From 40e1d1c87c03f6199872b42400c465035c9f33c8 Mon Sep 17 00:00:00 2001
From: Claude <noreply@anthropic.com>
Date: Wed, 19 Aug 2026 10:24:00 +0000
Subject: [PATCH] test: migrate `math/base/special/rempio2` to ULP-based
 assertions

Replaces the computed relative tolerance checks (`delta <= EPS*abs(x)`)
in `test/test.js` and `test/test.native.js` with ULP-based assertions
using `@stdlib/assert/is-almost-same-value`, mirroring the idiom already
used by the float32 counterpart `math/base/special/rempio2f`.

The reconstruction checks over the positive, negative, and multiples of
pi/4 input ranges assert equality to within 1 ULP. For the tiny positive
and tiny negative ranges, reconstruction is exact, and so the assertions
use exact equality.

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

Co-Authored-By: Claude <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_0126JBJYGMzjhQq8VHZUyEaa
---
 .../math/base/special/rempio2/test/test.js    | 33 ++++---------------
 .../base/special/rempio2/test/test.native.js  | 33 ++++---------------
 2 files changed, 12 insertions(+), 54 deletions(-)

diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2/test/test.js b/lib/node_modules/@stdlib/math/base/special/rempio2/test/test.js
index 4645d805c09a..e4d595e30878 100644
--- a/lib/node_modules/@stdlib/math/base/special/rempio2/test/test.js
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2/test/test.js
@@ -27,11 +27,10 @@ var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var incrspace = require( '@stdlib/array/base/incrspace' );
 var linspace = require( '@stdlib/array/base/linspace' );
 var randu = require( '@stdlib/random/base/randu' );
-var abs = require( '@stdlib/math/base/special/abs' );
 var pow = require( '@stdlib/math/base/special/pow' );
+var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 var NINF = require( '@stdlib/constants/float64/ninf' );
-var EPS = require( '@stdlib/constants/float64/eps' );
 var PIO2 = require( '@stdlib/constants/float64/half-pi' );
 var PIO4 = require( '@stdlib/constants/float64/fourth-pi' );
 var rempio2 = require( './../lib' );
@@ -70,8 +69,6 @@ tape( 'the function returns `0` and sets the elements of `y` to `NaN` if provide
 });
 
 tape( 'the function returns `n` and stores `r` as two double-precision floating point numbers in `y` such that `x - nπ/2 = r` (positive)', function test( t ) {
-	var delta;
-	var tol;
 	var x;
 	var y;
 	var z;
@@ -88,16 +85,12 @@ tape( 'the function returns `n` and stores `r` as two double-precision floating
 		t.strictEqual( isNumber( y[1] ), true, 'returns expected value' );
 
 		z = ( PIO2*n ) + ( y[0]+y[1] );
-		delta = abs( z - x );
-		tol = EPS * abs( x );
-		t.strictEqual( delta <= tol, true, 'returns expected value' );
+		t.strictEqual( isAlmostSameValue( z, x, 1 ), true, 'returns expected value' );
 	}
 	t.end();
 });
 
 tape( 'the function returns `n` and stores `r` as two double-precision floating point numbers in `y` such that `x - nπ/2 = r` (tiny positive)', function test( t ) {
-	var delta;
-	var tol;
 	var x;
 	var y;
 	var z;
@@ -114,16 +107,12 @@ tape( 'the function returns `n` and stores `r` as two double-precision floating
 		t.strictEqual( isNumber( y[1] ), true, 'returns expected value' );
 
 		z = ( PIO2*n ) + ( y[0]+y[1] );
-		delta = abs( z - x );
-		tol = EPS * abs( x );
-		t.strictEqual( delta <= tol, true, 'returns expected value' );
+		t.strictEqual( z, x, 'returns expected value' );
 	}
 	t.end();
 });
 
 tape( 'the function returns `n` and stores `r` as two double-precision floating point numbers in `y` such that `x - nπ/2 = r` (negative)', function test( t ) {
-	var delta;
-	var tol;
 	var x;
 	var y;
 	var z;
@@ -140,16 +129,12 @@ tape( 'the function returns `n` and stores `r` as two double-precision floating
 		t.strictEqual( isNumber( y[1] ), true, 'returns expected value' );
 
 		z = ( PIO2*n ) + ( y[0]+y[1] );
-		delta = abs( z - x );
-		tol = EPS * abs( x );
-		t.strictEqual( delta <= tol, true, 'returns expected value' );
+		t.strictEqual( isAlmostSameValue( z, x, 1 ), true, 'returns expected value' );
 	}
 	t.end();
 });
 
 tape( 'the function returns `n` and stores `r` as two double-precision floating point numbers in `y` such that `x - nπ/2 = r` (tiny negative)', function test( t ) {
-	var delta;
-	var tol;
 	var x;
 	var y;
 	var z;
@@ -166,16 +151,12 @@ tape( 'the function returns `n` and stores `r` as two double-precision floating
 		t.strictEqual( isNumber( y[1] ), true, 'returns expected value' );
 
 		z = ( PIO2*n ) + ( y[0]+y[1] );
-		delta = abs( z - x );
-		tol = EPS * abs( x );
-		t.strictEqual( delta <= tol, true, 'returns expected value' );
+		t.strictEqual( z, x, 'returns expected value' );
 	}
 	t.end();
 });
 
 tape( 'the function returns `n` and stores `r` as two double-precision floating point numbers in `y` such that `x - nπ/2 = r` (multiples of π/4)', function test( t ) {
-	var delta;
-	var tol;
 	var x;
 	var y;
 	var z;
@@ -192,9 +173,7 @@ tape( 'the function returns `n` and stores `r` as two double-precision floating
 		t.strictEqual( isNumber( y[1] ), true, 'returns expected value' );
 
 		z = ( PIO2*n ) + ( y[0]+y[1] );
-		delta = abs( z - x[i] );
-		tol = EPS * abs( x[i] );
-		t.strictEqual( delta <= tol, true, 'returns expected value' );
+		t.strictEqual( isAlmostSameValue( z, x[ i ], 1 ), true, 'returns expected value' );
 	}
 	t.end();
 });
diff --git a/lib/node_modules/@stdlib/math/base/special/rempio2/test/test.native.js b/lib/node_modules/@stdlib/math/base/special/rempio2/test/test.native.js
index aebecf791c36..0cd39b8ad88e 100644
--- a/lib/node_modules/@stdlib/math/base/special/rempio2/test/test.native.js
+++ b/lib/node_modules/@stdlib/math/base/special/rempio2/test/test.native.js
@@ -28,11 +28,10 @@ var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var incrspace = require( '@stdlib/array/base/incrspace' );
 var linspace = require( '@stdlib/array/base/linspace' );
 var randu = require( '@stdlib/random/base/randu' );
-var abs = require( '@stdlib/math/base/special/abs' );
 var pow = require( '@stdlib/math/base/special/pow' );
+var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 var NINF = require( '@stdlib/constants/float64/ninf' );
-var EPS = require( '@stdlib/constants/float64/eps' );
 var PIO2 = require( '@stdlib/constants/float64/half-pi' );
 var PIO4 = require( '@stdlib/constants/float64/fourth-pi' );
 var Float64Array = require( '@stdlib/array/float64' );
@@ -80,8 +79,6 @@ tape( 'the function returns `0` and sets the elements of `y` to `NaN` if provide
 });
 
 tape( 'the function returns `n` and stores `r` as two double-precision floating point numbers in `y` such that `x - nπ/2 = r` (positive)', opts, function test( t ) {
-	var delta;
-	var tol;
 	var x;
 	var y;
 	var z;
@@ -98,16 +95,12 @@ tape( 'the function returns `n` and stores `r` as two double-precision floating
 		t.strictEqual( isNumber( y[1] ), true, 'returns expected value' );
 
 		z = ( PIO2*n ) + ( y[0]+y[1] );
-		delta = abs( z - x );
-		tol = EPS * abs( x );
-		t.strictEqual( delta <= tol, true, 'can recover input value' );
+		t.strictEqual( isAlmostSameValue( z, x, 1 ), true, 'returns expected value' );
 	}
 	t.end();
 });
 
 tape( 'the function returns `n` and stores `r` as two double-precision floating point numbers in `y` such that `x - nπ/2 = r` (tiny positive)', opts, function test( t ) {
-	var delta;
-	var tol;
 	var x;
 	var y;
 	var z;
@@ -124,16 +117,12 @@ tape( 'the function returns `n` and stores `r` as two double-precision floating
 		t.strictEqual( isNumber( y[1] ), true, 'returns expected value' );
 
 		z = ( PIO2*n ) + ( y[0]+y[1] );
-		delta = abs( z - x );
-		tol = EPS * abs( x );
-		t.strictEqual( delta <= tol, true, 'can recover input value' );
+		t.strictEqual( z, x, 'returns expected value' );
 	}
 	t.end();
 });
 
 tape( 'the function returns `n` and stores `r` as two double-precision floating point numbers in `y` such that `x - nπ/2 = r` (negative)', opts, function test( t ) {
-	var delta;
-	var tol;
 	var x;
 	var y;
 	var z;
@@ -150,16 +139,12 @@ tape( 'the function returns `n` and stores `r` as two double-precision floating
 		t.strictEqual( isNumber( y[1] ), true, 'returns expected value' );
 
 		z = ( PIO2*n ) + ( y[0]+y[1] );
-		delta = abs( z - x );
-		tol = EPS * abs( x );
-		t.strictEqual( delta <= tol, true, 'can recover input value' );
+		t.strictEqual( isAlmostSameValue( z, x, 1 ), true, 'returns expected value' );
 	}
 	t.end();
 });
 
 tape( 'the function returns `n` and stores `r` as two double-precision floating point numbers in `y` such that `x - nπ/2 = r` (tiny negative)', opts, function test( t ) {
-	var delta;
-	var tol;
 	var x;
 	var y;
 	var z;
@@ -176,16 +161,12 @@ tape( 'the function returns `n` and stores `r` as two double-precision floating
 		t.strictEqual( isNumber( y[1] ), true, 'returns expected value' );
 
 		z = ( PIO2*n ) + ( y[0]+y[1] );
-		delta = abs( z - x );
-		tol = EPS * abs( x );
-		t.strictEqual( delta <= tol, true, 'can recover input value' );
+		t.strictEqual( z, x, 'returns expected value' );
 	}
 	t.end();
 });
 
 tape( 'the function returns `n` and stores `r` as two double-precision floating point numbers in `y` such that `x - nπ/2 = r` (multiples of π/4)', opts, function test( t ) {
-	var delta;
-	var tol;
 	var x;
 	var y;
 	var z;
@@ -202,9 +183,7 @@ tape( 'the function returns `n` and stores `r` as two double-precision floating
 		t.strictEqual( isNumber( y[1] ), true, 'returns expected value' );
 
 		z = ( PIO2*n ) + ( y[0]+y[1] );
-		delta = abs( z - x[i] );
-		tol = EPS * abs( x[i] );
-		t.strictEqual( delta <= tol, true, 'can recover input value' );
+		t.strictEqual( isAlmostSameValue( z, x[ i ], 1 ), true, 'returns expected value' );
 	}
 	t.end();
 });