test: validate implementation against Julia test fixtures

PR-URL: #5847
Reviewed-by: Athan Reines <[email protected]>

Author: anandkaranubc

lib/node_modules/@stdlib/math/base/special/kernel-cos/test/fixtures/julia/REQUIRE

@@ -0,0 +1,2 @@
+julia 1.5
+JSON 0.21

lib/node_modules/@stdlib/math/base/special/kernel-cos/test/fixtures/julia/large_negative.json

@@ -0,0 +1,74 @@
+#!/usr/bin/env julia
+#
+# @license Apache-2.0
+#
+# Copyright (c) 2025 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.
+# You may obtain a copy of the License at
+#
+#    http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import JSON
+
+"""
+	gen( domain, name )
+
+Generate fixture data and write to file.
+
+# Arguments
+
+* `domain`: domain
+* `name::AbstractString`: output filename
+
+# Examples
+
+``` julia
+julia> x = range( -1000.0, stop = 1000.0, length = 2001 );
+julia> gen( x, \"data.json\" );
+```
+"""
+function gen( domain, name )
+	x = collect( domain );
+	y = cos.( x );
+
+	# Store data to be written to file as a collection:
+	data = Dict([
+		("x", x),
+		("expected", y)
+	]);
+
+	# Based on the script directory, create an output filepath:
+	filepath = joinpath( dir, name );
+
+	# Write the data to the output filepath as JSON:
+	outfile = open( filepath, "w" );
+	write( outfile, JSON.json(data) );
+	write( outfile, "\n" );
+	close( outfile );
+end
+
+# Get the filename:
+file = @__FILE__;
+
+# Extract the directory in which this file resides:
+dir = dirname( file );
+
+# Values within the defined domain:
+x = range( -pi/4.0, stop = pi/4.0, length = 1000 )
+gen( x, "small_range.json" );
+
+# Positive values outside the defined domain:
+x = range( 40.0*pi/4.0, stop = 200*pi/4.0, length = 1000 )
+gen( x, "large_positive.json" );
+
+# Negative values outside the defined domain:
+x = range( -200*pi/4.0, stop = -40*pi/4.0, length = 1000 )
+gen( x, "large_negative.json" );

lib/node_modules/@stdlib/math/base/special/kernel-cos/test/fixtures/julia/large_positive.json

@@ -22,13 +22,17 @@
 
 var tape = require( 'tape' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
-var linspace = require( '@stdlib/array/base/linspace' );
 var rempio2 = require( '@stdlib/math/base/special/rempio2' );
-var PI = require( '@stdlib/constants/float64/pi' );
-var cos = require( '@stdlib/math/base/special/cos' );
 var kernelCos = require( './../lib' );
 
 
+// FIXTURES //
+
+var smallRange = require( './fixtures/julia/small_range.json' );
+var largePositive = require( './fixtures/julia/large_positive.json' );
+var largeNegative = require( './fixtures/julia/large_negative.json' );
+
+
 // TESTS //
 
 tape( 'main export is a function', function test( t ) {
@@ -39,52 +43,56 @@ tape( 'main export is a function', function test( t ) {
 
 tape( 'the function returns `NaN` if provided `NaN` for either parameter', function test( t ) {
 	var v = kernelCos( NaN, 0.0 );
-	t.equal( isnan( v ), true, 'returns NaN' );
+	t.equal( isnan( v ), true, 'returns expected value' );
 
 	v = kernelCos( 4.0, NaN );
-	t.equal( isnan( v ), true, 'returns NaN' );
+	t.equal( isnan( v ), true, 'returns expected value' );
 
 	v = kernelCos( NaN, NaN );
-	t.equal( isnan( v ), true, 'returns NaN' );
+	t.equal( isnan( v ), true, 'returns expected value' );
 	t.end();
 });
 
 tape( 'the function evaluates the cosine for input values on the interval `[-pi/4, pi/4]`', function test( t ) {
+	var expected;
 	var values;
 	var out;
 	var x;
 	var i;
 
-	values = linspace( -PI/4.0, PI/4.0, 1000 );
+	values = smallRange.x;
+	expected = smallRange.expected;
 	for ( i = 0; i < values.length; i++ ) {
 		x = values[ i ];
 		out = kernelCos( x, 0.0 );
-		t.strictEqual( out, cos( x ), 'returns expected value' );
+		t.strictEqual( out, expected[ i ], 'returns expected value' );
 	}
 	t.end();
 });
 
 tape( 'the function can be used to compute the cosine for input values outside of `[-pi/4, pi/4]` after argument reduction via `rempio2` (positive)', function test( t ) {
+	var expected;
 	var values;
 	var out;
 	var x;
 	var y;
 	var n;
 	var i;
 
-	values = linspace( 40.0*PI/4.0, 200*PI/4.0, 1000 );
-	y = new Array( 2 );
+	values = largePositive.x;
+	expected = largePositive.expected;
+	y = [ 0.0, 0.0 ];
 	for ( i = 0; i < values.length; i++ ) {
 		x = values[ i ];
 		n = rempio2( x, y );
 		switch ( n & 3 ) {
 		case 0:
 			out = kernelCos( y[ 0 ], y[ 1 ] );
-			t.strictEqual( out, cos( x ), 'returns expected value' );
+			t.strictEqual( out, expected[ i ], 'returns expected value' );
 			break;
 		case 2:
 			out = -kernelCos( y[ 0 ], y[ 1 ] );
-			t.strictEqual( out, cos( x ), 'returns expected value' );
+			t.strictEqual( out, expected[ i ], 'returns expected value' );
 			break;
 		default:
 			break;
@@ -94,26 +102,28 @@ tape( 'the function can be used to compute the cosine for input values outside o
 });
 
 tape( 'the function can be used to compute the cosine for input values outside of `[-pi/4, pi/4]` after argument reduction via `rempio2` (negative)', function test( t ) {
+	var expected;
 	var values;
 	var out;
 	var x;
 	var y;
 	var n;
 	var i;
 
-	values = linspace( -200.0*PI/4.0, -40.0*PI/4.0, 1000 );
-	y = new Array( 2 );
+	values = largeNegative.x;
+	expected = largeNegative.expected;
+	y = [ 0.0, 0.0 ];
 	for ( i = 0; i < values.length; i++ ) {
 		x = values[ i ];
 		n = rempio2( x, y );
 		switch ( n & 3 ) {
 		case 0:
 			out = kernelCos( y[ 0 ], y[ 1 ] );
-			t.strictEqual( out, cos( x ), 'returns expected value' );
+			t.strictEqual( out, expected[ i ], 'returns expected value' );
 			break;
 		case 2:
 			out = -kernelCos( y[ 0 ], y[ 1 ] );
-			t.strictEqual( out, cos( x ), 'returns expected value' );
+			t.strictEqual( out, expected[ i ], 'returns expected value' );
 			break;
 		default:
 			break;

lib/node_modules/@stdlib/math/base/special/kernel-cos/test/fixtures/julia/runner.jl

@@ -23,10 +23,9 @@
 var resolve = require( 'path' ).resolve;
 var tape = require( 'tape' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
-var linspace = require( '@stdlib/array/base/linspace' );
+var abs = require( '@stdlib/math/base/special/abs' );
+var EPS = require( '@stdlib/constants/float64/eps' );
 var rempio2 = require( '@stdlib/math/base/special/rempio2' );
-var PI = require( '@stdlib/constants/float64/pi' );
-var cos = require( '@stdlib/math/base/special/cos' );
 var tryRequire = require( '@stdlib/utils/try-require' );
 
 
@@ -38,6 +37,13 @@ var opts = {
 };
 
 
+// FIXTURES //
+
+var smallRange = require( './fixtures/julia/small_range.json' );
+var largePositive = require( './fixtures/julia/large_positive.json' );
+var largeNegative = require( './fixtures/julia/large_negative.json' );
+
+
 // TESTS //
 
 tape( 'main export is a function', opts, function test( t ) {
@@ -48,52 +54,66 @@ tape( 'main export is a function', opts, function test( t ) {
 
 tape( 'the function returns `NaN` if provided `NaN` for either parameter', opts, function test( t ) {
 	var v = kernelCos( NaN, 0.0 );
-	t.equal( isnan( v ), true, 'returns NaN' );
+	t.equal( isnan( v ), true, 'returns expected value' );
 
 	v = kernelCos( 4.0, NaN );
-	t.equal( isnan( v ), true, 'returns NaN' );
+	t.equal( isnan( v ), true, 'returns expected value' );
 
 	v = kernelCos( NaN, NaN );
-	t.equal( isnan( v ), true, 'returns NaN' );
+	t.equal( isnan( v ), true, 'returns expected value' );
 	t.end();
 });
 
 tape( 'the function evaluates the cosine for input values on the interval `[-pi/4, pi/4]`', opts, function test( t ) {
+	var expected;
 	var values;
 	var out;
 	var x;
 	var i;
 
-	values = linspace( -PI/4.0, PI/4.0, 1000 );
+	values = smallRange.x;
+	expected = smallRange.expected;
 	for ( i = 0; i < values.length; i++ ) {
 		x = values[ i ];
 		out = kernelCos( x, 0.0 );
-		t.strictEqual( out, cos( x ), 'returns expected value' );
+		t.strictEqual( out, expected[ i ], 'returns expected value' );
 	}
 	t.end();
 });
 
 tape( 'the function can be used to compute the cosine for input values outside of `[-pi/4, pi/4]` after argument reduction via `rempio2` (positive)', opts, function test( t ) {
+	var expected;
 	var values;
+	var delta;
+	var tol;
 	var out;
 	var x;
 	var y;
 	var n;
 	var i;
 
-	values = linspace( 40.0*PI/4.0, 200*PI/4.0, 1000 );
-	y = new Array( 2 );
+	values = largePositive.x;
+	expected = largePositive.expected;
+	y = [ 0.0, 0.0 ];
 	for ( i = 0; i < values.length; i++ ) {
 		x = values[ i ];
 		n = rempio2( x, y );
 		switch ( n & 3 ) {
 		case 0:
 			out = kernelCos( y[ 0 ], y[ 1 ] );
-			t.strictEqual( out, cos( x ), 'returns expected value' );
+			t.strictEqual( out, expected[ i ], 'returns expected value' );
 			break;
 		case 2:
 			out = -kernelCos( y[ 0 ], y[ 1 ] );
-			t.strictEqual( out, cos( x ), 'returns expected value' );
+			if ( out === expected[ i ] ) {
+				t.strictEqual( out, expected[ i ], 'returns expected value' );
+			} else {
+				delta = abs( out - expected[ i ] );
+
+				// NOTE: the tolerance here is larger than for the JavaScript implementation due to compiler optimizations which may be performed resulting in result divergence. For discussion, see https://github.com/stdlib-js/stdlib/pull/2298#discussion_r1624765205
+				tol = EPS * abs( expected[ i ] );
+				t.ok( delta <= tol, 'within tolerance. x: '+x+'. out: '+out+'. E: '+expected[i]+'. tol: '+tol+'. Δ: '+delta+'.' );
+			}
 			break;
 		default:
 			break;
@@ -103,26 +123,38 @@ tape( 'the function can be used to compute the cosine for input values outside o
 });
 
 tape( 'the function can be used to compute the cosine for input values outside of `[-pi/4, pi/4]` after argument reduction via `rempio2` (negative)', opts, function test( t ) {
+	var expected;
 	var values;
+	var delta;
+	var tol;
 	var out;
 	var x;
 	var y;
 	var n;
 	var i;
 
-	values = linspace( -200.0*PI/4.0, -40.0*PI/4.0, 1000 );
-	y = new Array( 2 );
+	values = largeNegative.x;
+	expected = largeNegative.expected;
+	y = [ 0.0, 0.0 ];
 	for ( i = 0; i < values.length; i++ ) {
 		x = values[ i ];
 		n = rempio2( x, y );
 		switch ( n & 3 ) {
 		case 0:
 			out = kernelCos( y[ 0 ], y[ 1 ] );
-			t.strictEqual( out, cos( x ), 'returns expected value' );
+			t.strictEqual( out, expected[ i ], 'returns expected value' );
 			break;
 		case 2:
 			out = -kernelCos( y[ 0 ], y[ 1 ] );
-			t.strictEqual( out, cos( x ), 'returns expected value' );
+			if ( out === expected[ i ] ) {
+				t.strictEqual( out, expected[ i ], 'returns expected value' );
+			} else {
+				delta = abs( out - expected[ i ] );
+
+				// NOTE: the tolerance here is larger than for the JavaScript implementation due to compiler optimizations which may be performed resulting in result divergence. For discussion, see https://github.com/stdlib-js/stdlib/pull/2298#discussion_r1624765205
+				tol = EPS * abs( expected[ i ] );
+				t.ok( delta <= tol, 'within tolerance. x: '+x+'. out: '+out+'. E: '+expected[i]+'. tol: '+tol+'. Δ: '+delta+'.' );
+			}
 			break;
 		default:
 			break;