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Fast Statistics 🚀

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A high performance native ruby extension (written in C++) for computation of descriptive statistics.


This gem provides fast computation of descriptive statistics (min, max, mean, median, 1st and 3rd quartiles, population standard deviation) for a multivariate dataset (represented as a 2D array) in ruby.

It is ~11x faster than an optimal algorithm in hand-written ruby, and ~4.7x faster than the next fastest available ruby gem or native extension (see benchmarks below).


Add this line to your application's Gemfile:

gem 'fast_statistics'

And then execute:

$ bundle install

Or install it yourself as:

$ gem install fast_statistics


Given you have some multivariate (2-dimensional) data:

data = [
  [0.6269, 0.3783, 0.1477, 0.2374],
  [0.4209, 0.1055, 0.8000, 0.2023],
  [0.1124, 0.1021, 0.1936, 0.8566],
  [0.6454, 0.5362, 0.4567, 0.8309],
  [0.4828, 0.1572, 0.5706, 0.4085],
  [0.5594, 0.0979, 0.4078, 0.5885],
  [0.8659, 0.5346, 0.5566, 0.6166],
  [0.7256, 0.5841, 0.8546, 0.3918]

You can compute descriptive statistics for all the inner arrays as follows:

require "fast_statistics"
# Result: 
# [{:min=>0.1477,
#   :max=>0.6269,
#   :mean=>0.347575,
#   :median=>0.30785,
#   :q1=>0.214975,
#   :q3=>0.44045,
#   :standard_deviation=>0.18100761551658537},
#  {:min=>0.1055,
#   :max=>0.8,
#   :mean=>0.38217500000000004,
#   :median=>0.3116,
#   :q1=>0.1781,
#   :q3=>0.515675,
#   :standard_deviation=>0.26691825878909076},
#  ...,
#  {:min=>0.3918,
#   :max=>0.8546,
#   :mean=>0.639025,
#   :median=>0.6548499999999999,
#   :q1=>0.536025,
#   :q3=>0.75785,
#   :standard_deviation=>0.1718318709523935}]


Some alternatives compared are:

You can reivew the benchmark implementations at benchmark/benchmark.rb and run the benchmark with rake benchmark.


Comparing calculated statistics with 10 values for 8 variables...
Test passed, results are equal to 6 decimal places!

Benchmarking with 100,000 values for 12 variables...
Warming up --------------------------------------
descriptive_statistics   1.000  i/100ms
           Custom ruby   1.000  i/100ms
                narray   1.000  i/100ms
ruby_native_statistics   1.000  i/100ms
        FastStatistics   3.000  i/100ms
Calculating -------------------------------------
descriptive_statistics   0.473  (± 0.0%) i/s -      3.000  in   6.354555s
           Custom ruby   2.518  (± 0.0%) i/s -     13.000  in   5.169084s
                narray   4.231  (± 0.0%) i/s -     22.000  in   5.210299s
ruby_native_statistics   5.962  (± 0.0%) i/s -     30.000  in   5.041869s
        FastStatistics   28.417  (±10.6%) i/s -    141.000  in   5.012229s

        FastStatistics:   28.4 i/s
ruby_native_statistics:    6.0 i/s - 4.77x  (± 0.00) slower
                narray:    4.2 i/s - 6.72x  (± 0.00) slower
           Custom ruby:    2.5 i/s - 11.29x  (± 0.00) slower
descriptive_statistics:    0.5 i/s - 60.09x  (± 0.00) slower

Background & Implementation

The inspiration for this gem was a use-case in an analytics ruby application, where we frequently had to compute descriptive statistics for fairly large multivariate datasets. Calculations in ruby were not fast enough, so I first explored performing the computations natively in this repository. The results were promising, so I decided to package it as a ruby gem.

Note: This is an early release and should be considered unstable, at least until I'm confident in the stability & performance in a real world application setting. Feel free to test it out in non-critical scenarios/environments (let me know in this discussion thread or by filing an issue if you use it!). I'm also not really an expert in C++, so reviews & suggestions are welcome.

How is the performance achieved?

The following factors combined help this gem achieve high performance compared to available native alternatives and hand-written computations in ruby:

  • It is written in C++ and so can leverage the speed of native execution.
  • It minimises the number of operations by calculating the statistics in as few operations as possible (1 sort + 2 loops). Most native alternatives don't provide a built in way to get all these statistics at once. Instead, they only provide APIs where you make single calls for individual statistics. Through such an API, building this set of summary statistics typically ends up looping through the data more times than is necessary.
  • This gem uses explicit 128-bit-wide SIMD intrinsics (on platforms where they are available) to parallelize computations for 2 variables at the same time where possible, giving an additional speed advantage while still being single threaded.

Limitations of the current implementation

The speed gains notwithstanding, there are some limitations in the current implementation:

  • The variables in the 2D array must all have the same number of data points (inner arrays must have the same length) and contain only numbers (i.e. no nil awareness is present).
  • There is currently no API to calculate single statistics (although this may be made available in the future).


Bug reports and pull requests are welcome on GitHub at


The gem is available as open source under the terms of the MIT License.


Fast computation of descriptive statistics in ruby using native code and SIMD




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