ssortsh

Sort a single-precision floating-point strided array using Shellsort.

Usage

var ssortsh = require( '@stdlib/blas/ext/base/ssortsh' );

ssortsh( N, order, x, stride )

Sorts a single-precision floating-point strided array x using Shellsort.

var Float32Array = require( '@stdlib/array/float32' );

var x = new Float32Array( [ 1.0, -2.0, 3.0, -4.0 ] );

ssortsh( x.length, 1.0, x, 1 );
// x => <Float32Array>[ -4.0, -2.0, 1.0, 3.0 ]

The function has the following parameters:

N: number of indexed elements.
order: sort order. If order < 0.0, the input strided array is sorted in decreasing order. If order > 0.0, the input strided array is sorted in increasing order. If order == 0.0, the input strided array is left unchanged.
x: input Float32Array.
stride: index increment.

The N and stride parameters determine which elements in x are accessed at runtime. For example, to sort every other element

var Float32Array = require( '@stdlib/array/float32' );
var floor = require( '@stdlib/math/base/special/floor' );

var x = new Float32Array( [ 1.0, -2.0, 3.0, -4.0 ] );
var N = floor( x.length / 2 );

ssortsh( N, -1.0, x, 2 );
// x => <Float32Array>[ 3.0, -2.0, 1.0, -4.0 ]

Note that indexing is relative to the first index. To introduce an offset, use typed array views.

var Float32Array = require( '@stdlib/array/float32' );
var floor = require( '@stdlib/math/base/special/floor' );

// Initial array...
var x0 = new Float32Array( [ 1.0, 2.0, 3.0, 4.0 ] );

// Create an offset view...
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var N = floor( x0.length/2 );

// Sort every other element...
ssortsh( N, -1.0, x1, 2 );
// x0 => <Float32Array>[ 1.0, 4.0, 3.0, 2.0 ]

ssortsh.ndarray( N, order, x, stride, offset )

Sorts a single-precision floating-point strided array x using Shellsort and alternative indexing semantics.

var Float32Array = require( '@stdlib/array/float32' );

var x = new Float32Array( [ 1.0, -2.0, 3.0, -4.0 ] );

ssortsh.ndarray( x.length, 1.0, x, 1, 0 );
// x => <Float32Array>[ -4.0, -2.0, 1.0, 3.0 ]

The function has the following additional parameters:

offset: starting index.

While typed array views mandate a view offset based on the underlying buffer, the offset parameter supports indexing semantics based on a starting index. For example, to access only the last three elements of x

var Float32Array = require( '@stdlib/array/float32' );

var x = new Float32Array( [ 1.0, -2.0, 3.0, -4.0, 5.0, -6.0 ] );

ssortsh.ndarray( 3, 1.0, x, 1, x.length-3 );
// x => <Float32Array>[ 1.0, -2.0, 3.0, -6.0, -4.0, 5.0 ]

Notes

If N <= 0 or order == 0.0, both functions return x unchanged.
The algorithm distinguishes between -0 and +0. When sorted in increasing order, -0 is sorted before +0. When sorted in decreasing order, -0 is sorted after +0.
The algorithm sorts NaN values to the end. When sorted in increasing order, NaN values are sorted last. When sorted in decreasing order, NaN values are sorted first.
The algorithm has space complexity O(1) and worst case time complexity O(N^(4/3)).
The algorithm is efficient for shorter strided arrays (typically N <= 50).
The algorithm is unstable, meaning that the algorithm may change the order of strided array elements which are equal or equivalent (e.g., NaN values).
The input strided array is sorted in-place (i.e., the input strided array is mutated).

Examples

var round = require( '@stdlib/math/base/special/round' );
var randu = require( '@stdlib/random/base/randu' );
var Float32Array = require( '@stdlib/array/float32' );
var ssortsh = require( '@stdlib/blas/ext/base/ssortsh' );

var rand;
var sign;
var x;
var i;

x = new Float32Array( 10 );
for ( i = 0; i < x.length; i++ ) {
    rand = round( randu()*100.0 );
    sign = randu();
    if ( sign < 0.5 ) {
        sign = -1.0;
    } else {
        sign = 1.0;
    }
    x[ i ] = sign * rand;
}
console.log( x );

ssortsh( x.length, -1.0, x, -1 );
console.log( x );

References

Shell, Donald L. 1959. "A High-Speed Sorting Procedure." Communications of the ACM 2 (7). Association for Computing Machinery: 30–32. doi:10.1145/368370.368387.
Sedgewick, Robert. 1986. "A new upper bound for Shellsort." Journal of Algorithms 7 (2): 159–73. doi:10.1016/0196-6774(86)90001-5.
Ciura, Marcin. 2001. "Best Increments for the Average Case of Shellsort." In Fundamentals of Computation Theory, 106–17. Springer Berlin Heidelberg. doi:10.1007/3-540-44669-9_12.