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* @license Apache-2.0
*
* Copyright (c) 2026 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.
*/
/* eslint-disable max-params, max-len */
'use strict';
// MODULES //
var gcopy = require( '@stdlib/blas/base/gcopy' ).ndarray;
var arraylike2object = require( '@stdlib/array/base/arraylike2object' );
var accessors = require( './accessors.js' );
// FUNCTIONS //
/**
* Calculates the forward difference of a strided array using alternative indexing semantics.
*
* @private
* @param {PositiveInteger} N - number of indexed elements
* @param {NumericArray} x - input array
* @param {integer} strideX - stride length for `x`
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @param {NonNegativeInteger} N1 - number of indexed elements for `prepend`
* @param {NumericArray} prepend - prepend array
* @param {integer} strideP - stride length for `prepend`
* @param {NonNegativeInteger} offsetP - starting index for `prepend`
* @param {NonNegativeInteger} N2 - number of indexed elements for `append`
* @param {NumericArray} append - append array
* @param {integer} strideA - stride length for `append`
* @param {NonNegativeInteger} offsetA - starting index for `append`
* @param {NumericArray} out - output array
* @param {integer} strideOut - stride length for `out`
* @param {NonNegativeInteger} offsetOut - starting index for `out`
* @returns {NumericArray} output array
*/
function base( N, x, strideX, offsetX, N1, prepend, strideP, offsetP, N2, append, strideA, offsetA, out, strideOut, offsetOut ) {
var total;
var prev;
var curr;
var ix;
var io;
var ip;
var ia;
var i;
total = N + N1 + N2;
if ( total <= 1 ) {
return out;
}
// Compute forward differences:
if ( N1 === 0 && N2 === 0 ) {
ix = offsetX;
io = offsetOut;
prev = x[ ix ];
for ( i = 1; i < N; i++ ) {
ix += strideX;
curr = x[ ix ];
out[ io ] = curr - prev;
prev = curr;
io += strideOut;
}
return out;
}
// Compute forward differences over the list of prepended values:
if ( N1 > 0 ) {
io = offsetOut;
ip = offsetP;
prev = prepend[ ip ];
for ( i = 1; i < N1; i++ ) {
ip += strideP;
curr = prepend[ ip ];
out[ io ] = curr - prev;
prev = curr;
io += strideOut;
}
if ( N > 0 ) {
curr = x[ offsetX ];
out[ io ] = curr - prev;
prev = curr;
io += strideOut;
} else if ( N2 > 0 ) {
curr = append[ offsetA ];
out[ io ] = curr - prev;
prev = curr;
io += strideOut;
}
} else if ( N > 0 ) {
prev = x[ offsetX ];
io = offsetOut;
} else {
prev = append[ offsetA ];
io = offsetOut;
}
// Compute forward differences over the input array:
if ( N > 0 ) {
ix = offsetX;
if ( N1 === 0 ) {
prev = x[ ix ];
ix += strideX;
for ( i = 1; i < N; i++ ) {
curr = x[ ix ];
out[ io ] = curr - prev;
prev = curr;
io += strideOut;
ix += strideX;
}
} else {
ix += strideX;
for ( i = 1; i < N; i++ ) {
curr = x[ ix ];
out[ io ] = curr - prev;
prev = curr;
io += strideOut;
ix += strideX;
}
}
if ( N2 > 0 ) {
curr = append[ offsetA ];
out[ io ] = curr - prev;
prev = curr;
io += strideOut;
}
}
// Compute forward differences over the list of appended values:
if ( N2 > 0 ) {
ia = offsetA + strideA;
for ( i = 1; i < N2; i++ ) {
curr = append[ ia ];
out[ io ] = curr - prev;
prev = curr;
io += strideOut;
ia += strideA;
}
}
return out;
}
// MAIN //
/**
* Calculates the k-th discrete forward difference of a strided array using alternative indexing semantics.
*
* @param {PositiveInteger} N - number of indexed elements
* @param {PositiveInteger} k - number of times to recursively compute differences
* @param {NumericArray} x - input array
* @param {integer} strideX - stride length for `x`
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @param {NonNegativeInteger} N1 - number of indexed elements for `prepend`
* @param {NumericArray} prepend - prepend array
* @param {integer} strideP - stride length for `prepend`
* @param {NonNegativeInteger} offsetP - starting index for `prepend`
* @param {NonNegativeInteger} N2 - number of indexed elements for `append`
* @param {NumericArray} append - append array
* @param {integer} strideA - stride length for `append`
* @param {NonNegativeInteger} offsetA - starting index for `append`
* @param {NumericArray} out - output array
* @param {integer} strideOut - stride length for `out`
* @param {NonNegativeInteger} offsetOut - starting index for `out`
* @param {NumericArray} workspace - workspace array
* @param {integer} strideW - stride length for `workspace`
* @param {NonNegativeInteger} offsetW - starting index for `workspace`
* @returns {NumericArray} output array
*
* @example
* var x = [ 2.0, 4.0, 7.0, 11.0, 16.0 ];
* var p = [ 1.0 ];
* var a = [ 22.0 ];
* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0 ];
* var w = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
*
* gdiff( x.length, 2, x, 1, 0, 1, p, 1, 0, 1, a, 1, 0, out, 1, 0, w, 1, 0 );
*
* console.log( out );
* // => [ 1.0, 1.0, 1.0, 1.0, 1.0 ]
*/
function gdiff( N, k, x, strideX, offsetX, N1, prepend, strideP, offsetP, N2, append, strideA, offsetA, out, strideOut, offsetOut, workspace, strideW, offsetW ) {
var total;
var ox;
var op;
var oa;
var oo;
var ow;
var io;
var n;
var i;
total = N + N1 + N2;
// If `k` is greater than or equal to the total number of elements, the k-th forward difference results in an empty array, so this function is a no-op...
if ( total <= 1 || k >= total ) {
return out;
}
// Dispatch to the accessor path when any array uses the accessor protocol...
ox = arraylike2object( x );
op = arraylike2object( prepend );
oa = arraylike2object( append );
oo = arraylike2object( out );
ow = arraylike2object( workspace );
if ( ox.accessorProtocol || op.accessorProtocol || oa.accessorProtocol || oo.accessorProtocol || ow.accessorProtocol ) {
accessors( N, k, ox, strideX, offsetX, N1, op, strideP, offsetP, N2, oa, strideA, offsetA, oo, strideOut, offsetOut, ow, strideW, offsetW );
return oo.data;
}
// If `k` is equal to zero, there are no differences to compute, so we merely copy the various arrays into the output array...
if ( k === 0 ) {
// Copy `prepend` into output array:
gcopy( N1, prepend, strideP, offsetP, out, strideOut, offsetOut );
// Copy `x` into output array:
io = offsetOut + ( N1 * strideOut );
gcopy( N, x, strideX, offsetX, out, strideOut, io );
// Copy `append` into output array:
io = offsetOut + ( ( N1 + N ) * strideOut );
gcopy( N2, append, strideA, offsetA, out, strideOut, io );
return out;
}
// If `k` is equal to one, we can compute the forward difference while writing directly to the output array...
if ( k === 1 ) {
base( N, x, strideX, offsetX, N1, prepend, strideP, offsetP, N2, append, strideA, offsetA, out, strideOut, offsetOut );
return out;
}
// Compute the first forward difference:
base( N, x, strideX, offsetX, N1, prepend, strideP, offsetP, N2, append, strideA, offsetA, workspace, strideW, offsetW );
// Recursively compute the next forward differences...
n = total - 1;
for ( i = 1; i < k-1; i++ ) {
base( n, workspace, strideW, offsetW, 0, prepend, strideP, offsetP, 0, append, strideA, offsetA, workspace, strideW, offsetW );
n -= 1;
}
// For the last forward difference, ensure that results are written to the output array:
base( n, workspace, strideW, offsetW, 0, prepend, strideP, offsetP, 0, append, strideA, offsetA, out, strideOut, offsetOut );
return out;
}
// EXPORTS //
module.exports = gdiff;
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