function broadcastShapes( shapes ) {
	var ndims;
	var out;
	var dim;
	var sh;
	var n1;
	var n2;
	var d;
	var M;
	var N;
	var i;
	var j;

	M = shapes.length;
	out = [];
	if ( M === 0 ) {
		return out;
	}
	sh = shapes[ 0 ];
	N = sh.length;

	// If provided a single input shape array, then the broadcast shape is input shape...
	if ( M === 1 ) {
		// Need to manually copy to output shape, as shapes could be array-like objects...
		for ( i = 0; i < N; i++ ) {
			out.push( sh[ i ] );
		}
		return out;
	}
	// Determine the maximum dimensionality...
	ndims = [ N ];
	for ( i = 1; i < M; i++ ) {
		ndims.push( shapes[ i ].length );
		if ( ndims[ i ] > N ) {
			N = ndims[ i ];
		}
	}
	// Initialize the output array...
	for ( i = 0; i < N; i++ ) {
		out.push( 0 );
	}
	// Compute the broadcast shape...
	i = N - 1;
	while ( i >= 0 ) {
		n1 = ndims[ 0 ] - N + i;
		if ( n1 >= 0 ) {
			dim = sh[ n1 ];
		} else {
			dim = 1;
		}
		for ( j = 1; j < M; j++ ) {
			n2 = ndims[ j ] - N + i;
			if ( n2 >= 0 ) {
				d = shapes[ j ][ n2 ];
			} else {
				d = 1;
			}
			if ( dim === 1 ) {
				dim = d;
				continue;
			}
			if ( d === 1 || dim === d ) {
				// When either `d` is `1` or `d` equals the current output shape dimension, the current output shape dimension remains the same...
				continue;
			}
			// The current shape cannot be broadcast against one of the other shapes...
			return null;
		}
		out[ i ] = dim;
		i -= 1;
	}
	return out;
}
Broadcasts array shapes to a single shape.

## Notes

-   Two respective dimensions in two shape arrays are compatible if

    1.  the dimensions are equal.
    2.  one dimension is `1`.

-   The function returns `null` if provided incompatible shapes (i.e., shapes which cannot be broadcast with one another).

@param {Array<NonNegativeIntegerArray>} shapes - array of shape arrays
@returns {(NonNegativeIntegerArray|null)} broadcast shape (or `null`)

@example
var shapes = [
    [ 8, 1, 6, 1 ],
    [ 7, 1, 5 ]
];

var out = broadcastShapes( shapes );
// returns [ 8, 7, 6, 5 ]

@example
var shapes = [
    [ 5, 4 ],
    [ 1 ]
];

var out = broadcastShapes( shapes );
// returns [ 5, 4 ]

@example
var shapes = [
    [ 5, 4 ],
    [ 4 ]
];

var out = broadcastShapes( shapes );
// returns [ 5, 4 ]

@example
var shapes = [
    [ 15, 3, 5 ],
    [ 15, 1, 5 ]
];

var out = broadcastShapes( shapes );
// returns [ 15, 3, 5 ]

@example
var shapes = [
    [ 15, 3, 5 ],
    [ 3, 5 ]
];

var out = broadcastShapes( shapes );
// returns [ 15, 3, 5 ]

@example
var shapes = [
    [ 15, 3, 5 ],
    [ 3, 1 ]
];

var out = broadcastShapes( shapes );
// returns [ 15, 3, 5 ]

@example
var shapes = [
    [ 8, 1, 1, 6, 1 ],
    [ 1, 7, 1, 5 ],
    [ 8, 4, 1, 6, 5 ]
];

var out = broadcastShapes( shapes );
// returns [ 8, 4, 7, 6, 5 ]

@example
var shapes = [
    [ 8, 1, 1, 6, 1 ],
    [ 0 ]
];

var out = broadcastShapes( shapes );
// returns [ 8, 1, 1, 6, 0 ]

@example
var shapes = [
    [ 8, 1, 1, 6, 1 ],
    [ 8, 0, 1, 6, 1 ]
];

var out = broadcastShapes( shapes );
// returns [ 8, 0, 1, 6, 1 ]

@example
var shapes = [
    [ 8, 8, 1, 6, 1 ],
    [ 8, 0, 1, 6, 1 ]
];

var out = broadcastShapes( shapes );
// returns null

@example
var shapes = [
    [ 8, 0, 1, 6, 1 ],
    [ 8, 8, 1, 6, 1 ]
];

var out = broadcastShapes( shapes );
// returns null

@example
var shapes = [
    []
];

var out = broadcastShapes( shapes );
// returns []

@example
var shapes = [
    [],
    []
];

var out = broadcastShapes( shapes );
// returns []

@example
var shapes = [];

var out = broadcastShapes( shapes );
// returns []

@example
var shapes = [
    [ 3, 2, 1 ],
    []
];

var out = broadcastShapes( shapes );
// returns [ 3, 2, 1 ]

@example
var shapes = [
    [],
    [ 3, 2, 1 ]
];

var out = broadcastShapes( shapes );
// returns [ 3, 2, 1 ]