fix: update implementation to preserve signed zeros

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---

Author: kgryte

lib/node_modules/@stdlib/blas/ext/base/dsumkbn2/lib/ndarray.js

@@ -53,6 +53,7 @@ var abs = require( '@stdlib/math/base/special/abs' );
 function dsumkbn2( N, x, strideX, offsetX ) {
 	var sum;
 	var ccs;
+	var flg;
 	var ix;
 	var cs;
 	var cc;
@@ -68,10 +69,28 @@ function dsumkbn2( N, x, strideX, offsetX ) {
 	if ( strideX === 0 ) {
 		return N * x[ ix ];
 	}
-	sum = 0.0;
+	v = x[ ix ];
+	sum = v;
+
+	// In order to preserve the sign of zero which can be lost during compensated summation below, find the first non-zero element...
+	if ( sum === 0.0 ) {
+		for ( i = 1; i < N; i++ ) {
+			v = x[ ix ];
+			if ( v !== 0.0 ) {
+				flg = true;
+				break;
+			}
+			sum += v;
+			ix += strideX;
+		}
+	} else {
+		flg = true;
+		ix += strideX;
+		i = 1;
+	}
 	ccs = 0.0; // second order correction term for lost low order bits
 	cs = 0.0; // first order correction term for lost low order bits
-	for ( i = 0; i < N; i++ ) {
+	for ( ; i < N; i++ ) {
 		v = x[ ix ];
 		t = sum + v;
 		if ( abs( sum ) >= abs( v ) ) {
@@ -90,7 +109,7 @@ function dsumkbn2( N, x, strideX, offsetX ) {
 		ccs += cc;
 		ix += strideX;
 	}
-	return sum + cs + ccs;
+	return ( flg ) ? sum+cs+ccs : sum;
 }
 
 

lib/node_modules/@stdlib/blas/ext/base/dsumkbn2/src/main.c

@@ -69,6 +69,7 @@ double API_SUFFIX(stdlib_strided_dsumkbn2_ndarray)( const CBLAS_INT N, const dou
 	double v;
 	double t;
 	double c;
+	int flg;
 
 	if ( N <= 0 ) {
 		return 0.0;
@@ -77,10 +78,29 @@ double API_SUFFIX(stdlib_strided_dsumkbn2_ndarray)( const CBLAS_INT N, const dou
 	if ( strideX == 0 ) {
 		return N * X[ ix ];
 	}
-	sum = 0.0;
+	v = X[ ix ];
+	sum = v;
+	flg = 0;
+
+	// In order to preserve the sign of zero which can be lost during compensated summation below, find the first non-zero element...
+	if ( sum == 0.0 ) {
+		for ( i = 1; i < N; i++ ) {
+			v = X[ ix ];
+			if ( v != 0.0 ) {
+				flg = 1;
+				break;
+			}
+			sum += v;
+			ix += strideX;
+		}
+	} else {
+		flg = 1;
+		ix += strideX;
+		i = 1;
+	}
 	ccs = 0.0; // second order correction term for lost lower order bits
 	cs = 0.0; // first order correction term for lost low order bits
-	for ( i = 0; i < N; i++ ) {
+	for ( ; i < N; i++ ) {
 		v = X[ ix ];
 		t = sum + v;
 		if ( stdlib_base_abs( sum ) >= stdlib_base_abs( v ) ) {
@@ -99,5 +119,5 @@ double API_SUFFIX(stdlib_strided_dsumkbn2_ndarray)( const CBLAS_INT N, const dou
 		ccs += cc;
 		ix += strideX;
 	}
-	return sum + cs + ccs;
+	return ( flg == 1 ) ? sum+cs+ccs : sum;
 }

lib/node_modules/@stdlib/blas/ext/base/dsumkbn2/test/test.ndarray.js

@@ -22,6 +22,7 @@
 
 var tape = require( 'tape' );
 var isPositiveZero = require( '@stdlib/math/base/assert/is-positive-zero' );
+var isNegativeZero = require( '@stdlib/math/base/assert/is-negative-zero' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var Float64Array = require( '@stdlib/array/float64' );
 var dsumkbn2 = require( './../lib/ndarray.js' );
@@ -67,14 +68,14 @@ tape( 'the function calculates the sum of all strided array elements', function
 	t.end();
 });
 
-tape( 'the function does not preserve the sign of zero', function test( t ) {
+tape( 'the function preserves the sign of zero', function test( t ) {
 	var x;
 	var v;
 
 	x = new Float64Array( [ -0.0, -0.0, -0.0 ] );
 
 	v = dsumkbn2( x.length, x, 1, 0 );
-	t.strictEqual( isPositiveZero( v ), true, 'returns expected value' );
+	t.strictEqual( isNegativeZero( v ), true, 'returns expected value' );
 
 	x = new Float64Array( [ 0.0, -0.0, -0.0 ] );
 

lib/node_modules/@stdlib/blas/ext/base/dsumkbn2/test/test.ndarray.native.js

@@ -23,6 +23,7 @@
 var resolve = require( 'path' ).resolve;
 var tape = require( 'tape' );
 var isPositiveZero = require( '@stdlib/math/base/assert/is-positive-zero' );
+var isNegativeZero = require( '@stdlib/math/base/assert/is-negative-zero' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var Float64Array = require( '@stdlib/array/float64' );
 var tryRequire = require( '@stdlib/utils/try-require' );
@@ -76,14 +77,14 @@ tape( 'the function calculates the sum of all strided array elements', opts, fun
 	t.end();
 });
 
-tape( 'the function does not preserve the sign of zero', opts, function test( t ) {
+tape( 'the function preserves the sign of zero', opts, function test( t ) {
 	var x;
 	var v;
 
 	x = new Float64Array( [ -0.0, -0.0, -0.0 ] );
 
 	v = dsumkbn2( x.length, x, 1, 0 );
-	t.strictEqual( isPositiveZero( v ), true, 'returns expected value' );
+	t.strictEqual( isNegativeZero( v ), true, 'returns expected value' );
 
 	x = new Float64Array( [ 0.0, -0.0, -0.0 ] );