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From ericbarnh...@apache.org
Subject [18/37] commons-numbers git commit: NUBERS-17: Added further 4D functionality to Complex Utils (real 2 complex and complex 2 real)
Date Fri, 26 Jan 2018 14:00:09 GMT
NUBERS-17: Added further 4D functionality to Complex Utils (real 2 complex and complex 2 real)


Project: http://git-wip-us.apache.org/repos/asf/commons-numbers/repo
Commit: http://git-wip-us.apache.org/repos/asf/commons-numbers/commit/1de701b3
Tree: http://git-wip-us.apache.org/repos/asf/commons-numbers/tree/1de701b3
Diff: http://git-wip-us.apache.org/repos/asf/commons-numbers/diff/1de701b3

Branch: refs/heads/master
Commit: 1de701b3e3c9dce998a1a0a7ed747ee5aa76cef4
Parents: 48464a3
Author: Eric Barnhill <ericbarnhill@apache.org>
Authored: Wed Jul 12 10:16:39 2017 +0200
Committer: Eric Barnhill <ericbarnhill@apache.org>
Committed: Wed Jul 12 10:16:39 2017 +0200

----------------------------------------------------------------------
 .../commons/numbers/complex/ComplexUtils.java   |  136 +-
 .../commons/numbers/complex/CStandardTest.java  |  282 ----
 .../commons/numbers/complex/ComplexTest.java    | 1366 ------------------
 3 files changed, 126 insertions(+), 1658 deletions(-)
----------------------------------------------------------------------


http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/1de701b3/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/ComplexUtils.java
----------------------------------------------------------------------
diff --git a/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/ComplexUtils.java b/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/ComplexUtils.java
index 4718ac5..e41709c 100644
--- a/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/ComplexUtils.java
+++ b/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/ComplexUtils.java
@@ -356,6 +356,24 @@ public class ComplexUtils {
     }
 
     /**
+     * Converts a 4D real {@code double[][][][]} array to a {@code Complex [][][][]}
+     * array.
+     *
+     * @param d 4D complex interleaved array
+     * @return 4D {@code Complex} array
+     *
+     * @since 1.0
+     */
+    public static Complex[][][][] real2Complex(double[][][][] d) {
+        final int w = d.length;
+        final Complex[][][][] c = new Complex[w][][][];
+        for (int x = 0; x < w; x++) {
+            c[x] = ComplexUtils.real2Complex(d[x]);
+        }
+        return c;
+    }
+
+    /**
      * Converts real component of {@code Complex[]} array to a {@code double[]}
      * array.
      *
@@ -463,6 +481,41 @@ public class ComplexUtils {
     }
 
     /**
+     * Converts real component of a 4D {@code Complex[][][][]} array to a 4D
+     * {@code double[][][][]} array.
+     *
+     * @param c 4D complex interleaved array
+     * @return array of real component
+     *
+     * @since 1.0
+     */
+    public static double[][][][] complex2Real(Complex[][][][] c) {
+        final int length = c.length;
+        double[][][][] d = new double[length][][][];
+        for (int n = 0; n < length; n++) {
+            d[n] = complex2Real(c[n]);
+        }
+        return d;
+    }
+
+    /**
+     * Converts real component of a 4D {@code Complex[][][][]} array to a 4D
+     * {@code float[][][][]} array.
+     *
+     * @param c 4D {@code Complex} array
+     * @return {@code float[][][][]} of real component
+     * @since 1.0
+     */
+    public static float[][][][] complex2RealFloat(Complex[][][][] c) {
+        final int length = c.length;
+        float[][][][] f = new float[length][][][];
+        for (int n = 0; n < length; n++) {
+            f[n] = complex2RealFloat(c[n]);
+        }
+        return f;
+    }
+
+    /**
      * Converts a {@code double[]} array to an imaginary {@code Complex[]}
      * array.
      *
@@ -510,8 +563,7 @@ public class ComplexUtils {
      */
     public static Complex[][] imaginary2Complex(double[][] i) {
         int w = i.length;
-        int h = i[0].length;
-        Complex[][] c = new Complex[w][h];
+        Complex[][] c = new Complex[w][];
         for (int n = 0; n < w; n++) {
             c[n] = ComplexUtils.imaginary2Complex(i[n]);
         }
@@ -529,13 +581,27 @@ public class ComplexUtils {
      */
     public static Complex[][][] imaginary2Complex(double[][][] i) {
         int w = i.length;
-        int h = i[0].length;
-        int d = i[0].length;
-        Complex[][][] c = new Complex[w][h][d];
-        for (int x = 0; x < w; x++) {
-            for (int y = 0; y < h; y++) {
-                c[x][y] = ComplexUtils.imaginary2Complex(i[x][y]);
-            }
+        Complex[][][] c = new Complex[w][][];
+        for (int n = 0; n < w; n++) {
+            c[n] = ComplexUtils.imaginary2Complex(i[n]);
+        }
+        return c;
+    }
+
+    /**
+     * Converts a 4D imaginary array {@code double[][][][]} to a 4D {@code Complex[][][][]}
+     * array.
+     *
+     * @param d 4D complex imaginary array
+     * @return 4D {@code Complex} array
+     *
+     * @since 1.0
+     */
+    public static Complex[][][][] imaginary2Complex(double[][][][] i) {
+        int w = i.length;
+        Complex[][][][] c = new Complex[w][][][];
+        for (int n = 0; n < w; n++) {
+            c[n] = ComplexUtils.imaginary2Complex(i[n]);
         }
         return c;
     }
@@ -647,6 +713,41 @@ public class ComplexUtils {
         return f;
     }
 
+    /**
+     * Converts imaginary component of a 4D {@code Complex[][][][]} array to a 4D
+     * {@code double[][][][]} array.
+     *
+     * @param c 4D complex interleaved array
+     * @return 4D {@code Complex} array
+     *
+     * @since 1.0
+     */
+    public static double[][][][] complex2Imaginary(Complex[][][][] c) {
+        final int length = c.length;
+        double[][][][] i = new double[length][][][];
+        for (int n = 0; n < length; n++) {
+            i[n] = complex2Imaginary(c[n]);
+        }
+        return i;
+    }
+
+    /**
+     * Converts imaginary component of a 4D {@code Complex[][][][]} array to a 4D
+     * {@code float[][][][]} array.
+     *
+     * @param c 4D {@code Complex} array
+     * @return {@code float[][][][]} of imaginary component
+     * @since 1.0
+     */
+    public static float[][][][] complex2ImaginaryFloat(Complex[][][][] c) {
+        final int length = c.length;
+        float[][][][] f = new float[length][][][];
+        for (int n = 0; n < length; n++) {
+            f[n] = complex2ImaginaryFloat(c[n]);
+        }
+        return f;
+    }
+
     // INTERLEAVED METHODS
 
     /**
@@ -911,7 +1012,7 @@ public class ComplexUtils {
 
     /**
      * Converts a 3D {@code Complex[][][]} array to an interleaved complex
-     * {@code double[][][]} array. The third d level of the array is
+     * {@code double[][][]} array. The third level of the array is
      * interleaved.
      *
      * @param c 3D Complex array
@@ -925,6 +1026,21 @@ public class ComplexUtils {
     }
 
     /**
+     * Converts a 4D {@code Complex[][][][]} array to an interleaved complex
+     * {@code double[][][][]} array. The fourth level of the array is
+     * interleaved.
+     *
+     * @param c 4D Complex array
+     * @return complex interleaved array alternating real and
+     *         imaginary values
+     *
+     * @since 1.0
+     */
+    public static double[][][][] complex2Interleaved(Complex[][][][] c) {
+        return complex2Interleaved(c, 3);
+    }
+
+    /**
      * Converts a 2D {@code Complex[][]} array to an interleaved complex
      * {@code float[][]} array.
      *

http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/1de701b3/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/CStandardTest.java
----------------------------------------------------------------------
diff --git a/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/CStandardTest.java b/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/CStandardTest.java
deleted file mode 100644
index 9c178f2..0000000
--- a/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/CStandardTest.java
+++ /dev/null
@@ -1,282 +0,0 @@
-/*
- * 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.
- */
-
-package org.apache.commons.numbers.complex;
-
-import org.apache.commons.numbers.complex.Complex;
-import org.apache.commons.numbers.complex.ComplexUtils;
-import org.junit.Assert;
-import org.junit.Ignore;
-import org.junit.Test;
-
-public class CStandardTest {
-
-    private double inf = Double.POSITIVE_INFINITY;
-    private double negInf = Double.NEGATIVE_INFINITY;
-    private double nan = Double.NaN;
-    private double pi = Math.PI;
-    private double piOverFour = Math.PI / 4.0;
-    private double piOverTwo = Math.PI / 2.0;
-    private double threePiOverFour = 3.0*Math.PI/4.0;
-    private Complex oneOne = new Complex(1, 1);
-    private Complex oneZero = new Complex(1, 0);
-    private Complex oneInf = new Complex(1, inf);
-    private Complex oneNegInf = new Complex(1, negInf);
-    private Complex oneNaN = new Complex(1, nan);
-    private Complex zeroInf = new Complex(0, inf);
-    private Complex zeroNegInf = new Complex(0,negInf);
-    private Complex zeroNaN = new Complex(0, nan);
-    private Complex zeroPiTwo = new Complex(0.0, piOverTwo);
-    private Complex negZeroZero = new Complex(-0.0, 0);
-    private Complex negZeroNan = new Complex(-0.0, nan);
-    private Complex negI = new Complex(0.0, -1.0);
-    private Complex infOne = new Complex(inf, 1);
-    private Complex infZero = new Complex(inf, 0);
-    private Complex infNaN = new Complex(inf, nan);
-    private Complex infNegInf = new Complex(inf, negInf);
-    private Complex infInf = new Complex(inf, inf);
-    private Complex infPiTwo = new Complex(inf, piOverTwo);
-    private Complex infPiFour = new Complex(inf, piOverFour);
-    private Complex infPi = new Complex(inf, Math.PI);
-    private Complex negInfInf = new Complex(negInf, inf);
-    private Complex negInfZero = new Complex(negInf, 0);
-    private Complex negInfOne = new Complex(negInf, 1);
-    private Complex negInfNaN = new Complex(negInf, nan);
-    private Complex negInfNegInf = new Complex(negInf, negInf);
-    private Complex negInfPosInf = new Complex(negInf, inf);
-    private Complex negInfPi = new Complex(negInf, Math.PI);
-    private Complex nanInf = new Complex(nan, inf);
-    private Complex nanNegInf = new Complex(nan, negInf);
-    private Complex nanZero = new Complex(nan, 0);
-    private Complex nanOne = new Complex(nan, 1);
-    private Complex piTwoNaN = new Complex(piOverTwo, nan);
-    private Complex piNegInf = new Complex(Math.PI, negInf);
-    private Complex piTwoNegInf = new Complex(piOverTwo, negInf);
-    private Complex piTwoNegZero = new Complex(piOverTwo, -0.0);
-    private Complex threePiFourNegInf = new Complex(threePiOverFour,negInf);
-    private Complex piFourNegInf = new Complex(piOverFour, negInf);
-    
-    public void assertComplex(Complex c1, Complex c2, double realTol, double imagTol) {
-        Assert.assertEquals(c1.getReal(), c2.getReal(), realTol);
-        Assert.assertEquals(c1.getImaginary(), c2.getImaginary(), imagTol);
-    }
-
-    public void assertComplex(Complex c1, Complex c2) {
-        Assert.assertEquals(c1.getReal(), c2.getReal(),0.0);
-        Assert.assertEquals(c1.getImaginary(), c2.getImaginary(), 0.0);
-    }
-
-
-    /**
-     * ISO C Standard G.6.3
-     */
-    @Test
-    public void testSqrt1() {
-        Complex z1 = new Complex(-2.0, 0.0);
-        Complex z2 = new Complex(0.0, Math.sqrt(2));
-        assertComplex(z1.sqrt(), z2);
-        z1 = new Complex(-2.0, -0.0);
-        z2 = new Complex(0.0, -Math.sqrt(2));
-        assertComplex(z1.sqrt(), z2);
-    }
-
-    @Test
-    public void testImplicitTrig() {
-        Complex z1 = new Complex(3.0);
-        Complex z2 = new Complex(0.0, 3.0); 
-        assertComplex(z1.asin(), negI.multiply(z2.asinh()));
-        assertComplex(z1.atan(), negI.multiply(z2.atanh()), Math.ulp(1), Math.ulp(1));
-        assertComplex(z1.cos(), z2.cosh());
-        assertComplex(z1.sin(), negI.multiply(z2.sinh()));
-        assertComplex(z1.tan(), negI.multiply(z1.tanh()));
-    }
-
-    /**
-     * ISO C Standard G.6.1.1
-     */
-    @Test
-    public void testAcos() {
-        assertComplex(oneOne.acos().conj(), oneOne.conj().acos(), Math.ulp(1), Math.ulp(1));
-        assertComplex(Complex.ZERO.acos(), piTwoNegZero);
-        assertComplex(negZeroZero.acos(), piTwoNegZero);
-        assertComplex(zeroNaN.acos(), piTwoNaN);
-        assertComplex(oneInf.acos(), piTwoNegInf);
-        assertComplex(oneNaN.acos(), Complex.NaN);
-        assertComplex(negInfOne.acos(), piNegInf);
-        assertComplex(infOne.acos(), zeroNegInf);
-        assertComplex(negInfPosInf.acos(), threePiFourNegInf);
-        assertComplex(infInf.acos(), piFourNegInf);
-        assertComplex(infNaN.acos(), nanInf);
-        assertComplex(negInfNaN.acos(), nanNegInf);
-        assertComplex(nanOne.acos(), Complex.NaN);
-        assertComplex(nanInf.acos(), nanNegInf);
-        assertComplex(Complex.NaN.acos(), Complex.NaN);
-    }
-
-    /**
-     * ISO C Standard G.6.2.2
-     */
-    @Test
-    public void testAsinh() {
-        // TODO: test for which Asinh is odd
-        assertComplex(oneOne.conj().asinh(), oneOne.asinh().conj());
-        assertComplex(Complex.ZERO.asinh(), Complex.ZERO);
-        assertComplex(oneInf.asinh(), infPiTwo);
-        assertComplex(oneNaN.asinh(), Complex.NaN);
-        assertComplex(infOne.asinh(), infZero);
-        assertComplex(infInf.asinh(), infPiFour);
-        assertComplex(infNaN.asinh(), infNaN);
-        assertComplex(nanZero.asinh(), nanZero);
-        assertComplex(nanOne.asinh(), Complex.NaN);
-        assertComplex(nanInf.asinh(), infNaN);
-        assertComplex(Complex.NaN, Complex.NaN);
-    }
-
-    /**
-     * ISO C Standard G.6.2.3
-     */
-    @Test
-    public void testAtanh() {
-        assertComplex(oneOne.conj().atanh(), oneOne.atanh().conj());
-        assertComplex(Complex.ZERO.atanh(), Complex.ZERO);
-        assertComplex(zeroNaN.atanh(), zeroNaN);
-        assertComplex(oneZero.atanh(), infZero);
-        assertComplex(oneInf.atanh(),zeroPiTwo);
-        assertComplex(oneNaN.atanh(), Complex.NaN);
-        assertComplex(infOne.atanh(), zeroPiTwo);
-        assertComplex(infInf.atanh(), zeroPiTwo);
-        assertComplex(infNaN.atanh(), zeroNaN);
-        assertComplex(nanOne.atanh(), Complex.NaN);
-        assertComplex(nanInf.atanh(), zeroPiTwo);
-        assertComplex(Complex.NaN.atanh(), Complex.NaN);
-    }
-
-    /**
-     * ISO C Standard G.6.2.4
-     */
-    @Test
-    public void testCosh() {
-        assertComplex(oneOne.cosh().conj(), oneOne.conj().cosh());
-        assertComplex(Complex.ZERO.cosh(), Complex.ONE);
-        assertComplex(zeroInf.cosh(), nanZero);
-        assertComplex(zeroNaN.cosh(), nanZero);
-        assertComplex(oneInf.cosh(), Complex.NaN);
-        assertComplex(oneNaN.cosh(), Complex.NaN);
-        assertComplex(infZero.cosh(), infZero);
-        // the next test does not appear to make sense:
-        // (inf + iy) = inf + cis(y)
-        // skipped
-        assertComplex(infInf.cosh(), infNaN);
-        assertComplex(infNaN.cosh(), infNaN);
-        assertComplex(nanZero.cosh(), nanZero);
-        assertComplex(nanOne.cosh(), Complex.NaN);
-        assertComplex(Complex.NaN.cosh(), Complex.NaN);
-    }
-
-    /**
-     * ISO C Standard G.6.2.5
-     */
-    @Test
-    public void testSinh() {
-        assertComplex(oneOne.sinh().conj(), oneOne.conj().sinh()); // AND CSINH IS ODD
-        assertComplex(Complex.ZERO.sinh(), Complex.ZERO);
-        assertComplex(zeroInf.sinh(), zeroNaN);
-        assertComplex(zeroNaN.sinh(), zeroNaN);
-        assertComplex(oneInf.sinh(), Complex.NaN);
-        assertComplex(oneNaN.sinh(), Complex.NaN);
-        assertComplex(infZero.sinh(), infZero);
-        // skipped test similar to previous section
-        assertComplex(infInf.sinh(), infNaN);
-        assertComplex(infNaN.sinh(), infNaN);
-        assertComplex(nanZero.sinh(), nanZero);
-        assertComplex(nanOne.sinh(), Complex.NaN);
-        assertComplex(Complex.NaN.sinh(), Complex.NaN);
-    }
-
-    /**
-     * ISO C Standard G.6.2.6
-     */
-    @Test
-    public void testTanh() {
-        assertComplex(oneOne.tanh().conj(), oneOne.conj().tanh()); // AND CSINH IS ODD
-        assertComplex(Complex.ZERO.tanh(), Complex.ZERO);
-        assertComplex(oneInf.tanh(), Complex.NaN);
-        assertComplex(oneNaN.tanh(), Complex.NaN);
-        //Do Not Understand the Next Test
-        assertComplex(infInf.tanh(), oneZero);
-        assertComplex(infNaN.tanh(), oneZero);
-        assertComplex(nanZero.tanh(), nanZero);
-        assertComplex(nanOne.tanh(), Complex.NaN);
-        assertComplex(Complex.NaN.tanh(), Complex.NaN);
-    }
-
-    /**
-     * ISO C Standard G.6.3.1
-     */
-    @Test
-    public void testExp() {
-        assertComplex(oneOne.conj().exp(), oneOne.exp().conj());
-        assertComplex(Complex.ZERO.exp(), oneZero);
-        assertComplex(negZeroZero.exp(), oneZero);
-        assertComplex(oneInf.exp(), Complex.NaN);
-        assertComplex(oneNaN.exp(), Complex.NaN);
-        assertComplex(infZero.exp(), infZero);
-        // Do not understand next test
-        assertComplex(negInfInf.exp(), Complex.ZERO);
-        assertComplex(infInf.exp(), infNaN);
-        assertComplex(negInfNaN.exp(), Complex.ZERO);
-        assertComplex(infNaN.exp(), infNaN);
-        assertComplex(nanZero.exp(), nanZero);
-        assertComplex(nanOne.exp(), Complex.NaN);
-        assertComplex(Complex.NaN.exp(), Complex.NaN);
-    }
-
-    /**
-     * ISO C Standard G.6.3.2
-     */
-    @Test
-    public void testLog() {
-        assertComplex(oneOne.log().conj(), oneOne.conj().log());
-        assertComplex(negZeroZero.log(), negInfPi); 
-        assertComplex(Complex.ZERO.log(), negInfZero);
-        assertComplex(oneInf.log(), infPiTwo);
-        assertComplex(oneNaN.log(), Complex.NaN);
-        assertComplex(negInfOne.log(), infPi);
-        assertComplex(infOne.log(), infZero);
-        assertComplex(infInf.log(), infPiFour);
-        assertComplex(infNaN.log(), infNaN);
-        assertComplex(nanOne.log(), Complex.NaN);
-        assertComplex(nanInf.log(), infNaN);
-        assertComplex(Complex.NaN.log(), Complex.NaN);
-    }
-
-    /**
-     * ISO C Standard G.6.4.2
-     */
-    @Test
-    public void testSqrt2() {
-        assertComplex(oneOne.sqrt().conj(), oneOne.conj().sqrt());
-        assertComplex(Complex.ZERO.sqrt(), Complex.ZERO);
-        assertComplex(oneInf.sqrt(), infInf);
-        assertComplex(negInfOne.sqrt(), zeroNaN);
-        assertComplex(infOne.sqrt(), infZero);
-        assertComplex(negInfNaN.sqrt(), nanInf);
-        assertComplex(infNaN.sqrt(), infNaN);
-        assertComplex(nanOne.sqrt(), Complex.NaN);
-        assertComplex(Complex.NaN.sqrt(), Complex.NaN);
-    }
-}

http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/1de701b3/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/ComplexTest.java
----------------------------------------------------------------------
diff --git a/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/ComplexTest.java b/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/ComplexTest.java
deleted file mode 100644
index 99a9624..0000000
--- a/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/ComplexTest.java
+++ /dev/null
@@ -1,1366 +0,0 @@
-/*
- * 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.
- */
-
-package org.apache.commons.numbers.complex;
-
-import java.util.List;
-
-import org.apache.commons.numbers.complex.Complex;
-import org.apache.commons.numbers.complex.ComplexUtils;
-import org.junit.Assert;
-import org.junit.Ignore;
-import org.junit.Test;
-
-
-/**
- */
-public class ComplexTest {
-
-
-    private double inf = Double.POSITIVE_INFINITY;
-    private double neginf = Double.NEGATIVE_INFINITY;
-    private double nan = Double.NaN;
-    private double pi = Math.PI;
-    private Complex oneInf = new Complex(1, inf);
-    private Complex oneNegInf = new Complex(1, neginf);
-    private Complex infOne = new Complex(inf, 1);
-    private Complex infZero = new Complex(inf, 0);
-    private Complex infNaN = new Complex(inf, nan);
-    private Complex infNegInf = new Complex(inf, neginf);
-    private Complex infInf = new Complex(inf, inf);
-    private Complex negInfInf = new Complex(neginf, inf);
-    private Complex negInfZero = new Complex(neginf, 0);
-    private Complex negInfOne = new Complex(neginf, 1);
-    private Complex negInfNaN = new Complex(neginf, nan);
-    private Complex negInfNegInf = new Complex(neginf, neginf);
-    private Complex oneNaN = new Complex(1, nan);
-    private Complex zeroInf = new Complex(0, inf);
-    private Complex zeroNaN = new Complex(0, nan);
-    private Complex nanInf = new Complex(nan, inf);
-    private Complex nanNegInf = new Complex(nan, neginf);
-    private Complex nanZero = new Complex(nan, 0);
-
-    @Test
-    public void testConstructor() {
-        Complex z = new Complex(3.0, 4.0);
-        Assert.assertEquals(3.0, z.getReal(), 0);
-        Assert.assertEquals(4.0, z.getImaginary(), 0);
-    }
-
-    @Test
-    public void testAbs() {
-        Complex z = new Complex(3.0, 4.0);
-        Assert.assertEquals(5.0, z.abs(), 0);
-    }
-
-    @Test
-    public void testAbsNaN() {
-        Assert.assertTrue(Double.isNaN(Complex.NaN.abs()));
-        Complex z = new Complex(inf, nan);
-        Assert.assertTrue(Double.isNaN(z.abs()));
-    }
-
-    @Test
-    public void testAbsInfinite() {
-        Complex z = new Complex(inf, 0);
-        Assert.assertEquals(inf, z.abs(), 0);
-        z = new Complex(0, neginf);
-        Assert.assertEquals(inf, z.abs(), 0);
-        z = new Complex(inf, neginf);
-        Assert.assertEquals(inf, z.abs(), 0);
-    }
-
-    @Test
-    public void testAdd() {
-        Complex x = new Complex(3.0, 4.0);
-        Complex y = new Complex(5.0, 6.0);
-        Complex z = x.add(y);
-        Assert.assertEquals(8.0, z.getReal(), 0);
-        Assert.assertEquals(10.0, z.getImaginary(), 0);
-    }
-
-    @Test
-    public void testAddNaN() {
-        Complex x = new Complex(3.0, 4.0);
-        Complex z = x.add(Complex.NaN);
-        Assert.assertSame(Complex.NaN, z);
-        z = new Complex(1, nan);
-        Complex w = x.add(z);
-        Assert.assertSame(Complex.NaN, w);
-    }
-
-    @Test
-    public void testAddInf() {
-        Complex x = new Complex(1, 1);
-        Complex z = new Complex(inf, 0);
-        Complex w = x.add(z);
-        Assert.assertEquals(w.getImaginary(), 1, 0);
-        Assert.assertEquals(inf, w.getReal(), 0);
-
-        x = new Complex(neginf, 0);
-        Assert.assertTrue(Double.isNaN(x.add(z).getReal()));
-    }
-
-
-    @Test
-    public void testScalarAdd() {
-        Complex x = new Complex(3.0, 4.0);
-        double yDouble = 2.0;
-        Complex yComplex = new Complex(yDouble);
-        Assert.assertEquals(x.add(yComplex), x.add(yDouble));
-    }
-
-    @Test
-    public void testScalarAddNaN() {
-        Complex x = new Complex(3.0, 4.0);
-        double yDouble = Double.NaN;
-        Complex yComplex = new Complex(yDouble);
-        Assert.assertEquals(x.add(yComplex), x.add(yDouble));
-    }
-
-    @Test
-    public void testScalarAddInf() {
-        Complex x = new Complex(1, 1);
-        double yDouble = Double.POSITIVE_INFINITY;
-
-        Complex yComplex = new Complex(yDouble);
-        Assert.assertEquals(x.add(yComplex), x.add(yDouble));
-
-        x = new Complex(neginf, 0);
-        Assert.assertEquals(x.add(yComplex), x.add(yDouble));
-    }
-
-    @Test
-    public void testConjugate() {
-        Complex x = new Complex(3.0, 4.0);
-        Complex z = x.conjugate();
-        Assert.assertEquals(3.0, z.getReal(), 1.0e-5);
-        Assert.assertEquals(-4.0, z.getImaginary(), 1.0e-5);
-    }
-
-    @Test
-    public void testConjugateInfinite() {
-        Complex z = new Complex(0, inf);
-        Assert.assertEquals(neginf, z.conjugate().getImaginary(), 0);
-        z = new Complex(0, neginf);
-        Assert.assertEquals(inf, z.conjugate().getImaginary(), 0);
-    }
-
-    @Test
-    public void testDivide() {
-        Complex x = new Complex(3.0, 4.0);
-        Complex y = new Complex(5.0, 6.0);
-        Complex z = x.divide(y);
-        Assert.assertEquals(39.0 / 61.0, z.getReal(), 1.0e-5);
-        Assert.assertEquals(2.0 / 61.0, z.getImaginary(), 1.0e-5);
-    }
-
-    @Test
-    public void testDivideReal() {
-        Complex x = new Complex(2d, 3d);
-        Complex y = new Complex(2d, 0d);
-        Assert.assertEquals(new Complex(1d, 1.5), x.divide(y));
-
-    }
-
-    @Test
-    public void testDivideImaginary() {
-        Complex x = new Complex(2d, 3d);
-        Complex y = new Complex(0d, 2d);
-        Assert.assertEquals(new Complex(1.5d, -1d), x.divide(y));
-    }
-
-    @Test
-    public void testDivideInf() {
-        Complex x = new Complex(3, 4);
-        Complex w = new Complex(neginf, inf);
-        Assert.assertTrue(x.divide(w).equals(Complex.ZERO));
-
-        Complex z = w.divide(x);
-        Assert.assertTrue(Double.isNaN(z.getReal()));
-        Assert.assertEquals(inf, z.getImaginary(), 0);
-
-        w = new Complex(inf, inf);
-        z = w.divide(x);
-        Assert.assertTrue(Double.isNaN(z.getImaginary()));
-        Assert.assertEquals(inf, z.getReal(), 0);
-
-        w = new Complex(1, inf);
-        z = w.divide(w);
-        Assert.assertTrue(Double.isNaN(z.getReal()));
-        Assert.assertTrue(Double.isNaN(z.getImaginary()));
-    }
-
-    @Test
-    public void testDivideZero() {
-        Complex x = new Complex(3.0, 4.0);
-        Complex z = x.divide(Complex.ZERO);
-        // Assert.assertEquals(z, Complex.INF); // See MATH-657
-        Assert.assertEquals(z, Complex.NaN);
-    }
-
-    @Test
-    public void testDivideZeroZero() {
-        Complex x = new Complex(0.0, 0.0);
-        Complex z = x.divide(Complex.ZERO);
-        Assert.assertEquals(z, Complex.NaN);
-    }
-
-    @Test
-    public void testDivideNaNInf() {
-       Complex z = oneInf.divide(Complex.ONE);
-       Assert.assertTrue(Double.isNaN(z.getReal()));
-       Assert.assertEquals(inf, z.getImaginary(), 0);
-
-       z = negInfNegInf.divide(oneNaN);
-       Assert.assertTrue(Double.isNaN(z.getReal()));
-       Assert.assertTrue(Double.isNaN(z.getImaginary()));
-
-       z = negInfInf.divide(Complex.ONE);
-       Assert.assertTrue(Double.isNaN(z.getReal()));
-       Assert.assertTrue(Double.isNaN(z.getImaginary()));
-    }
-
-    @Test
-    public void testScalarDivide() {
-        Complex x = new Complex(3.0, 4.0);
-        double yDouble = 2.0;
-        Complex yComplex = new Complex(yDouble);
-        Assert.assertEquals(x.divide(yComplex), x.divide(yDouble));
-    }
-
-    @Test
-    public void testScalarDivideNaN() {
-        Complex x = new Complex(3.0, 4.0);
-        double yDouble = Double.NaN;
-        Complex yComplex = new Complex(yDouble);
-        Assert.assertEquals(x.divide(yComplex), x.divide(yDouble));
-    }
-
-    @Test
-    public void testScalarDivideZero() {
-        Complex x = new Complex(1,1);
-        TestUtils.assertEquals(x.divide(Complex.ZERO), x.divide(0), 0);
-    }
-
-    @Test
-    public void testReciprocal() {
-        Complex z = new Complex(5.0, 6.0);
-        Complex act = z.reciprocal();
-        double expRe = 5.0 / 61.0;
-        double expIm = -6.0 / 61.0;
-        Assert.assertEquals(expRe, act.getReal(), Math.ulp(expRe));
-        Assert.assertEquals(expIm, act.getImaginary(), Math.ulp(expIm));
-    }
-
-    @Test
-    public void testReciprocalReciprocal() {
-        Complex z = new Complex(5.0, 6.0);
-        Complex zRR = z.reciprocal().reciprocal();
-        final double tol = 1e-14;
-        Assert.assertEquals(zRR.getReal(), z.getReal(), tol);
-        Assert.assertEquals(zRR.getImaginary(), z.getImaginary(), tol);
-    }
-
-    @Test
-    public void testReciprocalReal() {
-        Complex z = new Complex(-2.0, 0.0);
-        Assert.assertTrue(Complex.equals(new Complex(-0.5, 0.0), z.reciprocal()));
-    }
-
-    @Test
-    public void testReciprocalImaginary() {
-        Complex z = new Complex(0.0, -2.0);
-        Assert.assertEquals(new Complex(0.0, 0.5), z.reciprocal());
-    }
-
-    @Test
-    public void testReciprocalInf() {
-        Complex z = new Complex(neginf, inf);
-        Assert.assertTrue(z.reciprocal().equals(Complex.ZERO));
-
-        z = new Complex(1, inf).reciprocal();
-        Assert.assertEquals(z, Complex.ZERO);
-    }
-
-    @Test
-    public void testReciprocalZero() {
-        Assert.assertEquals(Complex.ZERO.reciprocal(), Complex.INF);
-    }
-
-    @Test
-    public void testMultiply() {
-        Complex x = new Complex(3.0, 4.0);
-        Complex y = new Complex(5.0, 6.0);
-        Complex z = x.multiply(y);
-        Assert.assertEquals(-9.0, z.getReal(), 1.0e-5);
-        Assert.assertEquals(38.0, z.getImaginary(), 1.0e-5);
-    }
-
-    @Test
-    public void testMultiplyNaN() {
-        Complex x = new Complex(3.0, 4.0);
-        Complex z = x.multiply(Complex.NaN);
-        Assert.assertSame(Complex.NaN, z);
-        z = Complex.NaN.multiply(5);
-        Assert.assertSame(Complex.NaN, z);
-    }
-
-    @Test
-    public void testMultiplyNaNInf() {
-        Complex z = new Complex(1,1);
-        Complex w = z.multiply(infOne);
-        Assert.assertEquals(w.getReal(), inf, 0);
-        Assert.assertEquals(w.getImaginary(), inf, 0);
-
-        // [MATH-164]
-        Assert.assertTrue(new Complex( 1,0).multiply(infInf).equals(Complex.INF));
-        Assert.assertTrue(new Complex(-1,0).multiply(infInf).equals(Complex.INF));
-        Assert.assertTrue(new Complex( 1,0).multiply(negInfZero).equals(Complex.INF));
-
-        w = oneInf.multiply(oneNegInf);
-        Assert.assertEquals(w.getReal(), inf, 0);
-        Assert.assertEquals(w.getImaginary(), inf, 0);
-
-        w = negInfNegInf.multiply(oneNaN);
-        Assert.assertTrue(Double.isNaN(w.getReal()));
-        Assert.assertTrue(Double.isNaN(w.getImaginary()));
-
-        z = new Complex(1, neginf);
-        Assert.assertSame(Complex.INF, z.multiply(z));
-    }
-
-    @Test
-    public void testScalarMultiply() {
-        Complex x = new Complex(3.0, 4.0);
-        double yDouble = 2.0;
-        Complex yComplex = new Complex(yDouble);
-        Assert.assertEquals(x.multiply(yComplex), x.multiply(yDouble));
-        int zInt = -5;
-        Complex zComplex = new Complex(zInt);
-        Assert.assertEquals(x.multiply(zComplex), x.multiply(zInt));
-    }
-
-    @Test
-    public void testScalarMultiplyNaN() {
-        Complex x = new Complex(3.0, 4.0);
-        double yDouble = Double.NaN;
-        Complex yComplex = new Complex(yDouble);
-        Assert.assertEquals(x.multiply(yComplex), x.multiply(yDouble));
-    }
-
-    @Test
-    public void testScalarMultiplyInf() {
-        Complex x = new Complex(1, 1);
-        double yDouble = Double.POSITIVE_INFINITY;
-        Complex yComplex = new Complex(yDouble);
-        Assert.assertEquals(x.multiply(yComplex), x.multiply(yDouble));
-
-        yDouble = Double.NEGATIVE_INFINITY;
-        yComplex = new Complex(yDouble);
-        Assert.assertEquals(x.multiply(yComplex), x.multiply(yDouble));
-    }
-
-    @Test
-    public void testNegate() {
-        Complex x = new Complex(3.0, 4.0);
-        Complex z = x.negate();
-        Assert.assertEquals(-3.0, z.getReal(), 1.0e-5);
-        Assert.assertEquals(-4.0, z.getImaginary(), 1.0e-5);
-    }
-
-    @Test
-    public void testSubtract() {
-        Complex x = new Complex(3.0, 4.0);
-        Complex y = new Complex(5.0, 6.0);
-        Complex z = x.subtract(y);
-        Assert.assertEquals(-2.0, z.getReal(), 1.0e-5);
-        Assert.assertEquals(-2.0, z.getImaginary(), 1.0e-5);
-    }
-
-    @Test
-    public void testSubtractNaN() {
-        Complex x = new Complex(3.0, 4.0);
-        Complex z = x.subtract(Complex.NaN);
-        Assert.assertSame(Complex.NaN, z);
-        z = new Complex(1, nan);
-        Complex w = x.subtract(z);
-        Assert.assertSame(Complex.NaN, w);
-    }
-
-    @Test
-    public void testSubtractInf() {
-        Complex x = new Complex(1, 1);
-        Complex z = new Complex(neginf, 0);
-        Complex w = x.subtract(z);
-        Assert.assertEquals(w.getImaginary(), 1, 0);
-        Assert.assertEquals(inf, w.getReal(), 0);
-
-        x = new Complex(neginf, 0);
-        Assert.assertTrue(Double.isNaN(x.subtract(z).getReal()));
-    }
-
-    @Test
-    public void testScalarSubtract() {
-        Complex x = new Complex(3.0, 4.0);
-        double yDouble = 2.0;
-        Complex yComplex = new Complex(yDouble);
-        Assert.assertEquals(x.subtract(yComplex), x.subtract(yDouble));
-    }
-
-    @Test
-    public void testScalarSubtractNaN() {
-        Complex x = new Complex(3.0, 4.0);
-        double yDouble = Double.NaN;
-        Complex yComplex = new Complex(yDouble);
-        Assert.assertEquals(x.subtract(yComplex), x.subtract(yDouble));
-    }
-
-    @Test
-    public void testScalarSubtractInf() {
-        Complex x = new Complex(1, 1);
-        double yDouble = Double.POSITIVE_INFINITY;
-        Complex yComplex = new Complex(yDouble);
-        Assert.assertEquals(x.subtract(yComplex), x.subtract(yDouble));
-
-        x = new Complex(neginf, 0);
-        Assert.assertEquals(x.subtract(yComplex), x.subtract(yDouble));
-    }
-
-
-    @Test
-    public void testEqualsNull() {
-        Complex x = new Complex(3.0, 4.0);
-        Assert.assertFalse(x.equals(null));
-    }
-
-    @Test(expected=NullPointerException.class)
-    public void testFloatingPointEqualsPrecondition1() {
-        Complex.equals(new Complex(3.0, 4.0), null, 3);
-    }
-    @Test(expected=NullPointerException.class)
-    public void testFloatingPointEqualsPrecondition2() {
-        Complex.equals(null, new Complex(3.0, 4.0), 3);
-    }
-
-    @Test
-    public void testEqualsClass() {
-        Complex x = new Complex(3.0, 4.0);
-        Assert.assertFalse(x.equals(this));
-    }
-
-    @Test
-    public void testEqualsSame() {
-        Complex x = new Complex(3.0, 4.0);
-        Assert.assertTrue(x.equals(x));
-    }
-
-    @Test
-    public void testFloatingPointEquals() {
-        double re = -3.21;
-        double im = 456789e10;
-
-        final Complex x = new Complex(re, im);
-        Complex y = new Complex(re, im);
-
-        Assert.assertTrue(x.equals(y));
-        Assert.assertTrue(Complex.equals(x, y));
-
-        final int maxUlps = 5;
-        for (int i = 0; i < maxUlps; i++) {
-            re = Math.nextUp(re);
-            im = Math.nextUp(im);
-        }
-        y = new Complex(re, im);
-        Assert.assertTrue(Complex.equals(x, y, maxUlps));
-
-        re = Math.nextUp(re);
-        im = Math.nextUp(im);
-        y = new Complex(re, im);
-        Assert.assertFalse(Complex.equals(x, y, maxUlps));
-    }
-
-    @Test
-    public void testFloatingPointEqualsNaN() {
-        Complex c = new Complex(Double.NaN, 1);
-        Assert.assertFalse(Complex.equals(c, c));
-
-        c = new Complex(1, Double.NaN);
-        Assert.assertFalse(Complex.equals(c, c));
-    }
-
-    @Test
-    public void testFloatingPointEqualsWithAllowedDelta() {
-        final double re = 153.0000;
-        final double im = 152.9375;
-        final double tol1 = 0.0625;
-        final Complex x = new Complex(re, im);
-        final Complex y = new Complex(re + tol1, im + tol1);
-        Assert.assertTrue(Complex.equals(x, y, tol1));
-
-        final double tol2 = 0.0624;
-        Assert.assertFalse(Complex.equals(x, y, tol2));
-    }
-
-    @Test
-    public void testFloatingPointEqualsWithAllowedDeltaNaN() {
-        final Complex x = new Complex(0, Double.NaN);
-        final Complex y = new Complex(Double.NaN, 0);
-        Assert.assertFalse(Complex.equals(x, Complex.ZERO, 0.1));
-        Assert.assertFalse(Complex.equals(x, x, 0.1));
-        Assert.assertFalse(Complex.equals(x, y, 0.1));
-    }
-
-    @Test
-    public void testFloatingPointEqualsWithRelativeTolerance() {
-        final double tol = 1e-4;
-        final double re = 1;
-        final double im = 1e10;
-
-        final double f = 1 + tol;
-        final Complex x = new Complex(re, im);
-        final Complex y = new Complex(re * f, im * f);
-        Assert.assertTrue(Complex.equalsWithRelativeTolerance(x, y, tol));
-    }
-
-    @Test
-    public void testFloatingPointEqualsWithRelativeToleranceNaN() {
-        final Complex x = new Complex(0, Double.NaN);
-        final Complex y = new Complex(Double.NaN, 0);
-        Assert.assertFalse(Complex.equalsWithRelativeTolerance(x, Complex.ZERO, 0.1));
-        Assert.assertFalse(Complex.equalsWithRelativeTolerance(x, x, 0.1));
-        Assert.assertFalse(Complex.equalsWithRelativeTolerance(x, y, 0.1));
-    }
-
-    @Test
-    public void testEqualsTrue() {
-        Complex x = new Complex(3.0, 4.0);
-        Complex y = new Complex(3.0, 4.0);
-        Assert.assertTrue(x.equals(y));
-    }
-
-    @Test
-    public void testEqualsRealDifference() {
-        Complex x = new Complex(0.0, 0.0);
-        Complex y = new Complex(0.0 + Double.MIN_VALUE, 0.0);
-        assertFalseComplex(x, y);
-    }
-
-    @Test
-    public void testEqualsImaginaryDifference() {
-        Complex x = new Complex(0.0, 0.0);
-        Complex y = new Complex(0.0, 0.0 + Double.MIN_VALUE);
-        assertFalseComplex(x, y);
-    }
-
-    @Test
-    public void testEqualsNaN() {
-        Complex realNaN = new Complex(Double.NaN, 0.0);
-        Complex imaginaryNaN = new Complex(0.0, Double.NaN);
-        Complex complexNaN = Complex.NaN;
-        Assert.assertTrue(realNaN.equals(imaginaryNaN));
-        Assert.assertTrue(imaginaryNaN.equals(complexNaN));
-        Assert.assertTrue(realNaN.equals(complexNaN));
-    }
-
-    @Test
-    public void testHashCode() {
-        Complex x = new Complex(0.0, 0.0);
-        Complex y = new Complex(0.0, 0.0 + Double.MIN_VALUE);
-        Assert.assertFalse(x.hashCode()==y.hashCode());
-        y = new Complex(0.0 + Double.MIN_VALUE, 0.0);
-        Assert.assertFalse(x.hashCode()==y.hashCode());
-        Complex realNaN = new Complex(Double.NaN, 0.0);
-        Complex imaginaryNaN = new Complex(0.0, Double.NaN);
-        Assert.assertEquals(realNaN.hashCode(), imaginaryNaN.hashCode());
-        Assert.assertEquals(imaginaryNaN.hashCode(), Complex.NaN.hashCode());
-
-        // MATH-1118
-        // "equals" and "hashCode" must be compatible: if two objects have
-        // different hash codes, "equals" must return false.
-        final String msg = "'equals' not compatible with 'hashCode'";
-
-        x = new Complex(0.0, 0.0);
-        y = new Complex(0.0, -0.0);
-        Assert.assertTrue(x.hashCode() != y.hashCode());
-        //Assert.assertFalse(msg, x.equals(y));
-
-        x = new Complex(0.0, 0.0);
-        y = new Complex(-0.0, 0.0);
-        Assert.assertTrue(x.hashCode() != y.hashCode());
-        //Assert.assertFalse(msg, x.equals(y));
-    }
-
-    @Test
-    public void testAcos() {
-        Complex z = new Complex(3, 4);
-        Complex expected = new Complex(0.936812, -2.30551);
-        TestUtils.assertEquals(expected, z.acos(), 1.0e-5);
-        TestUtils.assertEquals(new Complex(Math.acos(0), 0),
-                Complex.ZERO.acos(), 1.0e-12);
-    }
-
-    @Test
-    public void testAcosInf() {
-        TestUtils.assertSame(Complex.NaN, oneInf.acos());
-        TestUtils.assertSame(Complex.NaN, oneNegInf.acos());
-        TestUtils.assertSame(Complex.NaN, infOne.acos());
-        TestUtils.assertSame(Complex.NaN, negInfOne.acos());
-        TestUtils.assertSame(Complex.NaN, infInf.acos());
-        TestUtils.assertSame(Complex.NaN, infNegInf.acos());
-        TestUtils.assertSame(Complex.NaN, negInfInf.acos());
-        TestUtils.assertSame(Complex.NaN, negInfNegInf.acos());
-    }
-
-    @Test
-    public void testAsin() {
-        Complex z = new Complex(3, 4);
-        Complex expected = new Complex(0.633984, 2.30551);
-        TestUtils.assertEquals(expected, z.asin(), 1.0e-5);
-    }
-
-    @Test
-    public void testAsinInf() {
-        TestUtils.assertSame(Complex.NaN, oneInf.asin());
-        TestUtils.assertSame(Complex.NaN, oneNegInf.asin());
-        TestUtils.assertSame(Complex.NaN, infOne.asin());
-        TestUtils.assertSame(Complex.NaN, negInfOne.asin());
-        TestUtils.assertSame(Complex.NaN, infInf.asin());
-        TestUtils.assertSame(Complex.NaN, infNegInf.asin());
-        TestUtils.assertSame(Complex.NaN, negInfInf.asin());
-        TestUtils.assertSame(Complex.NaN, negInfNegInf.asin());
-    }
-
-    @Test
-    public void testAtan() {
-        Complex z = new Complex(3, 4);
-        Complex expected = new Complex(1.44831, 0.158997);
-        TestUtils.assertEquals(expected, z.atan(), 1.0e-5);
-    }
-
-    @Test
-    public void testAtanInf() {
-        TestUtils.assertSame(Complex.NaN, oneInf.atan());
-        TestUtils.assertSame(Complex.NaN, oneNegInf.atan());
-        TestUtils.assertSame(Complex.NaN, infOne.atan());
-        TestUtils.assertSame(Complex.NaN, negInfOne.atan());
-        TestUtils.assertSame(Complex.NaN, infInf.atan());
-        TestUtils.assertSame(Complex.NaN, infNegInf.atan());
-        TestUtils.assertSame(Complex.NaN, negInfInf.atan());
-        TestUtils.assertSame(Complex.NaN, negInfNegInf.atan());
-    }
-
-    @Test
-    public void testCos() {
-        Complex z = new Complex(3, 4);
-        Complex expected = new Complex(-27.03495, -3.851153);
-        TestUtils.assertEquals(expected, z.cos(), 1.0e-5);
-    }
-
-    @Test
-    public void testCosInf() {
-        TestUtils.assertSame(infNegInf, oneInf.cos());
-        TestUtils.assertSame(infInf, oneNegInf.cos());
-        TestUtils.assertSame(Complex.NaN, infOne.cos());
-        TestUtils.assertSame(Complex.NaN, negInfOne.cos());
-        TestUtils.assertSame(Complex.NaN, infInf.cos());
-        TestUtils.assertSame(Complex.NaN, infNegInf.cos());
-        TestUtils.assertSame(Complex.NaN, negInfInf.cos());
-        TestUtils.assertSame(Complex.NaN, negInfNegInf.cos());
-    }
-
-    @Test
-    public void testCosh() {
-        Complex z = new Complex(3, 4);
-        Complex expected = new Complex(-6.58066, -7.58155);
-        TestUtils.assertEquals(expected, z.cosh(), 1.0e-5);
-    }
-
-    @Test
-    public void testCoshInf() {
-        TestUtils.assertSame(Complex.NaN, oneInf.cosh());
-        TestUtils.assertSame(Complex.NaN, oneNegInf.cosh());
-        TestUtils.assertSame(infInf, infOne.cosh());
-        TestUtils.assertSame(infNegInf, negInfOne.cosh());
-        TestUtils.assertSame(Complex.NaN, infInf.cosh());
-        TestUtils.assertSame(Complex.NaN, infNegInf.cosh());
-        TestUtils.assertSame(Complex.NaN, negInfInf.cosh());
-        TestUtils.assertSame(Complex.NaN, negInfNegInf.cosh());
-    }
-
-    @Test
-    public void testExp() {
-        final double tol = Math.ulp(1d);
-        Complex z = new Complex(3, 4);
-        Complex expected = new Complex(-13.12878, -15.20078);
-        TestUtils.assertEquals(expected, z.exp(), 1.0e-5);
-        TestUtils.assertEquals(Complex.ONE,
-                Complex.ZERO.exp(), tol);
-        Complex iPi = Complex.I.multiply(new Complex(pi,0));
-        TestUtils.assertEquals(Complex.ONE.negate(),
-                iPi.exp(), tol);
-    }
-
-    @Test
-    public void testExpInf1() {
-        TestUtils.assertSame(Complex.NaN, oneInf.exp());
-    }
-
-    @Test
-    public void testExpInf2() {
-        TestUtils.assertSame(Complex.NaN, oneNegInf.exp());
-    }
-
-    @Test
-    public void testExpInf3() {
-        TestUtils.assertSame(infInf, infOne.exp());
-    }
-
-    @Test
-    @Ignore
-    public void testJava() {// TODO more debug
-        System.out.println(">>testJava()");
-        // MathTest#testExpSpecialCases() checks the following:
-        // Assert.assertEquals("exp of -infinity should be 0.0", 0.0, Math.exp(Double.NEGATIVE_INFINITY), Precision.EPSILON);
-        // Let's check how well Math works:
-        System.out.println("Math.exp="+Math.exp(Double.NEGATIVE_INFINITY));
-        String props[] = {
-        "java.version", //    Java Runtime Environment version
-        "java.vendor", // Java Runtime Environment vendor
-        "java.vm.specification.version", //   Java Virtual Machine specification version
-        "java.vm.specification.vendor", //    Java Virtual Machine specification vendor
-        "java.vm.specification.name", //  Java Virtual Machine specification name
-        "java.vm.version", // Java Virtual Machine implementation version
-        "java.vm.vendor", //  Java Virtual Machine implementation vendor
-        "java.vm.name", //    Java Virtual Machine implementation name
-        "java.specification.version", //  Java Runtime Environment specification version
-        "java.specification.vendor", //   Java Runtime Environment specification vendor
-        "java.specification.name", // Java Runtime Environment specification name
-        "java.class.version", //  Java class format version number
-        };
-        for(String t : props) {
-            System.out.println(t + "=" + System.getProperty(t));
-        }
-        System.out.println("<<testJava()");
-    }
-
-    @Test
-    public void testExpInf4() {
-        final Complex exp = negInfOne.exp();
-        TestUtils.assertSame(Complex.ZERO, exp);
-    }
-
-    @Test
-    public void testExpInf5() {
-        TestUtils.assertSame(Complex.NaN, infInf.exp());
-    }
-
-    @Test
-    public void testExpInf6() {
-        TestUtils.assertSame(Complex.NaN, infNegInf.exp());
-    }
-
-    @Test
-    public void testExpInf7() {
-        TestUtils.assertSame(Complex.NaN, negInfInf.exp());
-    }
-
-    @Test
-    public void testExpInf8() {
-        TestUtils.assertSame(Complex.NaN, negInfNegInf.exp());
-    }
-
-    @Test
-    public void testLog() {
-        Complex z = new Complex(3, 4);
-        Complex expected = new Complex(1.60944, 0.927295);
-        TestUtils.assertEquals(expected, z.log(), 1.0e-5);
-    }
-
-    @Test
-    public void testLogInf() {
-        final double tol = Math.ulp(1d);
-        TestUtils.assertEquals(new Complex(inf, pi / 2),
-                oneInf.log(), tol);
-        TestUtils.assertEquals(new Complex(inf, -pi / 2),
-                oneNegInf.log(), tol);
-        TestUtils.assertEquals(infZero, infOne.log(), tol);
-        TestUtils.assertEquals(new Complex(inf, pi),
-                negInfOne.log(), tol);
-        TestUtils.assertEquals(new Complex(inf, pi / 4),
-                infInf.log(), tol);
-        TestUtils.assertEquals(new Complex(inf, -pi / 4),
-                infNegInf.log(), tol);
-        TestUtils.assertEquals(new Complex(inf, 3d * pi / 4),
-                negInfInf.log(), tol);
-        TestUtils.assertEquals(new Complex(inf, - 3d * pi / 4),
-                negInfNegInf.log(), tol);
-    }
-
-    @Test
-    public void testLogZero() {
-        TestUtils.assertSame(negInfZero, Complex.ZERO.log());
-    }
-
-    @Test
-    public void testPow() {
-        Complex x = new Complex(3, 4);
-        Complex y = new Complex(5, 6);
-        Complex expected = new Complex(-1.860893, 11.83677);
-        TestUtils.assertEquals(expected, x.pow(y), 1.0e-5);
-    }
-
-   @Test
-   public void testPowInf() {
-       TestUtils.assertSame(Complex.NaN,Complex.ONE.pow(oneInf));
-       TestUtils.assertSame(Complex.NaN,Complex.ONE.pow(oneNegInf));
-       TestUtils.assertSame(Complex.NaN,Complex.ONE.pow(infOne));
-       TestUtils.assertSame(Complex.NaN,Complex.ONE.pow(infInf));
-       TestUtils.assertSame(Complex.NaN,Complex.ONE.pow(infNegInf));
-       TestUtils.assertSame(Complex.NaN,Complex.ONE.pow(negInfInf));
-       TestUtils.assertSame(Complex.NaN,Complex.ONE.pow(negInfNegInf));
-       TestUtils.assertSame(Complex.NaN,infOne.pow(Complex.ONE));
-       TestUtils.assertSame(Complex.NaN,negInfOne.pow(Complex.ONE));
-       TestUtils.assertSame(Complex.NaN,infInf.pow(Complex.ONE));
-       TestUtils.assertSame(Complex.NaN,infNegInf.pow(Complex.ONE));
-       TestUtils.assertSame(Complex.NaN,negInfInf.pow(Complex.ONE));
-       TestUtils.assertSame(Complex.NaN,negInfNegInf.pow(Complex.ONE));
-       TestUtils.assertSame(Complex.NaN,negInfNegInf.pow(infNegInf));
-       TestUtils.assertSame(Complex.NaN,negInfNegInf.pow(negInfNegInf));
-       TestUtils.assertSame(Complex.NaN,negInfNegInf.pow(infInf));
-       TestUtils.assertSame(Complex.NaN,infInf.pow(infNegInf));
-       TestUtils.assertSame(Complex.NaN,infInf.pow(negInfNegInf));
-       TestUtils.assertSame(Complex.NaN,infInf.pow(infInf));
-       TestUtils.assertSame(Complex.NaN,infNegInf.pow(infNegInf));
-       TestUtils.assertSame(Complex.NaN,infNegInf.pow(negInfNegInf));
-       TestUtils.assertSame(Complex.NaN,infNegInf.pow(infInf));
-   }
-
-   /*
-   @Test
-   public void testPowZero() {
-       final double tol = Math.ulp(1d);
-       TestUtils.assertEquals(Complex.ZERO,
-              Complex.ZERO.pow(Complex.ONE), tol);
-       TestUtils.assertEquals(Complex.ZERO,
-               Complex.ZERO.pow(new Complex(2, 0)), tol);
-       TestUtils.assertSame(Complex.NaN,
-               Complex.ZERO.pow(Complex.ZERO));
-       TestUtils.assertSame(Complex.NaN,
-               Complex.ZERO.pow(Complex.I));
-       TestUtils.assertEquals(Complex.ONE,
-               Complex.ONE.pow(Complex.ZERO), tol);
-       TestUtils.assertEquals(Complex.ONE,
-               Complex.I.pow(Complex.ZERO), tol);
-       TestUtils.assertEquals(Complex.ONE,
-               new Complex(-1, 3).pow(Complex.ZERO), tol);
-   }
-   */
-
-    @Test
-    public void testScalarPow() {
-        Complex x = new Complex(3, 4);
-        double yDouble = 5.0;
-        Complex yComplex = new Complex(yDouble);
-        Assert.assertEquals(x.pow(yComplex), x.pow(yDouble));
-    }
-
-    @Test
-    public void testScalarPowNaNBase() {
-        Complex x = Complex.NaN;
-        double yDouble = 5.0;
-        Complex yComplex = new Complex(yDouble);
-        Assert.assertEquals(x.pow(yComplex), x.pow(yDouble));
-    }
-
-    @Test
-    public void testScalarPowNaNExponent() {
-        Complex x = new Complex(3, 4);
-        double yDouble = Double.NaN;
-        Complex yComplex = new Complex(yDouble);
-        Assert.assertEquals(x.pow(yComplex), x.pow(yDouble));
-    }
-
-   @Test
-   public void testScalarPowInf() {
-       TestUtils.assertSame(Complex.NaN,Complex.ONE.pow(Double.POSITIVE_INFINITY));
-       TestUtils.assertSame(Complex.NaN,Complex.ONE.pow(Double.NEGATIVE_INFINITY));
-       TestUtils.assertSame(Complex.NaN,infOne.pow(1.0));
-       TestUtils.assertSame(Complex.NaN,negInfOne.pow(1.0));
-       TestUtils.assertSame(Complex.NaN,infInf.pow(1.0));
-       TestUtils.assertSame(Complex.NaN,infNegInf.pow(1.0));
-       TestUtils.assertSame(Complex.NaN,negInfInf.pow(10));
-       TestUtils.assertSame(Complex.NaN,negInfNegInf.pow(1.0));
-       TestUtils.assertSame(Complex.NaN,negInfNegInf.pow(Double.POSITIVE_INFINITY));
-       TestUtils.assertSame(Complex.NaN,negInfNegInf.pow(Double.POSITIVE_INFINITY));
-       TestUtils.assertSame(Complex.NaN,infInf.pow(Double.POSITIVE_INFINITY));
-       TestUtils.assertSame(Complex.NaN,infInf.pow(Double.NEGATIVE_INFINITY));
-       TestUtils.assertSame(Complex.NaN,infNegInf.pow(Double.NEGATIVE_INFINITY));
-       TestUtils.assertSame(Complex.NaN,infNegInf.pow(Double.POSITIVE_INFINITY));
-   }
-
-   /*
-   @Test
-   public void testScalarPowZero() {
-       final double tol = Math.ulp(1d);
-       TestUtils.assertEquals(Complex.ZERO, Complex.ZERO.pow(1.0), tol);
-       TestUtils.assertEquals(Complex.ZERO, Complex.ZERO.pow(2.0), tol);
-       TestUtils.assertSame(Complex.NaN, Complex.ZERO.pow(0.0));
-       TestUtils.assertSame(Complex.NaN, Complex.ZERO.pow(-1.0));
-       TestUtils.assertEquals(Complex.ONE, Complex.ONE.pow(0.0), tol);
-       TestUtils.assertEquals(Complex.ONE, Complex.I.pow(0.0), tol);
-       TestUtils.assertEquals(Complex.ONE, new Complex(-1, 3).pow(0.0), tol);
-   }
-   */
-
-    @Test
-    public void testSin() {
-        Complex z = new Complex(3, 4);
-        Complex expected = new Complex(3.853738, -27.01681);
-        TestUtils.assertEquals(expected, z.sin(), 1.0e-5);
-    }
-
-    @Test
-    public void testSinInf() {
-        TestUtils.assertSame(infInf, oneInf.sin());
-        TestUtils.assertSame(infNegInf, oneNegInf.sin());
-        TestUtils.assertSame(Complex.NaN, infOne.sin());
-        TestUtils.assertSame(Complex.NaN, negInfOne.sin());
-        TestUtils.assertSame(Complex.NaN, infInf.sin());
-        TestUtils.assertSame(Complex.NaN, infNegInf.sin());
-        TestUtils.assertSame(Complex.NaN, negInfInf.sin());
-        TestUtils.assertSame(Complex.NaN, negInfNegInf.sin());
-    }
-
-    @Test
-    public void testSinh() {
-        Complex z = new Complex(3, 4);
-        Complex expected = new Complex(-6.54812, -7.61923);
-        TestUtils.assertEquals(expected, z.sinh(), 1.0e-5);
-    }
-
-    @Test
-    public void testSinhInf() {
-        TestUtils.assertSame(Complex.NaN, oneInf.sinh());
-        TestUtils.assertSame(Complex.NaN, oneNegInf.sinh());
-        TestUtils.assertSame(infInf, infOne.sinh());
-        TestUtils.assertSame(negInfInf, negInfOne.sinh());
-        TestUtils.assertSame(Complex.NaN, infInf.sinh());
-        TestUtils.assertSame(Complex.NaN, infNegInf.sinh());
-        TestUtils.assertSame(Complex.NaN, negInfInf.sinh());
-        TestUtils.assertSame(Complex.NaN, negInfNegInf.sinh());
-    }
-
-    @Test
-    public void testSqrtRealPositive() {
-        Complex z = new Complex(3, 4);
-        Complex expected = new Complex(2, 1);
-        TestUtils.assertEquals(expected, z.sqrt(), 1.0e-5);
-    }
-
-    @Test
-    public void testSqrtRealZero() {
-        Complex z = new Complex(0.0, 4);
-        Complex expected = new Complex(1.41421, 1.41421);
-        TestUtils.assertEquals(expected, z.sqrt(), 1.0e-5);
-    }
-
-    @Test
-    public void testSqrtRealNegative() {
-        Complex z = new Complex(-3.0, 4);
-        Complex expected = new Complex(1, 2);
-        TestUtils.assertEquals(expected, z.sqrt(), 1.0e-5);
-    }
-
-    @Test
-    public void testSqrtImaginaryZero() {
-        Complex z = new Complex(-3.0, 0.0);
-        Complex expected = new Complex(0.0, 1.73205);
-        TestUtils.assertEquals(expected, z.sqrt(), 1.0e-5);
-    }
-
-    @Test
-    public void testSqrtImaginaryNegative() {
-        Complex z = new Complex(-3.0, -4.0);
-        Complex expected = new Complex(1.0, -2.0);
-        TestUtils.assertEquals(expected, z.sqrt(), 1.0e-5);
-    }
-
-    @Test
-    public void testSqrtPolar() {
-        final double tol = 1e-12;
-        double r = 1;
-        for (int i = 0; i < 5; i++) {
-            r += i;
-            double theta = 0;
-            for (int j = 0; j < 11; j++) {
-                theta += pi / 12;
-                Complex z = ComplexUtils.polar2Complex(r, theta);
-                Complex sqrtz = ComplexUtils.polar2Complex(Math.sqrt(r), theta / 2);
-                TestUtils.assertEquals(sqrtz, z.sqrt(), tol);
-            }
-        }
-    }
-
-    @Test
-    public void testSqrtInf() {
-        TestUtils.assertSame(infNaN, oneInf.sqrt());
-        TestUtils.assertSame(infNaN, oneNegInf.sqrt());
-        TestUtils.assertSame(infZero, infOne.sqrt());
-        TestUtils.assertSame(zeroInf, negInfOne.sqrt());
-        TestUtils.assertSame(infNaN, infInf.sqrt());
-        TestUtils.assertSame(infNaN, infNegInf.sqrt());
-        TestUtils.assertSame(nanInf, negInfInf.sqrt());
-        TestUtils.assertSame(nanNegInf, negInfNegInf.sqrt());
-    }
-
-    @Test
-    public void testSqrt1z() {
-        Complex z = new Complex(3, 4);
-        Complex expected = new Complex(4.08033, -2.94094);
-        TestUtils.assertEquals(expected, z.sqrt1z(), 1.0e-5);
-    }
-
-    @Test
-    public void testTan() {
-        Complex z = new Complex(3, 4);
-        Complex expected = new Complex(-0.000187346, 0.999356);
-        TestUtils.assertEquals(expected, z.tan(), 1.0e-5);
-        /* Check that no overflow occurs (MATH-722) */
-        Complex actual = new Complex(3.0, 1E10).tan();
-        expected = new Complex(0, 1);
-        TestUtils.assertEquals(expected, actual, 1.0e-5);
-        actual = new Complex(3.0, -1E10).tan();
-        expected = new Complex(0, -1);
-        TestUtils.assertEquals(expected, actual, 1.0e-5);
-    }
-
-    @Test
-    public void testTanInf() {
-        TestUtils.assertSame(Complex.valueOf(0.0, 1.0), oneInf.tan());
-        TestUtils.assertSame(Complex.valueOf(0.0, -1.0), oneNegInf.tan());
-        TestUtils.assertSame(Complex.NaN, infOne.tan());
-        TestUtils.assertSame(Complex.NaN, negInfOne.tan());
-        TestUtils.assertSame(Complex.NaN, infInf.tan());
-        TestUtils.assertSame(Complex.NaN, infNegInf.tan());
-        TestUtils.assertSame(Complex.NaN, negInfInf.tan());
-        TestUtils.assertSame(Complex.NaN, negInfNegInf.tan());
-    }
-
-   @Test
-   public void testTanCritical() {
-        TestUtils.assertSame(infNaN, new Complex(pi/2, 0).tan());
-        TestUtils.assertSame(negInfNaN, new Complex(-pi/2, 0).tan());
-    }
-
-    @Test
-    public void testTanh() {
-        Complex z = new Complex(3, 4);
-        Complex expected = new Complex(1.00071, 0.00490826);
-        TestUtils.assertEquals(expected, z.tanh(), 1.0e-5);
-        /* Check that no overflow occurs (MATH-722) */
-        Complex actual = new Complex(1E10, 3.0).tanh();
-        expected = new Complex(1, 0);
-        TestUtils.assertEquals(expected, actual, 1.0e-5);
-        actual = new Complex(-1E10, 3.0).tanh();
-        expected = new Complex(-1, 0);
-        TestUtils.assertEquals(expected, actual, 1.0e-5);
-    }
-
-    @Test
-    public void testTanhInf() {
-        TestUtils.assertSame(Complex.NaN, oneInf.tanh());
-        TestUtils.assertSame(Complex.NaN, oneNegInf.tanh());
-        TestUtils.assertSame(Complex.valueOf(1.0, 0.0), infOne.tanh());
-        TestUtils.assertSame(Complex.valueOf(-1.0, 0.0), negInfOne.tanh());
-        TestUtils.assertSame(Complex.NaN, infInf.tanh());
-        TestUtils.assertSame(Complex.NaN, infNegInf.tanh());
-        TestUtils.assertSame(Complex.NaN, negInfInf.tanh());
-        TestUtils.assertSame(Complex.NaN, negInfNegInf.tanh());
-    }
-
-    @Test
-    public void testTanhCritical() {
-        TestUtils.assertSame(nanInf, new Complex(0, pi/2).tanh());
-    }
-
-    /** test issue MATH-221 */
-    @Test
-    public void testMath221() {
-        Assert.assertTrue(Complex.equals(new Complex(0,-1),
-                                         new Complex(0,1).multiply(new Complex(-1,0))));
-    }
-
-    /**
-     * Test: computing <b>third roots</b> of z.
-     * <pre>
-     * <code>
-     * <b>z = -2 + 2 * i</b>
-     *   => z_0 =  1      +          i
-     *   => z_1 = -1.3660 + 0.3660 * i
-     *   => z_2 =  0.3660 - 1.3660 * i
-     * </code>
-     * </pre>
-     */
-    @Test
-    public void testNthRoot_normal_thirdRoot() {
-        // The complex number we want to compute all third-roots for.
-        Complex z = new Complex(-2,2);
-        // The List holding all third roots
-        Complex[] thirdRootsOfZ = z.nthRoot(3).toArray(new Complex[0]);
-        // Returned Collection must not be empty!
-        Assert.assertEquals(3, thirdRootsOfZ.length);
-        // test z_0
-        Assert.assertEquals(1.0,                  thirdRootsOfZ[0].getReal(),      1.0e-5);
-        Assert.assertEquals(1.0,                  thirdRootsOfZ[0].getImaginary(), 1.0e-5);
-        // test z_1
-        Assert.assertEquals(-1.3660254037844386,  thirdRootsOfZ[1].getReal(),      1.0e-5);
-        Assert.assertEquals(0.36602540378443843,  thirdRootsOfZ[1].getImaginary(), 1.0e-5);
-        // test z_2
-        Assert.assertEquals(0.366025403784439,    thirdRootsOfZ[2].getReal(),      1.0e-5);
-        Assert.assertEquals(-1.3660254037844384,  thirdRootsOfZ[2].getImaginary(), 1.0e-5);
-    }
-
-
-    /**
-     * Test: computing <b>fourth roots</b> of z.
-     * <pre>
-     * <code>
-     * <b>z = 5 - 2 * i</b>
-     *   => z_0 =  1.5164 - 0.1446 * i
-     *   => z_1 =  0.1446 + 1.5164 * i
-     *   => z_2 = -1.5164 + 0.1446 * i
-     *   => z_3 = -1.5164 - 0.1446 * i
-     * </code>
-     * </pre>
-     */
-    @Test
-    public void testNthRoot_normal_fourthRoot() {
-        // The complex number we want to compute all third-roots for.
-        Complex z = new Complex(5,-2);
-        // The List holding all fourth roots
-        Complex[] fourthRootsOfZ = z.nthRoot(4).toArray(new Complex[0]);
-        // Returned Collection must not be empty!
-        Assert.assertEquals(4, fourthRootsOfZ.length);
-        // test z_0
-        Assert.assertEquals(1.5164629308487783,     fourthRootsOfZ[0].getReal(),      1.0e-5);
-        Assert.assertEquals(-0.14469266210702247,   fourthRootsOfZ[0].getImaginary(), 1.0e-5);
-        // test z_1
-        Assert.assertEquals(0.14469266210702256,    fourthRootsOfZ[1].getReal(),      1.0e-5);
-        Assert.assertEquals(1.5164629308487783,     fourthRootsOfZ[1].getImaginary(), 1.0e-5);
-        // test z_2
-        Assert.assertEquals(-1.5164629308487783,    fourthRootsOfZ[2].getReal(),      1.0e-5);
-        Assert.assertEquals(0.14469266210702267,    fourthRootsOfZ[2].getImaginary(), 1.0e-5);
-        // test z_3
-        Assert.assertEquals(-0.14469266210702275,   fourthRootsOfZ[3].getReal(),      1.0e-5);
-        Assert.assertEquals(-1.5164629308487783,    fourthRootsOfZ[3].getImaginary(), 1.0e-5);
-    }
-
-    /**
-     * Test: computing <b>third roots</b> of z.
-     * <pre>
-     * <code>
-     * <b>z = 8</b>
-     *   => z_0 =  2
-     *   => z_1 = -1 + 1.73205 * i
-     *   => z_2 = -1 - 1.73205 * i
-     * </code>
-     * </pre>
-     */
-    @Test
-    public void testNthRoot_cornercase_thirdRoot_imaginaryPartEmpty() {
-        // The number 8 has three third roots. One we all already know is the number 2.
-        // But there are two more complex roots.
-        Complex z = new Complex(8,0);
-        // The List holding all third roots
-        Complex[] thirdRootsOfZ = z.nthRoot(3).toArray(new Complex[0]);
-        // Returned Collection must not be empty!
-        Assert.assertEquals(3, thirdRootsOfZ.length);
-        // test z_0
-        Assert.assertEquals(2.0,                thirdRootsOfZ[0].getReal(),      1.0e-5);
-        Assert.assertEquals(0.0,                thirdRootsOfZ[0].getImaginary(), 1.0e-5);
-        // test z_1
-        Assert.assertEquals(-1.0,               thirdRootsOfZ[1].getReal(),      1.0e-5);
-        Assert.assertEquals(1.7320508075688774, thirdRootsOfZ[1].getImaginary(), 1.0e-5);
-        // test z_2
-        Assert.assertEquals(-1.0,               thirdRootsOfZ[2].getReal(),      1.0e-5);
-        Assert.assertEquals(-1.732050807568877, thirdRootsOfZ[2].getImaginary(), 1.0e-5);
-    }
-
-
-    /**
-     * Test: computing <b>third roots</b> of z with real part 0.
-     * <pre>
-     * <code>
-     * <b>z = 2 * i</b>
-     *   => z_0 =  1.0911 + 0.6299 * i
-     *   => z_1 = -1.0911 + 0.6299 * i
-     *   => z_2 = -2.3144 - 1.2599 * i
-     * </code>
-     * </pre>
-     */
-    @Test
-    public void testNthRoot_cornercase_thirdRoot_realPartZero() {
-        // complex number with only imaginary part
-        Complex z = new Complex(0,2);
-        // The List holding all third roots
-        Complex[] thirdRootsOfZ = z.nthRoot(3).toArray(new Complex[0]);
-        // Returned Collection must not be empty!
-        Assert.assertEquals(3, thirdRootsOfZ.length);
-        // test z_0
-        Assert.assertEquals(1.0911236359717216,      thirdRootsOfZ[0].getReal(),      1.0e-5);
-        Assert.assertEquals(0.6299605249474365,      thirdRootsOfZ[0].getImaginary(), 1.0e-5);
-        // test z_1
-        Assert.assertEquals(-1.0911236359717216,     thirdRootsOfZ[1].getReal(),      1.0e-5);
-        Assert.assertEquals(0.6299605249474365,      thirdRootsOfZ[1].getImaginary(), 1.0e-5);
-        // test z_2
-        Assert.assertEquals(-2.3144374213981936E-16, thirdRootsOfZ[2].getReal(),      1.0e-5);
-        Assert.assertEquals(-1.2599210498948732,     thirdRootsOfZ[2].getImaginary(), 1.0e-5);
-    }
-
-    /**
-     * Test cornercases with NaN and Infinity.
-     */
-    @Test
-    public void testNthRoot_cornercase_NAN_Inf() {
-        // NaN + finite -> NaN
-        List<Complex> roots = oneNaN.nthRoot(3);
-        Assert.assertEquals(1,roots.size());
-        Assert.assertEquals(Complex.NaN, roots.get(0));
-
-        roots = nanZero.nthRoot(3);
-        Assert.assertEquals(1,roots.size());
-        Assert.assertEquals(Complex.NaN, roots.get(0));
-
-        // NaN + infinite -> NaN
-        roots = nanInf.nthRoot(3);
-        Assert.assertEquals(1,roots.size());
-        Assert.assertEquals(Complex.NaN, roots.get(0));
-
-        // finite + infinite -> Inf
-        roots = oneInf.nthRoot(3);
-        Assert.assertEquals(1,roots.size());
-        Assert.assertEquals(Complex.INF, roots.get(0));
-
-        // infinite + infinite -> Inf
-        roots = negInfInf.nthRoot(3);
-        Assert.assertEquals(1,roots.size());
-        Assert.assertEquals(Complex.INF, roots.get(0));
-    }
-
-    /**
-     * Test standard values
-     */
-    @Test
-    public void testGetArgument() {
-        Complex z = new Complex(1, 0);
-        Assert.assertEquals(0.0, z.getArgument(), 1.0e-12);
-
-        z = new Complex(1, 1);
-        Assert.assertEquals(Math.PI/4, z.getArgument(), 1.0e-12);
-
-        z = new Complex(0, 1);
-        Assert.assertEquals(Math.PI/2, z.getArgument(), 1.0e-12);
-
-        z = new Complex(-1, 1);
-        Assert.assertEquals(3 * Math.PI/4, z.getArgument(), 1.0e-12);
-
-        z = new Complex(-1, 0);
-        Assert.assertEquals(Math.PI, z.getArgument(), 1.0e-12);
-
-        z = new Complex(-1, -1);
-        Assert.assertEquals(-3 * Math.PI/4, z.getArgument(), 1.0e-12);
-
-        z = new Complex(0, -1);
-        Assert.assertEquals(-Math.PI/2, z.getArgument(), 1.0e-12);
-
-        z = new Complex(1, -1);
-        Assert.assertEquals(-Math.PI/4, z.getArgument(), 1.0e-12);
-
-    }
-
-    /**
-     * Verify atan2-style handling of infinite parts
-     */
-    @Test
-    public void testGetArgumentInf() {
-        Assert.assertEquals(Math.PI/4, infInf.getArgument(), 1.0e-12);
-        Assert.assertEquals(Math.PI/2, oneInf.getArgument(), 1.0e-12);
-        Assert.assertEquals(0.0, infOne.getArgument(), 1.0e-12);
-        Assert.assertEquals(Math.PI/2, zeroInf.getArgument(), 1.0e-12);
-        Assert.assertEquals(0.0, infZero.getArgument(), 1.0e-12);
-        Assert.assertEquals(Math.PI, negInfOne.getArgument(), 1.0e-12);
-        Assert.assertEquals(-3.0*Math.PI/4, negInfNegInf.getArgument(), 1.0e-12);
-        Assert.assertEquals(-Math.PI/2, oneNegInf.getArgument(), 1.0e-12);
-    }
-
-    /**
-     * Verify that either part NaN results in NaN
-     */
-    @Test
-    public void testGetArgumentNaN() {
-        Assert.assertTrue(Double.isNaN(nanZero.getArgument()));
-        Assert.assertTrue(Double.isNaN(zeroNaN.getArgument()));
-        Assert.assertTrue(Double.isNaN(Complex.NaN.getArgument()));
-    }
-
-    @Test
-    public void testSerial() {
-        Complex z = new Complex(3.0, 4.0);
-        Assert.assertEquals(z, TestUtils.serializeAndRecover(z));
-        Complex ncmplx = (Complex)TestUtils.serializeAndRecover(oneNaN);
-        Assert.assertEquals(nanZero, ncmplx);
-        Complex infcmplx = (Complex)TestUtils.serializeAndRecover(infInf);
-        Assert.assertEquals(infInf, infcmplx);
-        TestComplex tz = new TestComplex(3.0, 4.0);
-        Assert.assertEquals(tz, TestUtils.serializeAndRecover(tz));
-        TestComplex ntcmplx = (TestComplex)TestUtils.serializeAndRecover(new TestComplex(oneNaN));
-        Assert.assertEquals(nanZero, ntcmplx);
-        TestComplex inftcmplx = (TestComplex)TestUtils.serializeAndRecover(new TestComplex(infInf));
-        Assert.assertEquals(infInf, inftcmplx);
-    }
-
-    /**
-     * Class to test extending Complex
-     */
-    public static class TestComplex extends Complex {
-
-        /**
-         * Serialization identifier.
-         */
-        private static final long serialVersionUID = 3268726724160389237L;
-
-        public TestComplex(double real, double imaginary) {
-            super(real, imaginary);
-        }
-
-        public TestComplex(Complex other){
-            this(other.getReal(), other.getImaginary());
-        }
-
-        @Override
-        protected TestComplex createComplex(double real, double imaginary){
-            return new TestComplex(real, imaginary);
-        }
-
-    }
-
-    private static void assertFalseComplex(Complex a, Complex b) {
-        Assert.assertFalse("Difference not detected", new Double(a.getReal()).equals(new Double(b.getReal())) && new Double(a.getImaginary()).equals(new Double(b.getImaginary())));
-    }
-
-}


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