Memory estimate: 0 bytes, allocs estimate: 0.

julia> @benchmark x + y setup=((x, y) = (FastRational(rand(-20:20), rand(2:20)), FastRational(rand(-20:20), rand(2:20))))
BenchmarkTools.Trial: 10000 samples with 1000 evaluations.
 Range (min … max):  3.192 ns … 89.167 ns  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     3.215 ns              ┊ GC (median):    0.00%
 Time  (mean ± σ):   3.307 ns ±  1.820 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

    ▃█▆█▃▂
  ▄███████▅▄▃▃▃▃▃▃▃▃▃▂▂▂▂▂▂▂▂▂▂▂▁▂▂▂▂▁▂▂▂▂▂▂▁▂▂▂▂▂▂▂▂▂▁▂▂▂▂▂ ▃
  3.19 ns        Histogram: frequency by time        3.45 ns <

 Memory estimate: 0 bytes, allocs estimate: 0.

julia> @benchmark x + y setup=((x, y) = (Rational(rand(-20:20), rand(2:20)), Rational(rand(-20:20), rand(2:20))))
BenchmarkTools.Trial: 10000 samples with 996 evaluations.
 Range (min … max):  22.385 ns … 81.269 ns  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     32.777 ns              ┊ GC (median):    0.00%
 Time  (mean ± σ):   33.162 ns ±  4.743 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

                ▁  ▇  ▄▂ ▁▆▃  ▂█▃ ▁ ▇   ▁    ▁
  ▁▁▁▁▁▄▂▁▆▂▂█▄▃█▅▆█▇▇█████████████▅█▆▂▁█▇▁▂▁█▄▁▂▁▁▆▂▁▁▁▁▃▁▁▁ ▃
  22.4 ns         Histogram: frequency by time        45.8 ns <

 Memory estimate: 0 bytes, allocs estimate: 0.