diff --git a/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/README.md b/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/README.md
index 4f11f7b8c11c..ecfe246e4482 100644
--- a/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/README.md
+++ b/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/README.md
@@ -110,6 +110,7 @@ var v = gapxsumpw.ndarray( 4, 5.0, x, 2, 1 );
- If `N <= 0`, both functions return `0.0`.
- In general, pairwise summation is more numerically stable than ordinary recursive summation (i.e., "simple" summation), with slightly worse performance. While not the most numerically stable summation technique (e.g., compensated summation techniques such as the Kahan–Babuška-Neumaier algorithm are generally more numerically stable), pairwise summation strikes a reasonable balance between numerical stability and performance. If either numerical stability or performance is more desirable for your use case, consider alternative summation techniques.
+- Both functions support array-like objects having getter and setter accessors for array element access (e.g., [`@stdlib/array/base/accessor`][@stdlib/array/base/accessor])
- Depending on the environment, the typed versions ([`dapxsumpw`][@stdlib/blas/ext/base/dapxsumpw], [`sapxsumpw`][@stdlib/blas/ext/base/sapxsumpw], etc.) are likely to be significantly more performant.
@@ -176,6 +177,8 @@ console.log( v );
[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+[@stdlib/array/base/accessor]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/base/accessor
+
[@higham:1993a]: https://doi.org/10.1137/0914050
diff --git a/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/docs/types/index.d.ts b/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/docs/types/index.d.ts
index a31b1a049578..3e3d7879a36b 100644
--- a/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/docs/types/index.d.ts
+++ b/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/docs/types/index.d.ts
@@ -20,7 +20,12 @@
///
-import { NumericArray } from '@stdlib/types/array';
+import { NumericArray, Collection, AccessorArrayLike } from '@stdlib/types/array';
+
+/**
+* Input array.
+*/
+type InputArray = NumericArray | Collection | AccessorArrayLike;
/**
* Interface describing `gapxsumpw`.
@@ -41,7 +46,7 @@ interface Routine {
* var v = gapxsumpw( x.length, 5.0, x, 1 );
* // returns 16.0
*/
- ( N: number, alpha: number, x: NumericArray, strideX: number ): number;
+ ( N: number, alpha: number, x: InputArray, strideX: number ): number;
/**
* Adds a scalar constant to each strided array element and computes the sum using pairwise summation and alternative indexing semantics.
@@ -59,7 +64,7 @@ interface Routine {
* var v = gapxsumpw.ndarray( x.length, 5.0, x, 1, 0 );
* // returns 16.0
*/
- ndarray( N: number, alpha: number, x: NumericArray, strideX: number, offsetX: number ): number;
+ ndarray( N: number, alpha: number, x: InputArray, strideX: number, offsetX: number ): number;
}
/**
diff --git a/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/docs/types/test.ts b/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/docs/types/test.ts
index 38abe1d3c86e..2b57e1b21fde 100644
--- a/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/docs/types/test.ts
+++ b/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/docs/types/test.ts
@@ -16,6 +16,7 @@
* limitations under the License.
*/
+import AccessorArray = require( '@stdlib/array/base/accessor' );
import gapxsumpw = require( './index' );
@@ -26,6 +27,7 @@ import gapxsumpw = require( './index' );
const x = new Float64Array( 10 );
gapxsumpw( x.length, 5.0, x, 1 ); // $ExpectType number
+ gapxsumpw( x.length, 5.0, new AccessorArray( x ), 1 ); // $ExpectType number
}
// The compiler throws an error if the function is provided a first argument which is not a number...
@@ -100,6 +102,7 @@ import gapxsumpw = require( './index' );
const x = new Float64Array( 10 );
gapxsumpw.ndarray( x.length, 5.0, x, 1, 0 ); // $ExpectType number
+ gapxsumpw.ndarray( x.length, 5.0, new AccessorArray( x ), 1, 0 ); // $ExpectType number
}
// The compiler throws an error if the `ndarray` method is provided a first argument which is not a number...
diff --git a/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/lib/accessors.js b/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/lib/accessors.js
new file mode 100644
index 000000000000..76d74d9ea592
--- /dev/null
+++ b/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/lib/accessors.js
@@ -0,0 +1,143 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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 floor = require( '@stdlib/math/base/special/floor' );
+
+
+// VARIABLES //
+
+// Blocksize for pairwise summation (NOTE: decreasing the blocksize decreases rounding error as more pairs are summed, but also decreases performance. Because the inner loop is unrolled eight times, the blocksize is effectively `16`.):
+var BLOCKSIZE = 128;
+
+
+// MAIN //
+
+/**
+* Adds a scalar constant to each strided array element and computes the sum using pairwise summation.
+*
+* ## Method
+*
+* - This implementation uses pairwise summation, which accrues rounding error `O(log2 N)` instead of `O(N)`. The recursion depth is also `O(log2 N)`.
+*
+* ## References
+*
+* - Higham, Nicholas J. 1993. "The Accuracy of Floating Point Summation." _SIAM Journal on Scientific Computing_ 14 (4): 783–99. doi:[10.1137/0914050](https://doi.org/10.1137/0914050).
+*
+* @private
+* @param {PositiveInteger} N - number of indexed elements
+* @param {number} alpha - scalar constant
+* @param {Object} x - input array object
+* @param {Collection} x.data - input array data
+* @param {Array} x.accessors - array element accessors
+* @param {integer} strideX - stride length
+* @param {NonNegativeInteger} offsetX - starting index
+* @returns {number} sum
+*
+* @example
+* var toAccessorArray = require( '@stdlib/array/base/to-accessor-array' );
+* var arraylike2object = require( '@stdlib/array/base/arraylike2object' );
+*
+* var x = toAccessorArray( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
+*
+* var v = gapxsumpw( 4, 5.0, arraylike2object( x ), 2, 1 );
+* // returns 25.0
+*/
+function gapxsumpw( N, alpha, x, strideX, offsetX ) {
+ var xbuf;
+ var get;
+ var ix;
+ var s0;
+ var s1;
+ var s2;
+ var s3;
+ var s4;
+ var s5;
+ var s6;
+ var s7;
+ var M;
+ var s;
+ var n;
+ var i;
+
+ // Cache reference to array data:
+ xbuf = x.data;
+
+ // Cache a reference to the element accessor:
+ get = x.accessors[ 0 ];
+
+ ix = offsetX;
+ if ( strideX === 0 ) {
+ return N * ( alpha + get( xbuf, ix ) );
+ }
+ if ( N < 8 ) {
+ // Use simple summation...
+ s = 0.0;
+ for ( i = 0; i < N; i++ ) {
+ s += alpha + get( xbuf, ix );
+ ix += strideX;
+ }
+ return s;
+ }
+ if ( N <= BLOCKSIZE ) {
+ // Sum a block with 8 accumulators (by loop unrolling, we lower the effective blocksize to 16)...
+ s0 = alpha + get( xbuf, ix );
+ s1 = alpha + get( xbuf, ix+strideX );
+ s2 = alpha + get( xbuf, ix+(2*strideX) );
+ s3 = alpha + get( xbuf, ix+(3*strideX) );
+ s4 = alpha + get( xbuf, ix+(4*strideX) );
+ s5 = alpha + get( xbuf, ix+(5*strideX) );
+ s6 = alpha + get( xbuf, ix+(6*strideX) );
+ s7 = alpha + get( xbuf, ix+(7*strideX) );
+ ix += 8 * strideX;
+
+ M = N % 8;
+ for ( i = 8; i < N-M; i += 8 ) {
+ s0 += alpha + get( xbuf, ix );
+ s1 += alpha + get( xbuf, ix+strideX );
+ s2 += alpha + get( xbuf, ix+(2*strideX) );
+ s3 += alpha + get( xbuf, ix+(3*strideX) );
+ s4 += alpha + get( xbuf, ix+(4*strideX) );
+ s5 += alpha + get( xbuf, ix+(5*strideX) );
+ s6 += alpha + get( xbuf, ix+(6*strideX) );
+ s7 += alpha + get( xbuf, ix+(7*strideX) );
+ ix += 8 * strideX;
+ }
+ // Pairwise sum the accumulators:
+ s = ( (s0+s1) + (s2+s3) ) + ( (s4+s5) + (s6+s7) );
+
+ // Clean-up loop...
+ for ( i; i < N; i++ ) {
+ s += alpha + get( xbuf, ix );
+ ix += strideX;
+ }
+ return s;
+ }
+ // Recurse by dividing by two, but avoiding non-multiples of unroll factor...
+ n = floor( N/2 );
+ n -= n % 8;
+ return gapxsumpw( n, alpha, x, strideX, ix ) + gapxsumpw( N-n, alpha, x, strideX, ix+(n*strideX) ); // eslint-disable-line max-len
+}
+
+
+// EXPORTS //
+
+module.exports = gapxsumpw;
diff --git a/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/lib/ndarray.js b/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/lib/ndarray.js
index d22debfff295..f1c4cd330328 100644
--- a/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/lib/ndarray.js
+++ b/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/lib/ndarray.js
@@ -20,7 +20,9 @@
// MODULES //
+var arraylike2object = require( '@stdlib/array/base/arraylike2object' );
var floor = require( '@stdlib/math/base/special/floor' );
+var accessors = require( './accessors.js' );
// VARIABLES //
@@ -67,12 +69,17 @@ function gapxsumpw( N, alpha, x, strideX, offsetX ) {
var s7;
var M;
var s;
+ var o;
var n;
var i;
if ( N <= 0 ) {
return 0.0;
}
+ o = arraylike2object( x );
+ if ( o.accessorProtocol ) {
+ return accessors( N, alpha, o, strideX, offsetX );
+ }
ix = offsetX;
if ( strideX === 0 ) {
return N * ( alpha + x[ ix ] );
diff --git a/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/test/test.main.js b/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/test/test.main.js
index b632213c42a0..37a2df793436 100644
--- a/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/test/test.main.js
+++ b/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/test/test.main.js
@@ -21,8 +21,8 @@
// MODULES //
var tape = require( 'tape' );
-var floor = require( '@stdlib/math/base/special/floor' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var toAccessorArray = require( '@stdlib/array/base/to-accessor-array' );
var Float64Array = require( '@stdlib/array/float64' );
var gapxsumpw = require( './../lib' );
@@ -75,6 +75,41 @@ tape( 'the function adds a constant and calculates the sum of all strided array
t.end();
});
+tape( 'the function adds a constant and calculates the sum of all strided array elements (accessors)', function test( t ) {
+ var x;
+ var v;
+ var i;
+
+ x = [ 1.0, -2.0, -4.0, 5.0, 0.0, 3.0, 0.0, -3.0, 3.0 ];
+ v = gapxsumpw( x.length, 5.0, toAccessorArray( x ), 1 );
+ t.strictEqual( v, 48.0, 'returns expected value' );
+
+ x = [ 1.0, -2.0, -4.0, 5.0, 0.0, 3.0 ];
+ v = gapxsumpw( x.length, 5.0, toAccessorArray( x ), 1 );
+ t.strictEqual( v, 33.0, 'returns expected value' );
+
+ x = [ -4.0, -4.0 ];
+ v = gapxsumpw( x.length, 5.0, toAccessorArray( x ), 1 );
+ t.strictEqual( v, 2.0, 'returns expected value' );
+
+ x = [ NaN, 4.0 ];
+ v = gapxsumpw( x.length, 5.0, toAccessorArray( x ), 1 );
+ t.strictEqual( isnan( v ), true, 'returns expected value' );
+
+ x = [ 1.0, 1e100, 1.0, -1.0e100 ];
+ v = gapxsumpw( x.length, 5.0, toAccessorArray( x ), 1 );
+ t.strictEqual( v, 0.0, 'returns expected value' );
+
+ x = [];
+ for ( i = 0; i < 1000; i++ ) {
+ x.push( 1.0 );
+ }
+ v = gapxsumpw( x.length, 5.0, toAccessorArray( x ), 1 );
+ t.strictEqual( v, 6000.0, 'returns expected value' );
+
+ t.end();
+});
+
tape( 'if provided an `N` parameter less than or equal to `0`, the function returns `0.0`', function test( t ) {
var x;
var v;
@@ -103,7 +138,6 @@ tape( 'if provided an `N` parameter equal to `1`, the function returns the first
});
tape( 'the function supports a `stride` parameter', function test( t ) {
- var N;
var x;
var v;
@@ -118,15 +152,34 @@ tape( 'the function supports a `stride` parameter', function test( t ) {
2.0
];
- N = floor( x.length / 2 );
- v = gapxsumpw( N, 5.0, x, 2 );
+ v = gapxsumpw( 4, 5.0, x, 2 );
+
+ t.strictEqual( v, 25.0, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function supports a `stride` parameter (accessors)', function test( t ) {
+ var x;
+ var v;
+
+ x = [
+ 1.0, // 0
+ 2.0,
+ 2.0, // 1
+ -7.0,
+ -2.0, // 2
+ 3.0,
+ 4.0, // 3
+ 2.0
+ ];
+
+ v = gapxsumpw( 4, 5.0, toAccessorArray( x ), 2 );
t.strictEqual( v, 25.0, 'returns expected value' );
t.end();
});
tape( 'the function supports a negative `stride` parameter', function test( t ) {
- var N;
var x;
var v;
@@ -141,8 +194,28 @@ tape( 'the function supports a negative `stride` parameter', function test( t )
2.0
];
- N = floor( x.length / 2 );
- v = gapxsumpw( N, 5.0, x, -2 );
+ v = gapxsumpw( 4, 5.0, x, -2 );
+
+ t.strictEqual( v, 25.0, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function supports a negative `stride` parameter (accessors)', function test( t ) {
+ var x;
+ var v;
+
+ x = [
+ 1.0, // 3
+ 2.0,
+ 2.0, // 2
+ -7.0,
+ -2.0, // 1
+ 3.0,
+ 4.0, // 0
+ 2.0
+ ];
+
+ v = gapxsumpw( 4, 5.0, toAccessorArray( x ), -2 );
t.strictEqual( v, 25.0, 'returns expected value' );
t.end();
@@ -160,10 +233,21 @@ tape( 'if provided a `stride` parameter equal to `0`, the function returns the f
t.end();
});
+tape( 'if provided a `stride` parameter equal to `0`, the function returns the first element plus a constant repeated N times (accessors)', function test( t ) {
+ var x;
+ var v;
+
+ x = [ 1.0, -2.0, -4.0, 5.0, 3.0 ];
+
+ v = gapxsumpw( x.length, 5.0, toAccessorArray( x ), 0 );
+ t.strictEqual( v, x.length * (x[0]+5.0), 'returns expected value' );
+
+ t.end();
+});
+
tape( 'the function supports view offsets', function test( t ) {
var x0;
var x1;
- var N;
var v;
x0 = new Float64Array([
@@ -179,9 +263,8 @@ tape( 'the function supports view offsets', function test( t ) {
]);
x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
- N = floor(x1.length / 2);
- v = gapxsumpw( N, 5.0, x1, 2 );
+ v = gapxsumpw( 4, 5.0, x1, 2 );
t.strictEqual( v, 25.0, 'returns expected value' );
t.end();
diff --git a/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/test/test.ndarray.js b/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/test/test.ndarray.js
index 074753c77cda..a2bac292f1f8 100644
--- a/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/test/test.ndarray.js
+++ b/lib/node_modules/@stdlib/blas/ext/base/gapxsumpw/test/test.ndarray.js
@@ -21,8 +21,8 @@
// MODULES //
var tape = require( 'tape' );
-var floor = require( '@stdlib/math/base/special/floor' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var toAccessorArray = require( '@stdlib/array/base/to-accessor-array' );
var gapxsumpw = require( './../lib/ndarray.js' );
@@ -74,6 +74,41 @@ tape( 'the function adds a constant and calculates the sum of all strided array
t.end();
});
+tape( 'the function adds a constant and calculates the sum of all strided array elements (accessors)', function test( t ) {
+ var x;
+ var v;
+ var i;
+
+ x = [ 1.0, -2.0, -4.0, 5.0, 0.0, 3.0, 0.0, -3.0, 3.0 ];
+ v = gapxsumpw( x.length, 5.0, toAccessorArray( x ), 1, 0 );
+ t.strictEqual( v, 48.0, 'returns expected value' );
+
+ x = [ 1.0, -2.0, -4.0, 5.0, 0.0, 3.0 ];
+ v = gapxsumpw( x.length, 5.0, toAccessorArray( x ), 1, 0 );
+ t.strictEqual( v, 33.0, 'returns expected value' );
+
+ x = [ -4.0, -4.0 ];
+ v = gapxsumpw( x.length, 5.0, toAccessorArray( x ), 1, 0 );
+ t.strictEqual( v, 2.0, 'returns expected value' );
+
+ x = [ NaN, 4.0 ];
+ v = gapxsumpw( x.length, 5.0, toAccessorArray( x ), 1, 0 );
+ t.strictEqual( isnan( v ), true, 'returns expected value' );
+
+ x = [ 1.0, 1.0e100, 1.0, -1.0e100 ];
+ v = gapxsumpw( x.length, 5.0, toAccessorArray( x ), 1, 0 );
+ t.strictEqual( v, 0.0, 'returns expected value' );
+
+ x = [];
+ for ( i = 0; i < 1000; i++ ) {
+ x.push( 1.0 );
+ }
+ v = gapxsumpw( x.length, 5.0, toAccessorArray( x ), 1, 0 );
+ t.strictEqual( v, 6000.0, 'returns expected value' );
+
+ t.end();
+});
+
tape( 'if provided an `N` parameter less than or equal to `0`, the function returns `0.0`', function test( t ) {
var x;
var v;
@@ -102,7 +137,6 @@ tape( 'if provided an `N` parameter equal to `1`, the function returns the first
});
tape( 'the function supports a `stride` parameter', function test( t ) {
- var N;
var x;
var v;
@@ -117,15 +151,34 @@ tape( 'the function supports a `stride` parameter', function test( t ) {
2.0
];
- N = floor( x.length / 2 );
- v = gapxsumpw( N, 5.0, x, 2, 0 );
+ v = gapxsumpw( 4, 5.0, x, 2, 0 );
+
+ t.strictEqual( v, 25.0, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function supports a `stride` parameter (accessors)', function test( t ) {
+ var x;
+ var v;
+
+ x = [
+ 1.0, // 0
+ 2.0,
+ 2.0, // 1
+ -7.0,
+ -2.0, // 2
+ 3.0,
+ 4.0, // 3
+ 2.0
+ ];
+
+ v = gapxsumpw( 4, 5.0, toAccessorArray( x ), 2, 0 );
t.strictEqual( v, 25.0, 'returns expected value' );
t.end();
});
tape( 'the function supports a negative `stride` parameter', function test( t ) {
- var N;
var x;
var v;
@@ -140,8 +193,28 @@ tape( 'the function supports a negative `stride` parameter', function test( t )
2.0
];
- N = floor( x.length / 2 );
- v = gapxsumpw( N, 5.0, x, -2, 6 );
+ v = gapxsumpw( 4, 5.0, x, -2, 6 );
+
+ t.strictEqual( v, 25.0, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function supports a negative `stride` parameter (accessors)', function test( t ) {
+ var x;
+ var v;
+
+ x = [
+ 1.0, // 3
+ 2.0,
+ 2.0, // 2
+ -7.0,
+ -2.0, // 1
+ 3.0,
+ 4.0, // 0
+ 2.0
+ ];
+
+ v = gapxsumpw( 4, 5.0, toAccessorArray( x ), -2, 6 );
t.strictEqual( v, 25.0, 'returns expected value' );
t.end();
@@ -159,8 +232,19 @@ tape( 'if provided a `stride` parameter equal to `0`, the function returns the f
t.end();
});
+tape( 'if provided a `stride` parameter equal to `0`, the function returns the first element plus a constant repeated N times (accessors)', function test( t ) {
+ var x;
+ var v;
+
+ x = [ 1.0, -2.0, -4.0, 5.0, 3.0 ];
+
+ v = gapxsumpw( x.length, 5.0, toAccessorArray( x ), 0, 0 );
+ t.strictEqual( v, x.length * (x[0]+5.0), 'returns expected value' );
+
+ t.end();
+});
+
tape( 'the function supports an `offset` parameter', function test( t ) {
- var N;
var x;
var v;
@@ -174,9 +258,29 @@ tape( 'the function supports an `offset` parameter', function test( t ) {
3.0,
4.0 // 3
];
- N = floor( x.length / 2 );
- v = gapxsumpw( N, 5.0, x, 2, 1 );
+ v = gapxsumpw( 4, 5.0, x, 2, 1 );
+ t.strictEqual( v, 25.0, 'returns expected value' );
+
+ t.end();
+});
+
+tape( 'the function supports an `offset` parameter (accessors)', function test( t ) {
+ var x;
+ var v;
+
+ x = [
+ 2.0,
+ 1.0, // 0
+ 2.0,
+ -2.0, // 1
+ -2.0,
+ 2.0, // 2
+ 3.0,
+ 4.0 // 3
+ ];
+
+ v = gapxsumpw( 4, 5.0, toAccessorArray( x ), 2, 1 );
t.strictEqual( v, 25.0, 'returns expected value' );
t.end();