fix: update implementation to preserve signed zeros

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---

Author: kgryte

lib/node_modules/@stdlib/blas/ext/base/ssumkbn2/lib/ndarray.js

@@ -20,7 +20,7 @@
 
 // MODULES //
 
-var float64ToFloat32 = require( '@stdlib/number/float64/base/to-float32' );
+var f32 = require( '@stdlib/number/float64/base/to-float32' );
 var absf = require( '@stdlib/math/base/special/absf' );
 
 
@@ -54,6 +54,7 @@ var absf = require( '@stdlib/math/base/special/absf' );
 function ssumkbn2( N, x, strideX, offsetX ) {
 	var sum;
 	var ccs;
+	var flg;
 	var ix;
 	var cs;
 	var cc;
@@ -67,31 +68,49 @@ function ssumkbn2( N, x, strideX, offsetX ) {
 	}
 	ix = offsetX;
 	if ( strideX === 0 ) {
-		return float64ToFloat32( N * x[ ix ] );
+		return f32( N * x[ ix ] );
+	}
+	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 = f32( sum + v );
+			ix += strideX;
+		}
+	} else {
+		flg = true;
+		ix += strideX;
+		i = 1;
 	}
-	sum = 0.0;
 	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 = float64ToFloat32( sum+v );
+		t = f32( sum+v );
 		if ( absf( sum ) >= absf( v ) ) {
-			c = float64ToFloat32( float64ToFloat32( sum-t ) + v );
+			c = f32( f32( sum-t ) + v );
 		} else {
-			c = float64ToFloat32( float64ToFloat32( v-t ) + sum );
+			c = f32( f32( v-t ) + sum );
 		}
 		sum = t;
-		t = float64ToFloat32( cs+c );
+		t = f32( cs+c );
 		if ( absf( cs ) >= absf( c ) ) {
-			cc = float64ToFloat32( float64ToFloat32( cs-t ) + c );
+			cc = f32( f32( cs-t ) + c );
 		} else {
-			cc = float64ToFloat32( float64ToFloat32( c-t ) + cs );
+			cc = f32( f32( c-t ) + cs );
 		}
 		cs = t;
-		ccs = float64ToFloat32( ccs+cc );
+		ccs = f32( ccs+cc );
 		ix += strideX;
 	}
-	return float64ToFloat32( sum + float64ToFloat32( cs+ccs ) );
+	return ( flg ) ? f32( sum + f32( cs+ccs ) ) : sum;
 }
 
 

lib/node_modules/@stdlib/blas/ext/base/ssumkbn2/src/main.c

@@ -69,6 +69,7 @@ float API_SUFFIX(stdlib_strided_ssumkbn2_ndarray)( const CBLAS_INT N, const floa
 	float v;
 	float t;
 	float c;
+	int flg;
 
 	if ( N <= 0 ) {
 		return 0.0f;
@@ -77,10 +78,29 @@ float API_SUFFIX(stdlib_strided_ssumkbn2_ndarray)( const CBLAS_INT N, const floa
 	if ( strideX == 0 ) {
 		return N * X[ ix ];
 	}
-	sum = 0.0f;
+	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 == 0.0f ) {
+		for ( i = 1; i < N; i++ ) {
+			v = X[ ix ];
+			if ( v != 0.0f ) {
+				flg = 1;
+				break;
+			}
+			sum += v;
+			ix += strideX;
+		}
+	} else {
+		flg = 1;
+		ix += strideX;
+		i = 1;
+	}
 	ccs = 0.0f; // second order correction term for lost lower order bits
 	cs = 0.0f; // 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_absf( sum ) >= stdlib_base_absf( v ) ) {
@@ -99,5 +119,5 @@ float API_SUFFIX(stdlib_strided_ssumkbn2_ndarray)( const CBLAS_INT N, const floa
 		ccs += cc;
 		ix += strideX;
 	}
-	return sum + cs + ccs;
+	return ( flg == 1 ) ? sum+cs+ccs : sum;
 }

lib/node_modules/@stdlib/blas/ext/base/ssumkbn2/test/test.ndarray.js

@@ -22,6 +22,7 @@
 
 var tape = require( 'tape' );
 var isPositiveZerof = require( '@stdlib/math/base/assert/is-positive-zerof' );
+var isNegativeZerof = require( '@stdlib/math/base/assert/is-negative-zerof' );
 var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
 var Float32Array = require( '@stdlib/array/float32' );
 var ssumkbn2 = 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 Float32Array( [ -0.0, -0.0, -0.0 ] );
 
 	v = ssumkbn2( x.length, x, 1, 0 );
-	t.strictEqual( isPositiveZerof( v ), true, 'returns expected value' );
+	t.strictEqual( isNegativeZerof( v ), true, 'returns expected value' );
 
 	x = new Float32Array( [ 0.0, -0.0, -0.0 ] );
 

lib/node_modules/@stdlib/blas/ext/base/ssumkbn2/test/test.ndarray.native.js

@@ -24,6 +24,7 @@ var resolve = require( 'path' ).resolve;
 var tape = require( 'tape' );
 var isnanf = require( '@stdlib/math/base/assert/is-nanf' );
 var isPositiveZerof = require( '@stdlib/math/base/assert/is-positive-zerof' );
+var isNegativeZerof = require( '@stdlib/math/base/assert/is-negative-zerof' );
 var Float32Array = require( '@stdlib/array/float32' );
 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 Float32Array( [ -0.0, -0.0, -0.0 ] );
 
 	v = ssumkbn2( x.length, x, 1, 0 );
-	t.strictEqual( isPositiveZerof( v ), true, 'returns expected value' );
+	t.strictEqual( isNegativeZerof( v ), true, 'returns expected value' );
 
 	x = new Float32Array( [ 0.0, -0.0, -0.0 ] );