@stdlib/blas-ext-base-dsorthp/lib/ndarray.js

Sort a double-precision floating-point strided array using heapsort.

/**
* @license Apache-2.0
*
* Copyright (c) 2020 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
*    http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/

'use strict';

// MODULES //

var isPositiveZero = require( '@stdlib/math-base-assert-is-positive-zero' );
var isnan = require( '@stdlib/math-base-assert-is-nan' );
var floor = require( '@stdlib/math-base-special-floor' );


// MAIN //

/**
* Sorts a double-precision floating-point strided array using heapsort.
*
* ## Notes
*
* -   This implementation uses an in-place algorithm derived from the work of Floyd (1964).
*
* ## References
*
* -   Williams, John William Joseph. 1964. "Algorithm 232: Heapsort." _Communications of the ACM_ 7 (6). New York, NY, USA: Association for Computing Machinery: 347–49. doi:[10.1145/512274.512284](https://doi.org/10.1145/512274.512284).
* -   Floyd, Robert W. 1964. "Algorithm 245: Treesort." _Communications of the ACM_ 7 (12). New York, NY, USA: Association for Computing Machinery: 701. doi:[10.1145/355588.365103](https://doi.org/10.1145/355588.365103).
*
* @param {PositiveInteger} N - number of indexed elements
* @param {number} order - sort order
* @param {Float64Array} x - input array
* @param {integer} stride - index increment
* @param {NonNegativeInteger} offset - starting index
* @returns {Float64Array} input array
*
* @example
* var Float64Array = require( '@stdlib/array-float64' );
*
* var x = new Float64Array( [ 1.0, -2.0, 3.0, -4.0 ] );
*
* dsorthp( x.length, 1.0, x, 1, 0 );
* // x => <Float64Array>[ -4.0, -2.0, 1.0, 3.0 ]
*/
function dsorthp( N, order, x, stride, offset ) {
	var parent;
	var child;
	var v1;
	var v2;
	var n;
	var t;
	var i;
	var j;
	var k;

	if ( N <= 0 || order === 0.0 ) {
		return x;
	}
	// For a positive stride, sorting in decreasing order is equivalent to providing a negative stride and sorting in increasing order, and, for a negative stride, sorting in decreasing order is equivalent to providing a positive stride and sorting in increasing order...
	if ( order < 0.0 ) {
		stride *= -1;
		offset -= (N-1) * stride;
	}
	// Set the initial heap size:
	n = N;

	// Specify an initial "parent" index for building the heap:
	parent = floor( N / 2 );

	// Continue looping until the array is sorted...
	while ( true ) {
		if ( parent > 0 ) {
			// We need to build the heap...
			parent -= 1;
			t = x[ offset+(parent*stride) ];
		} else {
			// Reduce the heap size:
			n -= 1;

			// Check if the heap is empty, and, if so, we are finished sorting...
			if ( n === 0 ) {
				return x;
			}
			// Store the last heap value in a temporary variable in order to make room for the heap root being placed into its sorted position:
			i = offset + (n*stride);
			t = x[ i ];

			// Move the heap root to its sorted position:
			x[ i ] = x[ offset ];
		}
		// We need to "sift down", pushing `t` down the heap to in order to replace the parent and satisfy the heap property...

		// Start at the parent index:
		j = parent;

		// Get the "left" child index:
		child = (j*2) + 1;

		while ( child < n ) {
			// Find the largest child...
			k = child + 1;
			if ( k < n ) {
				v1 = x[ offset+(k*stride) ];
				v2 = x[ offset+(child*stride) ];

				// Check if a "right" child exists and is "bigger"...
				if ( v1 > v2 || isnan( v1 ) || (v1 === v2 && isPositiveZero( v1 ) ) ) { // eslint-disable-line max-len
					child += 1;
				}
			}
			// Check if the largest child is bigger than `t`...
			v1 = x[ offset+(child*stride) ];
			if ( v1 > t || isnan( v1 ) || ( v1 === t && isPositiveZero( v1 ) ) ) { // eslint-disable-line max-len
				// Insert the larger child value:
				x[ offset+(j*stride) ] = v1;

				// Update `j` to point to the child index:
				j = child;

				// Get the "left" child index and repeat...
				child = (j*2) + 1;
			} else {
				// We've found `t`'s place in the heap...
				break;
			}
		}
		// Insert `t` into the heap:
		x[ offset+(j*stride) ] = t;
	}
}


// EXPORTS //

module.exports = dsorthp;