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van der Corput low-discrepancy sequences


Pure JS implementation of van der Corput low-discrepancy sequences.

With npm:

$ npm install vdc

In the browser:

<script src="vdc.js"></script>

The browser exposes a variable VDC

The exported function VDC accepts a opts object with the following fields:

  • b (default 2) base for the sequence.
  • n (default 0) starting index for the sequence.

Calling without arguments will default to the aforementioned values.

The object returned by VDC exposes a next() method to get the next element.

The field last holds the most recently generated value (accessing the field does not trigger a recalculation)

For example:

//var VDC = require('vdc') // uncomment this line if in node 
var opts = {'n':0, 'b':2};
var generator = VDC(opts);
for(var i = 0; i != 10; ++i) console.log(;

The expected output is

0       (0/1)
0.5     (1/2)
0.25    (1/4)
0.75    (3/4)
0.125   (1/8)
0.625   (5/8)
0.375   (3/8)
0.875   (7/8)
0.0625  (1/16)
0.5625  (9/16)

make test will run the nodejs-based test.

make baseline will generate the test baselines using Mathematica by explicitly extracting and reversing the digits. The implementation is based off a tutorial

VanDerCorput[base_][len_] := Table[
  With[{digits = Reverse@IntegerDigits[n, base]},
   Sum[2^(-ii)*digits[[ii]], {ii, Length[digits]}]
   ], {n, len}]

0 is the first value. Some sources (notably Wikipedia) start the sequence at 1/2, but others (Glasserman "Monte Carlo Methods in Financial Engineering") claim that the original sequence definition started at 0.

Please consult the attached LICENSE file for details. All rights not explicitly granted by the Apache 2.0 license are reserved by the Original Author.