fix: update implementation to preserve signed zeros

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---

Author: kgryte

lib/node_modules/@stdlib/blas/ext/base/gsumkbn2/lib/accessors.js

@@ -59,6 +59,7 @@ function gsumkbn2( N, x, strideX, offsetX ) {
 	var get;
 	var sum;
 	var ccs;
+	var flg;
 	var ix;
 	var cs;
 	var cc;
@@ -77,11 +78,28 @@ function gsumkbn2( N, x, strideX, offsetX ) {
 	if ( strideX === 0 ) {
 		return N * get( xbuf, ix );
 	}
+	v = get( xbuf, ix );
+	sum = v;
 
-	sum = 0.0;
+	// 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 = get( xbuf, 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 = get( xbuf, ix );
 		t = sum + v;
 		if ( abs( sum ) >= abs( v ) ) {
@@ -100,7 +118,7 @@ function gsumkbn2( 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/gsumkbn2/lib/ndarray.js

@@ -53,6 +53,7 @@ var accessors = require( './accessors.js' );
 function gsumkbn2( N, x, strideX, offsetX ) {
 	var sum;
 	var ccs;
+	var flg;
 	var ix;
 	var cs;
 	var cc;
@@ -73,10 +74,28 @@ function gsumkbn2( 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 ) ) {
@@ -95,7 +114,7 @@ function gsumkbn2( 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/gsumkbn2/test/test.ndarray.js

@@ -23,6 +23,7 @@
 var tape = require( 'tape' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var isPositiveZero = require( '@stdlib/math/base/assert/is-positive-zero' );
+var isNegativeZero = require( '@stdlib/math/base/assert/is-negative-zero' );
 var toAccessorArray = require( '@stdlib/array/base/to-accessor-array' );
 var gsumkbn2 = require( './../lib/ndarray.js' );
 
@@ -94,14 +95,14 @@ tape( 'the function calculates the sum of all strided array elements (accessors)
 	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 = [ -0.0, -0.0, -0.0 ];
 
 	v = gsumkbn2( x.length, x, 1, 0 );
-	t.strictEqual( isPositiveZero( v ), true, 'returns expected value' );
+	t.strictEqual( isNegativeZero( v ), true, 'returns expected value' );
 
 	x = [ 0.0, -0.0, -0.0 ];
 
@@ -111,14 +112,14 @@ tape( 'the function does not preserve the sign of zero', function test( t ) {
 	t.end();
 });
 
-tape( 'the function does not preserve the sign of zero (accessors)', function test( t ) {
+tape( 'the function preserves the sign of zero (accessors)', function test( t ) {
 	var x;
 	var v;
 
 	x = toAccessorArray( [ -0.0, -0.0, -0.0 ] );
 
 	v = gsumkbn2( x.length, x, 1, 0 );
-	t.strictEqual( isPositiveZero( v ), true, 'returns expected value' );
+	t.strictEqual( isNegativeZero( v ), true, 'returns expected value' );
 
 	x = toAccessorArray( [ 0.0, -0.0, -0.0 ] );