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+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math3.analysis.integration;
+
+import org.apache.commons.math3.exception.MaxCountExceededException;
+import org.apache.commons.math3.exception.NotStrictlyPositiveException;
+import org.apache.commons.math3.exception.NumberIsTooLargeException;
+import org.apache.commons.math3.exception.NumberIsTooSmallException;
+import org.apache.commons.math3.exception.TooManyEvaluationsException;
+import org.apache.commons.math3.util.FastMath;
+
+/**
+ * Implements <a href="http://mathworld.wolfram.com/SimpsonsRule.html">
+ * Simpson's Rule</a> for integration of real univariate functions. For
+ * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,
+ * chapter 3.
+ * <p>
+ * This implementation employs the basic trapezoid rule to calculate Simpson's
+ * rule.</p>
+ *
+ * @since 1.2
+ */
+public class SimpsonIntegrator extends BaseAbstractUnivariateIntegrator {
+
+    /** Maximal number of iterations for Simpson. */
+    public static final int SIMPSON_MAX_ITERATIONS_COUNT = 64;
+
+    /**
+     * Build a Simpson integrator with given accuracies and iterations counts.
+     * @param relativeAccuracy relative accuracy of the result
+     * @param absoluteAccuracy absolute accuracy of the result
+     * @param minimalIterationCount minimum number of iterations
+     * @param maximalIterationCount maximum number of iterations
+     * (must be less than or equal to {@link #SIMPSON_MAX_ITERATIONS_COUNT})
+     * @exception NotStrictlyPositiveException if minimal number of iterations
+     * is not strictly positive
+     * @exception NumberIsTooSmallException if maximal number of iterations
+     * is lesser than or equal to the minimal number of iterations
+     * @exception NumberIsTooLargeException if maximal number of iterations
+     * is greater than {@link #SIMPSON_MAX_ITERATIONS_COUNT}
+     */
+    public SimpsonIntegrator(final double relativeAccuracy,
+                             final double absoluteAccuracy,
+                             final int minimalIterationCount,
+                             final int maximalIterationCount)
+        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
+        super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
+        if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) {
+            throw new NumberIsTooLargeException(maximalIterationCount,
+                                                SIMPSON_MAX_ITERATIONS_COUNT, false);
+        }
+    }
+
+    /**
+     * Build a Simpson integrator with given iteration counts.
+     * @param minimalIterationCount minimum number of iterations
+     * @param maximalIterationCount maximum number of iterations
+     * (must be less than or equal to {@link #SIMPSON_MAX_ITERATIONS_COUNT})
+     * @exception NotStrictlyPositiveException if minimal number of iterations
+     * is not strictly positive
+     * @exception NumberIsTooSmallException if maximal number of iterations
+     * is lesser than or equal to the minimal number of iterations
+     * @exception NumberIsTooLargeException if maximal number of iterations
+     * is greater than {@link #SIMPSON_MAX_ITERATIONS_COUNT}
+     */
+    public SimpsonIntegrator(final int minimalIterationCount,
+                             final int maximalIterationCount)
+        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
+        super(minimalIterationCount, maximalIterationCount);
+        if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) {
+            throw new NumberIsTooLargeException(maximalIterationCount,
+                                                SIMPSON_MAX_ITERATIONS_COUNT, false);
+        }
+    }
+
+    /**
+     * Construct an integrator with default settings.
+     * (max iteration count set to {@link #SIMPSON_MAX_ITERATIONS_COUNT})
+     */
+    public SimpsonIntegrator() {
+        super(DEFAULT_MIN_ITERATIONS_COUNT, SIMPSON_MAX_ITERATIONS_COUNT);
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    protected double doIntegrate()
+        throws TooManyEvaluationsException, MaxCountExceededException {
+
+        TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
+        if (getMinimalIterationCount() == 1) {
+            return (4 * qtrap.stage(this, 1) - qtrap.stage(this, 0)) / 3.0;
+        }
+
+        // Simpson's rule requires at least two trapezoid stages.
+        double olds = 0;
+        double oldt = qtrap.stage(this, 0);
+        while (true) {
+            final double t = qtrap.stage(this, getIterations());
+            incrementCount();
+            final double s = (4 * t - oldt) / 3.0;
+            if (getIterations() >= getMinimalIterationCount()) {
+                final double delta = FastMath.abs(s - olds);
+                final double rLimit =
+                    getRelativeAccuracy() * (FastMath.abs(olds) + FastMath.abs(s)) * 0.5;
+                if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
+                    return s;
+                }
+            }
+            olds = s;
+            oldt = t;
+        }
+
+    }
+
+}