Originally posted at http://ceruleanjs.joeyrobert.org/.

CeruleanJS has a pseudo-legal move generation algorithm. It generates all possible moves for a position (even ones that put the king in check or castle the king through check) and the full legality is tested during the addMove() function. This is because the move needs to be added before check detection can work. Fast move generation is key to a strong chess engine: the more moves you can generate and evaluate per second, the stronger it will be. This post is about my experiences optimizing CeruleanJS’s move generation.

At the start of this document, CeruleanJS was weighing in at a measly 200,000 moves/s on my MacBook Pro. Cerulean (the original C implementation) managed 20,000,000 moves/s in a single thread. CeruleanJS hopes to achieve this level of performance, the question is: can it?

Faster Piece List

A piece list is a cache of which board indices are occupied by which side. CeruleanJS has two piece lists, one for each white and black. Think of it as a way to optimize looping over all 64 squares. Instead we only need to loop over the pieces we’re generating moves for (maximum 32).

The first iteration of CeruleanJS contained a dead simple piece list implementation:

class PieceList {
    constructor() {
        this.indices = [];
    }

    push(index) {
        this.indices.push(index);
    }

    remove(index) {
        let reverseIndex = this.indices.indexOf(index);
        this.indices.splice(reverseIndex, 1);
    }
}

There’s a couple things wrong with this implementation. First, the indices array is set to an initial length of 0, so each push has to allocate more memory to store the new item. Second, removing an index is expensive. It requires a linear scan of the indices array to remove a specified index, which is O(n). Third, indices is spliced to remove the found index. This reduces the size of the array, but forces all values after reverseIndex to be shifted by one. I’m can’t speculate on the internals of the JS Array data structure, but this may cause a rewrite of up to 16 squares (again, O(n)). What data structure would allow quick creation and removal?

What if we implement a scheme such that when an index is removed, it is replaced by current last element in the list? A piece list only needs to contain at most 16 pieces. We can do the allocation for all 16 elements up front. Also, what if we maintain a reverse board array that maps board index to index in piece list? This would remove the linear scan needed to find the object to remove.

class PieceList {
    constructor() {
        this.indices = new Array(16);
        this.reverse = new Array(constants.WIDTH * constants.HEIGHT);
        this.length = 0;
    }

    push(index) {
        this.reverse[index] = this.length;
        this.indices[this.length] = index;
        this.length++;
    }

    remove(index) {
        this.length--;
        var reverseIndex = this.reverse[index];
        this.indices[reverseIndex] = this.indices[this.length];
        this.reverse[this.indices[reverseIndex]] = reverseIndex;
        this.indices[this.length] = undefined;
        this.reverse[index] = undefined;
    }
}

This allows for an O(1) piece list implementation for both adding and removing items.

Remove ‘let’ keyword in tight loops

The let keyword is a relatively new addition to ES6, which allows variables to be defined at the block level (for, if, while, do, switch, or { }). This is great for encapsulating variables in a for loop or if statement.

However when let is used two levels deep in nested for loops, all that variable allocation and deallocation can be expensive and can generate a lot of garbage.

The solution is to use a single variable declared outside of any loop and to modify this value as necessary. This trades off safety for performance, but resulted in a large performance increase for Cerulean :).

Switch expensive lookups from Objects to Arrays

A significant performance increase was noticed when two lookup objects were converted to arrays. These lookup objects were used in tight loops (generateMoves(), addMove(), subtractMove()) where the additional overhead of casting a value to a string was cost prohibitive.

Add history less

CeruleanJS uses an internal history array to restore unrecoverable information (i.e. information that cannot be inferred) during the subtractMove() function. Some examples of unrecoverable information are:

• En passant
• Castling
• Half move clock
• Zobrist keys (these are recoverable but are loaded from the history array for simplicity)

It makes sense for addMove() and subtractMove() to be exact inverses of each other, where addMove() pushes a new array to the history array, and subtractMove() pops this off. This however would generate an array for every move. As it turns out, at each node in the search tree, all subsequent moves share the same history. Therefore we only need to save to the history array once per move generation instead of once for every move in every move generation, saving dozens of array allocations.

Move as a 32-bit integer

This may seem obvious to other chess programmers, but using a single 32-bit integer to represent a move object is significantly faster than using an object-structure like an array. CeruleanJS initially used a simple array [from, to, promotion]. [] in JavaScript is short for new Array(), so in reality you’re doing a lot of object allocation. Integers create less garbage in this respect.

Cerulean’s move data structure is:

ORDER  BITS   CAP PRO TO      FROM
000000 000000 000 000 0000000 0000000
^ MSB                           LSB ^

This breaksdown to the following distribution:

• 7 bits for FROM index
• 7 bits for TO index
• 3 bits for PROmotion piece (Q/R/B/N)
• 3 bits for CAPtured piece (any or empty)
• 6 bits for BITS (metadata)
• 6 bits for ORDERing

This dense move structure requires less data to be saved on the board’s internal history array.

Have your move generator help you out

Your pseudolegal move generator has a lot of information about the move your generating. Is it a pawn move? Is it a capture? Is it a double push? Save this information in a metadata field in your move and base your addMove()/subtractMove() functions on it.

Originally CeruleanJS only passed in [from, to, promotion] and inferred all other information from the board state. This proved to add a lot of overhead to addMove()/subtractMove() when this information is available earlier in the pseudolegal move generator. For a capture for instance — you’d be essentially double checking that the board[to] is occupied by an opponent square: in generateMoves() and addMove().

CeruleanJS switched to a “bits” based addMove()/subtractMove() functions, where the “bits” flag in a move is used to switch() to specialized move for that bit type.

Pass moves array by reference

The move generator is a single function, generateMoves() loops over all pieces for a side and has a big switch statement for the piece we’re looking at (pawn, knight, bishop, rook, queen, king). This calls a bunch of other functions pawnMoves(), rookMoves(), etc.

Originally these functions returned a list which was concatenated to the main move list.

Instead of using concat, we can use a single move array that is passed by reference to all the sub functions (pawnMoves(moves), etc.), which then modify it. Using a single array with a mutable state that is passed by reference to other objects that modify it is considered bad practice almost anywhere that codes JavaScript. However, by doing this we reduce the amount of garbage arrays (and .concat()) created during the move generation process.

Use TypedArrays (Uint32Array) for Board and Piece List

This makes the lookup of board positions significantly faster. Roughly a 2x speed increase was noticed when switching to this. This is because less checks are required on item access in JavaScript.

An additional increase of 14% was seen switching from Arrays to Uint32Array in the PieceList.

Testing showed this would not be as advantageous for Move lists (due to the number Uint32Array allocations, which can be as large as 218 in one turn!). A possible optimization here is to use one move list per depth and maintain the list of preallocated move lists in the board. More testing is needed on this front.

Future Improvements

A number of other data structures in my application could be switched to TypedArrays, namely Zobrist keys, which are looked up frequently during the addMove()/subtractMove() cycle. However, this did not prove to be as beneficial since Zobrist keys are currently a multi-dimensional data structure. JavaScript only supports a 1 dimensional TypedArray and the multiplication required to generate the key look took away any possible speed improvements.

As a whole, these improvements gave a 10-15x speed boost for CeruleanJS, which clocks in at around 2,500,000 moves/s. The performance remains an order of magnitude slower than Cerulean in C (and 2 orders of magnitude slower then a well optimized state-of-the-art chess move generator), but it will suffice for a sufficiently strong JavaScript chess engine.

Until next time, happy chessing!