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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.MathIllegalArgumentException;
+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 the <a href="http://en.wikipedia.org/wiki/Midpoint_method">
+ * Midpoint Rule</a> for integration of real univariate functions. For
+ * reference, see <b>Numerical Mathematics</b>, ISBN 0387989595,
+ * chapter 9.2.
+ * <p>
+ * The function should be integrable.</p>
+ *
+ * @since 3.3
+ */
+public class MidPointIntegrator extends BaseAbstractUnivariateIntegrator {
+
+    /** Maximum number of iterations for midpoint. */
+    public static final int MIDPOINT_MAX_ITERATIONS_COUNT = 64;
+
+    /**
+     * Build a midpoint 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 #MIDPOINT_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 #MIDPOINT_MAX_ITERATIONS_COUNT}
+     */
+    public MidPointIntegrator(final double relativeAccuracy,
+                              final double absoluteAccuracy,
+                              final int minimalIterationCount,
+                              final int maximalIterationCount)
+        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
+        super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
+        if (maximalIterationCount > MIDPOINT_MAX_ITERATIONS_COUNT) {
+            throw new NumberIsTooLargeException(maximalIterationCount,
+                                                MIDPOINT_MAX_ITERATIONS_COUNT, false);
+        }
+    }
+
+    /**
+     * Build a midpoint 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 #MIDPOINT_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 #MIDPOINT_MAX_ITERATIONS_COUNT}
+     */
+    public MidPointIntegrator(final int minimalIterationCount,
+                              final int maximalIterationCount)
+        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
+        super(minimalIterationCount, maximalIterationCount);
+        if (maximalIterationCount > MIDPOINT_MAX_ITERATIONS_COUNT) {
+            throw new NumberIsTooLargeException(maximalIterationCount,
+                                                MIDPOINT_MAX_ITERATIONS_COUNT, false);
+        }
+    }
+
+    /**
+     * Construct a midpoint integrator with default settings.
+     * (max iteration count set to {@link #MIDPOINT_MAX_ITERATIONS_COUNT})
+     */
+    public MidPointIntegrator() {
+        super(DEFAULT_MIN_ITERATIONS_COUNT, MIDPOINT_MAX_ITERATIONS_COUNT);
+    }
+
+    /**
+     * Compute the n-th stage integral of midpoint rule.
+     * This function should only be called by API <code>integrate()</code> in the package.
+     * To save time it does not verify arguments - caller does.
+     * <p>
+     * The interval is divided equally into 2^n sections rather than an
+     * arbitrary m sections because this configuration can best utilize the
+     * already computed values.</p>
+     *
+     * @param n the stage of 1/2 refinement. Must be larger than 0.
+     * @param previousStageResult Result from the previous call to the
+     * {@code stage} method.
+     * @param min Lower bound of the integration interval.
+     * @param diffMaxMin Difference between the lower bound and upper bound
+     * of the integration interval.
+     * @return the value of n-th stage integral
+     * @throws TooManyEvaluationsException if the maximal number of evaluations
+     * is exceeded.
+     */
+    private double stage(final int n,
+                         double previousStageResult,
+                         double min,
+                         double diffMaxMin)
+        throws TooManyEvaluationsException {
+
+        // number of new points in this stage
+        final long np = 1L << (n - 1);
+        double sum = 0;
+
+        // spacing between adjacent new points
+        final double spacing = diffMaxMin / np;
+
+        // the first new point
+        double x = min + 0.5 * spacing;
+        for (long i = 0; i < np; i++) {
+            sum += computeObjectiveValue(x);
+            x += spacing;
+        }
+        // add the new sum to previously calculated result
+        return 0.5 * (previousStageResult + sum * spacing);
+    }
+
+
+    /** {@inheritDoc} */
+    @Override
+    protected double doIntegrate()
+        throws MathIllegalArgumentException, TooManyEvaluationsException, MaxCountExceededException {
+
+        final double min = getMin();
+        final double diff = getMax() - min;
+        final double midPoint = min + 0.5 * diff;
+
+        double oldt = diff * computeObjectiveValue(midPoint);
+
+        while (true) {
+            incrementCount();
+            final int i = getIterations();
+            final double t = stage(i, oldt, min, diff);
+            if (i >= getMinimalIterationCount()) {
+                final double delta = FastMath.abs(t - oldt);
+                final double rLimit =
+                        getRelativeAccuracy() * (FastMath.abs(oldt) + FastMath.abs(t)) * 0.5;
+                if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
+                    return t;
+                }
+            }
+            oldt = t;
+        }
+
+    }
+
+}