chore: update the signum implementation and improve test coverage

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---

Author: prajjwalbajpai

lib/node_modules/@stdlib/lapack/base/dlasv2/lib/base.js

@@ -22,28 +22,10 @@
 
 // MODULES //
 
-var signum = require( '@stdlib/math/base/special/signum' );
+var dlamch = require( '@stdlib/lapack/base/dlamch' );
 var sqrt = require( '@stdlib/math/base/special/sqrt' );
 var abs = require( '@stdlib/math/base/special/abs' );
-
-
-// FUNCTIONS //
-
-/**
-* Returns `x` multipled by `signum( y )`.
-*
-* @private
-* @param {number} x - scalar element
-* @param {number} y - scalar element
-* @returns {number} computed value
-*
-* @example
-* var out = sign( 1.0, -0.9 );
-* // out => -1.0
-*/
-function sign( x, y ) {
-	return x * signum( y );
-}
+var copysign = require( '@stdlib/math/base/special/copysign' );
 
 
 // MAIN //
@@ -62,6 +44,7 @@ function sign( x, y ) {
 *
 * @example
 * var Float64Array = require( '@stdlib/array/float64' );
+*
 * var out = new Float64Array( 6 );
 *
 * out = dlasv2( 2.0, 3.0, 4.0, out, 1, 0 );
@@ -139,9 +122,7 @@ function dlasv2( F, G, H, out, strideOut, offsetOut ) {
 		gasmal = true;
 		if ( ga > fa ) {
 			PMAX = 2;
-
-			// TODO: replace 1.11022302E-16 with dlamch( 'E' )
-			if ( ( fa / ga ) < 1.11022302E-16 ) {
+			if ( ( fa / ga ) < dlamch( 'E' ) ) {
 				// Case of very large GA
 				gasmal = false;
 				ssmax = ga;
@@ -193,9 +174,9 @@ function dlasv2( F, G, H, out, strideOut, offsetOut ) {
 			if ( mm === 0.0 ) {
 				// Note that M is very tiny
 				if ( l === 0.0 ) {
-					t = sign( 2.0, ft ) * sign( 1.0, gt );
+					t = copysign( 2.0, ft ) * copysign( 1.0, gt );
 				} else {
-					t = ( ( gt / sign( d, ft ) ) + ( m / t ) );
+					t = ( ( gt / copysign( d, ft ) ) + ( m / t ) );
 				}
 			} else {
 				t = ( ( m / ( s + t ) ) + ( m / ( r + l ) ) ) * ( 1.0 + a );
@@ -221,16 +202,16 @@ function dlasv2( F, G, H, out, strideOut, offsetOut ) {
 
 	// Correct signs 0f ssmax and ssmin
 	if ( PMAX === 1 ) {
-		tsign = sign( 1.0, csr ) * sign( 1.0, csl ) * sign( 1.0, F );
+		tsign = copysign( 1.0, csr ) * copysign( 1.0, csl ) * copysign( 1.0, F );
 	}
 	if ( PMAX === 2 ) {
-		tsign = sign( 1.0, snr ) * sign( 1.0, csl ) * sign( 1.0, G );
+		tsign = copysign( 1.0, snr ) * copysign( 1.0, csl ) * copysign( 1.0, G );
 	}
 	if ( PMAX === 3 ) {
-		tsign = sign( 1.0, snr ) * sign( 1.0, snl ) * sign( 1.0, H );
+		tsign = copysign( 1.0, snr ) * copysign( 1.0, snl ) * copysign( 1.0, H );
 	}
-	ssmax = sign( ssmax, tsign );
-	ssmin = sign( ssmin, tsign * sign( 1.0, F ) * sign( 1.0, H ) );
+	ssmax = copysign( ssmax, tsign );
+	ssmin = copysign( ssmin, tsign * copysign( 1.0, F ) * copysign( 1.0, H ) );
 
 	out[ offsetOut ] = ssmin;
 	out[ offsetOut + strideOut ] = ssmax;

lib/node_modules/@stdlib/lapack/base/dlasv2/test/test.dlasv2.js

@@ -133,3 +133,47 @@ tape( 'the function correctly computes svd of diagonal matrix', function test( t
 	isApprox( t, out, expected, 1.0 );
 	t.end();
 });
+
+tape( 'the function correctly computes svd of diagonal matrix with a very large `G`', function test( t ) {
+	var expected;
+	var out;
+
+	expected = new Float64Array( [ 2.0e-20, 1.0e+20, 1.0, 2.0e-20, 1.0e-20, 1.0 ] );
+	out = new Float64Array( 6 );
+	out = dlasv2( 2.0, 1.0e+20, 1.0, out );
+	isApprox( t, out, expected, 1.0 );
+	t.end();
+});
+
+tape( 'the function computes svd of diagonal matrix with a very large `G` when `H` is greater than 1', function test( t ) {
+	var expected;
+	var out;
+
+	expected = new Float64Array( [ 6.0e-20, 1.0e+20, 1.0, 2.0e-20, 3.0e-20, 1.0 ] );
+	out = new Float64Array( 6 );
+	out = dlasv2( 2.0, 1.0e+20, 3.0, out );
+	isApprox( t, out, expected, 1.0 );
+	t.end();
+});
+
+tape( 'the function correctly computes svd of diagonal matrix with an infinite `F`', function test( t ) {
+	var expected;
+	var out;
+
+	expected = new Float64Array( [ 1.0, Infinity, 0.0, 1.0, 0.0, 1.0 ] );
+	out = new Float64Array( 6 );
+	out = dlasv2( Infinity, 2.0, 1.0, out );
+	isApprox( t, out, expected, 1.0 );
+	t.end();
+});
+
+tape( 'the function computes svd of diagonal matrix with tiny off-diagonal entries when `F` and `H` are equal', function test( t ) {
+	var expected;
+	var out;
+
+	expected = new Float64Array( [ 3.0, 3.0, 0.7071067811865475, 0.7071067811865475, 0.7071067811865475, 0.7071067811865475 ] );
+	out = new Float64Array( 6 );
+	out = dlasv2( 3.0, 5e-324, 3.0, out );
+	isApprox( t, out, expected, 1.0 );
+	t.end();
+});