From 6ad90d9896caf2772d112e3e5bccd4664d585d20 Mon Sep 17 00:00:00 2001
From: Athan Reines <kgryte+claude@gmail.com>
Date: Mon, 12 Oct 2026 22:30:10 +0000
Subject: [PATCH] test: migrate `blas/base/zaxpy` to ULP-based assertions

Replace the relative-tolerance `isApprox` helper with ULP difference
testing via `@stdlib/assert/is-almost-same-value`, tightening each
assertion to the minimum required ULP bound.

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_01TpH47f7GqLWYmKXoVNEzuu

---
type: pre_commit_static_analysis_report
description: Results of running static analysis checks when committing changes.
report:
  - task: lint_filenames
    status: passed
  - task: lint_editorconfig
    status: skipped
  - task: lint_markdown_pkg_readmes
    status: na
  - task: lint_markdown_docs
    status: na
  - task: lint_markdown
    status: na
  - task: lint_package_json
    status: na
  - task: lint_repl_help
    status: na
  - task: lint_javascript_src
    status: na
  - task: lint_javascript_cli
    status: na
  - task: lint_javascript_examples
    status: na
  - task: lint_javascript_tests
    status: passed
  - task: lint_javascript_benchmarks
    status: na
  - task: lint_python
    status: na
  - task: lint_r
    status: na
  - task: lint_c_src
    status: na
  - task: lint_c_examples
    status: na
  - task: lint_c_benchmarks
    status: na
  - task: lint_c_tests_fixtures
    status: na
  - task: lint_shell
    status: na
  - task: lint_typescript_declarations
    status: passed
  - task: lint_typescript_tests
    status: na
  - task: lint_license_headers
    status: passed
---
---
 .../blas/base/zaxpy/test/test.ndarray.js      | 33 +++++++----------
 .../base/zaxpy/test/test.ndarray.native.js    | 35 +++++++------------
 .../blas/base/zaxpy/test/test.zaxpy.js        | 31 ++++++----------
 .../blas/base/zaxpy/test/test.zaxpy.native.js | 31 ++++++----------
 4 files changed, 47 insertions(+), 83 deletions(-)

diff --git a/lib/node_modules/@stdlib/blas/base/zaxpy/test/test.ndarray.js b/lib/node_modules/@stdlib/blas/base/zaxpy/test/test.ndarray.js
index bc313d9c0b05..68e81de7b21a 100644
--- a/lib/node_modules/@stdlib/blas/base/zaxpy/test/test.ndarray.js
+++ b/lib/node_modules/@stdlib/blas/base/zaxpy/test/test.ndarray.js
@@ -24,8 +24,7 @@ var tape = require( 'tape' );
 var Float64Array = require( '@stdlib/array/float64' );
 var Complex128Array = require( '@stdlib/array/complex128' );
 var Complex128 = require( '@stdlib/complex/float64/ctor' );
-var EPS = require( '@stdlib/constants/float64/eps' );
-var abs = require( '@stdlib/math/base/special/abs' );
+var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
 var zaxpy = require( './../lib/ndarray.js' );
 
 
@@ -38,22 +37,14 @@ var zaxpy = require( './../lib/ndarray.js' );
 * @param {Object} t - test object
 * @param {Collection} actual - actual values
 * @param {Collection} expected - expected values
-* @param {number} rtol - relative tolerance
+* @param {NonNegativeInteger} ulp - maximum allowed ULP difference
 */
-function isApprox( t, actual, expected, rtol ) {
-	var delta;
-	var tol;
+function isApprox( t, actual, expected, ulp ) {
 	var i;
 
 	t.strictEqual( actual.length, expected.length, 'returns expected value' );
 	for ( i = 0; i < expected.length; i++ ) {
-		if ( actual[ i ] === expected[ i ] ) {
-			t.strictEqual( actual[ i ], expected[ i ], 'returns expected value' );
-		} else {
-			delta = abs( actual[ i ] - expected[ i ] );
-			tol = rtol * EPS * abs( expected[ i ] );
-			t.ok( delta <= tol, 'within tolerance. actual: '+actual[ i ]+'. expected: '+expected[ i ]+'. delta: '+delta+'. tol: '+tol+'.' );
-		}
+		t.strictEqual( isAlmostSameValue( actual[ i ], expected[ i ], ulp ), true, 'returns expected value' );
 	}
 }
 
@@ -131,7 +122,7 @@ tape( 'the function scales elements from `x` by `alpha` and adds the result to `
 		0.8,
 		-0.7
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 24 );
 	t.end();
 });
 
@@ -195,7 +186,7 @@ tape( 'the function supports an `x` stride', function test( t ) {
 		0.8,
 		-0.7
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 8 );
 	t.end();
 });
 
@@ -259,7 +250,7 @@ tape( 'the function supports an `x` offset', function test( t ) {
 		0.8,
 		-0.7
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 11 );
 	t.end();
 });
 
@@ -323,7 +314,7 @@ tape( 'the function supports a `y` stride', function test( t ) {
 		0.32,  // 4
 		-1.16  // 4
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 6 );
 	t.end();
 });
 
@@ -387,7 +378,7 @@ tape( 'the function supports a `y` offset', function test( t ) {
 		0.8,
 		-0.7
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 1 );
 	t.end();
 });
 
@@ -513,7 +504,7 @@ tape( 'the function supports a negative `x` stride', function test( t ) {
 		0.8,
 		-0.7
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 24 );
 	t.end();
 });
 
@@ -577,7 +568,7 @@ tape( 'the function supports a negative `y` stride', function test( t ) {
 		0.52,  // 1
 		-1.51  // 1
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 8 );
 	t.end();
 });
 
@@ -641,6 +632,6 @@ tape( 'the function supports complex access patterns', function test( t ) {
 		0.32,  // 1
 		-1.16  // 1
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 6 );
 	t.end();
 });
diff --git a/lib/node_modules/@stdlib/blas/base/zaxpy/test/test.ndarray.native.js b/lib/node_modules/@stdlib/blas/base/zaxpy/test/test.ndarray.native.js
index c0951fb971ad..54e7e6f33bec 100644
--- a/lib/node_modules/@stdlib/blas/base/zaxpy/test/test.ndarray.native.js
+++ b/lib/node_modules/@stdlib/blas/base/zaxpy/test/test.ndarray.native.js
@@ -25,8 +25,7 @@ var tape = require( 'tape' );
 var Float64Array = require( '@stdlib/array/float64' );
 var Complex128Array = require( '@stdlib/array/complex128' );
 var Complex128 = require( '@stdlib/complex/float64/ctor' );
-var EPS = require( '@stdlib/constants/float64/eps' );
-var abs = require( '@stdlib/math/base/special/abs' );
+var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
 var tryRequire = require( '@stdlib/utils/try-require' );
 
 
@@ -47,22 +46,14 @@ var opts = {
 * @param {Object} t - test object
 * @param {Collection} actual - actual values
 * @param {Collection} expected - expected values
-* @param {number} rtol - relative tolerance
+* @param {NonNegativeInteger} ulp - maximum allowed ULP difference
 */
-function isApprox( t, actual, expected, rtol ) {
-	var delta;
-	var tol;
+function isApprox( t, actual, expected, ulp ) {
 	var i;
 
 	t.strictEqual( actual.length, expected.length, 'returns expected value' );
 	for ( i = 0; i < expected.length; i++ ) {
-		if ( actual[ i ] === expected[ i ] ) {
-			t.strictEqual( actual[ i ], expected[ i ], 'returns expected value' );
-		} else {
-			delta = abs( actual[ i ] - expected[ i ] );
-			tol = rtol * EPS * abs( expected[ i ] );
-			t.ok( delta <= tol, 'within tolerance. actual: '+actual[ i ]+'. expected: '+expected[ i ]+'. delta: '+delta+'. tol: '+tol+'.' );
-		}
+		t.strictEqual( isAlmostSameValue( actual[ i ], expected[ i ], ulp ), true, 'returns expected value' );
 	}
 }
 
@@ -140,7 +131,7 @@ tape( 'the function scales elements from `x` by `alpha` and adds the result to `
 		0.8,
 		-0.7
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 24 );
 	t.end();
 });
 
@@ -204,7 +195,7 @@ tape( 'if dcabs1( alpha ) === 0.0; the function returns the second input array u
 		0.8,
 		-0.7
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 0 );
 	t.end();
 });
 
@@ -268,7 +259,7 @@ tape( 'the function supports an `x` stride', opts, function test( t ) {
 		0.8,
 		-0.7
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 8 );
 	t.end();
 });
 
@@ -332,7 +323,7 @@ tape( 'the function supports an `x` offset', opts, function test( t ) {
 		0.8,
 		-0.7
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 11 );
 	t.end();
 });
 
@@ -396,7 +387,7 @@ tape( 'the function supports a `y` stride', opts, function test( t ) {
 		0.32,  // 4
 		-1.16  // 4
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 6 );
 	t.end();
 });
 
@@ -460,7 +451,7 @@ tape( 'the function supports a `y` offset', opts, function test( t ) {
 		0.8,
 		-0.7
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 1 );
 	t.end();
 });
 
@@ -563,7 +554,7 @@ tape( 'the function supports a negative `x` stride', opts, function test( t ) {
 		0.8,
 		-0.7
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 24 );
 	t.end();
 });
 
@@ -627,7 +618,7 @@ tape( 'the function supports a negative `y` stride', opts, function test( t ) {
 		0.52,  // 1
 		-1.51  // 1
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 8 );
 	t.end();
 });
 
@@ -691,6 +682,6 @@ tape( 'the function supports complex access patterns', opts, function test( t )
 		0.32,  // 1
 		-1.16  // 1
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 6 );
 	t.end();
 });
diff --git a/lib/node_modules/@stdlib/blas/base/zaxpy/test/test.zaxpy.js b/lib/node_modules/@stdlib/blas/base/zaxpy/test/test.zaxpy.js
index c02ccd798e51..5f9b67edb3e0 100644
--- a/lib/node_modules/@stdlib/blas/base/zaxpy/test/test.zaxpy.js
+++ b/lib/node_modules/@stdlib/blas/base/zaxpy/test/test.zaxpy.js
@@ -24,8 +24,7 @@ var tape = require( 'tape' );
 var Float64Array = require( '@stdlib/array/float64' );
 var Complex128Array = require( '@stdlib/array/complex128' );
 var Complex128 = require( '@stdlib/complex/float64/ctor' );
-var EPS = require( '@stdlib/constants/float64/eps' );
-var abs = require( '@stdlib/math/base/special/abs' );
+var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
 var zaxpy = require( './../lib/zaxpy.js' );
 
 
@@ -38,22 +37,14 @@ var zaxpy = require( './../lib/zaxpy.js' );
 * @param {Object} t - test object
 * @param {Collection} actual - actual values
 * @param {Collection} expected - expected values
-* @param {number} rtol - relative tolerance
+* @param {NonNegativeInteger} ulp - maximum allowed ULP difference
 */
-function isApprox( t, actual, expected, rtol ) {
-	var delta;
-	var tol;
+function isApprox( t, actual, expected, ulp ) {
 	var i;
 
 	t.strictEqual( actual.length, expected.length, 'returns expected value' );
 	for ( i = 0; i < expected.length; i++ ) {
-		if ( actual[ i ] === expected[ i ] ) {
-			t.strictEqual( actual[ i ], expected[ i ], 'returns expected value' );
-		} else {
-			delta = abs( actual[ i ] - expected[ i ] );
-			tol = rtol * EPS * abs( expected[ i ] );
-			t.ok( delta <= tol, 'within tolerance. actual: '+actual[ i ]+'. expected: '+expected[ i ]+'. delta: '+delta+'. tol: '+tol+'.' );
-		}
+		t.strictEqual( isAlmostSameValue( actual[ i ], expected[ i ], ulp ), true, 'returns expected value' );
 	}
 }
 
@@ -131,7 +122,7 @@ tape( 'the function scales elements from `x` by `alpha` and adds the result to `
 		0.8,
 		-0.7
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 24 );
 	t.end();
 });
 
@@ -195,7 +186,7 @@ tape( 'the function supports an `x` stride', function test( t ) {
 		0.8,
 		-0.7
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 8 );
 	t.end();
 });
 
@@ -259,7 +250,7 @@ tape( 'the function supports a `y` stride', function test( t ) {
 		0.32,  // 4
 		-1.16  // 4
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 6 );
 	t.end();
 });
 
@@ -385,7 +376,7 @@ tape( 'the function supports negative `x` strides', function test( t ) {
 		0.8,
 		-0.7
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 24 );
 	t.end();
 });
 
@@ -449,7 +440,7 @@ tape( 'the function supports negative `y` strides', function test( t ) {
 		0.52,  // 1
 		-1.51  // 1
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 8 );
 	t.end();
 });
 
@@ -513,7 +504,7 @@ tape( 'the function supports complex access patterns', function test( t ) {
 		0.32,  // 1
 		-1.16  // 1
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 6 );
 	t.end();
 });
 
@@ -579,6 +570,6 @@ tape( 'the function supports view offsets', function test( t ) {
 		-0.96  // 4
 	]);
 
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 24 );
 	t.end();
 });
diff --git a/lib/node_modules/@stdlib/blas/base/zaxpy/test/test.zaxpy.native.js b/lib/node_modules/@stdlib/blas/base/zaxpy/test/test.zaxpy.native.js
index d3e7808edfb8..ff77475878ae 100644
--- a/lib/node_modules/@stdlib/blas/base/zaxpy/test/test.zaxpy.native.js
+++ b/lib/node_modules/@stdlib/blas/base/zaxpy/test/test.zaxpy.native.js
@@ -25,8 +25,7 @@ var tape = require( 'tape' );
 var Float64Array = require( '@stdlib/array/float64' );
 var Complex128Array = require( '@stdlib/array/complex128' );
 var Complex128 = require( '@stdlib/complex/float64/ctor' );
-var EPS = require( '@stdlib/constants/float64/eps' );
-var abs = require( '@stdlib/math/base/special/abs' );
+var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
 var tryRequire = require( '@stdlib/utils/try-require' );
 
 
@@ -47,22 +46,14 @@ var opts = {
 * @param {Object} t - test object
 * @param {Collection} actual - actual values
 * @param {Collection} expected - expected values
-* @param {number} rtol - relative tolerance
+* @param {NonNegativeInteger} ulp - maximum allowed ULP difference
 */
-function isApprox( t, actual, expected, rtol ) {
-	var delta;
-	var tol;
+function isApprox( t, actual, expected, ulp ) {
 	var i;
 
 	t.strictEqual( actual.length, expected.length, 'returns expected value' );
 	for ( i = 0; i < expected.length; i++ ) {
-		if ( actual[ i ] === expected[ i ] ) {
-			t.strictEqual( actual[ i ], expected[ i ], 'returns expected value' );
-		} else {
-			delta = abs( actual[ i ] - expected[ i ] );
-			tol = rtol * EPS * abs( expected[ i ] );
-			t.ok( delta <= tol, 'within tolerance. actual: '+actual[ i ]+'. expected: '+expected[ i ]+'. delta: '+delta+'. tol: '+tol+'.' );
-		}
+		t.strictEqual( isAlmostSameValue( actual[ i ], expected[ i ], ulp ), true, 'returns expected value' );
 	}
 }
 
@@ -140,7 +131,7 @@ tape( 'the function scales elements from `x` by `alpha` and adds the result to `
 		0.8,
 		-0.7
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 24 );
 	t.end();
 });
 
@@ -204,7 +195,7 @@ tape( 'the function supports an `x` stride', opts, function test( t ) {
 		0.8,
 		-0.7
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 8 );
 	t.end();
 });
 
@@ -268,7 +259,7 @@ tape( 'the function supports a `y` stride', opts, function test( t ) {
 		0.32,  // 4
 		-1.16  // 4
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 6 );
 	t.end();
 });
 
@@ -394,7 +385,7 @@ tape( 'the function supports negative `x` strides', opts, function test( t ) {
 		0.8,
 		-0.7
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 24 );
 	t.end();
 });
 
@@ -458,7 +449,7 @@ tape( 'the function supports negative `y` strides', opts, function test( t ) {
 		0.52,  // 1
 		-1.51  // 1
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 8 );
 	t.end();
 });
 
@@ -522,7 +513,7 @@ tape( 'the function supports complex access patterns', opts, function test( t )
 		0.32,  // 1
 		-1.16  // 1
 	]);
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 6 );
 	t.end();
 });
 
@@ -588,6 +579,6 @@ tape( 'the function supports view offsets', opts, function test( t ) {
 		-0.96  // 4
 	]);
 
-	isApprox( t, viewY, expected, 14.0 );
+	isApprox( t, viewY, expected, 24 );
 	t.end();
 });