feat: refactor JavaScript implementation and add C ndarray implementation for blas/base/dnrm2

PR-URL: #2941
Ref: #2039
Co-authored-by: Athan Reines <[email protected]>
Reviewed-by: Athan Reines <[email protected]> 
Signed-off-by: Athan Reines <[email protected]>

Author: aman-095

lib/node_modules/@stdlib/blas/base/dnrm2/README.md

@@ -91,7 +91,7 @@ var z = dnrm2( 4, x1, 2 );
 // returns 5.0
 ```
 
-If either `N` or `stride` is less than or equal to `0`, the function returns `0`.
+If `N` is less than or equal to `0`, the function returns `0`.
 
 #### dnrm2.ndarray( N, x, stride, offset )
 
@@ -207,6 +207,28 @@ The function accepts the following arguments:
 double c_dnrm2( const CBLAS_INT N, const double *X, const CBLAS_INT stride );
 ```
 
+#### c_dnrm2_ndarray( N, \*X, stride, offset )
+
+Computes the L2-norm of a double-precision floating-point vector using alternative indexing semantics.
+
+```c
+const double x[] = { 1.0, -2.0, 2.0 };
+
+double v = c_dnrm2( 3, x, -1, 2 );
+// returns 3.0
+```
+
+The function accepts the following arguments:
+
+-   **N**: `[in] CBLAS_INT` number of indexed elements.
+-   **X**: `[in] double*` input array.
+-   **stride**: `[in] CBLAS_INT` index increment for `X`.
+-   **offset**: `[in] CBLAS_INT` starting index for `X`.
+
+```c
+double c_dnrm2_ndarray( const CBLAS_INT N, const double *X, const CBLAS_INT stride, const CBLAS_INT offset );
+```
+
 </section>
 
 <!-- /.usage -->
@@ -244,6 +266,12 @@ int main( void ) {
 
     // Print the result:
     printf( "L2-norm: %lf\n", l2 );
+
+    // Compute the L2-norm:
+    l2 = c_dnrm2_ndarray( N, x, -strideX, N-1 );
+
+    // Print the result:
+    printf( "L2-norm: %lf\n", l2 );
 }
 ```
 

lib/node_modules/@stdlib/blas/base/dnrm2/benchmark/c/benchmark.length.c

@@ -94,7 +94,7 @@ static double rand_double( void ) {
 * @param len          array length
 * @return elapsed time in seconds
 */
-static double benchmark( int iterations, int len ) {
+static double benchmark1( int iterations, int len ) {
 	double elapsed;
 	double x[ len ];
 	double z;
@@ -120,6 +120,39 @@ static double benchmark( int iterations, int len ) {
 	return elapsed;
 }
 
+/**
+* Runs a benchmark.
+*
+* @param iterations   number of iterations
+* @param len          array length
+* @return elapsed time in seconds
+*/
+static double benchmark2( int iterations, int len ) {
+	double elapsed;
+	double x[ len ];
+	double z;
+	double t;
+	int i;
+
+	for ( i = 0; i < len; i++ ) {
+		x[ i ] = ( rand_double() * 20000.0 ) - 10000.0;
+	}
+	z = 0.0;
+	t = tic();
+	for ( i = 0; i < iterations; i++ ) {
+		z = c_dnrm2_ndarray( len, x, 1, 0 );
+		if ( z != z ) {
+			printf( "should not return NaN\n" );
+			break;
+		}
+	}
+	elapsed = tic() - t;
+	if ( z != z ) {
+		printf( "should not return NaN\n" );
+	}
+	return elapsed;
+}
+
 /**
 * Main execution sequence.
 */
@@ -142,7 +175,14 @@ int main( void ) {
 		for ( j = 0; j < REPEATS; j++ ) {
 			count += 1;
 			printf( "# c::%s:len=%d\n", NAME, len );
-			elapsed = benchmark( iter, len );
+			elapsed = benchmark1( iter, len );
+			print_results( iter, elapsed );
+			printf( "ok %d benchmark finished\n", count );
+		}
+		for ( j = 0; j < REPEATS; j++ ) {
+			count += 1;
+			printf( "# c::%s:ndarray:len=%d\n", NAME, len );
+			elapsed = benchmark2( iter, len );
 			print_results( iter, elapsed );
 			printf( "ok %d benchmark finished\n", count );
 		}

lib/node_modules/@stdlib/blas/base/dnrm2/docs/repl.txt

@@ -8,7 +8,7 @@
     Indexing is relative to the first index. To introduce an offset, use a typed
     array view.
 
-    If `N <= 0` or `stride <= 0`, the function returns `0`.
+    If `N <= 0`, the function returns `0`.
 
     Parameters
     ----------

lib/node_modules/@stdlib/blas/base/dnrm2/examples/c/example.c

@@ -34,4 +34,10 @@ int main( void ) {
 
 	// Print the result:
 	printf( "L2-norm: %lf\n", l2 );
+
+	// Compute the L2-norm:
+	l2 = c_dnrm2_ndarray( N, x, -strideX, N-1 );
+
+	// Print the result:
+	printf( "L2-norm: %lf\n", l2 );
 }

lib/node_modules/@stdlib/blas/base/dnrm2/include/stdlib/blas/base/dnrm2.h

@@ -36,6 +36,11 @@ extern "C" {
 */
 double API_SUFFIX(c_dnrm2)( const CBLAS_INT N, const double *X, const CBLAS_INT stride );
 
+/**
+* Computes the L2-norm of a double-precision floating-point vector using alternative indexing semantics.
+*/
+double API_SUFFIX(c_dnrm2_ndarray)( const CBLAS_INT N, const double *X, const CBLAS_INT stride, const CBLAS_INT offset );
+
 #ifdef __cplusplus
 }
 #endif

lib/node_modules/@stdlib/blas/base/dnrm2/lib/dnrm2.js

@@ -20,9 +20,8 @@
 
 // MODULES //
 
-var sqrt = require( '@stdlib/math/base/special/sqrt' );
-var abs = require( '@stdlib/math/base/special/abs' );
-var pow = require( '@stdlib/math/base/special/pow' );
+var stride2offset = require( '@stdlib/strided/base/stride2offset' );
+var ndarray = require( './ndarray.js' );
 
 
 // MAIN //
@@ -32,7 +31,7 @@ var pow = require( '@stdlib/math/base/special/pow' );
 *
 * @param {PositiveInteger} N - number of indexed elements
 * @param {Float64Array} x - input array
-* @param {PositiveInteger} stride - stride length
+* @param {integer} stride - stride length
 * @returns {number} L2-norm
 *
 * @example
@@ -44,32 +43,8 @@ var pow = require( '@stdlib/math/base/special/pow' );
 * // returns 3.0
 */
 function dnrm2( N, x, stride ) {
-	var scale;
-	var ssq;
-	var ax;
-	var i;
-
-	if ( N <= 0 || stride <= 0 ) {
-		return 0.0;
-	}
-	if ( N === 1 ) {
-		return abs( x[ 0 ] );
-	}
-	scale = 0.0;
-	ssq = 1.0;
-	N *= stride;
-	for ( i = 0; i < N; i += stride ) {
-		if ( x[ i ] !== 0.0 ) {
-			ax = abs( x[ i ] );
-			if ( scale < ax ) {
-				ssq = 1.0 + ( ssq * pow( scale/ax, 2 ) );
-				scale = ax;
-			} else {
-				ssq += pow( ax/scale, 2 );
-			}
-		}
-	}
-	return scale * sqrt( ssq );
+	var ox = stride2offset( N, stride );
+	return ndarray( N, x, stride, ox );
 }
 
 

lib/node_modules/@stdlib/blas/base/dnrm2/lib/dnrm2.native.js

@@ -30,7 +30,7 @@ var addon = require( './../src/addon.node' );
 *
 * @param {PositiveInteger} N - number of indexed elements
 * @param {Float64Array} x - input array
-* @param {PositiveInteger} stride - stride length
+* @param {integer} stride - stride length
 * @returns {number} L2-norm
 *
 * @example

lib/node_modules/@stdlib/blas/base/dnrm2/lib/ndarray.js

@@ -1,7 +1,7 @@
 /**
 * @license Apache-2.0
 *
-* Copyright (c) 2020 The Stdlib Authors.
+* Copyright (c) 2023 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.
@@ -20,9 +20,19 @@
 
 // MODULES //
 
-var sqrt = require( '@stdlib/math/base/special/sqrt' );
+var FLOAT64_MAX = require( '@stdlib/constants/float64/max' );
 var abs = require( '@stdlib/math/base/special/abs' );
-var pow = require( '@stdlib/math/base/special/pow' );
+var abs2 = require( '@stdlib/math/base/special/abs2' );
+var sqrt = require( '@stdlib/math/base/special/sqrt' );
+
+
+// VARIABLES //
+
+// Blue's scaling constants:
+var tsml = 1.4916681462400413E-154;
+var tbig = 1.9979190722022350E+146;
+var ssml = 4.4989137945431964E+161;
+var sbig = 1.1113793747425387E-162;
 
 
 // MAIN //
@@ -41,38 +51,83 @@ var pow = require( '@stdlib/math/base/special/pow' );
 *
 * var x = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
 *
-* var out = dnrm2( 4, x, 2, 1 );
+* var z = dnrm2( 4, x, 2, 1 );
 * // returns 5.0
 */
 function dnrm2( N, x, stride, offset ) {
-	var scale;
-	var ssq;
+	var notbig;
+	var sumsq;
+	var abig;
+	var amed;
+	var asml;
+	var ymax;
+	var ymin;
+	var scl;
 	var ax;
 	var ix;
 	var i;
 
 	if ( N <= 0 ) {
 		return 0.0;
 	}
-	if ( N === 1 ) {
-		return abs( x[ offset ] );
-	}
 	ix = offset;
-	scale = 0.0;
-	ssq = 1.0;
+
+	// Initialize loop values for accumulation:
+	notbig = true;
+
+	sumsq = 0.0;
+	abig = 0.0;
+	amed = 0.0;
+	asml = 0.0;
+	scl = 1.0;
+
+	// Compute the sum of squares using 3 accumulators--`abig` (sum of squares scaled down to avoid overflow), `asml` (sum of squares scaled up to avoid underflow), `amed` (sum of squares that do not require scaling)--and thresholds and multipliers--`tbig` (values bigger than this are scaled down by `sbig`) and `tsml` (values smaller than this are scaled up by `ssml`)...
 	for ( i = 0; i < N; i++ ) {
-		if ( x[ ix ] !== 0.0 ) {
-			ax = abs( x[ ix ] );
-			if ( scale < ax ) {
-				ssq = 1.0 + ( ssq * pow( scale/ax, 2 ) );
-				scale = ax;
-			} else {
-				ssq += pow( ax/scale, 2 );
+		ax = abs( x[ ix ] );
+		if ( ax > tbig ) {
+			abig += abs2( ax * sbig );
+			notbig = false;
+		} else if ( ax < tsml ) {
+			if ( notbig ) {
+				asml += abs2( ax * ssml );
 			}
+		} else {
+			amed += ( ax * ax );
 		}
 		ix += stride;
 	}
-	return scale * sqrt( ssq );
+	// Combine `abig` and `amed` or `amed` and `asml` if more than one accumulator was used...
+	if ( abig > 0.0 ) {
+		// Combine `abig` and `amed` if `abig` > 0...
+		if ( amed > 0.0 || ( amed > FLOAT64_MAX ) || ( amed !== amed ) ) {
+			abig += ( ( amed * sbig ) * sbig );
+		}
+		scl = 1.0 / sbig;
+		sumsq = abig;
+	} else if ( asml > 0.0 ) {
+		// Combine `amed` and `asml` if `asml` > 0...
+		if ( amed > 0.0 || amed > FLOAT64_MAX || ( amed !== amed ) ) {
+			amed = sqrt( amed );
+			asml = sqrt( asml ) / ssml;
+			if ( asml > amed ) {
+				ymin = amed;
+				ymax = asml;
+			} else {
+				ymin = asml;
+				ymax = amed;
+			}
+			scl = 1.0;
+			sumsq = ( ymax * ymax ) * ( 1.0 + abs2( ymin / ymax ) );
+		} else {
+			scl = 1.0 / ssml;
+			sumsq = asml;
+		}
+	} else {
+		// All values are mid-range...
+		scl = 1.0;
+		sumsq = amed;
+	}
+	return sqrt( sumsq ) * scl;
 }
 
 

lib/node_modules/@stdlib/blas/base/dnrm2/lib/ndarray.native.js

@@ -20,9 +20,7 @@
 
 // MODULES //
 
-var minViewBufferIndex = require( '@stdlib/strided/base/min-view-buffer-index' );
-var offsetView = require( '@stdlib/strided/base/offset-view' );
-var addon = require( './dnrm2.native.js' );
+var addon = require( './../src/addon.node' );
 
 
 // MAIN //
@@ -45,13 +43,7 @@ var addon = require( './dnrm2.native.js' );
 * // returns 5.0
 */
 function dnrm2( N, x, stride, offset ) {
-	var view;
-	offset = minViewBufferIndex( N, stride, offset );
-	if ( stride < 0 ) {
-		stride *= -1;
-	}
-	view = offsetView( x, offset );
-	return addon( N, view, stride );
+	return addon.ndarray( N, x, stride, offset );
 }