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From er...@apache.org
Subject [10/31] commons-numbers git commit: Multimodule project setup.
Date Fri, 20 Jan 2017 14:45:57 GMT
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/c4541327/commons-numbers-core/src/test/java/org/apache/commons/numbers/core/PrecisionTest.java
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diff --git a/commons-numbers-core/src/test/java/org/apache/commons/numbers/core/PrecisionTest.java b/commons-numbers-core/src/test/java/org/apache/commons/numbers/core/PrecisionTest.java
new file mode 100644
index 0000000..188c949
--- /dev/null
+++ b/commons-numbers-core/src/test/java/org/apache/commons/numbers/core/PrecisionTest.java
@@ -0,0 +1,547 @@
+/*
+ * 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.numbers.core;
+
+import java.math.BigDecimal;
+
+import org.junit.Assert;
+import org.junit.Test;
+
+/**
+ * Test cases for the {@link Precision} class.
+ *
+ */
+public class PrecisionTest {
+    @Test
+    public void testEqualsWithRelativeTolerance() {
+        Assert.assertTrue(Precision.equalsWithRelativeTolerance(0d, 0d, 0d));
+        Assert.assertTrue(Precision.equalsWithRelativeTolerance(0d, 1 / Double.NEGATIVE_INFINITY, 0d));
+
+        final double eps = 1e-14;
+        Assert.assertFalse(Precision.equalsWithRelativeTolerance(1.987654687654968, 1.987654687654988, eps));
+        Assert.assertTrue(Precision.equalsWithRelativeTolerance(1.987654687654968, 1.987654687654987, eps));
+        Assert.assertFalse(Precision.equalsWithRelativeTolerance(1.987654687654968, 1.987654687654948, eps));
+        Assert.assertTrue(Precision.equalsWithRelativeTolerance(1.987654687654968, 1.987654687654949, eps));
+
+        Assert.assertFalse(Precision.equalsWithRelativeTolerance(Precision.SAFE_MIN, 0.0, eps));
+
+        Assert.assertFalse(Precision.equalsWithRelativeTolerance(1.0000000000001e-300, 1e-300, eps));
+        Assert.assertTrue(Precision.equalsWithRelativeTolerance(1.00000000000001e-300, 1e-300, eps));
+
+        Assert.assertFalse(Precision.equalsWithRelativeTolerance(Double.NEGATIVE_INFINITY, 1.23, eps));
+        Assert.assertFalse(Precision.equalsWithRelativeTolerance(Double.POSITIVE_INFINITY, 1.23, eps));
+
+        Assert.assertTrue(Precision.equalsWithRelativeTolerance(Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY, eps));
+        Assert.assertTrue(Precision.equalsWithRelativeTolerance(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY, eps));
+        Assert.assertFalse(Precision.equalsWithRelativeTolerance(Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY, eps));
+
+        Assert.assertFalse(Precision.equalsWithRelativeTolerance(Double.NaN, 1.23, eps));
+        Assert.assertFalse(Precision.equalsWithRelativeTolerance(Double.NaN, Double.NaN, eps));
+    }
+
+    @Test
+    public void testEqualsIncludingNaN() {
+        double[] testArray = {
+            Double.NaN,
+            Double.POSITIVE_INFINITY,
+            Double.NEGATIVE_INFINITY,
+            1d,
+            0d };
+        for (int i = 0; i < testArray.length; i++) {
+            for (int j = 0; j < testArray.length; j++) {
+                if (i == j) {
+                    Assert.assertTrue(Precision.equalsIncludingNaN(testArray[i], testArray[j]));
+                    Assert.assertTrue(Precision.equalsIncludingNaN(testArray[j], testArray[i]));
+                } else {
+                    Assert.assertTrue(!Precision.equalsIncludingNaN(testArray[i], testArray[j]));
+                    Assert.assertTrue(!Precision.equalsIncludingNaN(testArray[j], testArray[i]));
+                }
+            }
+        }
+    }
+
+    @Test
+    public void testEqualsWithAllowedDelta() {
+        Assert.assertTrue(Precision.equals(153.0000, 153.0000, .0625));
+        Assert.assertTrue(Precision.equals(153.0000, 153.0625, .0625));
+        Assert.assertTrue(Precision.equals(152.9375, 153.0000, .0625));
+        Assert.assertFalse(Precision.equals(153.0000, 153.0625, .0624));
+        Assert.assertFalse(Precision.equals(152.9374, 153.0000, .0625));
+        Assert.assertFalse(Precision.equals(Double.NaN, Double.NaN, 1.0));
+        Assert.assertTrue(Precision.equals(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY, 1.0));
+        Assert.assertTrue(Precision.equals(Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY, 1.0));
+        Assert.assertFalse(Precision.equals(Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY, 1.0));
+    }
+
+    @Test
+    public void testMath475() {
+        final double a = 1.7976931348623182E16;
+        final double b = Math.nextUp(a);
+
+        double diff = Math.abs(a - b);
+        // Because they are adjacent floating point numbers, "a" and "b" are
+        // considered equal even though the allowed error is smaller than
+        // their difference.
+        Assert.assertTrue(Precision.equals(a, b, 0.5 * diff));
+
+        final double c = Math.nextUp(b);
+        diff = Math.abs(a - c);
+        // Because "a" and "c" are not adjacent, the tolerance is taken into
+        // account for assessing equality.
+        Assert.assertTrue(Precision.equals(a, c, diff));
+        Assert.assertFalse(Precision.equals(a, c, (1 - 1e-16) * diff));
+    }
+
+    @Test
+    public void testEqualsIncludingNaNWithAllowedDelta() {
+        Assert.assertTrue(Precision.equalsIncludingNaN(153.0000, 153.0000, .0625));
+        Assert.assertTrue(Precision.equalsIncludingNaN(153.0000, 153.0625, .0625));
+        Assert.assertTrue(Precision.equalsIncludingNaN(152.9375, 153.0000, .0625));
+        Assert.assertTrue(Precision.equalsIncludingNaN(Double.NaN, Double.NaN, 1.0));
+        Assert.assertTrue(Precision.equalsIncludingNaN(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY, 1.0));
+        Assert.assertTrue(Precision.equalsIncludingNaN(Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY, 1.0));
+        Assert.assertFalse(Precision.equalsIncludingNaN(Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY, 1.0));
+        Assert.assertFalse(Precision.equalsIncludingNaN(153.0000, 153.0625, .0624));
+        Assert.assertFalse(Precision.equalsIncludingNaN(152.9374, 153.0000, .0625));
+    }
+
+    // Tests for floating point equality
+    @Test
+    public void testFloatEqualsWithAllowedUlps() {
+        Assert.assertTrue("+0.0f == -0.0f",Precision.equals(0.0f, -0.0f));
+        Assert.assertTrue("+0.0f == -0.0f (1 ulp)",Precision.equals(0.0f, -0.0f, 1));
+        float oneFloat = 1.0f;
+        Assert.assertTrue("1.0f == 1.0f + 1 ulp",Precision.equals(oneFloat, Float.intBitsToFloat(1 + Float.floatToIntBits(oneFloat))));
+        Assert.assertTrue("1.0f == 1.0f + 1 ulp (1 ulp)",Precision.equals(oneFloat, Float.intBitsToFloat(1 + Float.floatToIntBits(oneFloat)), 1));
+        Assert.assertFalse("1.0f != 1.0f + 2 ulp (1 ulp)",Precision.equals(oneFloat, Float.intBitsToFloat(2 + Float.floatToIntBits(oneFloat)), 1));
+
+        Assert.assertTrue(Precision.equals(153.0f, 153.0f, 1));
+
+        // These tests need adjusting for floating point precision
+//        Assert.assertTrue(Precision.equals(153.0f, 153.00000000000003f, 1));
+//        Assert.assertFalse(Precision.equals(153.0f, 153.00000000000006f, 1));
+//        Assert.assertTrue(Precision.equals(153.0f, 152.99999999999997f, 1));
+//        Assert.assertFalse(Precision.equals(153f, 152.99999999999994f, 1));
+//
+//        Assert.assertTrue(Precision.equals(-128.0f, -127.99999999999999f, 1));
+//        Assert.assertFalse(Precision.equals(-128.0f, -127.99999999999997f, 1));
+//        Assert.assertTrue(Precision.equals(-128.0f, -128.00000000000003f, 1));
+//        Assert.assertFalse(Precision.equals(-128.0f, -128.00000000000006f, 1));
+
+        Assert.assertTrue(Precision.equals(Float.POSITIVE_INFINITY, Float.POSITIVE_INFINITY, 1));
+        Assert.assertTrue(Precision.equals(Double.MAX_VALUE, Float.POSITIVE_INFINITY, 1));
+
+        Assert.assertTrue(Precision.equals(Float.NEGATIVE_INFINITY, Float.NEGATIVE_INFINITY, 1));
+        Assert.assertTrue(Precision.equals(-Float.MAX_VALUE, Float.NEGATIVE_INFINITY, 1));
+
+        Assert.assertFalse(Precision.equals(Float.NaN, Float.NaN, 1));
+        Assert.assertFalse(Precision.equals(Float.NaN, Float.NaN, 0));
+        Assert.assertFalse(Precision.equals(Float.NaN, 0, 0));
+        Assert.assertFalse(Precision.equals(Float.NaN, Float.POSITIVE_INFINITY, 0));
+        Assert.assertFalse(Precision.equals(Float.NaN, Float.NEGATIVE_INFINITY, 0));
+
+        Assert.assertFalse(Precision.equals(Float.NEGATIVE_INFINITY, Float.POSITIVE_INFINITY, 100000));
+    }
+
+    @Test
+    public void testEqualsWithAllowedUlps() {
+        Assert.assertTrue(Precision.equals(0.0, -0.0, 1));
+
+        Assert.assertTrue(Precision.equals(1.0, 1 + Math.ulp(1d), 1));
+        Assert.assertFalse(Precision.equals(1.0, 1 + 2 * Math.ulp(1d), 1));
+
+        final double nUp1 = Math.nextAfter(1d, Double.POSITIVE_INFINITY);
+        final double nnUp1 = Math.nextAfter(nUp1, Double.POSITIVE_INFINITY);
+        Assert.assertTrue(Precision.equals(1.0, nUp1, 1));
+        Assert.assertTrue(Precision.equals(nUp1, nnUp1, 1));
+        Assert.assertFalse(Precision.equals(1.0, nnUp1, 1));
+
+        Assert.assertTrue(Precision.equals(0.0, Math.ulp(0d), 1));
+        Assert.assertTrue(Precision.equals(0.0, -Math.ulp(0d), 1));
+
+        Assert.assertTrue(Precision.equals(153.0, 153.0, 1));
+
+        Assert.assertTrue(Precision.equals(153.0, 153.00000000000003, 1));
+        Assert.assertFalse(Precision.equals(153.0, 153.00000000000006, 1));
+        Assert.assertTrue(Precision.equals(153.0, 152.99999999999997, 1));
+        Assert.assertFalse(Precision.equals(153, 152.99999999999994, 1));
+
+        Assert.assertTrue(Precision.equals(-128.0, -127.99999999999999, 1));
+        Assert.assertFalse(Precision.equals(-128.0, -127.99999999999997, 1));
+        Assert.assertTrue(Precision.equals(-128.0, -128.00000000000003, 1));
+        Assert.assertFalse(Precision.equals(-128.0, -128.00000000000006, 1));
+
+        Assert.assertTrue(Precision.equals(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY, 1));
+        Assert.assertTrue(Precision.equals(Double.MAX_VALUE, Double.POSITIVE_INFINITY, 1));
+
+        Assert.assertTrue(Precision.equals(Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY, 1));
+        Assert.assertTrue(Precision.equals(-Double.MAX_VALUE, Double.NEGATIVE_INFINITY, 1));
+
+        Assert.assertFalse(Precision.equals(Double.NaN, Double.NaN, 1));
+        Assert.assertFalse(Precision.equals(Double.NaN, Double.NaN, 0));
+        Assert.assertFalse(Precision.equals(Double.NaN, 0, 0));
+        Assert.assertFalse(Precision.equals(Double.NaN, Double.POSITIVE_INFINITY, 0));
+        Assert.assertFalse(Precision.equals(Double.NaN, Double.NEGATIVE_INFINITY, 0));
+
+        Assert.assertFalse(Precision.equals(Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY, 100000));
+    }
+
+    @Test
+    public void testEqualsIncludingNaNWithAllowedUlps() {
+        Assert.assertTrue(Precision.equalsIncludingNaN(0.0, -0.0, 1));
+
+        Assert.assertTrue(Precision.equalsIncludingNaN(1.0, 1 + Math.ulp(1d), 1));
+        Assert.assertFalse(Precision.equalsIncludingNaN(1.0, 1 + 2 * Math.ulp(1d), 1));
+
+        final double nUp1 = Math.nextAfter(1d, Double.POSITIVE_INFINITY);
+        final double nnUp1 = Math.nextAfter(nUp1, Double.POSITIVE_INFINITY);
+        Assert.assertTrue(Precision.equalsIncludingNaN(1.0, nUp1, 1));
+        Assert.assertTrue(Precision.equalsIncludingNaN(nUp1, nnUp1, 1));
+        Assert.assertFalse(Precision.equalsIncludingNaN(1.0, nnUp1, 1));
+
+        Assert.assertTrue(Precision.equalsIncludingNaN(0.0, Math.ulp(0d), 1));
+        Assert.assertTrue(Precision.equalsIncludingNaN(0.0, -Math.ulp(0d), 1));
+
+        Assert.assertTrue(Precision.equalsIncludingNaN(153.0, 153.0, 1));
+
+        Assert.assertTrue(Precision.equalsIncludingNaN(153.0, 153.00000000000003, 1));
+        Assert.assertFalse(Precision.equalsIncludingNaN(153.0, 153.00000000000006, 1));
+        Assert.assertTrue(Precision.equalsIncludingNaN(153.0, 152.99999999999997, 1));
+        Assert.assertFalse(Precision.equalsIncludingNaN(153, 152.99999999999994, 1));
+
+        Assert.assertTrue(Precision.equalsIncludingNaN(-128.0, -127.99999999999999, 1));
+        Assert.assertFalse(Precision.equalsIncludingNaN(-128.0, -127.99999999999997, 1));
+        Assert.assertTrue(Precision.equalsIncludingNaN(-128.0, -128.00000000000003, 1));
+        Assert.assertFalse(Precision.equalsIncludingNaN(-128.0, -128.00000000000006, 1));
+
+        Assert.assertTrue(Precision.equalsIncludingNaN(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY, 1));
+        Assert.assertTrue(Precision.equalsIncludingNaN(Double.MAX_VALUE, Double.POSITIVE_INFINITY, 1));
+
+        Assert.assertTrue(Precision.equalsIncludingNaN(Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY, 1));
+        Assert.assertTrue(Precision.equalsIncludingNaN(-Double.MAX_VALUE, Double.NEGATIVE_INFINITY, 1));
+
+        Assert.assertTrue(Precision.equalsIncludingNaN(Double.NaN, Double.NaN, 1));
+
+        Assert.assertFalse(Precision.equalsIncludingNaN(Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY, 100000));
+    }
+
+    @Test
+    public void testCompareToEpsilon() {
+        Assert.assertEquals(0, Precision.compareTo(152.33, 152.32, .011));
+        Assert.assertTrue(Precision.compareTo(152.308, 152.32, .011) < 0);
+        Assert.assertTrue(Precision.compareTo(152.33, 152.318, .011) > 0);
+        Assert.assertEquals(0, Precision.compareTo(Double.MIN_VALUE, +0.0, Double.MIN_VALUE));
+        Assert.assertEquals(0, Precision.compareTo(Double.MIN_VALUE, -0.0, Double.MIN_VALUE));
+    }
+
+    @Test
+    public void testCompareToMaxUlps() {
+        double a     = 152.32;
+        double delta = Math.ulp(a);
+        for (int i = 0; i <= 10; ++i) {
+            if (i <= 5) {
+                Assert.assertEquals( 0, Precision.compareTo(a, a + i * delta, 5));
+                Assert.assertEquals( 0, Precision.compareTo(a, a - i * delta, 5));
+            } else {
+                Assert.assertEquals(-1, Precision.compareTo(a, a + i * delta, 5));
+                Assert.assertEquals(+1, Precision.compareTo(a, a - i * delta, 5));
+            }
+        }
+
+        Assert.assertEquals( 0, Precision.compareTo(-0.0, 0.0, 0));
+
+        Assert.assertEquals(-1, Precision.compareTo(-Double.MIN_VALUE, -0.0, 0));
+        Assert.assertEquals( 0, Precision.compareTo(-Double.MIN_VALUE, -0.0, 1));
+        Assert.assertEquals(-1, Precision.compareTo(-Double.MIN_VALUE, +0.0, 0));
+        Assert.assertEquals( 0, Precision.compareTo(-Double.MIN_VALUE, +0.0, 1));
+
+        Assert.assertEquals(+1, Precision.compareTo( Double.MIN_VALUE, -0.0, 0));
+        Assert.assertEquals( 0, Precision.compareTo( Double.MIN_VALUE, -0.0, 1));
+        Assert.assertEquals(+1, Precision.compareTo( Double.MIN_VALUE, +0.0, 0));
+        Assert.assertEquals( 0, Precision.compareTo( Double.MIN_VALUE, +0.0, 1));
+
+        Assert.assertEquals(-1, Precision.compareTo(-Double.MIN_VALUE, Double.MIN_VALUE, 0));
+        Assert.assertEquals(-1, Precision.compareTo(-Double.MIN_VALUE, Double.MIN_VALUE, 1));
+        Assert.assertEquals( 0, Precision.compareTo(-Double.MIN_VALUE, Double.MIN_VALUE, 2));
+
+        Assert.assertEquals( 0, Precision.compareTo(Double.MAX_VALUE, Double.POSITIVE_INFINITY, 1));
+        Assert.assertEquals(-1, Precision.compareTo(Double.MAX_VALUE, Double.POSITIVE_INFINITY, 0));
+
+        Assert.assertEquals(+1, Precision.compareTo(Double.MAX_VALUE, Double.NaN, Integer.MAX_VALUE));
+        Assert.assertEquals(+1, Precision.compareTo(Double.NaN, Double.MAX_VALUE, Integer.MAX_VALUE));
+    }
+
+    @Test
+    public void testRoundDouble() {
+        double x = 1.234567890;
+        Assert.assertEquals(1.23, Precision.round(x, 2), 0.0);
+        Assert.assertEquals(1.235, Precision.round(x, 3), 0.0);
+        Assert.assertEquals(1.2346, Precision.round(x, 4), 0.0);
+
+        // JIRA MATH-151
+        Assert.assertEquals(39.25, Precision.round(39.245, 2), 0.0);
+        Assert.assertEquals(39.24, Precision.round(39.245, 2, BigDecimal.ROUND_DOWN), 0.0);
+        double xx = 39.0;
+        xx += 245d / 1000d;
+        Assert.assertEquals(39.25, Precision.round(xx, 2), 0.0);
+
+        // BZ 35904
+        Assert.assertEquals(30.1d, Precision.round(30.095d, 2), 0.0d);
+        Assert.assertEquals(30.1d, Precision.round(30.095d, 1), 0.0d);
+        Assert.assertEquals(33.1d, Precision.round(33.095d, 1), 0.0d);
+        Assert.assertEquals(33.1d, Precision.round(33.095d, 2), 0.0d);
+        Assert.assertEquals(50.09d, Precision.round(50.085d, 2), 0.0d);
+        Assert.assertEquals(50.19d, Precision.round(50.185d, 2), 0.0d);
+        Assert.assertEquals(50.01d, Precision.round(50.005d, 2), 0.0d);
+        Assert.assertEquals(30.01d, Precision.round(30.005d, 2), 0.0d);
+        Assert.assertEquals(30.65d, Precision.round(30.645d, 2), 0.0d);
+
+        Assert.assertEquals(1.24, Precision.round(x, 2, BigDecimal.ROUND_CEILING), 0.0);
+        Assert.assertEquals(1.235, Precision.round(x, 3, BigDecimal.ROUND_CEILING), 0.0);
+        Assert.assertEquals(1.2346, Precision.round(x, 4, BigDecimal.ROUND_CEILING), 0.0);
+        Assert.assertEquals(-1.23, Precision.round(-x, 2, BigDecimal.ROUND_CEILING), 0.0);
+        Assert.assertEquals(-1.234, Precision.round(-x, 3, BigDecimal.ROUND_CEILING), 0.0);
+        Assert.assertEquals(-1.2345, Precision.round(-x, 4, BigDecimal.ROUND_CEILING), 0.0);
+
+        Assert.assertEquals(1.23, Precision.round(x, 2, BigDecimal.ROUND_DOWN), 0.0);
+        Assert.assertEquals(1.234, Precision.round(x, 3, BigDecimal.ROUND_DOWN), 0.0);
+        Assert.assertEquals(1.2345, Precision.round(x, 4, BigDecimal.ROUND_DOWN), 0.0);
+        Assert.assertEquals(-1.23, Precision.round(-x, 2, BigDecimal.ROUND_DOWN), 0.0);
+        Assert.assertEquals(-1.234, Precision.round(-x, 3, BigDecimal.ROUND_DOWN), 0.0);
+        Assert.assertEquals(-1.2345, Precision.round(-x, 4, BigDecimal.ROUND_DOWN), 0.0);
+
+        Assert.assertEquals(1.23, Precision.round(x, 2, BigDecimal.ROUND_FLOOR), 0.0);
+        Assert.assertEquals(1.234, Precision.round(x, 3, BigDecimal.ROUND_FLOOR), 0.0);
+        Assert.assertEquals(1.2345, Precision.round(x, 4, BigDecimal.ROUND_FLOOR), 0.0);
+        Assert.assertEquals(-1.24, Precision.round(-x, 2, BigDecimal.ROUND_FLOOR), 0.0);
+        Assert.assertEquals(-1.235, Precision.round(-x, 3, BigDecimal.ROUND_FLOOR), 0.0);
+        Assert.assertEquals(-1.2346, Precision.round(-x, 4, BigDecimal.ROUND_FLOOR), 0.0);
+
+        Assert.assertEquals(1.23, Precision.round(x, 2, BigDecimal.ROUND_HALF_DOWN), 0.0);
+        Assert.assertEquals(1.235, Precision.round(x, 3, BigDecimal.ROUND_HALF_DOWN), 0.0);
+        Assert.assertEquals(1.2346, Precision.round(x, 4, BigDecimal.ROUND_HALF_DOWN), 0.0);
+        Assert.assertEquals(-1.23, Precision.round(-x, 2, BigDecimal.ROUND_HALF_DOWN), 0.0);
+        Assert.assertEquals(-1.235, Precision.round(-x, 3, BigDecimal.ROUND_HALF_DOWN), 0.0);
+        Assert.assertEquals(-1.2346, Precision.round(-x, 4, BigDecimal.ROUND_HALF_DOWN), 0.0);
+        Assert.assertEquals(1.234, Precision.round(1.2345, 3, BigDecimal.ROUND_HALF_DOWN), 0.0);
+        Assert.assertEquals(-1.234, Precision.round(-1.2345, 3, BigDecimal.ROUND_HALF_DOWN), 0.0);
+
+        Assert.assertEquals(1.23, Precision.round(x, 2, BigDecimal.ROUND_HALF_EVEN), 0.0);
+        Assert.assertEquals(1.235, Precision.round(x, 3, BigDecimal.ROUND_HALF_EVEN), 0.0);
+        Assert.assertEquals(1.2346, Precision.round(x, 4, BigDecimal.ROUND_HALF_EVEN), 0.0);
+        Assert.assertEquals(-1.23, Precision.round(-x, 2, BigDecimal.ROUND_HALF_EVEN), 0.0);
+        Assert.assertEquals(-1.235, Precision.round(-x, 3, BigDecimal.ROUND_HALF_EVEN), 0.0);
+        Assert.assertEquals(-1.2346, Precision.round(-x, 4, BigDecimal.ROUND_HALF_EVEN), 0.0);
+        Assert.assertEquals(1.234, Precision.round(1.2345, 3, BigDecimal.ROUND_HALF_EVEN), 0.0);
+        Assert.assertEquals(-1.234, Precision.round(-1.2345, 3, BigDecimal.ROUND_HALF_EVEN), 0.0);
+        Assert.assertEquals(1.236, Precision.round(1.2355, 3, BigDecimal.ROUND_HALF_EVEN), 0.0);
+        Assert.assertEquals(-1.236, Precision.round(-1.2355, 3, BigDecimal.ROUND_HALF_EVEN), 0.0);
+
+        Assert.assertEquals(1.23, Precision.round(x, 2, BigDecimal.ROUND_HALF_UP), 0.0);
+        Assert.assertEquals(1.235, Precision.round(x, 3, BigDecimal.ROUND_HALF_UP), 0.0);
+        Assert.assertEquals(1.2346, Precision.round(x, 4, BigDecimal.ROUND_HALF_UP), 0.0);
+        Assert.assertEquals(-1.23, Precision.round(-x, 2, BigDecimal.ROUND_HALF_UP), 0.0);
+        Assert.assertEquals(-1.235, Precision.round(-x, 3, BigDecimal.ROUND_HALF_UP), 0.0);
+        Assert.assertEquals(-1.2346, Precision.round(-x, 4, BigDecimal.ROUND_HALF_UP), 0.0);
+        Assert.assertEquals(1.235, Precision.round(1.2345, 3, BigDecimal.ROUND_HALF_UP), 0.0);
+        Assert.assertEquals(-1.235, Precision.round(-1.2345, 3, BigDecimal.ROUND_HALF_UP), 0.0);
+
+        Assert.assertEquals(-1.23, Precision.round(-1.23, 2, BigDecimal.ROUND_UNNECESSARY), 0.0);
+        Assert.assertEquals(1.23, Precision.round(1.23, 2, BigDecimal.ROUND_UNNECESSARY), 0.0);
+
+        try {
+            Precision.round(1.234, 2, BigDecimal.ROUND_UNNECESSARY);
+            Assert.fail();
+        } catch (ArithmeticException ex) {
+            // expected
+        }
+
+        Assert.assertEquals(1.24, Precision.round(x, 2, BigDecimal.ROUND_UP), 0.0);
+        Assert.assertEquals(1.235, Precision.round(x, 3, BigDecimal.ROUND_UP), 0.0);
+        Assert.assertEquals(1.2346, Precision.round(x, 4, BigDecimal.ROUND_UP), 0.0);
+        Assert.assertEquals(-1.24, Precision.round(-x, 2, BigDecimal.ROUND_UP), 0.0);
+        Assert.assertEquals(-1.235, Precision.round(-x, 3, BigDecimal.ROUND_UP), 0.0);
+        Assert.assertEquals(-1.2346, Precision.round(-x, 4, BigDecimal.ROUND_UP), 0.0);
+
+        try {
+            Precision.round(1.234, 2, 1923);
+            Assert.fail();
+        } catch (IllegalArgumentException ex) {
+            // expected
+        }
+
+        // MATH-151
+        Assert.assertEquals(39.25, Precision.round(39.245, 2, BigDecimal.ROUND_HALF_UP), 0.0);
+
+        // special values
+        TestUtils.assertEquals(Double.NaN, Precision.round(Double.NaN, 2), 0.0);
+        Assert.assertEquals(0.0, Precision.round(0.0, 2), 0.0);
+        Assert.assertEquals(Double.POSITIVE_INFINITY, Precision.round(Double.POSITIVE_INFINITY, 2), 0.0);
+        Assert.assertEquals(Double.NEGATIVE_INFINITY, Precision.round(Double.NEGATIVE_INFINITY, 2), 0.0);
+        // comparison of positive and negative zero is not possible -> always equal thus do string comparison
+        Assert.assertEquals("-0.0", Double.toString(Precision.round(-0.0, 0)));
+        Assert.assertEquals("-0.0", Double.toString(Precision.round(-1e-10, 0)));
+    }
+
+    @Test
+    public void testRoundFloat() {
+        float x = 1.234567890f;
+        Assert.assertEquals(1.23f, Precision.round(x, 2), 0.0);
+        Assert.assertEquals(1.235f, Precision.round(x, 3), 0.0);
+        Assert.assertEquals(1.2346f, Precision.round(x, 4), 0.0);
+
+        // BZ 35904
+        Assert.assertEquals(30.1f, Precision.round(30.095f, 2), 0.0f);
+        Assert.assertEquals(30.1f, Precision.round(30.095f, 1), 0.0f);
+        Assert.assertEquals(50.09f, Precision.round(50.085f, 2), 0.0f);
+        Assert.assertEquals(50.19f, Precision.round(50.185f, 2), 0.0f);
+        Assert.assertEquals(50.01f, Precision.round(50.005f, 2), 0.0f);
+        Assert.assertEquals(30.01f, Precision.round(30.005f, 2), 0.0f);
+        Assert.assertEquals(30.65f, Precision.round(30.645f, 2), 0.0f);
+
+        Assert.assertEquals(1.24f, Precision.round(x, 2, BigDecimal.ROUND_CEILING), 0.0);
+        Assert.assertEquals(1.235f, Precision.round(x, 3, BigDecimal.ROUND_CEILING), 0.0);
+        Assert.assertEquals(1.2346f, Precision.round(x, 4, BigDecimal.ROUND_CEILING), 0.0);
+        Assert.assertEquals(-1.23f, Precision.round(-x, 2, BigDecimal.ROUND_CEILING), 0.0);
+        Assert.assertEquals(-1.234f, Precision.round(-x, 3, BigDecimal.ROUND_CEILING), 0.0);
+        Assert.assertEquals(-1.2345f, Precision.round(-x, 4, BigDecimal.ROUND_CEILING), 0.0);
+
+        Assert.assertEquals(1.23f, Precision.round(x, 2, BigDecimal.ROUND_DOWN), 0.0);
+        Assert.assertEquals(1.234f, Precision.round(x, 3, BigDecimal.ROUND_DOWN), 0.0);
+        Assert.assertEquals(1.2345f, Precision.round(x, 4, BigDecimal.ROUND_DOWN), 0.0);
+        Assert.assertEquals(-1.23f, Precision.round(-x, 2, BigDecimal.ROUND_DOWN), 0.0);
+        Assert.assertEquals(-1.234f, Precision.round(-x, 3, BigDecimal.ROUND_DOWN), 0.0);
+        Assert.assertEquals(-1.2345f, Precision.round(-x, 4, BigDecimal.ROUND_DOWN), 0.0);
+
+        Assert.assertEquals(1.23f, Precision.round(x, 2, BigDecimal.ROUND_FLOOR), 0.0);
+        Assert.assertEquals(1.234f, Precision.round(x, 3, BigDecimal.ROUND_FLOOR), 0.0);
+        Assert.assertEquals(1.2345f, Precision.round(x, 4, BigDecimal.ROUND_FLOOR), 0.0);
+        Assert.assertEquals(-1.24f, Precision.round(-x, 2, BigDecimal.ROUND_FLOOR), 0.0);
+        Assert.assertEquals(-1.235f, Precision.round(-x, 3, BigDecimal.ROUND_FLOOR), 0.0);
+        Assert.assertEquals(-1.2346f, Precision.round(-x, 4, BigDecimal.ROUND_FLOOR), 0.0);
+
+        Assert.assertEquals(1.23f, Precision.round(x, 2, BigDecimal.ROUND_HALF_DOWN), 0.0);
+        Assert.assertEquals(1.235f, Precision.round(x, 3, BigDecimal.ROUND_HALF_DOWN), 0.0);
+        Assert.assertEquals(1.2346f, Precision.round(x, 4, BigDecimal.ROUND_HALF_DOWN), 0.0);
+        Assert.assertEquals(-1.23f, Precision.round(-x, 2, BigDecimal.ROUND_HALF_DOWN), 0.0);
+        Assert.assertEquals(-1.235f, Precision.round(-x, 3, BigDecimal.ROUND_HALF_DOWN), 0.0);
+        Assert.assertEquals(-1.2346f, Precision.round(-x, 4, BigDecimal.ROUND_HALF_DOWN), 0.0);
+        Assert.assertEquals(1.234f, Precision.round(1.2345f, 3, BigDecimal.ROUND_HALF_DOWN), 0.0);
+        Assert.assertEquals(-1.234f, Precision.round(-1.2345f, 3, BigDecimal.ROUND_HALF_DOWN), 0.0);
+
+        Assert.assertEquals(1.23f, Precision.round(x, 2, BigDecimal.ROUND_HALF_EVEN), 0.0);
+        Assert.assertEquals(1.235f, Precision.round(x, 3, BigDecimal.ROUND_HALF_EVEN), 0.0);
+        Assert.assertEquals(1.2346f, Precision.round(x, 4, BigDecimal.ROUND_HALF_EVEN), 0.0);
+        Assert.assertEquals(-1.23f, Precision.round(-x, 2, BigDecimal.ROUND_HALF_EVEN), 0.0);
+        Assert.assertEquals(-1.235f, Precision.round(-x, 3, BigDecimal.ROUND_HALF_EVEN), 0.0);
+        Assert.assertEquals(-1.2346f, Precision.round(-x, 4, BigDecimal.ROUND_HALF_EVEN), 0.0);
+        Assert.assertEquals(1.234f, Precision.round(1.2345f, 3, BigDecimal.ROUND_HALF_EVEN), 0.0);
+        Assert.assertEquals(-1.234f, Precision.round(-1.2345f, 3, BigDecimal.ROUND_HALF_EVEN), 0.0);
+        Assert.assertEquals(1.236f, Precision.round(1.2355f, 3, BigDecimal.ROUND_HALF_EVEN), 0.0);
+        Assert.assertEquals(-1.236f, Precision.round(-1.2355f, 3, BigDecimal.ROUND_HALF_EVEN), 0.0);
+
+        Assert.assertEquals(1.23f, Precision.round(x, 2, BigDecimal.ROUND_HALF_UP), 0.0);
+        Assert.assertEquals(1.235f, Precision.round(x, 3, BigDecimal.ROUND_HALF_UP), 0.0);
+        Assert.assertEquals(1.2346f, Precision.round(x, 4, BigDecimal.ROUND_HALF_UP), 0.0);
+        Assert.assertEquals(-1.23f, Precision.round(-x, 2, BigDecimal.ROUND_HALF_UP), 0.0);
+        Assert.assertEquals(-1.235f, Precision.round(-x, 3, BigDecimal.ROUND_HALF_UP), 0.0);
+        Assert.assertEquals(-1.2346f, Precision.round(-x, 4, BigDecimal.ROUND_HALF_UP), 0.0);
+        Assert.assertEquals(1.235f, Precision.round(1.2345f, 3, BigDecimal.ROUND_HALF_UP), 0.0);
+        Assert.assertEquals(-1.235f, Precision.round(-1.2345f, 3, BigDecimal.ROUND_HALF_UP), 0.0);
+
+        Assert.assertEquals(-1.23f, Precision.round(-1.23f, 2, BigDecimal.ROUND_UNNECESSARY), 0.0);
+        Assert.assertEquals(1.23f, Precision.round(1.23f, 2, BigDecimal.ROUND_UNNECESSARY), 0.0);
+
+        try {
+            Precision.round(1.234f, 2, BigDecimal.ROUND_UNNECESSARY);
+            Assert.fail();
+        } catch (ArithmeticException ex) {
+            // success
+        }
+
+        Assert.assertEquals(1.24f, Precision.round(x, 2, BigDecimal.ROUND_UP), 0.0);
+        Assert.assertEquals(1.235f, Precision.round(x, 3, BigDecimal.ROUND_UP), 0.0);
+        Assert.assertEquals(1.2346f, Precision.round(x, 4, BigDecimal.ROUND_UP), 0.0);
+        Assert.assertEquals(-1.24f, Precision.round(-x, 2, BigDecimal.ROUND_UP), 0.0);
+        Assert.assertEquals(-1.235f, Precision.round(-x, 3, BigDecimal.ROUND_UP), 0.0);
+        Assert.assertEquals(-1.2346f, Precision.round(-x, 4, BigDecimal.ROUND_UP), 0.0);
+
+        try {
+            Precision.round(1.234f, 2, 1923);
+            Assert.fail();
+        } catch (IllegalArgumentException ex) {
+            // success
+        }
+
+        // special values
+        TestUtils.assertEquals(Float.NaN, Precision.round(Float.NaN, 2), 0.0f);
+        Assert.assertEquals(0.0f, Precision.round(0.0f, 2), 0.0f);
+        Assert.assertEquals(Float.POSITIVE_INFINITY, Precision.round(Float.POSITIVE_INFINITY, 2), 0.0f);
+        Assert.assertEquals(Float.NEGATIVE_INFINITY, Precision.round(Float.NEGATIVE_INFINITY, 2), 0.0f);
+        // comparison of positive and negative zero is not possible -> always equal thus do string comparison
+        Assert.assertEquals("-0.0", Float.toString(Precision.round(-0.0f, 0)));
+        Assert.assertEquals("-0.0", Float.toString(Precision.round(-1e-10f, 0)));
+
+        // MATH-1070
+        Assert.assertEquals(0.0f, Precision.round(0f, 2, BigDecimal.ROUND_UP), 0.0f);
+        Assert.assertEquals(0.05f, Precision.round(0.05f, 2, BigDecimal.ROUND_UP), 0.0f);
+        Assert.assertEquals(0.06f, Precision.round(0.051f, 2, BigDecimal.ROUND_UP), 0.0f);
+        Assert.assertEquals(0.06f, Precision.round(0.0505f, 2, BigDecimal.ROUND_UP), 0.0f);
+        Assert.assertEquals(0.06f, Precision.round(0.059f, 2, BigDecimal.ROUND_UP), 0.0f);
+    }
+
+
+    @Test
+    public void testIssue721() {
+        Assert.assertEquals(-53,   Math.getExponent(Precision.EPSILON));
+        Assert.assertEquals(-1022, Math.getExponent(Precision.SAFE_MIN));
+    }
+
+
+    @Test
+    public void testRepresentableDelta() {
+        int nonRepresentableCount = 0;
+        final double x = 100;
+        final int numTrials = 10000;
+        for (int i = 0; i < numTrials; i++) {
+            final double originalDelta = Math.random();
+            final double delta = Precision.representableDelta(x, originalDelta);
+            if (delta != originalDelta) {
+                ++nonRepresentableCount;
+            }
+        }
+
+        Assert.assertTrue(nonRepresentableCount / (double) numTrials > 0.9);
+    }
+
+    @Test
+    public void testMath843() {
+        final double afterEpsilon = Math.nextAfter(Precision.EPSILON,
+                                                   Double.POSITIVE_INFINITY);
+
+        // a) 1 + EPSILON is equal to 1.
+        Assert.assertTrue(1 + Precision.EPSILON == 1);
+
+        // b) 1 + "the number after EPSILON" is not equal to 1.
+        Assert.assertFalse(1 + afterEpsilon == 1);
+    }
+
+    @Test
+    public void testMath1127() {
+        Assert.assertFalse(Precision.equals(2.0, -2.0, 1));
+        Assert.assertTrue(Precision.equals(0.0, -0.0, 0));
+        Assert.assertFalse(Precision.equals(2.0f, -2.0f, 1));
+        Assert.assertTrue(Precision.equals(0.0f, -0.0f, 0));
+    }
+}

http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/c4541327/commons-numbers-core/src/test/java/org/apache/commons/numbers/core/TestUtils.java
----------------------------------------------------------------------
diff --git a/commons-numbers-core/src/test/java/org/apache/commons/numbers/core/TestUtils.java b/commons-numbers-core/src/test/java/org/apache/commons/numbers/core/TestUtils.java
new file mode 100644
index 0000000..6700958
--- /dev/null
+++ b/commons-numbers-core/src/test/java/org/apache/commons/numbers/core/TestUtils.java
@@ -0,0 +1,320 @@
+/*
+ * 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.numbers.core;
+
+import java.io.ByteArrayInputStream;
+import java.io.ByteArrayOutputStream;
+import java.io.IOException;
+import java.io.ObjectInputStream;
+import java.io.ObjectOutputStream;
+
+
+import org.junit.Assert;
+
+/**
+ * Test utilities.
+ * TODO: Cleanup (remove unused and obsolete methods).
+ */
+public class TestUtils {
+    /**
+     * Collection of static methods used in math unit tests.
+     */
+    private TestUtils() {
+        super();
+    }
+
+    /**
+     * Verifies that expected and actual are within delta, or are both NaN or
+     * infinities of the same sign.
+     */
+    public static void assertEquals(double expected, double actual, double delta) {
+        Assert.assertEquals(null, expected, actual, delta);
+    }
+
+    /**
+     * Verifies that expected and actual are within delta, or are both NaN or
+     * infinities of the same sign.
+     */
+    public static void assertEquals(String msg, double expected, double actual, double delta) {
+        // check for NaN
+        if(Double.isNaN(expected)){
+            Assert.assertTrue("" + actual + " is not NaN.",
+                Double.isNaN(actual));
+        } else {
+            Assert.assertEquals(msg, expected, actual, delta);
+        }
+    }
+
+    /**
+     * Verifies that the two arguments are exactly the same, either
+     * both NaN or infinities of same sign, or identical floating point values.
+     */
+    public static void assertSame(double expected, double actual) {
+     Assert.assertEquals(expected, actual, 0);
+    }
+
+    /**
+     * Verifies that two double arrays have equal entries, up to tolerance
+     */
+    public static void assertEquals(double expected[], double observed[], double tolerance) {
+        assertEquals("Array comparison failure", expected, observed, tolerance);
+    }
+
+    /**
+     * Serializes an object to a bytes array and then recovers the object from the bytes array.
+     * Returns the deserialized object.
+     *
+     * @param o  object to serialize and recover
+     * @return  the recovered, deserialized object
+     */
+    public static Object serializeAndRecover(Object o) {
+        try {
+            // serialize the Object
+            ByteArrayOutputStream bos = new ByteArrayOutputStream();
+            ObjectOutputStream so = new ObjectOutputStream(bos);
+            so.writeObject(o);
+
+            // deserialize the Object
+            ByteArrayInputStream bis = new ByteArrayInputStream(bos.toByteArray());
+            ObjectInputStream si = new ObjectInputStream(bis);
+            return si.readObject();
+        } catch (IOException ioe) {
+            return null;
+        } catch (ClassNotFoundException cnfe) {
+            return null;
+        }
+    }
+
+    /**
+     * Verifies that serialization preserves equals and hashCode.
+     * Serializes the object, then recovers it and checks equals and hash code.
+     *
+     * @param object  the object to serialize and recover
+     */
+    public static void checkSerializedEquality(Object object) {
+        Object object2 = serializeAndRecover(object);
+        Assert.assertEquals("Equals check", object, object2);
+        Assert.assertEquals("HashCode check", object.hashCode(), object2.hashCode());
+    }
+
+    /**
+     * Verifies that the relative error in actual vs. expected is less than or
+     * equal to relativeError.  If expected is infinite or NaN, actual must be
+     * the same (NaN or infinity of the same sign).
+     *
+     * @param expected expected value
+     * @param actual  observed value
+     * @param relativeError  maximum allowable relative error
+     */
+    public static void assertRelativelyEquals(double expected, double actual,
+            double relativeError) {
+        assertRelativelyEquals(null, expected, actual, relativeError);
+    }
+
+    /**
+     * Verifies that the relative error in actual vs. expected is less than or
+     * equal to relativeError.  If expected is infinite or NaN, actual must be
+     * the same (NaN or infinity of the same sign).
+     *
+     * @param msg  message to return with failure
+     * @param expected expected value
+     * @param actual  observed value
+     * @param relativeError  maximum allowable relative error
+     */
+    public static void assertRelativelyEquals(String msg, double expected,
+            double actual, double relativeError) {
+        if (Double.isNaN(expected)) {
+            Assert.assertTrue(msg, Double.isNaN(actual));
+        } else if (Double.isNaN(actual)) {
+            Assert.assertTrue(msg, Double.isNaN(expected));
+        } else if (Double.isInfinite(actual) || Double.isInfinite(expected)) {
+            Assert.assertEquals(expected, actual, relativeError);
+        } else if (expected == 0.0) {
+            Assert.assertEquals(msg, actual, expected, relativeError);
+        } else {
+            double absError = Math.abs(expected) * relativeError;
+            Assert.assertEquals(msg, expected, actual, absError);
+        }
+    }
+
+    /**
+     * Fails iff values does not contain a number within epsilon of x.
+     *
+     * @param msg  message to return with failure
+     * @param values double array to search
+     * @param x value sought
+     * @param epsilon  tolerance
+     */
+    public static void assertContains(String msg, double[] values,
+            double x, double epsilon) {
+        for (double value : values) {
+            if (Precision.equals(value, x, epsilon)) {
+                return;
+            }
+        }
+        Assert.fail(msg + " Unable to find " + x);
+    }
+
+    /**
+     * Fails iff values does not contain a number within epsilon of x.
+     *
+     * @param values double array to search
+     * @param x value sought
+     * @param epsilon  tolerance
+     */
+    public static void assertContains(double[] values, double x,
+            double epsilon) {
+       assertContains(null, values, x, epsilon);
+    }
+
+    /** verifies that two arrays are close (sup norm) */
+    public static void assertEquals(String msg, double[] expected, double[] observed, double tolerance) {
+        StringBuilder out = new StringBuilder(msg);
+        if (expected.length != observed.length) {
+            out.append("\n Arrays not same length. \n");
+            out.append("expected has length ");
+            out.append(expected.length);
+            out.append(" observed length = ");
+            out.append(observed.length);
+            Assert.fail(out.toString());
+        }
+        boolean failure = false;
+        for (int i=0; i < expected.length; i++) {
+            if (!equalsIncludingNaN(expected[i], observed[i], tolerance)) {
+                failure = true;
+                out.append("\n Elements at index ");
+                out.append(i);
+                out.append(" differ. ");
+                out.append(" expected = ");
+                out.append(expected[i]);
+                out.append(" observed = ");
+                out.append(observed[i]);
+            }
+        }
+        if (failure) {
+            Assert.fail(out.toString());
+        }
+    }
+
+    /** verifies that two arrays are close (sup norm) */
+    public static void assertEquals(String msg, float[] expected, float[] observed, float tolerance) {
+        StringBuilder out = new StringBuilder(msg);
+        if (expected.length != observed.length) {
+            out.append("\n Arrays not same length. \n");
+            out.append("expected has length ");
+            out.append(expected.length);
+            out.append(" observed length = ");
+            out.append(observed.length);
+            Assert.fail(out.toString());
+        }
+        boolean failure = false;
+        for (int i=0; i < expected.length; i++) {
+            if (!equalsIncludingNaN(expected[i], observed[i], tolerance)) {
+                failure = true;
+                out.append("\n Elements at index ");
+                out.append(i);
+                out.append(" differ. ");
+                out.append(" expected = ");
+                out.append(expected[i]);
+                out.append(" observed = ");
+                out.append(observed[i]);
+            }
+        }
+        if (failure) {
+            Assert.fail(out.toString());
+        }
+    }
+
+    /**
+     * Updates observed counts of values in quartiles.
+     * counts[0] <-> 1st quartile ... counts[3] <-> top quartile
+     */
+    public static void updateCounts(double value, long[] counts, double[] quartiles) {
+        if (value < quartiles[0]) {
+            counts[0]++;
+        } else if (value > quartiles[2]) {
+            counts[3]++;
+        } else if (value > quartiles[1]) {
+            counts[2]++;
+        } else {
+            counts[1]++;
+        }
+    }
+
+    /**
+     * Eliminates points with zero mass from densityPoints and densityValues parallel
+     * arrays.  Returns the number of positive mass points and collapses the arrays so
+     * that the first <returned value> elements of the input arrays represent the positive
+     * mass points.
+     */
+    public static int eliminateZeroMassPoints(int[] densityPoints, double[] densityValues) {
+        int positiveMassCount = 0;
+        for (int i = 0; i < densityValues.length; i++) {
+            if (densityValues[i] > 0) {
+                positiveMassCount++;
+            }
+        }
+        if (positiveMassCount < densityValues.length) {
+            int[] newPoints = new int[positiveMassCount];
+            double[] newValues = new double[positiveMassCount];
+            int j = 0;
+            for (int i = 0; i < densityValues.length; i++) {
+                if (densityValues[i] > 0) {
+                    newPoints[j] = densityPoints[i];
+                    newValues[j] = densityValues[i];
+                    j++;
+                }
+            }
+            System.arraycopy(newPoints,0,densityPoints,0,positiveMassCount);
+            System.arraycopy(newValues,0,densityValues,0,positiveMassCount);
+        }
+        return positiveMassCount;
+    }
+
+    /**
+     * Returns true if the arguments are both NaN, are equal or are within the range
+     * of allowed error (inclusive).
+     *
+     * @param x first value
+     * @param y second value
+     * @param eps the amount of absolute error to allow.
+     * @return {@code true} if the values are equal or within range of each other,
+     * or both are NaN.
+     * @since 2.2
+     */
+    private static boolean equalsIncludingNaN(double x, double y, double eps) {
+        return equalsIncludingNaN(x, y) || (Math.abs(y - x) <= eps);
+    }
+
+    /**
+     * Returns true if the arguments are both NaN or they are
+     * equal as defined by {@link #equals(double,double) equals(x, y, 1)}.
+     *
+     * @param x first value
+     * @param y second value
+     * @return {@code true} if the values are equal or both are NaN.
+     * @since 2.2
+     */
+    private static boolean equalsIncludingNaN(double x, double y) {
+        return (x != x || y != y) ? !(x != x ^ y != y) : Precision.equals(x, y, 1);
+    }
+
+
+}
+
+

http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/c4541327/commons-numbers-quaternion/LICENSE.txt
----------------------------------------------------------------------
diff --git a/commons-numbers-quaternion/LICENSE.txt b/commons-numbers-quaternion/LICENSE.txt
new file mode 100644
index 0000000..261eeb9
--- /dev/null
+++ b/commons-numbers-quaternion/LICENSE.txt
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
+      and distribution as defined by Sections 1 through 9 of this document.
+
+      "Licensor" shall mean the copyright owner or entity authorized by
+      the copyright owner that is granting the License.
+
+      "Legal Entity" shall mean the union of the acting entity and all
+      other entities that control, are controlled by, or are under common
+      control with that entity. For the purposes of this definition,
+      "control" means (i) the power, direct or indirect, to cause the
+      direction or management of such entity, whether by contract or
+      otherwise, or (ii) ownership of fifty percent (50%) or more of the
+      outstanding shares, or (iii) beneficial ownership of such entity.
+
+      "You" (or "Your") shall mean an individual or Legal Entity
+      exercising permissions granted by this License.
+
+      "Source" form shall mean the preferred form for making modifications,
+      including but not limited to software source code, documentation
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+      "Work" shall mean the work of authorship, whether in Source or
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+      (an example is provided in the Appendix below).
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+      "Derivative Works" shall mean any work, whether in Source or Object
+      form, that is based on (or derived from) the Work and for which the
+      editorial revisions, annotations, elaborations, or other modifications
+      represent, as a whole, an original work of authorship. For the purposes
+      of this License, Derivative Works shall not include works that remain
+      separable from, or merely link (or bind by name) to the interfaces of,
+      the Work and Derivative Works thereof.
+
+      "Contribution" shall mean any work of authorship, including
+      the original version of the Work and any modifications or additions
+      to that Work or Derivative Works thereof, that is intentionally
+      submitted to Licensor for inclusion in the Work by the copyright owner
+      or by an individual or Legal Entity authorized to submit on behalf of
+      the copyright owner. For the purposes of this definition, "submitted"
+      means any form of electronic, verbal, or written communication sent
+      to the Licensor or its representatives, including but not limited to
+      communication on electronic mailing lists, source code control systems,
+      and issue tracking systems that are managed by, or on behalf of, the
+      Licensor for the purpose of discussing and improving the Work, but
+      excluding communication that is conspicuously marked or otherwise
+      designated in writing by the copyright owner as "Not a Contribution."
+
+      "Contributor" shall mean Licensor and any individual or Legal Entity
+      on behalf of whom a Contribution has been received by Licensor and
+      subsequently incorporated within the Work.
+
+   2. Grant of Copyright License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+      copyright license to reproduce, prepare Derivative Works of,
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+      Work and such Derivative Works in Source or Object form.
+
+   3. Grant of Patent License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+      (except as stated in this section) patent license to make, have made,
+      use, offer to sell, sell, import, and otherwise transfer the Work,
+      where such license applies only to those patent claims licensable
+      by such Contributor that are necessarily infringed by their
+      Contribution(s) alone or by combination of their Contribution(s)
+      with the Work to which such Contribution(s) was submitted. If You
+      institute patent litigation against any entity (including a
+      cross-claim or counterclaim in a lawsuit) alleging that the Work
+      or a Contribution incorporated within the Work constitutes direct
+      or contributory patent infringement, then any patent licenses
+      granted to You under this License for that Work shall terminate
+      as of the date such litigation is filed.
+
+   4. Redistribution. You may reproduce and distribute copies of the
+      Work or Derivative Works thereof in any medium, with or without
+      modifications, and in Source or Object form, provided that You
+      meet the following conditions:
+
+      (a) You must give any other recipients of the Work or
+          Derivative Works a copy of this License; and
+
+      (b) You must cause any modified files to carry prominent notices
+          stating that You changed the files; and
+
+      (c) You must retain, in the Source form of any Derivative Works
+          that You distribute, all copyright, patent, trademark, and
+          attribution notices from the Source form of the Work,
+          excluding those notices that do not pertain to any part of
+          the Derivative Works; and
+
+      (d) If the Work includes a "NOTICE" text file as part of its
+          distribution, then any Derivative Works that You distribute must
+          include a readable copy of the attribution notices contained
+          within such NOTICE file, excluding those notices that do not
+          pertain to any part of the Derivative Works, in at least one
+          of the following places: within a NOTICE text file distributed
+          as part of the Derivative Works; within the Source form or
+          documentation, if provided along with the Derivative Works; or,
+          within a display generated by the Derivative Works, if and
+          wherever such third-party notices normally appear. The contents
+          of the NOTICE file are for informational purposes only and
+          do not modify the License. You may add Your own attribution
+          notices within Derivative Works that You distribute, alongside
+          or as an addendum to the NOTICE text from the Work, provided
+          that such additional attribution notices cannot be construed
+          as modifying the License.
+
+      You may add Your own copyright statement to Your modifications and
+      may provide additional or different license terms and conditions
+      for use, reproduction, or distribution of Your modifications, or
+      for any such Derivative Works as a whole, provided Your use,
+      reproduction, and distribution of the Work otherwise complies with
+      the conditions stated in this License.
+
+   5. Submission of Contributions. Unless You explicitly state otherwise,
+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
+      this License, without any additional terms or conditions.
+      Notwithstanding the above, nothing herein shall supersede or modify
+      the terms of any separate license agreement you may have executed
+      with Licensor regarding such Contributions.
+
+   6. Trademarks. This License does not grant permission to use the trade
+      names, trademarks, service marks, or product names of the Licensor,
+      except as required for reasonable and customary use in describing the
+      origin of the Work and reproducing the content of the NOTICE file.
+
+   7. Disclaimer of Warranty. Unless required by applicable law or
+      agreed to in writing, Licensor provides the Work (and each
+      Contributor provides its Contributions) on an "AS IS" BASIS,
+      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
+      implied, including, without limitation, any warranties or conditions
+      of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
+      PARTICULAR PURPOSE. You are solely responsible for determining the
+      appropriateness of using or redistributing the Work and assume any
+      risks associated with Your exercise of permissions under this License.
+
+   8. Limitation of Liability. In no event and under no legal theory,
+      whether in tort (including negligence), contract, or otherwise,
+      unless required by applicable law (such as deliberate and grossly
+      negligent acts) or agreed to in writing, shall any Contributor be
+      liable to You for damages, including any direct, indirect, special,
+      incidental, or consequential damages of any character arising as a
+      result of this License or out of the use or inability to use the
+      Work (including but not limited to damages for loss of goodwill,
+      work stoppage, computer failure or malfunction, or any and all
+      other commercial damages or losses), even if such Contributor
+      has been advised of the possibility of such damages.
+
+   9. Accepting Warranty or Additional Liability. While redistributing
+      the Work or Derivative Works thereof, You may choose to offer,
+      and charge a fee for, acceptance of support, warranty, indemnity,
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+      on Your own behalf and on Your sole responsibility, not on behalf
+      of any other Contributor, and only if You agree to indemnify,
+      defend, and hold each Contributor harmless for any liability
+      incurred by, or claims asserted against, such Contributor by reason
+      of your accepting any such warranty or additional liability.
+
+   END OF TERMS AND CONDITIONS
+
+   APPENDIX: How to apply the Apache License to your work.
+
+      To apply the Apache License to your work, attach the following
+      boilerplate notice, with the fields enclosed by brackets "[]"
+      replaced with your own identifying information. (Don't include
+      the brackets!)  The text should be enclosed in the appropriate
+      comment syntax for the file format. We also recommend that a
+      file or class name and description of purpose be included on the
+      same "printed page" as the copyright notice for easier
+      identification within third-party archives.
+
+   Copyright [yyyy] [name of copyright owner]
+
+   Licensed 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.

http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/c4541327/commons-numbers-quaternion/NOTICE.txt
----------------------------------------------------------------------
diff --git a/commons-numbers-quaternion/NOTICE.txt b/commons-numbers-quaternion/NOTICE.txt
new file mode 100644
index 0000000..ea6ae07
--- /dev/null
+++ b/commons-numbers-quaternion/NOTICE.txt
@@ -0,0 +1,6 @@
+Apache Commons Numbers
+Copyright 2001-2016 The Apache Software Foundation
+
+This product includes software developed at
+The Apache Software Foundation (http://www.apache.org/).
+

http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/c4541327/commons-numbers-quaternion/README.md
----------------------------------------------------------------------
diff --git a/commons-numbers-quaternion/README.md b/commons-numbers-quaternion/README.md
new file mode 100644
index 0000000..ab9f829
--- /dev/null
+++ b/commons-numbers-quaternion/README.md
@@ -0,0 +1,98 @@
+<!---
+ 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.
+-->
+<!---
+ +======================================================================+
+ |****                                                              ****|
+ |****      THIS FILE IS GENERATED BY THE COMMONS BUILD PLUGIN      ****|
+ |****                    DO NOT EDIT DIRECTLY                      ****|
+ |****                                                              ****|
+ +======================================================================+
+ | TEMPLATE FILE: readme-md-template.md                                 |
+ | commons-build-plugin/trunk/src/main/resources/commons-xdoc-templates |
+ +======================================================================+
+ |                                                                      |
+ | 1) Re-generate using: mvn commons:readme-md                          |
+ |                                                                      |
+ | 2) Set the following properties in the component's pom:              |
+ |    - commons.componentid (required, alphabetic, lower case)          |
+ |    - commons.release.version (required)                              |
+ |                                                                      |
+ | 3) Example Properties                                                |
+ |                                                                      |
+ |  <properties>                                                        |
+ |    <commons.componentid>math</commons.componentid>                   |
+ |    <commons.release.version>1.2</commons.release.version>            |
+ |  </properties>                                                       |
+ |                                                                      |
+ +======================================================================+
+--->
+Apache Commons Numbers Quaternion
+===================
+
+Quaternion numbers.
+
+Documentation
+-------------
+
+More information can be found on the [homepage](https://commons.apache.org/proper/commons-numbers).
+The [JavaDoc](https://commons.apache.org/proper/commons-numbers/javadocs/api-release) can be browsed.
+Questions related to the usage of Apache Commons Numbers Quaternion should be posted to the [user mailing list][ml].
+
+Where can I get the latest release?
+-----------------------------------
+You can download source and binaries from our [download page](https://commons.apache.org/proper/commons-numbers/download_numbers.cgi).
+
+Alternatively you can pull it from the central Maven repositories:
+
+```xml
+<dependency>
+  <groupId>org.apache.commons</groupId>
+  <artifactId>commons-numbers-quaternion</artifactId>
+  <version>1.0</version>
+</dependency>
+```
+
+Contributing
+------------
+
+We accept PRs via github. The [developer mailing list][ml] is the main channel of communication for contributors.
+There are some guidelines which will make applying PRs easier for us:
++ No tabs! Please use spaces for indentation.
++ Respect the code style.
++ Create minimal diffs - disable on save actions like reformat source code or organize imports. If you feel the source code should be reformatted create a separate PR for this change.
++ Provide JUnit tests for your changes and make sure your changes don't break any existing tests by running ```mvn clean test```.
+
+If you plan to contribute on a regular basis, please consider filing a [contributor license agreement](https://www.apache.org/licenses/#clas).
+You can learn more about contributing via GitHub in our [contribution guidelines](CONTRIBUTING.md).
+
+License
+-------
+Code is under the [Apache Licence v2](https://www.apache.org/licenses/LICENSE-2.0.txt).
+
+Donations
+---------
+You like Apache Commons Numbers Quaternion? Then [donate back to the ASF](https://www.apache.org/foundation/contributing.html) to support the development.
+
+Additional Resources
+--------------------
+
++ [Apache Commons Homepage](https://commons.apache.org/)
++ [Apache Bugtracker (JIRA)](https://issues.apache.org/jira/)
++ [Apache Commons Twitter Account](https://twitter.com/ApacheCommons)
++ #apachecommons IRC channel on freenode.org
+
+[ml]:https://commons.apache.org/mail-lists.html

http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/c4541327/commons-numbers-quaternion/pom.xml
----------------------------------------------------------------------
diff --git a/commons-numbers-quaternion/pom.xml b/commons-numbers-quaternion/pom.xml
new file mode 100644
index 0000000..76a59e3
--- /dev/null
+++ b/commons-numbers-quaternion/pom.xml
@@ -0,0 +1,53 @@
+<?xml version="1.0"?>
+<!--
+   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.
+-->
+<project xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/xsd/maven-4.0.0.xsd"
+         xmlns="http://maven.apache.org/POM/4.0.0"
+         xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
+  <modelVersion>4.0.0</modelVersion>
+
+  <parent>
+    <groupId>org.apache.commons</groupId>
+    <artifactId>commons-numbers-parent</artifactId>
+    <version>1.0-SNAPSHOT</version>
+  </parent>
+
+  <groupId>org.apache.commons</groupId>
+  <artifactId>commons-numbers-quaternion</artifactId>
+  <version>1.0-SNAPSHOT</version>
+  <name>Apache Commons Numbers Quaternion</name>
+
+  <description>Quaternion numbers.</description>
+
+  <properties>
+    <!-- This value must reflect the current name of the base package. -->
+    <commons.osgi.symbolicName>org.apache.commons.numbers.quaternion</commons.osgi.symbolicName>
+    <!-- OSGi -->
+    <commons.osgi.export>org.apache.commons.numbers.quaternion</commons.osgi.export>
+    <!-- Workaround to avoid duplicating config files. -->
+    <numbers.parent.dir>${basedir}/..</numbers.parent.dir>
+  </properties>
+
+  <dependencies>
+    <dependency>
+      <groupId>org.apache.commons</groupId>
+      <artifactId>commons-numbers-core</artifactId>
+      <version>1.0-SNAPSHOT</version>
+    </dependency>
+  </dependencies>
+
+</project>

http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/c4541327/commons-numbers-quaternion/src/main/java/org/apache/commons/numbers/quaternion/Quaternion.java
----------------------------------------------------------------------
diff --git a/commons-numbers-quaternion/src/main/java/org/apache/commons/numbers/quaternion/Quaternion.java b/commons-numbers-quaternion/src/main/java/org/apache/commons/numbers/quaternion/Quaternion.java
new file mode 100644
index 0000000..1722f9b
--- /dev/null
+++ b/commons-numbers-quaternion/src/main/java/org/apache/commons/numbers/quaternion/Quaternion.java
@@ -0,0 +1,455 @@
+/*
+ * 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.numbers.quaternion;
+
+import java.util.Arrays;
+import java.io.Serializable;
+import org.apache.commons.numbers.core.Precision;
+
+/**
+ * This class implements <a href="http://mathworld.wolfram.com/Quaternion.html">
+ * quaternions</a> (Hamilton's hypercomplex numbers).
+ *
+ * <p>Instance of this class are guaranteed to be immutable.</p>
+ */
+public final class Quaternion implements Serializable {
+    /** Serializable version identifier. */
+    private static final long serialVersionUID = 20170118L;
+    /** Error message. */
+    private static final String ZERO_NORM_MSG = "Norm is zero";
+
+    /** Identity quaternion. */
+    public static final Quaternion IDENTITY = new Quaternion(1, 0, 0, 0);
+    /** Zero quaternion. */
+    public static final Quaternion ZERO = new Quaternion(0, 0, 0, 0);
+    /** i */
+    public static final Quaternion I = new Quaternion(0, 1, 0, 0);
+    /** j */
+    public static final Quaternion J = new Quaternion(0, 0, 1, 0);
+    /** k */
+    public static final Quaternion K = new Quaternion(0, 0, 0, 1);
+
+    /** First component (scalar part). */
+    private final double q0;
+    /** Second component (first vector part). */
+    private final double q1;
+    /** Third component (second vector part). */
+    private final double q2;
+    /** Fourth component (third vector part). */
+    private final double q3;
+
+    /**
+     * Builds a quaternion from its components.
+     *
+     * @param a Scalar component.
+     * @param b First vector component.
+     * @param c Second vector component.
+     * @param d Third vector component.
+     */
+    public Quaternion(final double a,
+                      final double b,
+                      final double c,
+                      final double d) {
+        q0 = a;
+        q1 = b;
+        q2 = c;
+        q3 = d;
+    }
+
+    /**
+     * Builds a quaternion from scalar and vector parts.
+     *
+     * @param scalar Scalar part of the quaternion.
+     * @param v Components of the vector part of the quaternion.
+     *
+     * @throws IllegalArgumentException if the array length is not 3.
+     */
+    public Quaternion(final double scalar,
+                      final double[] v) {
+        if (v.length != 3) {
+        	throw new IllegalArgumentException("Size of array must be 3");
+        }
+
+        q0 = scalar;
+        q1 = v[0];
+        q2 = v[1];
+        q3 = v[2];
+    }
+
+    /**
+     * Builds a pure quaternion from a vector (assuming that the scalar
+     * part is zero).
+     *
+     * @param v Components of the vector part of the pure quaternion.
+     */
+    public Quaternion(final double[] v) {
+        this(0, v);
+    }
+
+    /**
+     * Returns the conjugate quaternion of the instance.
+     *
+     * @return the conjugate quaternion
+     */
+    public Quaternion getConjugate() {
+        return new Quaternion(q0, -q1, -q2, -q3);
+    }
+
+    /**
+     * Returns the Hamilton product of two quaternions.
+     *
+     * @param q1 First quaternion.
+     * @param q2 Second quaternion.
+     * @return the product {@code q1} and {@code q2}, in that order.
+     */
+    public static Quaternion multiply(final Quaternion q1,
+                                      final Quaternion q2) {
+        // Components of the first quaternion.
+        final double q1a = q1.q0;
+        final double q1b = q1.q1;
+        final double q1c = q1.q2;
+        final double q1d = q1.q3;
+
+        // Components of the second quaternion.
+        final double q2a = q2.q0;
+        final double q2b = q2.q1;
+        final double q2c = q2.q2;
+        final double q2d = q2.q3;
+
+        // Components of the product.
+        final double w = q1a * q2a - q1b * q2b - q1c * q2c - q1d * q2d;
+        final double x = q1a * q2b + q1b * q2a + q1c * q2d - q1d * q2c;
+        final double y = q1a * q2c - q1b * q2d + q1c * q2a + q1d * q2b;
+        final double z = q1a * q2d + q1b * q2c - q1c * q2b + q1d * q2a;
+
+        return new Quaternion(w, x, y, z);
+    }
+
+    /**
+     * Returns the Hamilton product of the instance by a quaternion.
+     *
+     * @param q Quaternion.
+     * @return the product of this instance with {@code q}, in that order.
+     */
+    public Quaternion multiply(final Quaternion q) {
+        return multiply(this, q);
+    }
+
+    /**
+     * Computes the sum of two quaternions.
+     *
+     * @param q1 Quaternion.
+     * @param q2 Quaternion.
+     * @return the sum of {@code q1} and {@code q2}.
+     */
+    public static Quaternion add(final Quaternion q1,
+                                 final Quaternion q2) {
+        return new Quaternion(q1.q0 + q2.q0,
+                              q1.q1 + q2.q1,
+                              q1.q2 + q2.q2,
+                              q1.q3 + q2.q3);
+    }
+
+    /**
+     * Computes the sum of the instance and another quaternion.
+     *
+     * @param q Quaternion.
+     * @return the sum of this instance and {@code q}
+     */
+    public Quaternion add(final Quaternion q) {
+        return add(this, q);
+    }
+
+    /**
+     * Subtracts two quaternions.
+     *
+     * @param q1 First Quaternion.
+     * @param q2 Second quaternion.
+     * @return the difference between {@code q1} and {@code q2}.
+     */
+    public static Quaternion subtract(final Quaternion q1,
+                                      final Quaternion q2) {
+        return new Quaternion(q1.q0 - q2.q0,
+                              q1.q1 - q2.q1,
+                              q1.q2 - q2.q2,
+                              q1.q3 - q2.q3);
+    }
+
+    /**
+     * Subtracts a quaternion from the instance.
+     *
+     * @param q Quaternion.
+     * @return the difference between this instance and {@code q}.
+     */
+    public Quaternion subtract(final Quaternion q) {
+        return subtract(this, q);
+    }
+
+    /**
+     * Computes the dot-product of two quaternions.
+     *
+     * @param q1 Quaternion.
+     * @param q2 Quaternion.
+     * @return the dot product of {@code q1} and {@code q2}.
+     */
+    public static double dotProduct(final Quaternion q1,
+                                    final Quaternion q2) {
+        return q1.q0 * q2.q0 +
+            q1.q1 * q2.q1 +
+            q1.q2 * q2.q2 +
+            q1.q3 * q2.q3;
+    }
+
+    /**
+     * Computes the dot-product of the instance by a quaternion.
+     *
+     * @param q Quaternion.
+     * @return the dot product of this instance and {@code q}.
+     */
+    public double dotProduct(final Quaternion q) {
+        return dotProduct(this, q);
+    }
+
+    /**
+     * Computes the norm of the quaternion.
+     *
+     * @return the norm.
+     */
+    public double getNorm() {
+        return Math.sqrt(q0 * q0 +
+                         q1 * q1 +
+                         q2 * q2 +
+                         q3 * q3);
+    }
+
+    /**
+     * Computes the normalized quaternion (the versor of the instance).
+     * The norm of the quaternion must not be zero.
+     *
+     * @return a normalized quaternion.
+     * @throws IllegalStateException if the norm of the quaternion is zero.
+     */
+    public Quaternion normalize() {
+        final double norm = getNorm();
+
+        if (norm < Precision.SAFE_MIN) {
+            throw new IllegalStateException(ZERO_NORM_MSG);
+        }
+
+        return new Quaternion(q0 / norm,
+                              q1 / norm,
+                              q2 / norm,
+                              q3 / norm);
+    }
+
+    /**
+     * {@inheritDoc}
+     */
+    @Override
+    public boolean equals(Object other) {
+        if (this == other) {
+            return true;
+        }
+        if (other instanceof Quaternion) {
+            final Quaternion q = (Quaternion) other;
+            return q0 == q.q0 &&
+                q1 == q.q1 &&
+                q2 == q.q2 &&
+                q3 == q.q3;
+        }
+
+        return false;
+    }
+
+    /**
+     * {@inheritDoc}
+     */
+    @Override
+    public int hashCode() {
+        return Arrays.hashCode(new double[] { q0, q1, q2, q3 });
+    }
+
+    /**
+     * Checks whether this instance is equal to another quaternion
+     * within a given tolerance.
+     *
+     * @param q Quaternion with which to compare the current quaternion.
+     * @param eps Tolerance.
+     * @return {@code true} if the each of the components are equal
+     * within the allowed absolute error.
+     */
+    public boolean equals(final Quaternion q,
+                          final double eps) {
+        return Precision.equals(q0, q.q0, eps) &&
+            Precision.equals(q1, q.q1, eps) &&
+            Precision.equals(q2, q.q2, eps) &&
+            Precision.equals(q3, q.q3, eps);
+    }
+
+    /**
+     * Checks whether the instance is a unit quaternion within a given
+     * tolerance.
+     *
+     * @param eps Tolerance (absolute error).
+     * @return {@code true} if the norm is 1 within the given tolerance,
+     * {@code false} otherwise
+     */
+    public boolean isUnitQuaternion(double eps) {
+        return Precision.equals(getNorm(), 1d, eps);
+    }
+
+    /**
+     * Checks whether the instance is a pure quaternion within a given
+     * tolerance.
+     *
+     * @param eps Tolerance (absolute error).
+     * @return {@code true} if the scalar part of the quaternion is zero.
+     */
+    public boolean isPureQuaternion(double eps) {
+        return Math.abs(q0) <= eps;
+    }
+
+    /**
+     * Returns the polar form of the quaternion.
+     *
+     * @return the unit quaternion with positive scalar part.
+     */
+    public Quaternion getPositivePolarForm() {
+        if (q0 < 0) {
+            final Quaternion unitQ = normalize();
+            // The quaternion of rotation (normalized quaternion) q and -q
+            // are equivalent (i.e. represent the same rotation).
+            return new Quaternion(-unitQ.q0,
+                                  -unitQ.q1,
+                                  -unitQ.q2,
+                                  -unitQ.q3);
+        } else {
+            return this.normalize();
+        }
+    }
+
+    /**
+     * Returns the inverse of this instance.
+     * The norm of the quaternion must not be zero.
+     *
+     * @return the inverse.
+     * @throws IllegalArgumentException if the norm (squared) of the quaternion is zero.
+     */
+    public Quaternion getInverse() {
+        final double squareNorm = q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3;
+        if (squareNorm < Precision.SAFE_MIN) {
+            throw new IllegalStateException(ZERO_NORM_MSG);
+        }
+
+        return new Quaternion(q0 / squareNorm,
+                              -q1 / squareNorm,
+                              -q2 / squareNorm,
+                              -q3 / squareNorm);
+    }
+
+    /**
+     * Gets the first component of the quaternion (scalar part).
+     *
+     * @return the scalar part.
+     */
+    public double getQ0() {
+        return q0;
+    }
+
+    /**
+     * Gets the second component of the quaternion (first component
+     * of the vector part).
+     *
+     * @return the first component of the vector part.
+     */
+    public double getQ1() {
+        return q1;
+    }
+
+    /**
+     * Gets the third component of the quaternion (second component
+     * of the vector part).
+     *
+     * @return the second component of the vector part.
+     */
+    public double getQ2() {
+        return q2;
+    }
+
+    /**
+     * Gets the fourth component of the quaternion (third component
+     * of the vector part).
+     *
+     * @return the third component of the vector part.
+     */
+    public double getQ3() {
+        return q3;
+    }
+
+    /**
+     * Gets the scalar part of the quaternion.
+     *
+     * @return the scalar part.
+     * @see #getQ0()
+     */
+    public double getScalarPart() {
+        return q0;
+    }
+
+    /**
+     * Gets the three components of the vector part of the quaternion.
+     *
+     * @return the vector part.
+     * @see #getQ1()
+     * @see #getQ2()
+     * @see #getQ3()
+     */
+    public double[] getVectorPart() {
+        return new double[] { q1, q2, q3 };
+    }
+
+    /**
+     * Multiplies the instance by a scalar.
+     *
+     * @param alpha Scalar factor.
+     * @return a scaled quaternion.
+     */
+    public Quaternion multiply(final double alpha) {
+        return new Quaternion(alpha * q0,
+                              alpha * q1,
+                              alpha * q2,
+                              alpha * q3);
+    }
+
+    /**
+     * {@inheritDoc}
+     */
+    @Override
+    public String toString() {
+        final String sp = " ";
+        final StringBuilder s = new StringBuilder();
+        s.append("[")
+            .append(q0).append(sp)
+            .append(q1).append(sp)
+            .append(q2).append(sp)
+            .append(q3)
+            .append("]");
+
+        return s.toString();
+    }
+}

http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/c4541327/commons-numbers-quaternion/src/main/java/org/apache/commons/numbers/quaternion/package-info.java
----------------------------------------------------------------------
diff --git a/commons-numbers-quaternion/src/main/java/org/apache/commons/numbers/quaternion/package-info.java b/commons-numbers-quaternion/src/main/java/org/apache/commons/numbers/quaternion/package-info.java
new file mode 100644
index 0000000..a8696ec
--- /dev/null
+++ b/commons-numbers-quaternion/src/main/java/org/apache/commons/numbers/quaternion/package-info.java
@@ -0,0 +1,20 @@
+/*
+ * 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.
+ */
+/**
+ * Quaternion number type.
+ */
+package org.apache.commons.numbers.quaternion;


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