.../commons/numbers/complex/CStandardTest.java | 265 ++++
4 files changed, 1585 insertions(+)
----------------------------------------------------------------------
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/15136c2d/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/.Complex.java.swo
----------------------------------------------------------------------
diff --git
a/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/.Complex.java.swo
b/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/.Complex.java.swo
new file mode 100644
index 0000000..7720390
Binary files /dev/null and
b/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/.Complex.java.swo
differ
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/15136c2d/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java.orig
----------------------------------------------------------------------
diff --git
a/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java.orig
b/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java.orig
new file mode 100644
index 0000000..d3c7ce0
--- /dev/null
+++
b/commons-numbers-complex/src/main/java/org/apache/commons/numbers/complex/Complex.java.orig
@@ -0,0 +1,1320 @@
+/*
+ * 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.io.Serializable;
+import java.util.ArrayList;
+import java.util.List;
+import org.apache.commons.numbers.core.Precision;
+/**
+ * Representation of a Complex number, i.e., a number which has both
a
+ * real and imaginary part.
+ * <p>
+ * Implementations of arithmetic operations handle {@code NaN} and
+ * infinite values according to the rules for {@link
java.lang.Double}, i.e.
+ * {@link #equals} is an equivalence relation for all instances that
have
+ * a {@code NaN} in either real or imaginary part, e.g. the
following are
+ * considered equal:
+ * <ul>
+ * <li>{@code 1 + NaNi}</li>
+ * <li>{@code NaN + i}</li>
+ * <li>{@code NaN + NaNi}</li>
+ * </ul><p>
+ * Note that this contradicts the IEEE-754 standard for floating
+ * point numbers (according to which the test {@code x == x} must
fail if
+ * {@code x} is {@code NaN}). The method
+ * {@link
org.apache.commons.numbers.core.Precision#equals(double,double,int)
+ * equals for primitive double} in class {@code Precision} conforms
with
+ * IEEE-754 while this class conforms with the standard behavior for
Java
+ * object types.</p>
+ *
+ */
+public class Complex implements Serializable {
+ /** The square root of -1. A number representing "0.0 + 1.0i" */
+ public static final Complex I = new Complex(0.0, 1.0);
+ // CHECKSTYLE: stop ConstantName
+ /** A complex number representing "NaN + NaNi" */
+ public static final Complex NaN = new Complex(Double.NaN,
Double.NaN);
+ // CHECKSTYLE: resume ConstantName
+ /** A complex number representing "+INF + INFi" */
+ public static final Complex INF = new
Complex(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY);
+ /** A complex number representing "1.0 + 0.0i" */
+ public static final Complex ONE = new Complex(1.0, 0.0);
+ /** A complex number representing "0.0 + 0.0i" */
+ public static final Complex ZERO = new Complex(0.0, 0.0);
+
+ /** Serializable version identifier */
+ private static final long serialVersionUID = 201701120L;
+
+ /** The imaginary part. */
+ private final double imaginary;
+ /** The real part. */
+ private final double real;
+ /** Record whether this complex number is equal to NaN. */
+ private final transient boolean isNaN;
+ /** Record whether this complex number is infinite. */
+ private final transient boolean isInfinite;
+
+ /**
+ * Create a complex number given only the real part.
+ *
+ * @param real Real part.
+ */
+ public Complex(double real) {
+ this(real, 0.0);
+ }
+
+ /**
+ * Create a complex number given the real and imaginary parts.
+ *
+ * @param real Real part.
+ * @param imaginary Imaginary part.
+ */
+ public Complex(double real, double imaginary) {
+ this.real = real;
+ this.imaginary = imaginary;
+
+ isNaN = Double.isNaN(real) || Double.isNaN(imaginary);
+ isInfinite = !isNaN &&
+ (Double.isInfinite(real) ||
Double.isInfinite(imaginary));
+ }
+
+ /**
+ * Return the absolute value of this complex number.
+ * Returns {@code NaN} if either real or imaginary part is
{@code NaN}
+ * and {@code Double.POSITIVE_INFINITY} if neither part is
{@code NaN},
+ * but at least one part is infinite.
+ * This code follows the <a
href="http://www.iso-9899.info/wiki/The_Standard";>ISO C Standard</a>,
Annex G, in calculating the returned value (i.e. the hypot(x,y)
method)
+ *
+ * @return the absolute value.
+ */
+ public double abs() {
+ if (isNaN) {
+ return Double.NaN;
+ }
+ if (isInfinite()) {
+ return Double.POSITIVE_INFINITY;
+ }
+ if (Math.abs(real) < Math.abs(imaginary)) {
+ if (imaginary == 0.0) {
+ return Math.abs(real);
+ }
+ double q = real / imaginary;
+ return Math.abs(imaginary) * Math.sqrt(1 + q * q);
+ } else {
+ if (real == 0.0) {
+ return Math.abs(imaginary);
+ }
+ double q = imaginary / real;
+ return Math.abs(real) * Math.sqrt(1 + q * q);
+ }
+ }
+
+ /**
+ * Returns a {@code Complex} whose value is
+ * {@code (this + addend)}.
+ * Uses the definitional formula
+ * <p>
+ * {@code (a + bi) + (c + di) = (a+c) + (b+d)i}
+ * </p>
+ * If either {@code this} or {@code addend} has a {@code NaN}
value in
+ * either part, {@link #NaN} is returned; otherwise {@code
Infinite}
+ * and {@code NaN} values are returned in the parts of the
result
+ * according to the rules for {@link java.lang.Double}
arithmetic.
+ *
+ * @param addend Value to be added to this {@code Complex}.
+ * @return {@code this + addend}.
+ */
+ public Complex add(Complex addend) {
+ checkNotNull(addend);
+ if (isNaN || addend.isNaN) {
+ return NaN;
+ }
+
+ return createComplex(real + addend.getReal(),
+ imaginary + addend.getImaginary());
+ }
+
+ /**
+ * Returns a {@code Complex} whose value is {@code (this +
addend)},
+ * with {@code addend} interpreted as a real number.
+ *
+ * @param addend Value to be added to this {@code Complex}.
+ * @return {@code this + addend}.
+ * @see #add(Complex)
+ */
+ public Complex add(double addend) {
+ if (isNaN || Double.isNaN(addend)) {
+ return NaN;
+ }
+
+ return createComplex(real + addend, imaginary);
+ }
+
+ /**
+ * Returns the conjugate of this complex number.
+ * The conjugate of {@code a + bi} is {@code a - bi}.
+ * <p>
+ * {@link #NaN} is returned if either the real or imaginary
+ * part of this Complex number equals {@code Double.NaN}.
+ * </p><p>
+ * If the imaginary part is infinite, and the real part is not
+ * {@code NaN}, the returned value has infinite imaginary part
+ * of the opposite sign, e.g. the conjugate of
+ * {@code 1 + POSITIVE_INFINITY i} is {@code 1 -
NEGATIVE_INFINITY i}.
+ * </p>
+ * @return the conjugate of this Complex object.
+ */
+ public Complex conjugate() {
+ if (isNaN) {
+ return NaN;
+ }
+
+ return createComplex(real, -imaginary);
+ }
+
+ /**
+ * Returns a {@code Complex} whose value is
+ * {@code (this / divisor)}.
+ * Implements the definitional formula
+ * <pre>
+ * <code>
+ * a + bi ac + bd + (bc - ad)i
+ * ----------- = -------------------------
+ * c + di c<sup>2</sup> + d<sup>2</sup>
+ * </code>
+ * </pre>
+ * but uses
+ * <a href="http://doi.acm.org/10.1145/1039813.1039814";>
+ * prescaling of operands</a> to limit the effects of overflows
and
+ * underflows in the computation.
+ * <p>
+ * {@code Infinite} and {@code NaN} values are handled according
to the
+ * following rules, applied in the order presented:
+ * <ul>
+ * <li>If either {@code this} or {@code divisor} has a {@code
NaN} value
+ * in either part, {@link #NaN} is returned.
+ * </li>
+ * <li>If {@code divisor} equals {@link #ZERO}, {@link #NaN} is
returned.
+ * </li>
+ * <li>If {@code this} and {@code divisor} are both infinite,
+ * {@link #NaN} is returned.
+ * </li>
+ * <li>If {@code this} is finite (i.e., has no {@code Infinite}
or
+ * {@code NaN} parts) and {@code divisor} is infinite (one or
both parts
+ * infinite), {@link #ZERO} is returned.
+ * </li>
+ * <li>If {@code this} is infinite and {@code divisor} is
finite,
+ * {@code NaN} values are returned in the parts of the result
if the
+ * {@link java.lang.Double} rules applied to the definitional
formula
+ * force {@code NaN} results.
+ * </li>
+ * </ul>
+ *
+ * @param divisor Value by which this {@code Complex} is to be
divided.
+ * @return {@code this / divisor}.
+ */
+ public Complex divide(Complex divisor) {
+ checkNotNull(divisor);
+ if (isNaN || divisor.isNaN) {
+ return NaN;
+ }
+
+ final double c = divisor.getReal();
+ final double d = divisor.getImaginary();
+ if (c == 0.0 && d == 0.0) {
+ return NaN;
+ }
+
+ if (divisor.isInfinite() && !isInfinite()) {
+ return ZERO;
+ }
+
+ if (Math.abs(c) < Math.abs(d)) {
+ double q = c / d;
+ double denominator = c * q + d;
+ return createComplex((real * q + imaginary) /
denominator,
+ (imaginary * q - real) / denominator);
+ } else {
+ double q = d / c;
+ double denominator = d * q + c;
+ return createComplex((imaginary * q + real) /
denominator,
+ (imaginary - real * q) / denominator);
+ }
+ }
+
+ /**
+ * Returns a {@code Complex} whose value is {@code (this /
divisor)},
+ * with {@code divisor} interpreted as a real number.
+ *
+ * @param divisor Value by which this {@code Complex} is to be
divided.
+ * @return {@code this / divisor}.
+ * @see #divide(Complex)
+ */
+ public Complex divide(double divisor) {
+ if (isNaN || Double.isNaN(divisor)) {
+ return NaN;
+ }
+ if (divisor == 0d) {
+ return NaN;
+ }
+ if (Double.isInfinite(divisor)) {
+ return !isInfinite() ? ZERO : NaN;
+ }
+ return createComplex(real / divisor,
+ imaginary / divisor);
+ }
+
+ /**
+ * Returns the multiplicative inverse this instance.
+ *
+ * @return {@code 1 / this}.
+ * @see #divide(Complex)
+ */
+ public Complex reciprocal() {
+ if (isNaN) {
+ return NaN;
+ }
+
+ if (real == 0.0 && imaginary == 0.0) {
+ return INF;
+ }
+
+ if (isInfinite) {
+ return ZERO;
+ }
+
+ if (Math.abs(real) < Math.abs(imaginary)) {
+ double q = real / imaginary;
+ double scale = 1. / (real * q + imaginary);
+ return createComplex(scale * q, -scale);
+ } else {
+ double q = imaginary / real;
+ double scale = 1. / (imaginary * q + real);
+ return createComplex(scale, -scale * q);
+ }
+ }
+
+ /**
+ * Test for equality with another object.
+ * If both the real and imaginary parts of two complex numbers
+ * are exactly the same, and neither is {@code Double.NaN}, the
two
+ * Complex objects are considered to be equal.
+ * The behavior is the same as for JDK's {@link
Double#equals(Object)
+ * Double}:
+ * <ul>
+ * <li>All {@code NaN} values are considered to be equal,
+ * i.e, if either (or both) real and imaginary parts of the
complex
+ * number are equal to {@code Double.NaN}, the complex number
is equal
+ * to {@code NaN}.
+ * </li>
+ * <li>
+ * Instances constructed with different representations of
zero (i.e.
+ * either "0" or "-0") are <em>not</em> considered to be
equal.
+ * </li>
+ * </ul>
+ *
+ * @param other Object to test for equality with this instance.
+ * @return {@code true} if the objects are equal, {@code false}
if object
+ * is {@code null}, not an instance of {@code Complex}, or not
equal to
+ * this instance.
+ */
+ @Override
+ public boolean equals(Object other) {
+ if (this == other) {
+ return true;
+ }
+ if (other instanceof Complex){
+ Complex c = (Complex) other;
+ if (c.isNaN) {
+ return isNaN;
+ } else {
+ return equals(real, c.real) &&
+ equals(imaginary, c.imaginary);
+ }
+ }
+ return false;
+ }
+
+ /**
+ * Test for the floating-point equality between Complex objects.
+ * It returns {@code true} if both arguments are equal or within
the
+ * range of allowed error (inclusive).
+ *
+ * @param x First value (cannot be {@code null}).
+ * @param y Second value (cannot be {@code null}).
+ * @param maxUlps {@code (maxUlps - 1)} is the number of
floating point
+ * values between the real (resp. imaginary) parts of {@code x}
and
+ * {@code y}.
+ * @return {@code true} if there are fewer than {@code maxUlps}
floating
+ * point values between the real (resp. imaginary) parts of
{@code x}
+ * and {@code y}.
+ *
+ * @see Precision#equals(double,double,int)
+ */
+ public static boolean equals(Complex x, Complex y, int maxUlps)
{
+ return Precision.equals(x.real, y.real, maxUlps) &&
+ Precision.equals(x.imaginary, y.imaginary, maxUlps);
+ }
+
+ /**
+ * Returns {@code true} iff the values are equal as defined by
+ * {@link #equals(Complex,Complex,int) equals(x, y, 1)}.
+ *
+ * @param x First value (cannot be {@code null}).
+ * @param y Second value (cannot be {@code null}).
+ * @return {@code true} if the values are equal.
+ */
+ public static boolean equals(Complex x, Complex y) {
+ return equals(x, y, 1);
+ }
+
+ /**
+ * Returns {@code true} if, both for the real part and for the
imaginary
+ * part, there is no double value strictly between the arguments
or the
+ * difference between them is within the range of allowed error
+ * (inclusive). Returns {@code false} if either of the
arguments is NaN.
+ *
+ * @param x First value (cannot be {@code null}).
+ * @param y Second value (cannot be {@code null}).
+ * @param eps Amount of allowed absolute error.
+ * @return {@code true} if the values are two adjacent floating
point
+ * numbers or they are within range of each other.
+ *
+ * @see Precision#equals(double,double,double)
+ */
+ public static boolean equals(Complex x, Complex y, double eps) {
+ return Precision.equals(x.real, y.real, eps) &&
+ Precision.equals(x.imaginary, y.imaginary, eps);
+ }
+
+ /**
+ * Returns {@code true} if, both for the real part and for the
imaginary
+ * part, there is no double value strictly between the arguments
or the
+ * relative difference between them is smaller or equal to the
given
+ * tolerance. Returns {@code false} if either of the arguments
is NaN.
+ *
+ * @param x First value (cannot be {@code null}).
+ * @param y Second value (cannot be {@code null}).
+ * @param eps Amount of allowed relative error.
+ * @return {@code true} if the values are two adjacent floating
point
+ * numbers or they are within range of each other.
+ *
+ * @see
Precision#equalsWithRelativeTolerance(double,double,double)
+ */
+ public static boolean equalsWithRelativeTolerance(Complex x,
Complex y,
+ double eps) {
+ return Precision.equalsWithRelativeTolerance(x.real, y.real,
eps) &&
+ Precision.equalsWithRelativeTolerance(x.imaginary,
y.imaginary, eps);
+ }
+
+ /**
+ * Get a hashCode for the complex number.
+ * Any {@code Double.NaN} value in real or imaginary part
produces
+ * the same hash code {@code 7}.
+ *
+ * @return a hash code value for this object.
+ */
+ @Override
+ public int hashCode() {
+ if (isNaN) {
+ return 7;
+ }
+<<<<<<< HEAD
+ return 37 * 17 * (hash(imaginary) +
+ hash(real));
+ }
+
+ private int hash(double d) {
+ final long v = Double.doubleToLongBits(d);
+ return (int)(v^(v>>>32));
+ //return new Double(d).hashCode();
+=======
+ return 37 * (17 * hash(imaginary) +
+ hash(real));
+>>>>>>> eb-test
+ }
+
+ /**
+ * Access the imaginary part.
+ *
+ * @return the imaginary part.
+ */
+ public double getImaginary() {
+ return imaginary;
+ }
+
+ /**
+ * Access the real part.
+ *
+ * @return the real part.
+ */
+ public double getReal() {
+ return real;
+ }
+
+ /**
+ * Checks whether either or both parts of this complex number is
+ * {@code NaN}.
+ *
+ * @return true if either or both parts of this complex number
is
+ * {@code NaN}; false otherwise.
+ */
+ public boolean isNaN() {
+ return isNaN;
+ }
+
+ /**
+ * Checks whether either the real or imaginary part of this
complex number
+ * takes an infinite value (either {@code
Double.POSITIVE_INFINITY} or
+ * {@code Double.NEGATIVE_INFINITY}) and neither part
+ * is {@code NaN}.
+ *
+ * @return true if one or both parts of this complex number are
infinite
+ * and neither part is {@code NaN}.
+ */
+ public boolean isInfinite() {
+ return isInfinite;
+ }
+
+ /**
+ * Returns a {@code Complex} whose value is {@code this *
factor}.
+ * Implements preliminary checks for {@code NaN} and infinity
followed by
+ * the definitional formula:
+ * <p>
+ * {@code (a + bi)(c + di) = (ac - bd) + (ad + bc)i}
+ * </p>
+ * Returns {@link #NaN} if either {@code this} or {@code factor}
has one or
+ * more {@code NaN} parts.
+ * <p>
+ * Returns {@link #INF} if neither {@code this} nor {@code
factor} has one
+ * or more {@code NaN} parts and if either {@code this} or
{@code factor}
+ * has one or more infinite parts (same result is returned
regardless of
+ * the sign of the components).
+ * </p><p>
+ * Returns finite values in components of the result per the
definitional
+ * formula in all remaining cases.</p>
+ *
+ * @param factor value to be multiplied by this {@code
Complex}.
+ * @return {@code this * factor}.
+ */
+ public Complex multiply(Complex factor) {
+ checkNotNull(factor);
+ if (isNaN || factor.isNaN) {
+ return NaN;
+ }
+ if (Double.isInfinite(real) ||
+ Double.isInfinite(imaginary) ||
+ Double.isInfinite(factor.real) ||
+ Double.isInfinite(factor.imaginary)) {
+ // we don't use isInfinite() to avoid testing for NaN
again
+ return INF;
+ }
+ return createComplex(real * factor.real - imaginary *
factor.imaginary,
+ real * factor.imaginary + imaginary *
factor.real);
+ }
+
+ /**
+ * Returns a {@code Complex} whose value is {@code this *
factor}, with {@code factor}
+ * interpreted as a integer number.
+ *
+ * @param factor value to be multiplied by this {@code
Complex}.
+ * @return {@code this * factor}.
+ * @see #multiply(Complex)
+ */
+ public Complex multiply(final int factor) {
+ if (isNaN) {
+ return NaN;
+ }
+ if (Double.isInfinite(real) ||
+ Double.isInfinite(imaginary)) {
+ return INF;
+ }
+ return createComplex(real * factor, imaginary * factor);
+ }
+
+ /**
+ * Returns a {@code Complex} whose value is {@code this *
factor}, with {@code factor}
+ * interpreted as a real number.
+ *
+ * @param factor value to be multiplied by this {@code
Complex}.
+ * @return {@code this * factor}.
+ * @see #multiply(Complex)
+ */
+ public Complex multiply(double factor) {
+ if (isNaN || Double.isNaN(factor)) {
+ return NaN;
+ }
+ if (Double.isInfinite(real) ||
+ Double.isInfinite(imaginary) ||
+ Double.isInfinite(factor)) {
+ // we don't use isInfinite() to avoid testing for NaN
again
+ return INF;
+ }
+ return createComplex(real * factor, imaginary * factor);
+ }
+
+ /**
+ * Returns a {@code Complex} whose value is {@code (-this)}.
+ * Returns {@code NaN} if either real or imaginary
+ * part of this Complex number is {@code Double.NaN}.
+ *
+ * @return {@code -this}.
+ */
+ public Complex negate() {
+ if (isNaN) {
+ return NaN;
+ }
+
+ return createComplex(-real, -imaginary);
+ }
+
+ /**
+ * Returns a {@code Complex} whose value is
+ * {@code (this - subtrahend)}.
+ * Uses the definitional formula
+ * <p>
+ * {@code (a + bi) - (c + di) = (a-c) + (b-d)i}
+ * </p>
+ * If either {@code this} or {@code subtrahend} has a {@code
NaN]} value in either part,
+ * {@link #NaN} is returned; otherwise infinite and {@code NaN}
values are
+ * returned in the parts of the result according to the rules
for
+ * {@link java.lang.Double} arithmetic.
+ *
+ * @param subtrahend value to be subtracted from this {@code
Complex}.
+ * @return {@code this - subtrahend}.
+ */
+ public Complex subtract(Complex subtrahend) {
+ checkNotNull(subtrahend);
+ if (isNaN || subtrahend.isNaN) {
+ return NaN;
+ }
+
+ return createComplex(real - subtrahend.getReal(),
+ imaginary - subtrahend.getImaginary());
+ }
+
+ /**
+ * Returns a {@code Complex} whose value is
+ * {@code (this - subtrahend)}.
+ *
+ * @param subtrahend value to be subtracted from this {@code
Complex}.
+ * @return {@code this - subtrahend}.
+ * @see #subtract(Complex)
+ */
+ public Complex subtract(double subtrahend) {
+ if (isNaN || Double.isNaN(subtrahend)) {
+ return NaN;
+ }
+ return createComplex(real - subtrahend, imaginary);
+ }
+
+ /**
+ * Compute the
+ * <a href="http://mathworld.wolfram.com/InverseCosine.html";
TARGET="_top">
+ * inverse cosine</a> of this complex number.
+ * Implements the formula:
+ * <p>
+ * {@code acos(z) = -i (log(z + i (sqrt(1 - z<sup>2</sup>))))}
+ * </p>
+ * Returns {@link Complex#NaN} if either real or imaginary part
of the
+ * input argument is {@code NaN} or infinite.
+ *
+ * @return the inverse cosine of this complex number.
+ */
+ public Complex acos() {
+ if (isNaN) {
+ return NaN;
+ }
+
+ return
this.add(this.sqrt1z().multiply(I)).log().multiply(I.negate());
+ }
+
+ /**
+ * Compute the
+ * <a href="http://mathworld.wolfram.com/InverseSine.html";
TARGET="_top">
+ * inverse sine</a> of this complex number.
+ * Implements the formula:
+ * <p>
+ * {@code asin(z) = -i (log(sqrt(1 - z<sup>2</sup>) + iz))}
+ * </p><p>
+ * Returns {@link Complex#NaN} if either real or imaginary part
of the
+ * input argument is {@code NaN} or infinite.</p>
+ *
+ * @return the inverse sine of this complex number.
+ */
+ public Complex asin() {
+ if (isNaN) {
+ return NaN;
+ }
+
+ return
sqrt1z().add(this.multiply(I)).log().multiply(I.negate());
+ }
+
+ /**
+ * Compute the
+ * <a href="http://mathworld.wolfram.com/InverseTangent.html";
TARGET="_top">
+ * inverse tangent</a> of this complex number.
+ * Implements the formula:
+ * <p>
+ * {@code atan(z) = (i/2) log((i + z)/(i - z))}
+ * </p><p>
+ * Returns {@link Complex#NaN} if either real or imaginary part
of the
+ * input argument is {@code NaN} or infinite.</p>
+ *
+ * @return the inverse tangent of this complex number
+ */
+ public Complex atan() {
+ if (isNaN) {
+ return NaN;
+ }
+
+ return this.add(I).divide(I.subtract(this)).log()
+ .multiply(I.divide(createComplex(2.0, 0.0)));
+ }
+
+ /**
+ * Compute the
+ * <a href="http://mathworld.wolfram.com/Cosine.html";
TARGET="_top">
+ * cosine</a> of this complex number.
+ * Implements the formula:
+ * <p>
+ * {@code cos(a + bi) = cos(a)cosh(b) - sin(a)sinh(b)i}
+ * </p><p>
+ * where the (real) functions on the right-hand side are
+ * {@link Math#sin}, {@link Math#cos},
+ * {@link Math#cosh} and {@link Math#sinh}.
+ * </p><p>
+ * Returns {@link Complex#NaN} if either real or imaginary part
of the
+ * input argument is {@code NaN}.
+ * </p><p>
+ * Infinite values in real or imaginary parts of the input may
result in
+ * infinite or NaN values returned in parts of the result.</p>
+ * <pre>
+ * Examples:
+ * <code>
+ * cos(1 ± INFINITY i) = 1 \u2213 INFINITY i
+ * cos(±INFINITY + i) = NaN + NaN i
+ * cos(±INFINITY ± INFINITY i) = NaN + NaN i
+ * </code>
+ * </pre>
+ *
+ * @return the cosine of this complex number.
+ */
+ public Complex cos() {
+ if (isNaN) {
+ return NaN;
+ }
+
+ return createComplex(Math.cos(real) * Math.cosh(imaginary),
+ -Math.sin(real) *
Math.sinh(imaginary));
+ }
+
+ /**
+ * Compute the
+ * <a href="http://mathworld.wolfram.com/HyperbolicCosine.html";
TARGET="_top">
+ * hyperbolic cosine</a> of this complex number.
+ * Implements the formula:
+ * <pre>
+ * <code>
+ * cosh(a + bi) = cosh(a)cos(b) + sinh(a)sin(b)i
+ * </code>
+ * </pre>
+ * where the (real) functions on the right-hand side are
+ * {@link Math#sin}, {@link Math#cos},
+ * {@link Math#cosh} and {@link Math#sinh}.
+ * <p>
+ * Returns {@link Complex#NaN} if either real or imaginary part
of the
+ * input argument is {@code NaN}.
+ * </p>
+ * Infinite values in real or imaginary parts of the input may
result in
+ * infinite or NaN values returned in parts of the result.
+ * <pre>
+ * Examples:
+ * <code>
+ * cosh(1 ± INFINITY i) = NaN + NaN i
+ * cosh(±INFINITY + i) = INFINITY ± INFINITY i
+ * cosh(±INFINITY ± INFINITY i) = NaN + NaN i
+ * </code>
+ * </pre>
+ *
+ * @return the hyperbolic cosine of this complex number.
+ */
+ public Complex cosh() {
+ if (isNaN) {
+ return NaN;
+ }
+
+ return createComplex(Math.cosh(real) * Math.cos(imaginary),
+ Math.sinh(real) * Math.sin(imaginary));
+ }
+
+ /**
+ * Compute the
+ * <a
href="http://mathworld.wolfram.com/ExponentialFunction.html";
TARGET="_top">
+ * exponential function</a> of this complex number.
+ * Implements the formula:
+ * <pre>
+ * <code>
+ * exp(a + bi) = exp(a)cos(b) + exp(a)sin(b)i
+ * </code>
+ * </pre>
+ * where the (real) functions on the right-hand side are
+ * {@link Math#exp}, {@link Math#cos}, and
+ * {@link Math#sin}.
+ * <p>
+ * Returns {@link Complex#NaN} if either real or imaginary part
of the
+ * input argument is {@code NaN}.
+ * </p>
+ * Infinite values in real or imaginary parts of the input may
result in
+ * infinite or NaN values returned in parts of the result.
+ * <pre>
+ * Examples:
+ * <code>
+ * exp(1 ± INFINITY i) = NaN + NaN i
+ * exp(INFINITY + i) = INFINITY + INFINITY i
+ * exp(-INFINITY + i) = 0 + 0i
+ * exp(±INFINITY ± INFINITY i) = NaN + NaN i
+ * </code>
+ * </pre>
+ *
+ * @return <code><i>e</i><sup>this</sup></code>.
+ */
+ public Complex exp() {
+ if (isNaN) {
+ return NaN;
+ }
+
+ double expReal = Math.exp(real);
+ return createComplex(expReal * Math.cos(imaginary),
+ expReal * Math.sin(imaginary));
+ }
+
+ /**
+ * Compute the
+ * <a href="http://mathworld.wolfram.com/NaturalLogarithm.html";
TARGET="_top">
+ * natural logarithm</a> of this complex number.
+ * Implements the formula:
+ * <pre>
+ * <code>
+ * log(a + bi) = ln(|a + bi|) + arg(a + bi)i
+ * </code>
+ * </pre>
+ * where ln on the right hand side is {@link Math#log},
+ * {@code |a + bi|} is the modulus, {@link Complex#abs}, and
+ * {@code arg(a + bi) = }{@link Math#atan2}(b, a).
+ * <p>
+ * Returns {@link Complex#NaN} if either real or imaginary part
of the
+ * input argument is {@code NaN}.
+ * </p>
+ * Infinite (or critical) values in real or imaginary parts of
the input may
+ * result in infinite or NaN values returned in parts of the
result.
+ * <pre>
+ * Examples:
+ * <code>
+ * log(1 ± INFINITY i) = INFINITY ± (π/2)i
+ * log(INFINITY + i) = INFINITY + 0i
+ * log(-INFINITY + i) = INFINITY + πi
+ * log(INFINITY ± INFINITY i) = INFINITY ±
(π/4)i
+ * log(-INFINITY ± INFINITY i) = INFINITY ±
(3π/4)i
+ * log(0 + 0i) = -INFINITY + 0i
+ * </code>
+ * </pre>
+ *
+ * @return the value <code>ln this</code>, the natural
logarithm
+ * of {@code this}.
+ */
+ public Complex log() {
+ if (isNaN) {
+ return NaN;
+ }
+ return createComplex(Math.log(abs()),
+ Math.atan2(imaginary, real));
+ }
+
+ /**
+ * Returns of value of this complex number raised to the power
of {@code x}.
+ * Implements the formula:
+ * <pre>
+ * <code>
+ * y<sup>x</sup> = exp(x·log(y))
+ * </code>
+ * </pre>
+ * where {@code exp} and {@code log} are {@link #exp} and
+ * {@link #log}, respectively.
+ * <p>
+ * Returns {@link Complex#NaN} if either real or imaginary part
of the
+ * input argument is {@code NaN} or infinite, or if {@code y}
+ * equals {@link Complex#ZERO}.</p>
+ *
+ * @param x exponent to which this {@code Complex} is to be
raised.
+ * @return <code> this<sup>x</sup></code>.
+ */
+ public Complex pow(Complex x) {
+ checkNotNull(x);
+ if (real == 0 && imaginary == 0) {
+ if (x.real > 0 && x.imaginary == 0) {
+ // 0 raised to positive number is 0
+ return ZERO;
+ } else {
+ // 0 raised to anything else is NaN
+ return NaN;
+ }
+ }
+ return this.log().multiply(x).exp();
+ }
+
+ /**
+ * Returns of value of this complex number raised to the power
of {@code x}.
+ *
+ * @param x exponent to which this {@code Complex} is to be
raised.
+ * @return <code>this<sup>x</sup></code>.
+ * @see #pow(Complex)
+ */
+ public Complex pow(double x) {
+ if (real == 0 && imaginary == 0) {
+ if (x > 0) {
+ // 0 raised to positive number is 0
+ return ZERO;
+ } else {
+ // 0 raised to anything else is NaN
+ return NaN;
+ }
+ }
+ return this.log().multiply(x).exp();
+ }
+
+ /**
+ * Compute the
+ * <a href="http://mathworld.wolfram.com/Sine.html";
TARGET="_top">
+ * sine</a>
+ * of this complex number.
+ * Implements the formula:
+ * <pre>
+ * <code>
+ * sin(a + bi) = sin(a)cosh(b) - cos(a)sinh(b)i
+ * </code>
+ * </pre>
+ * where the (real) functions on the right-hand side are
+ * {@link Math#sin}, {@link Math#cos},
+ * {@link Math#cosh} and {@link Math#sinh}.
+ * <p>
+ * Returns {@link Complex#NaN} if either real or imaginary part
of the
+ * input argument is {@code NaN}.
+ * </p><p>
+ * Infinite values in real or imaginary parts of the input may
result in
+ * infinite or {@code NaN} values returned in parts of the
result.
+ * <pre>
+ * Examples:
+ * <code>
+ * sin(1 ± INFINITY i) = 1 ± INFINITY i
+ * sin(±INFINITY + i) = NaN + NaN i
+ * sin(±INFINITY ± INFINITY i) = NaN + NaN i
+ * </code>
+ * </pre>
+ *
+ * @return the sine of this complex number.
+ */
+ public Complex sin() {
+ if (isNaN) {
+ return NaN;
+ }
+
+ return createComplex(Math.sin(real) * Math.cosh(imaginary),
+ Math.cos(real) * Math.sinh(imaginary));
+ }
+
+ /**
+ * Compute the
+ * <a href="http://mathworld.wolfram.com/HyperbolicSine.html";
TARGET="_top">
+ * hyperbolic sine</a> of this complex number.
+ * Implements the formula:
+ * <pre>
+ * <code>
+ * sinh(a + bi) = sinh(a)cos(b)) + cosh(a)sin(b)i
+ * </code>
+ * </pre>
+ * where the (real) functions on the right-hand side are
+ * {@link Math#sin}, {@link Math#cos},
+ * {@link Math#cosh} and {@link Math#sinh}.
+ * <p>
+ * Returns {@link Complex#NaN} if either real or imaginary part
of the
+ * input argument is {@code NaN}.
+ * </p><p>
+ * Infinite values in real or imaginary parts of the input may
result in
+ * infinite or NaN values returned in parts of the result.
+ * <pre>
+ * Examples:
+ * <code>
+ * sinh(1 ± INFINITY i) = NaN + NaN i
+ * sinh(±INFINITY + i) = ± INFINITY + INFINITY i
+ * sinh(±INFINITY ± INFINITY i) = NaN + NaN i
+ * </code>
+ * </pre>
+ *
+ * @return the hyperbolic sine of {@code this}.
+ */
+ public Complex sinh() {
+ if (isNaN) {
+ return NaN;
+ }
+
+ return createComplex(Math.sinh(real) * Math.cos(imaginary),
+ Math.cosh(real) * Math.sin(imaginary));
+ }
+
+ /**
+ * Compute the
+ * <a href="http://mathworld.wolfram.com/SquareRoot.html";
TARGET="_top">
+ * square root</a> of this complex number.
+ * Implements the following algorithm to compute {@code sqrt(a +
bi)}:
+ * <ol><li>Let {@code t = sqrt((|a| + |a + bi|) / 2)}</li>
+ * <li><pre>if {@code a ≥ 0} return {@code t + (b/2t)i}
+ * else return {@code |b|/2t + sign(b)t i }</pre></li>
+ * </ol>
+ * where <ul>
+ * <li>{@code |a| = }{@link Math#abs}(a)</li>
+ * <li>{@code |a + bi| = }{@link Complex#abs}(a + bi)</li>
+ * <li>{@code sign(b) = }{@link Math#copySign(double,double)
copySign(1d, b)}
+ * </ul>
+ * <p>
+ * Returns {@link Complex#NaN} if either real or imaginary part
of the
+ * input argument is {@code NaN}.
+ * </p>
+ * Infinite values in real or imaginary parts of the input may
result in
+ * infinite or NaN values returned in parts of the result.
+ * <pre>
+ * Examples:
+ * <code>
+ * sqrt(1 ± INFINITY i) = INFINITY + NaN i
+ * sqrt(INFINITY + i) = INFINITY + 0i
+ * sqrt(-INFINITY + i) = 0 + INFINITY i
+ * sqrt(INFINITY ± INFINITY i) = INFINITY + NaN i
+ * sqrt(-INFINITY ± INFINITY i) = NaN ± INFINITY
i
+ * </code>
+ * </pre>
+ *
+ * @return the square root of {@code this}.
+ */
+ public Complex sqrt() {
+ if (isNaN) {
+ return NaN;
+ }
+
+ if (real == 0.0 && imaginary == 0.0) {
+ return createComplex(0.0, 0.0);
+ }
+
+ double t = Math.sqrt((Math.abs(real) + abs()) / 2.0);
+ if (real >= 0.0) {
+ return createComplex(t, imaginary / (2.0 * t));
+ } else {
+ return createComplex(Math.abs(imaginary) / (2.0 * t),
+ Math.copySign(1d, imaginary) * t);
+ }
+ }
+
+ /**
+ * Compute the
+ * <a href="http://mathworld.wolfram.com/SquareRoot.html";
TARGET="_top">
+ * square root</a> of <code>1 - this<sup>2</sup></code> for this
complex
+ * number.
+ * Computes the result directly as
+ * {@code sqrt(ONE.subtract(z.multiply(z)))}.
+ * <p>
+ * Returns {@link Complex#NaN} if either real or imaginary part
of the
+ * input argument is {@code NaN}.
+ * </p>
+ * Infinite values in real or imaginary parts of the input may
result in
+ * infinite or NaN values returned in parts of the result.
+ *
+ * @return the square root of <code>1 - this<sup>2</sup></code>.
+ */
+ public Complex sqrt1z() {
+ return createComplex(1.0,
0.0).subtract(this.multiply(this)).sqrt();
+ }
+
+ /**
+ * Compute the
+ * <a href="http://mathworld.wolfram.com/Tangent.html";
TARGET="_top">
+ * tangent</a> of this complex number.
+ * Implements the formula:
+ * <pre>
+ * <code>
+ * tan(a + bi) = sin(2a)/(cos(2a)+cosh(2b)) +
[sinh(2b)/(cos(2a)+cosh(2b))]i
+ * </code>
+ * </pre>
+ * where the (real) functions on the right-hand side are
+ * {@link Math#sin}, {@link Math#cos}, {@link Math#cosh} and
+ * {@link Math#sinh}.
+ * <p>
+ * Returns {@link Complex#NaN} if either real or imaginary part
of the
+ * input argument is {@code NaN}.
+ * </p>
+ * Infinite (or critical) values in real or imaginary parts of
the input may
+ * result in infinite or NaN values returned in parts of the
result.
+ * <pre>
+ * Examples:
+ * <code>
+ * tan(a ± INFINITY i) = 0 ± i
+ * tan(±INFINITY + bi) = NaN + NaN i
+ * tan(±INFINITY ± INFINITY i) = NaN + NaN i
+ * tan(±π/2 + 0 i) = ±INFINITY + NaN i
+ * </code>
+ * </pre>
+ *
+ * @return the tangent of {@code this}.
+ */
+ public Complex tan() {
+ if (isNaN || Double.isInfinite(real)) {
+ return NaN;
+ }
+ if (imaginary > 20.0) {
+ return createComplex(0.0, 1.0);
+ }
+ if (imaginary < -20.0) {
+ return createComplex(0.0, -1.0);
+ }
+
+ double real2 = 2.0 * real;
+ double imaginary2 = 2.0 * imaginary;
+ double d = Math.cos(real2) + Math.cosh(imaginary2);
+
+ return createComplex(Math.sin(real2) / d,
+ Math.sinh(imaginary2) / d);
+ }
+
+ /**
+ * Compute the
+ * <a href="http://mathworld.wolfram.com/HyperbolicTangent.html";
TARGET="_top">
+ * hyperbolic tangent</a> of this complex number.
+ * Implements the formula:
+ * <pre>
+ * <code>
+ * tan(a + bi) = sinh(2a)/(cosh(2a)+cos(2b)) +
[sin(2b)/(cosh(2a)+cos(2b))]i
+ * </code>
+ * </pre>
+ * where the (real) functions on the right-hand side are
+ * {@link Math#sin}, {@link Math#cos}, {@link Math#cosh} and
+ * {@link Math#sinh}.
+ * <p>
+ * Returns {@link Complex#NaN} if either real or imaginary part
of the
+ * input argument is {@code NaN}.
+ * </p>
+ * Infinite values in real or imaginary parts of the input may
result in
+ * infinite or NaN values returned in parts of the result.
+ * <pre>
+ * Examples:
+ * <code>
+ * tanh(a ± INFINITY i) = NaN + NaN i
+ * tanh(±INFINITY + bi) = ±1 + 0 i
+ * tanh(±INFINITY ± INFINITY i) = NaN + NaN i
+ * tanh(0 + (π/2)i) = NaN + INFINITY i
+ * </code>
+ * </pre>
+ *
+ * @return the hyperbolic tangent of {@code this}.
+ */
+ public Complex tanh() {
+ if (isNaN || Double.isInfinite(imaginary)) {
+ return NaN;
+ }
+ if (real > 20.0) {
+ return createComplex(1.0, 0.0);
+ }
+ if (real < -20.0) {
+ return createComplex(-1.0, 0.0);
+ }
+ double real2 = 2.0 * real;
+ double imaginary2 = 2.0 * imaginary;
+ double d = Math.cosh(real2) + Math.cos(imaginary2);
+
+ return createComplex(Math.sinh(real2) / d,
+ Math.sin(imaginary2) / d);
+ }
+
+
+
+ /**
+ * Compute the argument of this complex number.
+ * The argument is the angle phi between the positive real axis
and
+ * the point representing this number in the complex plane.
+ * The value returned is between -PI (not inclusive)
+ * and PI (inclusive), with negative values returned for numbers
with
+ * negative imaginary parts.
+ * <p>
+ * If either real or imaginary part (or both) is NaN, NaN is
returned.
+ * Infinite parts are handled as {@code Math.atan2} handles
them,
+ * essentially treating finite parts as zero in the presence of
an
+ * infinite coordinate and returning a multiple of pi/4
depending on
+ * the signs of the infinite parts.
+ * See the javadoc for {@code Math.atan2} for full details.
+ *
+ * @return the argument of {@code this}.
+ */
+ public double getArgument() {
+ return Math.atan2(getImaginary(), getReal());
+ }
+
+ /**
+ * Computes the n-th roots of this complex number.
+ * The nth roots are defined by the formula:
+ * <pre>
+ * <code>
+ * z<sub>k</sub> = abs<sup>1/n</sup> (cos(phi + 2πk/n) + i
(sin(phi + 2πk/n))
+ * </code>
+ * </pre>
+ * for <i>{@code k=0, 1, ..., n-1}</i>, where {@code abs} and
{@code phi}
+ * are respectively the {@link #abs() modulus} and
+ * {@link #getArgument() argument} of this complex number.
+ * <p>
+ * If one or both parts of this complex number is NaN, a list
with just
+ * one element, {@link #NaN} is returned.
+ * if neither part is NaN, but at least one part is infinite,
the result
+ * is a one-element list containing {@link #INF}.
+ *
+ * @param n Degree of root.
+ * @return a List of all {@code n}-th roots of {@code this}.
+ */
+ public List<Complex> nthRoot(int n) {
+
+ if (n <= 0) {
+ throw new RuntimeException("cannot compute nth root for
null or negative n: {0}");
+ }
+
+ final List<Complex> result = new ArrayList<Complex>();
+
+ if (isNaN) {
+ result.add(NaN);
+ return result;
+ }
+ if (isInfinite()) {
+ result.add(INF);
+ return result;
+ }
+
+ // nth root of abs -- faster / more accurate to use a solver
here?
+ final double nthRootOfAbs = Math.pow(abs(), 1.0 / n);
+
+ // Compute nth roots of complex number with k = 0, 1, ...
n-1
+ final double nthPhi = getArgument() / n;
+ final double slice = 2 * Math.PI / n;
+ double innerPart = nthPhi;
+ for (int k = 0; k < n ; k++) {
+ // inner part
+ final double realPart = nthRootOfAbs *
Math.cos(innerPart);
+ final double imaginaryPart = nthRootOfAbs *
Math.sin(innerPart);
+ result.add(createComplex(realPart, imaginaryPart));
+ innerPart += slice;
+ }
+
+ return result;
+ }
+
+ /**
+ * Create a complex number given the real and imaginary parts.
+ *
+ * @param realPart Real part.
+ * @param imaginaryPart Imaginary part.
+ * @return a new complex number instance.
+ * @see #valueOf(double, double)
+ */
+ protected Complex createComplex(double realPart,
+ double imaginaryPart) {
+ return new Complex(realPart, imaginaryPart);
+ }
+
+ /**
+ * Create a complex number given the real and imaginary parts.
+ *
+ * @param realPart Real part.
+ * @param imaginaryPart Imaginary part.
+ * @return a Complex instance.
+ */
+ public static Complex valueOf(double realPart,
+ double imaginaryPart) {
+ if (Double.isNaN(realPart) ||
+ Double.isNaN(imaginaryPart)) {
+ return NaN;
+ }
+ return new Complex(realPart, imaginaryPart);
+ }
+
+ /**
+ * Create a complex number given only the real part.
+ *
+ * @param realPart Real part.
+ * @return a Complex instance.
+ */
+ public static Complex valueOf(double realPart) {
+ if (Double.isNaN(realPart)) {
+ return NaN;
+ }
+ return new Complex(realPart);
+ }
+
+ /**
+ * Resolve the transient fields in a deserialized Complex
Object.
+ * Subclasses will need to override {@link #createComplex} to
+ * deserialize properly.
+ *
+ * @return A Complex instance with all fields resolved.
+ */
+ protected final Object readResolve() {
+ return createComplex(real, imaginary);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public String toString() {
+ return "(" + real + ", " + imaginary + ")";
+ }
+
+ /**
+ * Checks that an object is not null.
+ *
+ * @param o Object to be checked.
+ */
+ private static void checkNotNull(Object o) {
+ if (o == null) {
+ throw new RuntimeException("Null Argument to Complex
Method");
+ }
+ }
+
+ /**
+ * Returns {@code true} if the values are equal according to
semantics of
+ * {@link Double#equals(Object)}.
+ *
+ * @param x Value
+ * @param y Value
+ * @return {@code new Double(x).equals(new Double(y))}
+ */
+ private static boolean equals(double x, double y) {
+ return new Double(x).equals(new Double(y));
+ }
+
+ /**
+ * Returns an integer hash code representing the given double
value.
+ *
+ * @param value the value to be hashed
+ * @return the hash code
+ */
+ private static int hash(double value) {
+ return new Double(value).hashCode();
+ }
+}
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/15136c2d/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/.CStandardTest.java.swo
----------------------------------------------------------------------
diff --git
a/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/.CStandardTest.java.swo
b/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/.CStandardTest.java.swo
new file mode 100644
index 0000000..430efd7
Binary files /dev/null and
b/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/.CStandardTest.java.swo
differ
http://git-wip-us.apache.org/repos/asf/commons-numbers/blob/15136c2d/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
new file mode 100644
index 0000000..88183de
--- /dev/null
+++
b/commons-numbers-complex/src/test/java/org/apache/commons/numbers/complex/CStandardTest.java
@@ -0,0 +1,265 @@
+/*
+ * 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 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);
+ 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 zeroPiTwo = new Complex(0.0, piOverTwo);
+ private Complex piTwoNaN = new Complex(piOverTwo, nan);
+ private Complex piNegInf = new Complex(Math.PI, negInf);
+ private Complex piTwoNegInf = new Complex(piOverTwo, negInf);
+ private Complex negInfPosInf = new Complex(negInf, inf);
+ private Complex piTwoNegZero = new Complex(piOverTwo, -0.0);
+ private Complex threePiFourNegInf = new
Complex(threePiOverFour,negInf);
+ private Complex piFourNegInf = new Complex(piOverFour, negInf);
+ private Complex infPiTwo = new Complex(inf, piOverTwo);
+ private Complex infPiFour = new Complex(inf, piOverFour);
+ private Complex negInfPi = new Complex(negInf, Math.PI);
+ /**
+ * ISO C Standard G.6.3
+ */
+ @Test
+ public void testSqrt() {
+ Complex z1 = new Complex(-2.0, 0.0);
+ Complex z2 = new Complex(0.0, Math.sqrt(2));
+ Assert.assertEquals(z1.sqrt(), z2);
+ z1 = new Complex(-2.0, -0.0);
+ z2 = new Complex(0.0, -Math.sqrt(2));
+ Assert.assertEquals(z1.sqrt(), z2);
+ }
+
+ @Test
+ public void testImplicitTrig() {
+ Complex z1 = new Complex(3.0);
+ Complex z2 = new Complex(0.0, 3.0);
+ Assert.assertEquals(z1.asin(), negI.multiply(z2.asinh()));
+ Assert.assertEquals(z1.atan(), negI.multiply(z2.atanh()));
+ Assert.assertEquals(z1.cos(), z2.cosh());
+ Assert.assertEquals(z1.sin(), negI.multiply(z2.sinh()));
+ Assert.assertEquals(z1.tan(), negI.multiply(z1.tanh()));
+ }
+
+ /**
+ * ISO C Standard G.6.1.1
+ */
+ @Test
+ public void testAcos() {
+ Assert.assertEquals(oneOne.acos().conj(),
oneOne.conj().acos());
+ Assert.assertEquals(Complex.ZERO.acos(), piTwoNegZero);
+ Assert.assertEquals(negZeroZero.acos(), piTwoNegZero);
+ Assert.assertEquals(zeroNaN.acos(), piTwoNaN);
+ Assert.assertEquals(oneInf.acos(), piTwoNegInf);
+ Assert.assertEquals(oneNaN.acos(), Complex.NaN);
+ Assert.assertEquals(negInfOne.acos(), piNegInf);
+ Assert.assertEquals(infOne.acos(), zeroInf);
+ Assert.assertEquals(negInfPosInf.acos(), threePiFourNegInf);
+ Assert.assertEquals(infInf.acos(), piFourNegInf);
+ Assert.assertEquals(infNaN.acos(), naNInf);
+ Assert.assertEquals(negInfNan.acos(), nanNegInf);
+ Assert.assertEquals(nanOne.acos(), Complex.NaN);
+ Assert.assertEquals(nanInf.acos(), nanNegInf);
+ Assert.assertEquals(Complex.NaN.acos(), Complex.NaN);
+ }
+
+ /**
+ * ISO C Standard G.6.2.2
+ */
+ @Test
+ public void testAsinh() {
+ // TODO: test for which Asinh is odd
+ Assert.assertEquals(oneOne.conj().asinh(),
oneOne.asinh().conj());
+ Assert.assertEquals(Complex.ZERO.asinh(), Complex.ZERO);
+ Assert.assertEquals(oneInf.asinh(), infPiTwo);
+ Assert.assertEquals(oneNaN.asinh(), Complex.NaN);
+ Assert.assertEquals(infOne.asinh(), infZero);
+ Assert.assertEquals(infInf.asinh(), infPiFour);
+ Assert.assertEquals(infNaN.asinh(), z1);
+ Assert.assertEquals(nanZero.asinh(), nanZero);
+ Assert.assertEquals(nanOne.asinh(), Complex.NaN);
+ Assert.assertEquals(nanInf.asinh(), infNan);
+ Assert.assertEquals(Complex.NaN, Complex.NaN);
+ }
+
+ /**
+ * ISO C Standard G.6.2.3
+ */
+ @Test
+ public void testAtanh() {
+ Assert.assertEquals(oneOne.conj().atanh(),
oneOne.atanh().conj());
+ Assert.assertEquals(Complex.ZERO.atanh(), Complex.ZERO);
+ Assert.assertEquals(zeroNaN.atanh(), zeroNaN);
+ Assert.assertEquals(oneZero.atanh(), infZero);
+ Assert.assertEquals(oneInf.atanh(),zeroPiTwo);
+ Assert.assertEquals(oneNaN.atanh(), Complex.NaN);
+ Assert.assertEquals(infOne.atanh(), zeroPiTwo);
+ Assert.assertEquals(infInf.atanh(), zeroPiTwo);
+ Assert.assertEquals(infNaN.atanh(), zeroNaN);
+ Assert.assertEquals(nanOne.atanh(), Complex.NaN);
+ Assert.assertEquals(nanInf.atanh(), zeroPiTwo);
+ Assert.assertEquals(Complex.NaN.atanh(), Complex.NaN);
+ }
+
+ /**
+ * ISO C Standard G.6.2.4
+ */
+ @Test
+ public void testCosh() {
+ Assert.assertEquals(oneOne.cosh().conj(),
oneOne.conj().cosh());
+ Assert.assertEquals(Complex.ZERO.cosh(), Complex.ONE);
+ Assert.assertEquals(zeroInf.cosh(), nanZero);
+ Assert.assertEquals(zeroNan.cosh(), nanZero);
+ Assert.assertEquals(oneInf.cosh(), Complex.NaN);
+ Assert.assertEquals(oneNan.cosh(), Complex.NaN);
+ Assert.assertEquals(infZero.cosh(), infZero);
+ // the next test does not appear to make sense:
+ // (inf + iy) = inf + cis(y)
+ // skipped
+ Assert.assertEquals(infInf.cosh(), infNaN);
+ Assert.assertEquals(infNaN.cosh(), infNaN);
+ Assert.assertEquals(nanZero.cosh(), nanZero);
+ Assert.assertEquals(nanOne.cosh(), Complex.NaN);
+ Assert.assertEquals(Complex.NaN.cosh(), Complex.NaN);
+ }
+
+ /**
+ * ISO C Standard G.6.2.5
+ */
+ @Test
+ public void testSinh() {
+ Assert.assertEquals(oneOne.sinh().conj(),
oneOne.conj().sinh()); // AND CSINH IS ODD
+ Assert.assertEquals(Complex.ZERO.sinh(), Complex.ZERO);
+ Assert.assertEquals(zeroInf.sinh(), zeroNaN);
+ Assert.assertEquals(zeroNaN.sinh(), zeroNaN);
+ Assert.assertEquals(oneInf.sinh(), Complex.NaN);
+ Assert.assertEquals(oneNaN.sinh(), Complex.NaN);
+ Assert.assertEquals(infZero.sinh(), infZero);
+ // skipped test similar to previous section
+ Assert.assertEquals(infInf.sinh(), infNaN);
+ Assert.assertEquals(infNaN.sinh(), infNaN);
+ Assert.assertEquals(nanZero.sinh(), nanZero);
+ Assert.assertEquals(nanOne.sinh(), Complex.NaN);
+ Assert.assertEquals(Complex.NaN.sinh(), Complex.NaN);
+ }
+
+ /**
+ * ISO C Standard G.6.2.6
+ */
+ @Test
+ public void testTanh() {
+ Assert.assertEquals(oneOne.tanh().conj(),
oneOne.conj().tanh()); // AND CSINH IS ODD
+ Assert.assertEquals(Complex.ZERO.tanh(), Complex.ZERO);
+ Assert.assertEquals(oneInf.tanh(), Complex.NaN);
+ Assert.assertEquals(oneNaN.tanh(), Complex.NaN);
+ //Do Not Understand the Next Test
+ Assert.assertEquals(infInf.tanh(), oneZero);
+ Assert.assertEquals(infNaN.tanh(), oneZero);
+ Assert.assertEquals(nanZero.tanh(), nanZero);
+ Assert.assertEquals(nanOne.tanh(), Complex.NaN);
+ Assert.assertEquals(Complex.NaN.tanh(), Complex.NaN);
+ }
+
+ /**
+ * ISO C Standard G.6.3.1
+ */
+ @Test
+ public void testExp() {
+ Assert.assertEquals(oneOne.conj().exp(),
oneOne.exp().conj());
+ Assert.assertEquals(Complex.ZERO.exp(), oneZero);
+ Assert.assertEquals(negZero.exp(), oneZero);
+ Assert.assertEquals(oneInf.exp(), Complex.NaN);
+ Assert.assertEquals(oneNaN.exp(), Complex.NaN);
+ Assert.assertEquals(infZero.exp(), infZero);
+ // Do not understand next test
+ Assert.assertEquals(negInfInf.exp(), Complex.ZERO);
+ Assert.assertEquals(infInf.exp(), infNaN);
+ Assert.assertEquals(negInfNaN.exp(), Complex.ZERO);
+ Assert.assertEquals(infNaN.exp(), infNaN);
+ Assert.assertEquals(nanZero.exp(), nanZero);
+ Assert.assertEquals(nanOne.exp(), Complex.NaN);
+ Assert.assertEquals(Complex.NaN.exp(), Complex.NaN);
+ }
+
+ /**
+ * ISO C Standard G.6.3.2
+ */
+ @Test
+ public void testLog() {
+ Assert.assertEquals(oneOne.log().conj(),
oneOne.conj().log());
+ Assert.assertEquals(negZeroZero.log(), negInfPi);
+ Assert.assertEquals(Complex.ZERO.log(), negInfZero);
+ Assert.assertEquals(oneInf.log(), infPiTwo);
+ Assert.assertEquals(oneNaN.log(), Complex.NaN);
+ Assert.assertEquals(negInfOne.log(), infPi);
+ Assert.assertEquals(infOne.log(), infZero);
+ Assert.assertEquals(infInf.log(), infPiFour);
+ Assert.assertEquals(infNaN.log(), infNaN);
+ Assert.assertEquals(nanOne.log(), Complex.NaN);
+ Assert.assertEquals(nanInf.log(), infNaN);
+ Assert.assertEquals(Complex.NaN.log(), Complex.NaN);
+ }
+
+ /**
+ * ISO C Standard G.6.4.2
+ */
+ @Test
+ public void testSqrt() {
+ Assert.assertEquals(oneOne.sqrt().conj(), oneOne.conj(),
sqrt());
+ Assert.assertEquals(Complex.ZERO.sqrt(), Complex.ZERO);
+ Assert.assertEquals(oneInf.sqrt(), infInf);
+ Assert.assertEquals(negInfOne.sqrt(), zeroNaN);
+ Assert.assertEquals(infOne.sqrt(), infZero);
+ Assert.assertEquals(negInfNaN.sqrt(), nanInf);
+ Assert.assertEquals(infNaN.sqrt(), infNaN);
+ Assert.assertEquals(nanOne.sqrt(), Complex.NaN);
+ Assert.assertEquals(Complex.NaN.sqrt(), Complex.NaN);
+ }
+}
