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test: migrate math/base/special/ellipj to ULP-based assertions #15264

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Merged
kgryte merged 1 commit into from
Sep 23, 2026
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test: migrate math/base/special/ellipj to ULP-based assertions #15264

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143 changes: 16 additions & 127 deletions lib/node_modules/@stdlib/math/base/special/ellipj/test/test.main.js
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Original file line number Diff line number Diff line change
Expand Up @@ -22,11 +22,10 @@

var tape = require( 'tape' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
var PINF = require( '@stdlib/constants/float64/pinf' );
var NINF = require( '@stdlib/constants/float64/ninf' );
var HALF_PI = require( '@stdlib/constants/float64/half-pi' );
var EPS = require( '@stdlib/constants/float64/eps' );
var abs = require( '@stdlib/math/base/special/abs' );
var ellipj = require( './../lib/main.js' );


Expand Down Expand Up @@ -88,8 +87,6 @@ tape( 'the function evaluates the Jacobi elliptic functions sn, cn dn (medium po
var cnExpected;
var dnExpected;
var sncndn;
var delta;
var tol;
var sn;
var cn;
var dn;
Expand All @@ -107,30 +104,9 @@ tape( 'the function evaluates the Jacobi elliptic functions sn, cn dn (medium po
sn = sncndn[0];
cn = sncndn[1];
dn = sncndn[2];

if ( sn === snExpected[i] ) {
t.strictEqual( sn, snExpected[i], 'u: '+u[i]+', m: '+m[i]+', sn: '+sn+', snExpected: '+snExpected[i] );
} else {
delta = abs( sn - snExpected[i] );
tol = 18.0 * EPS;
t.strictEqual( delta <= tol, true, 'within tolerance. u: '+u[i]+'. m: '+m[i]+', sn: '+sn+'. E: '+snExpected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
}

if ( cn === cnExpected[i] ) {
t.strictEqual( cn, cnExpected[i], 'u: '+u[i]+', m: '+m[i]+', cn: '+cn+', cnExpected: '+cnExpected[i] );
} else {
delta = abs( cn - cnExpected[i] );
tol = 14.0 * EPS;
t.strictEqual( delta <= tol, true, 'within tolerance. u: '+u[i]+'. m: '+m[i]+', cn: '+cn+'. E: '+cnExpected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
}

if ( dn === dnExpected[i] ) {
t.strictEqual( dn, dnExpected[i], 'u: '+u[i]+', m: '+m[i]+', dn: '+dn+', dnExpected: '+dnExpected[i] );
} else {
delta = abs( dn - dnExpected[i] );
tol = 40.0 * EPS;
t.strictEqual( delta <= tol, true, 'within tolerance. u: '+u[i]+'. m: '+m[i]+', dn: '+dn+'. E: '+dnExpected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
}
t.strictEqual( isAlmostSameValue( sn, snExpected[ i ], 4750 ), true, 'returns expected value' );

@kgryte kgryte Sep 21, 2026

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@Devansh-18155 How did you derive these ULP diffs? Given the previous deltas (e.g., 18*EPS), I am surprised by these large ULP differences.

@kgryte kgryte Sep 21, 2026

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This same comment applies to several other test assertions.

@Devansh-18155 Devansh-18155 Sep 21, 2026

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@kgryte ,Large ULP diffs because the previous test checks difference (18 * EPS), while isAlmostSameValue checks ULP, As an deltas of 2.3 * EPS which makes approx 4750 ULP.
I derived it by checking max ULP diff across dataset and we can keep this limits!

@kgryte kgryte Sep 21, 2026

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This still doesn't seem right. 1 unit of epsilon is roughly equal to 1 ULP, so, again, this large divergence is surprising. Can you provide exact test values demonstrating the large ULP difference?

@Devansh-18155 Devansh-18155 Sep 21, 2026

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@kgryte ,

Taken a test case from medium_positive_modulus.json :

  • u : 5.006645997054875
  • m : 0.8826190324290656
  • Computed sn : -0.000761851982413601
  • Expected sn : -0.000761851982414116
  • Difference : 5.15 e-16 ( approx 2.3 EPS)

The value is small (0.0007), 1 ULP is 1.08e-19. So difference is 2.3 * EPS in terms, it takes 4750 ULPs.

1 ULP =1 EPS but, if the numbers are closer to zero the ULP shrinks as well.

@kgryte kgryte Sep 23, 2026

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Oh, I see. The tolerances were previously computed incorrectly. They should have been scaled by the expected value.

t.strictEqual( isAlmostSameValue( cn, cnExpected[ i ], 9327 ), true, 'returns expected value' );
t.strictEqual( isAlmostSameValue( dn, dnExpected[ i ], 155 ), true, 'returns expected value' );
}
t.end();
});
Expand All @@ -140,8 +116,6 @@ tape( 'the function evaluates the Jacobi elliptic functions sn, cn dn (modulus n
var cnExpected;
var dnExpected;
var sncndn;
var delta;
var tol;
var sn;
var cn;
var dn;
Expand All @@ -159,30 +133,9 @@ tape( 'the function evaluates the Jacobi elliptic functions sn, cn dn (modulus n
sn = sncndn[0];
cn = sncndn[1];
dn = sncndn[2];

if ( sn === snExpected[i] ) {
t.strictEqual( sn, snExpected[i], 'u: '+u[i]+', m: '+m[i]+', sn: '+sn+', snExpected: '+snExpected[i] );
} else {
delta = abs( sn - snExpected[i] );
tol = 7.0 * EPS;
t.strictEqual( delta <= tol, true, 'within tolerance. u: '+u[i]+'. m: '+m[i]+', sn: '+sn+'. E: '+snExpected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
}

if ( cn === cnExpected[i] ) {
t.strictEqual( cn, cnExpected[i], 'u: '+u[i]+', m: '+m[i]+', cn: '+cn+', cnExpected: '+cnExpected[i] );
} else {
delta = abs( cn - cnExpected[i] );
tol = 5.0 * EPS;
t.strictEqual( delta <= tol, true, 'within tolerance. u: '+u[i]+'. m: '+m[i]+', cn: '+cn+'. E: '+cnExpected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
}

if ( dn === dnExpected[i] ) {
t.strictEqual( dn, dnExpected[i], 'u: '+u[i]+', m: '+m[i]+', dn: '+dn+', dnExpected: '+dnExpected[i] );
} else {
delta = abs( dn - dnExpected[i] );
tol = 5.0 * EPS;
t.strictEqual( delta <= tol, true, 'within tolerance. u: '+u[i]+'. m: '+m[i]+', dn: '+dn+'. E: '+dnExpected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
}
t.strictEqual( isAlmostSameValue( sn, snExpected[ i ], 9944 ), true, 'returns expected value' );
t.strictEqual( isAlmostSameValue( cn, cnExpected[ i ], 12 ), true, 'returns expected value' );
t.strictEqual( isAlmostSameValue( dn, dnExpected[ i ], 12 ), true, 'returns expected value' );
}
t.end();
});
Expand All @@ -192,8 +145,6 @@ tape( 'the function evaluates the Jacobi elliptic functions sn, cn dn (small pos
var cnExpected;
var dnExpected;
var sncndn;
var delta;
var tol;
var sn;
var cn;
var dn;
Expand All @@ -211,30 +162,9 @@ tape( 'the function evaluates the Jacobi elliptic functions sn, cn dn (small pos
sn = sncndn[0];
cn = sncndn[1];
dn = sncndn[2];

if ( sn === snExpected[i] ) {
t.strictEqual( sn, snExpected[i], 'u: '+u[i]+', m: '+m[i]+', sn: '+sn+', snExpected: '+snExpected[i] );
} else {
delta = abs( sn - snExpected[i] );
tol = 12.0 * EPS;
t.strictEqual( delta <= tol, true, 'within tolerance. u: '+u[i]+'. m: '+m[i]+', sn: '+sn+'. E: '+snExpected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
}

if ( cn === cnExpected[i] ) {
t.strictEqual( cn, cnExpected[i], 'u: '+u[i]+', m: '+m[i]+', cn: '+cn+', cnExpected: '+cnExpected[i] );
} else {
delta = abs( cn - cnExpected[i] );
tol = 12.0 * EPS;
t.strictEqual( delta <= tol, true, 'within tolerance. u: '+u[i]+'. m: '+m[i]+', cn: '+cn+'. E: '+cnExpected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
}

if ( dn === dnExpected[i] ) {
t.strictEqual( dn, dnExpected[i], 'u: '+u[i]+', m: '+m[i]+', dn: '+dn+', dnExpected: '+dnExpected[i] );
} else {
delta = abs( dn - dnExpected[i] );
tol = 1.0 * EPS;
t.strictEqual( delta <= tol, true, 'within tolerance. u: '+u[i]+'. m: '+m[i]+', dn: '+dn+'. E: '+dnExpected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
}
t.strictEqual( isAlmostSameValue( sn, snExpected[ i ], 9866 ), true, 'returns expected value' );
t.strictEqual( isAlmostSameValue( cn, cnExpected[ i ], 9792 ), true, 'returns expected value' );
t.strictEqual( isAlmostSameValue( dn, dnExpected[ i ], 1 ), true, 'returns expected value' );
}
t.end();
});
Expand All @@ -244,8 +174,6 @@ tape( 'the function evaluates the Jacobi elliptic functions sn, cn dn (zero modu
var cnExpected;
var dnExpected;
var sncndn;
var delta;
var tol;
var sn;
var cn;
var dn;
Expand All @@ -263,25 +191,9 @@ tape( 'the function evaluates the Jacobi elliptic functions sn, cn dn (zero modu
sn = sncndn[0];
cn = sncndn[1];
dn = sncndn[2];

if ( sn === snExpected[i] ) {
t.strictEqual( sn, snExpected[i], 'u: '+u[i]+', m: '+m[i]+', sn: '+sn+', snExpected: '+snExpected[i] );
} else {
delta = abs( sn - snExpected[i] );
tol = 1.0 * EPS;
t.strictEqual( delta <= tol, true, 'within tolerance. u: '+u[i]+'. m: '+m[i]+', sn: '+sn+'. E: '+snExpected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
}

if ( cn === cnExpected[i] ) {
t.strictEqual( cn, cnExpected[i], 'u: '+u[i]+', m: '+m[i]+', cn: '+cn+', cnExpected: '+cnExpected[i] );
} else {
delta = abs( cn - cnExpected[i] );
tol = 1.0 * EPS;
t.strictEqual( delta <= tol, true, 'within tolerance. u: '+u[i]+'. m: '+m[i]+', cn: '+cn+'. E: '+cnExpected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
}

// There is no reason for this to be anything but exactly identical, i.e. 1.0.
t.strictEqual( dn, dnExpected[i], 'u: '+u[i]+', m: '+m[i]+', dn: '+dn+', dnExpected: '+dnExpected[i] );
t.strictEqual( isAlmostSameValue( sn, snExpected[ i ], 1 ), true, 'returns expected value' );
t.strictEqual( isAlmostSameValue( cn, cnExpected[ i ], 1 ), true, 'returns expected value' );
t.strictEqual( isAlmostSameValue( dn, dnExpected[ i ], 0 ), true, 'returns expected value' );
}
t.end();
});
Expand All @@ -291,8 +203,6 @@ tape( 'the function evaluates the Jacobi elliptic functions sn, cn dn (unity mod
var cnExpected;
var dnExpected;
var sncndn;
var delta;
var tol;
var sn;
var cn;
var dn;
Expand All @@ -310,30 +220,9 @@ tape( 'the function evaluates the Jacobi elliptic functions sn, cn dn (unity mod
sn = sncndn[0];
cn = sncndn[1];
dn = sncndn[2];

if ( sn === snExpected[i] ) {
t.strictEqual( sn, snExpected[i], 'u: '+u[i]+', m: '+m[i]+', sn: '+sn+', snExpected: '+snExpected[i] );
} else {
delta = abs( sn - snExpected[i] );
tol = 1.0 * EPS;
t.strictEqual( delta <= tol, true, 'within tolerance. u: '+u[i]+'. m: '+m[i]+', sn: '+sn+'. E: '+snExpected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
}

if ( cn === cnExpected[i] ) {
t.strictEqual( cn, cnExpected[i], 'u: '+u[i]+', m: '+m[i]+', cn: '+cn+', cnExpected: '+cnExpected[i] );
} else {
delta = abs( cn - cnExpected[i] );
tol = 1.0 * EPS;
t.strictEqual( delta <= tol, true, 'within tolerance. u: '+u[i]+'. m: '+m[i]+', cn: '+cn+'. E: '+cnExpected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
}

if ( dn === dnExpected[i] ) {
t.strictEqual( dn, dnExpected[i], 'u: '+u[i]+', m: '+m[i]+', dn: '+dn+', dnExpected: '+dnExpected[i] );
} else {
delta = abs( dn - dnExpected[i] );
tol = 1.0 * EPS;
t.strictEqual( delta <= tol, true, 'within tolerance. u: '+u[i]+'. m: '+m[i]+', dn: '+dn+'. E: '+dnExpected[i]+'. Δ: '+delta+'. tol: '+tol+'.' );
}
t.strictEqual( isAlmostSameValue( sn, snExpected[ i ], 1 ), true, 'returns expected value' );
t.strictEqual( isAlmostSameValue( cn, cnExpected[ i ], 2 ), true, 'returns expected value' );
t.strictEqual( isAlmostSameValue( dn, dnExpected[ i ], 2 ), true, 'returns expected value' );
}
t.end();
});
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