From f68162e2709e5a57cd58bb6510ac93999094486c Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Fri, 14 Aug 2026 02:25:53 +0000
Subject: [PATCH] test: migrate `math/base/special/coversin` to ULP-based
 assertions

Migrate the relative tolerance test cases to ULP difference testing via
`@stdlib/assert/is-almost-same-value`, as proposed in the tracking issue.
Both the JavaScript and C implementations match the Julia fixtures exactly
across all 24000 values, so the minimum required ULP value is zero.

Ref: https://github.com/stdlib-js/stdlib/issues/11352

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_014wMuenVCso7e5Sw1pvi4Aj
---
 .../math/base/special/coversin/test/test.js   | 63 +++----------------
 .../base/special/coversin/test/test.native.js | 63 +++----------------
 2 files changed, 14 insertions(+), 112 deletions(-)

diff --git a/lib/node_modules/@stdlib/math/base/special/coversin/test/test.js b/lib/node_modules/@stdlib/math/base/special/coversin/test/test.js
index 42d14af0ac18..7667c1e08cb1 100644
--- a/lib/node_modules/@stdlib/math/base/special/coversin/test/test.js
+++ b/lib/node_modules/@stdlib/math/base/special/coversin/test/test.js
@@ -21,11 +21,10 @@
 // MODULES //
 
 var tape = require( 'tape' );
+var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 var NINF = require( '@stdlib/constants/float64/ninf' );
-var EPS = require( '@stdlib/constants/float64/eps' );
-var abs = require( '@stdlib/math/base/special/abs' );
 var coversin = require( './../lib' );
 
 
@@ -49,8 +48,6 @@ tape( 'main export is a function', function test( t ) {
 
 tape( 'the function computes the coversine (for -256*pi < x < 0)', function test( t ) {
 	var expected;
-	var delta;
-	var tol;
 	var x;
 	var y;
 	var i;
@@ -60,21 +57,13 @@ tape( 'the function computes the coversine (for -256*pi < x < 0)', function test
 
 	for ( i = 0; i < x.length; i++ ) {
 		y = coversin( x[i] );
-		if ( y === expected[ i ] ) {
-			t.strictEqual( y, expected[ i ], 'x: '+x[i]+'. E: '+expected[i] );
-		} else {
-			delta = abs( y - expected[i] );
-			tol = EPS * abs( expected[i] );
-			t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. Value: '+y+'. E: '+expected[i]+'. tol: '+tol+'. Δ: '+delta+'.' );
-		}
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
 	}
 	t.end();
 });
 
 tape( 'the function computes the coversine (for 0 < x < 256*pi)', function test( t ) {
 	var expected;
-	var delta;
-	var tol;
 	var x;
 	var y;
 	var i;
@@ -84,21 +73,13 @@ tape( 'the function computes the coversine (for 0 < x < 256*pi)', function test(
 
 	for ( i = 0; i < x.length; i++ ) {
 		y = coversin( x[i] );
-		if ( y === expected[ i ] ) {
-			t.strictEqual( y, expected[ i ], 'x: '+x[i]+'. E: '+expected[i] );
-		} else {
-			delta = abs( y - expected[i] );
-			tol = EPS * abs( expected[i] );
-			t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. Value: '+y+'. E: '+expected[i]+'. tol: '+tol+'. Δ: '+delta+'.' );
-		}
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
 	}
 	t.end();
 });
 
 tape( 'the function computes the coversine (for -2**60 (pi/2) < x < -2**20 (pi/2))', function test( t ) {
 	var expected;
-	var delta;
-	var tol;
 	var x;
 	var y;
 	var i;
@@ -108,21 +89,13 @@ tape( 'the function computes the coversine (for -2**60 (pi/2) < x < -2**20 (pi/2
 
 	for ( i = 0; i < x.length; i++ ) {
 		y = coversin( x[i] );
-		if ( y === expected[ i ] ) {
-			t.strictEqual( y, expected[ i ], 'x: '+x[i]+'. E: '+expected[i] );
-		} else {
-			delta = abs( y - expected[i] );
-			tol = EPS * abs( expected[i] );
-			t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. Value: '+y+'. E: '+expected[i]+'. tol: '+tol+'. Δ: '+delta+'.' );
-		}
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
 	}
 	t.end();
 });
 
 tape( 'the function computes the coversine (for 2**20 (pi/2) < x < 2**60 (pi/2))', function test( t ) {
 	var expected;
-	var delta;
-	var tol;
 	var x;
 	var y;
 	var i;
@@ -132,21 +105,13 @@ tape( 'the function computes the coversine (for 2**20 (pi/2) < x < 2**60 (pi/2))
 
 	for ( i = 0; i < x.length; i++ ) {
 		y = coversin( x[i] );
-		if ( y === expected[ i ] ) {
-			t.strictEqual( y, expected[ i ], 'x: '+x[i]+'. E: '+expected[i] );
-		} else {
-			delta = abs( y - expected[i] );
-			tol = EPS * abs( expected[i] );
-			t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. Value: '+y+'. E: '+expected[i]+'. tol: '+tol+'. Δ: '+delta+'.' );
-		}
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
 	}
 	t.end();
 });
 
 tape( 'the function computes the coversine (for x <= -2**60 (PI/2))', function test( t ) {
 	var expected;
-	var delta;
-	var tol;
 	var x;
 	var y;
 	var i;
@@ -156,21 +121,13 @@ tape( 'the function computes the coversine (for x <= -2**60 (PI/2))', function t
 
 	for ( i = 0; i < x.length; i++ ) {
 		y = coversin( x[i] );
-		if ( y === expected[ i ] ) {
-			t.strictEqual( y, expected[ i ], 'x: '+x[i]+'. E: '+expected[i] );
-		} else {
-			delta = abs( y - expected[i] );
-			tol = EPS * abs( expected[i] );
-			t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. Value: '+y+'. E: '+expected[i]+'. tol: '+tol+'. Δ: '+delta+'.' );
-		}
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
 	}
 	t.end();
 });
 
 tape( 'the function computes the coversine (for x >= 2**60 (PI/2))', function test( t ) {
 	var expected;
-	var delta;
-	var tol;
 	var x;
 	var y;
 	var i;
@@ -180,13 +137,7 @@ tape( 'the function computes the coversine (for x >= 2**60 (PI/2))', function te
 
 	for ( i = 0; i < x.length; i++ ) {
 		y = coversin( x[i] );
-		if ( y === expected[ i ] ) {
-			t.strictEqual( y, expected[ i ], 'x: '+x[i]+'. E: '+expected[i] );
-		} else {
-			delta = abs( y - expected[i] );
-			tol = EPS * abs( expected[i] );
-			t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. Value: '+y+'. E: '+expected[i]+'. tol: '+tol+'. Δ: '+delta+'.' );
-		}
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
 	}
 	t.end();
 });
diff --git a/lib/node_modules/@stdlib/math/base/special/coversin/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/coversin/test/test.native.js
index 7c03682b9a28..00a20912d6a8 100644
--- a/lib/node_modules/@stdlib/math/base/special/coversin/test/test.native.js
+++ b/lib/node_modules/@stdlib/math/base/special/coversin/test/test.native.js
@@ -22,11 +22,10 @@
 
 var resolve = require( 'path' ).resolve;
 var tape = require( 'tape' );
+var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 var NINF = require( '@stdlib/constants/float64/ninf' );
-var EPS = require( '@stdlib/constants/float64/eps' );
-var abs = require( '@stdlib/math/base/special/abs' );
 var tryRequire = require( '@stdlib/utils/try-require' );
 
 
@@ -58,8 +57,6 @@ tape( 'main export is a function', opts, function test( t ) {
 
 tape( 'the function computes the coversine (for -256*pi < x < 0)', opts, function test( t ) {
 	var expected;
-	var delta;
-	var tol;
 	var x;
 	var y;
 	var i;
@@ -69,21 +66,13 @@ tape( 'the function computes the coversine (for -256*pi < x < 0)', opts, functio
 
 	for ( i = 0; i < x.length; i++ ) {
 		y = coversin( x[i] );
-		if ( y === expected[ i ] ) {
-			t.strictEqual( y, expected[ i ], 'x: '+x[i]+'. E: '+expected[i] );
-		} else {
-			delta = abs( y - expected[i] );
-			tol = 2.0 * EPS * abs( expected[i] );
-			t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. Value: '+y+'. E: '+expected[i]+'. tol: '+tol+'. Δ: '+delta+'.' );
-		}
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
 	}
 	t.end();
 });
 
 tape( 'the function computes the coversine (for 0 < x < 256*pi)', opts, function test( t ) {
 	var expected;
-	var delta;
-	var tol;
 	var x;
 	var y;
 	var i;
@@ -93,21 +82,13 @@ tape( 'the function computes the coversine (for 0 < x < 256*pi)', opts, function
 
 	for ( i = 0; i < x.length; i++ ) {
 		y = coversin( x[i] );
-		if ( y === expected[ i ] ) {
-			t.strictEqual( y, expected[ i ], 'x: '+x[i]+'. E: '+expected[i] );
-		} else {
-			delta = abs( y - expected[i] );
-			tol = 4.0 * EPS * abs( expected[i] );
-			t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. Value: '+y+'. E: '+expected[i]+'. tol: '+tol+'. Δ: '+delta+'.' );
-		}
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
 	}
 	t.end();
 });
 
 tape( 'the function computes the coversine (for -2**60 (pi/2) < x < -2**20 (pi/2))', opts, function test( t ) {
 	var expected;
-	var delta;
-	var tol;
 	var x;
 	var y;
 	var i;
@@ -117,21 +98,13 @@ tape( 'the function computes the coversine (for -2**60 (pi/2) < x < -2**20 (pi/2
 
 	for ( i = 0; i < x.length; i++ ) {
 		y = coversin( x[i] );
-		if ( y === expected[ i ] ) {
-			t.strictEqual( y, expected[ i ], 'x: '+x[i]+'. E: '+expected[i] );
-		} else {
-			delta = abs( y - expected[i] );
-			tol = 4.6 * EPS * abs( expected[i] );
-			t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. Value: '+y+'. E: '+expected[i]+'. tol: '+tol+'. Δ: '+delta+'.' );
-		}
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
 	}
 	t.end();
 });
 
 tape( 'the function computes the coversine (for 2**20 (pi/2) < x < 2**60 (pi/2))', opts, function test( t ) {
 	var expected;
-	var delta;
-	var tol;
 	var x;
 	var y;
 	var i;
@@ -141,21 +114,13 @@ tape( 'the function computes the coversine (for 2**20 (pi/2) < x < 2**60 (pi/2))
 
 	for ( i = 0; i < x.length; i++ ) {
 		y = coversin( x[i] );
-		if ( y === expected[ i ] ) {
-			t.strictEqual( y, expected[ i ], 'x: '+x[i]+'. E: '+expected[i] );
-		} else {
-			delta = abs( y - expected[i] );
-			tol = 1.7 * EPS * abs( expected[i] );
-			t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. Value: '+y+'. E: '+expected[i]+'. tol: '+tol+'. Δ: '+delta+'.' );
-		}
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
 	}
 	t.end();
 });
 
 tape( 'the function computes the coversine (for x <= -2**60 (PI/2))', opts, function test( t ) {
 	var expected;
-	var delta;
-	var tol;
 	var x;
 	var y;
 	var i;
@@ -165,21 +130,13 @@ tape( 'the function computes the coversine (for x <= -2**60 (PI/2))', opts, func
 
 	for ( i = 0; i < x.length; i++ ) {
 		y = coversin( x[i] );
-		if ( y === expected[ i ] ) {
-			t.strictEqual( y, expected[ i ], 'x: '+x[i]+'. E: '+expected[i] );
-		} else {
-			delta = abs( y - expected[i] );
-			tol = 2.3 * EPS * abs( expected[i] );
-			t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. Value: '+y+'. E: '+expected[i]+'. tol: '+tol+'. Δ: '+delta+'.' );
-		}
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
 	}
 	t.end();
 });
 
 tape( 'the function computes the coversine (for x >= 2**60 (PI/2))', opts, function test( t ) {
 	var expected;
-	var delta;
-	var tol;
 	var x;
 	var y;
 	var i;
@@ -189,13 +146,7 @@ tape( 'the function computes the coversine (for x >= 2**60 (PI/2))', opts, funct
 
 	for ( i = 0; i < x.length; i++ ) {
 		y = coversin( x[i] );
-		if ( y === expected[ i ] ) {
-			t.strictEqual( y, expected[ i ], 'x: '+x[i]+'. E: '+expected[i] );
-		} else {
-			delta = abs( y - expected[i] );
-			tol = 3.6 * EPS * abs( expected[i] );
-			t.ok( delta <= tol, 'within tolerance. x: '+x[i]+'. Value: '+y+'. E: '+expected[i]+'. tol: '+tol+'. Δ: '+delta+'.' );
-		}
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
 	}
 	t.end();
 });