js-vdc/README.md

# VDC

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

## Installation

With [npm](http://npm.im/vdc):

```bash
$ npm install vdc
```

In the browser:

```html
<script src="vdc.js"></script>
```

The browser exposes a variable `VDC`

## Usage

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:

```js
//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(generator.next());
```

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)
```

## Testing

`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
<http://reference.wolfram.com/mathematica/CUDALink/tutorial/Applications.html>

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

## Notes

`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`.

## License

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.

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