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MATH-1694: Fix racy Jacobi coefficient cache in PolynomialsUtils #340

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Merged
aherbert merged 3 commits into from
Oct 29, 2026
+68 −31
Merged

MATH-1694: Fix racy Jacobi coefficient cache in PolynomialsUtils #340

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9b68d72
fix racy cache lookups in BaseRuleFactory and PolynomialsUtils
insaf021 Oct 26, 2026
665cafb
Use ConcurrentHashMap for Jacobi cache and build polynomial outside lock
insaf021 Oct 28, 2026
618cf4d
Drop BaseRuleFactory change, tracked separately as MATH-1693
insaf021 Oct 29, 2026
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60 changes: 29 additions & 31 deletions .../src/main/java/org/apache/commons/math4/legacy/analysis/polynomials/PolynomialsUtils.java
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Original file line number Diff line number Diff line change
Expand Up @@ -17,9 +17,9 @@
package org.apache.commons.math4.legacy.analysis.polynomials;

import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.concurrent.ConcurrentHashMap;

import org.apache.commons.numbers.fraction.BigFraction;
import org.apache.commons.numbers.combinatorics.BinomialCoefficient;
Expand Down Expand Up @@ -82,7 +82,7 @@ public final class PolynomialsUtils {
LEGENDRE_COEFFICIENTS.add(BigFraction.ONE);

// initialize map for Jacobi polynomials
JACOBI_COEFFICIENTS = new HashMap<>();
JACOBI_COEFFICIENTS = new ConcurrentHashMap<>();
}

/**
Expand Down Expand Up @@ -228,24 +228,21 @@ public static PolynomialFunction createJacobiPolynomial(final int degree, final
// select the appropriate list
final JacobiKey key = new JacobiKey(v, w);

if (!JACOBI_COEFFICIENTS.containsKey(key)) {
synchronized(JACOBI_COEFFICIENTS) {
if (!JACOBI_COEFFICIENTS.containsKey(key)) {
// allocate a new list for v, w
final List<BigFraction> list = new ArrayList<>();
JACOBI_COEFFICIENTS.put(key, list);
final List<BigFraction> coefficients = JACOBI_COEFFICIENTS.computeIfAbsent(key, k -> {
// allocate a new list for v, w
final List<BigFraction> list = new ArrayList<>();

// Pv,w,0(x) = 1;
list.add(BigFraction.ONE);
// Pv,w,0(x) = 1;
list.add(BigFraction.ONE);

// P1(x) = (v - w) / 2 + (2 + v + w) * X / 2
list.add(BigFraction.of(v - w, 2));
list.add(BigFraction.of(2 + v + w, 2));
}
}
}
// P1(x) = (v - w) / 2 + (2 + v + w) * X / 2
list.add(BigFraction.of(v - w, 2));
list.add(BigFraction.of(2 + v + w, 2));

return list;
});

return buildPolynomial(degree, JACOBI_COEFFICIENTS.get(key),
return buildPolynomial(degree, coefficients,
new RecurrenceCoefficientsGenerator() {
/** {@inheritDoc} */
@Override
Expand Down Expand Up @@ -368,26 +365,27 @@ private static PolynomialFunction buildPolynomial(final int degree,
// Synchronizing on a method parameter is not safe; however, in this
// case, the lock object is an immutable field that belongs to this
// class.
final double[] a;
synchronized (coefficients) {
final int maxDegree = (int) JdkMath.floor(JdkMath.sqrt(2.0 * coefficients.size())) - 1;
if (degree > maxDegree) {
computeUpToDegree(degree, maxDegree, generator, coefficients);
}
}

// coefficient for polynomial 0 is l [0]
// coefficients for polynomial 1 are l [1] ... l [2] (degrees 0 ... 1)
// coefficients for polynomial 2 are l [3] ... l [5] (degrees 0 ... 2)
// coefficients for polynomial 3 are l [6] ... l [9] (degrees 0 ... 3)
// coefficients for polynomial 4 are l[10] ... l[14] (degrees 0 ... 4)
// coefficients for polynomial 5 are l[15] ... l[20] (degrees 0 ... 5)
// coefficients for polynomial 6 are l[21] ... l[27] (degrees 0 ... 6)
// ...
final int start = degree * (degree + 1) / 2;

final double[] a = new double[degree + 1];
for (int i = 0; i <= degree; ++i) {
a[i] = coefficients.get(start + i).doubleValue();
// coefficient for polynomial 0 is l [0]
// coefficients for polynomial 1 are l [1] ... l [2] (degrees 0 ... 1)
// coefficients for polynomial 2 are l [3] ... l [5] (degrees 0 ... 2)
// coefficients for polynomial 3 are l [6] ... l [9] (degrees 0 ... 3)
// coefficients for polynomial 4 are l[10] ... l[14] (degrees 0 ... 4)
// coefficients for polynomial 5 are l[15] ... l[20] (degrees 0 ... 5)
// coefficients for polynomial 6 are l[21] ... l[27] (degrees 0 ... 6)
// ...
final int start = degree * (degree + 1) / 2;

a = new double[degree + 1];
for (int i = 0; i <= degree; ++i) {
a[i] = coefficients.get(start + i).doubleValue();
}
}

// build the polynomial
Expand Down
39 changes: 39 additions & 0 deletions .../test/java/org/apache/commons/math4/legacy/analysis/polynomials/PolynomialsUtilsTest.java
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Original file line number Diff line number Diff line change
Expand Up @@ -16,6 +16,13 @@
*/
package org.apache.commons.math4.legacy.analysis.polynomials;

import java.util.ArrayList;
import java.util.List;
import java.util.concurrent.CyclicBarrier;
import java.util.concurrent.ExecutorService;
import java.util.concurrent.Executors;
import java.util.concurrent.Future;

import org.apache.commons.math4.legacy.analysis.UnivariateFunction;
import org.apache.commons.math4.legacy.analysis.integration.IterativeLegendreGaussIntegrator;
import org.apache.commons.numbers.combinatorics.BinomialCoefficient;
Expand Down Expand Up @@ -291,6 +298,38 @@ public void testJacobiEvaluationAt1() {
}
}

@Test
public void testJacobiConcurrentCreation() throws Exception {
final int numThreads = 8;
final ExecutorService exec = Executors.newFixedThreadPool(numThreads);
try {
// Exponents not used elsewhere, so that every (v, w) list is
// created while the threads are racing.
for (int v = 20; v < 40; ++v) {
for (int w = 20; w < 40; ++w) {
final int fv = v;
final int fw = w;
final CyclicBarrier barrier = new CyclicBarrier(numThreads);
final List<Future<Double>> results = new ArrayList<>();
for (int t = 0; t < numThreads; ++t) {
final int degree = 1 + t % 4;
results.add(exec.submit(() -> {
barrier.await();
return PolynomialsUtils.createJacobiPolynomial(degree, fv, fw).value(1.0);
}));
}
for (int t = 0; t < numThreads; ++t) {
final int degree = 1 + t % 4;
final double binomial = BinomialCoefficient.value(v + degree, degree);
Assert.assertTrue(Precision.equals(binomial, results.get(t).get(), 1));
}
}
}
} finally {
exec.shutdownNow();
}
}

@Test
public void testJacobiOrthogonality() {
for (int v = 0; v < 5; ++v) {
Expand Down
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