# Barsort — a number sorting project gone haywire

This Javascript module sorts numbers around twice as quick as the famously fast Timsort. It is a stable sort and it produces primarily a sorting index.

Barsort.js performs great and is finally passing its tests, but there is one remaining problem with it — much of its source code is completely haywire. The expansive challenge of optimising and testing a general purpose sort has combined here with my self-indulgent code style, impatience and a few personal frailties, to produce possibly my most unpresentable work yet :

**Barsort algorithm basics — a “counting sort”**

The input numbers are first tallied into bins as though calculating a histogram (by dividing by a suitable factor and casting to integer to get a bin number). Like this:` for(var i=0; i<e; i++) `

{ kysbin[i]=(binperval*(kysval[i]-minv))>>0 }

These “counting bins” are subsequently indexed by a fewer number of “placement bins”. The core of the algorithm was first developed to sort data roughly into histogram bars ( without sorting *within* the bars). The “counting bins” were subdivisions of the bars to reduce spillage between the bars. Anyway, so the cumulative sum of the populations of the placement bins is calculated so that for each placement bin an anchor position in the sorting index (output) is known (for values of bins range).

Like this:

for(var bin=0; bin<nbin; bin++){

//fillbar is current bar to fill

barofbin[bin]=fillbar

//here it is being allocated a bins tally

barsfill[fillbar]+=cntofbin[bin]

//when bar is full...

while(barsfill[fillbar]>=fcap){

barsfill[fillbar+1]+=barsfill[fillbar]-fcap

barsfill[fillbar]=fcap

fillbar++ //...fill next bar

nxtcap+=kysperbar-fcap //nxtcap and kysperbar are floats

fcap=nxtcap >>>0 //fcap is integer

} //(it differs for each bar)

}

Finally some curious indirected lookup and updating is done for each input to use the base placement info to assign inputs their position in the sorting index.

Here is that final ‘curious’ code:

var bapos=new Array(nbar); bapos[0]=0

for(var i=0;i<nbar-1;i++){ bapos[i+1]=bapos[i]+barsfill[i] }

for(var i=st; i<ov; i++){

var binofel=kysbin[i]

//(change barofbin if barsfill is empty)

while( barsfill[barofbin[binofel]]===0 ){

barofbin[binofel]++

}

barsfill[barofbin[binofel]]--

sortix[ bapos[barofbin[binofel]]++ ]=i

//sort index gets ordered by bar

}

// (this was not the unpresentable part...)

The counting sort is used to get elements quite close to where they should be but they need to be fine-sorted afterwards. The classic “insertion sort” is perfect for fine sorting as long it never has to move any elements too far. In early versions barsort relied on just insertsort to tidy up, but to improve performance on problem cases it was necessary to deal with far misplaced elements. For this I tested both mergesort and combsort, mergesort won out. The resulting hybrid sort was rather tricky to create and optimise, and amounts to a decent stable sorting routine by itself, its just not as good on its own as the champion *Timsort*.

**Comparison with Timsort**

Timsort is also known as “Pythons sort” and “probably THE fastest in-memory sort available” It is based on a very proficient combination of insertsort and mergesort that must be somewhat more refined than Barsort’s combination of the same (although I have not studied Timsorts implementation well enough to emulate any of it).

It is significant that Timsort can sort strings and other data while Barsort will only sort numbers. Also, Timsort sorts inplace and Barsort primarily sorts an index, but these latter differences only effect their relative performance on test cases which required very little actual sorting.

What motivated the development of Barsort is that it is basically about twice as fast as the Javascript port of Timsort on common random distributions. Barsort is potentially one of the fastest general purpose numeric sorts ever cobbled together, despite large parts of its source code having been abandoned in a possibly unredeemable state.