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1.0.0 • Public • Published


Cartesian cross-product as a first class object. Naive cross-products can rapidly consume vast amounts of memory and degrade exponentially in performance. Generator based approaches conserve RAM, but are not typically performant. CXProduct supports high-speed, low memory virtual Cartesian cross-product creation and use through the use of lazy evaluation, i.e. rows of the cross-product are not created until needed by calling functions.


npm install cxproduct

Browser code can also be found in the browser directory at


new CXProduct(arrayOfArrays,{cache}={}) - Creates a virtual Cartesian cross-product based on the arrays. A copy of the top level wrapping array is created, which means the contained arrays are not. This way they can be manipulated (added to, deleted from) by code outside the CXProduct. If cache is true, then all get, has, indexOf will all cache results. DO NOT modify the arrays with an external program if caching is on unless you call flush() each time you make a modification.

The following methods are supported:

.add(array,...) - Adds the array to the collection of arrays already associated with the CXProduct. Invalidates the cache, if any.

.push(index,element) - Adds the element to the array at the index in the collection of arrays associated with the CXProduct. Invalidates the cache, if any.

.forEach(callback,{test,cache}={}) - Iterates over the CXProduct and invokes the callback for each row, optionally matching the row against a provided pattern or passing the provided boolean test. The callback takes the signature callback(row,index). The optional test has the signature test(array) and should return true or false. It is not recommended to loop through the CXProduct using get and a counter. The access algorithms are different and the one under forEach is optimized for forward moving access rather than random access.

.get(index,{test,cache}={}) - Return row at index. Allocates memory for the row. Repeated calls will not return the same object. Unless cache===true or the CXProduct was created with the cache=true option, no cache is created with the CXProduct since underlying collections may be changed by application code in a manner than changes the nature of the CXProduct.

.has(row,{cache}={}) - Returns true if row exists and false otherwise.

.indexable() - Returns a Proxy that can be index accessed like an array. Note, this will be a lot slower than .forEach if you are trying to iterate.

.indexOf(row,{cache}={}) - Return index where the row exists, returns -1 if row does not exist

.intersection(cxproduct) - Returns a new CXProduct that is an intersection of the current CXProduct with the one provided as an argument

.verify(index,row,{cache}={}) - Verifies that the index still contains the row in case the arrays defining the CXProduct have changed.


CXProduct is more performant than naive cross-product generation from a memory and speed perspective once the matrix is larger than 5x5. It is more performant than a generator approach once a matrix is larger than 3x3. At 3x3 performance is almost indistinguishable due to clock timing in JavaScript.

Basic Ops/Sec +/- Min Max Sample
construct 5x5 naive# 239 24 56 Infinity 100
construct 5x5 generator# Infinity Infinity 1786 Infinity 100
construct 5x5 CXProduct# Infinity Infinity 4082 Infinity 100
naive 5x5 forEach# 396 40 40 Infinity 100
generator 5x5 forEach# Infinity Infinity 29 Infinity 100
CXProduct 5x5 forEach# 372 37 171 Infinity 100
construct and iterate 3x3 naive# Infinity Infinity 962 Infinity 100
construct and iterate 3x3 generator# Infinity Infinity 1923 Infinity 100
construct and iterate 3x3 CXProduct# Infinity Infinity 2597 Infinity 100
construct and iterate 5x5 naive# 26 3 11 41 100
construct and iterate 5x5 generator# 16 2 13 21 100
construct and iterate 5x5 CXProduct# 118 12 66 Infinity 100
construct and iterate 6x6 naive# 3 0 3 3 100
construct and iterate 6x6 generator# 5 1 4 6 100
construct and iterate 6x6 CXProduct# 34 3 28 78 100

Building & Testing

Building, testing and quality assessment are conducted using Mocha, Chai, Istanbul, Benchtest, Code Climate, and Codacity.

For code quality assessment purposes, the cyclomatic complexity threshold is set to 10.

Updates (reverse chronological order)

2020-07-15 v1.0.0 Finally added unit and performance tests! Added caching. Calling interfaces changed to support caching. Added indexable.

2020-07-14 v0.0.3 Updated documentation.

2020-06-07 v0.0.2 Updated documentation.

2016-03-30 v0.0.1 First public commit.


This software is provided as-is under the MIT license.


Credit to Gavin Kistner for the core code:


npm i cxproduct

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