commons-numbers-examples/examples-jmh/src/main/java/org/apache/commons/numbers/examples/jmh/complex/ComplexPerformance.java - commons-numbers - Git at Google

 /*
  * 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.examples.jmh.complex;

 import org.apache.commons.numbers.complex.Complex;
 import org.openjdk.jmh.annotations.Benchmark;
 import org.openjdk.jmh.annotations.BenchmarkMode;
 import org.openjdk.jmh.annotations.Fork;
 import org.openjdk.jmh.annotations.Measurement;
 import org.openjdk.jmh.annotations.Mode;
 import org.openjdk.jmh.annotations.OutputTimeUnit;
 import org.openjdk.jmh.annotations.Param;
 import org.openjdk.jmh.annotations.Scope;
 import org.openjdk.jmh.annotations.Setup;
 import org.openjdk.jmh.annotations.State;
 import org.openjdk.jmh.annotations.Warmup;

 import java.util.Arrays;
 import java.util.SplittableRandom;
 import java.util.concurrent.TimeUnit;
 import java.util.function.BiFunction;
 import java.util.function.Predicate;
 import java.util.function.Supplier;
 import java.util.function.ToDoubleFunction;
 import java.util.function.UnaryOperator;
 import java.util.stream.Stream;

 /**
  * Executes a benchmark to measure the speed of operations in the {@link Complex} class.
  */
 @BenchmarkMode(Mode.AverageTime)
 @OutputTimeUnit(TimeUnit.NANOSECONDS)
 @Warmup(iterations = 5, time = 1, timeUnit = TimeUnit.SECONDS)
 @Measurement(iterations = 5, time = 1, timeUnit = TimeUnit.SECONDS)
 @State(Scope.Benchmark)
 @Fork(value = 1, jvmArgs = {"-server", "-Xms512M", "-Xmx512M"})
 public class ComplexPerformance {
     /**
      * An array of edge numbers that will produce edge case results from functions:
      * {@code +/-inf, +/-max, +/-min, +/-0, nan}.
      */
     private static final double[] EDGE_NUMBERS = {
         Double.POSITIVE_INFINITY, Double.NEGATIVE_INFINITY, Double.MAX_VALUE,
         -Double.MAX_VALUE, Double.MIN_VALUE, -Double.MIN_VALUE, 0.0, -0.0, Double.NaN};

     /**
      * Contains the size of numbers.
      */
     @State(Scope.Benchmark)
     public static class ComplexNumberSize {
         /**
          * The size of the data.
          */
         @Param({"1000"})
         private int size;

         /**
          * Gets the size.
          *
          * @return the size
          */
         public int getSize() {
             return size;
         }
     }

     /**
      * Contains an array of complex numbers.
      */
     @State(Scope.Benchmark)
     public static class ComplexNumbers extends ComplexNumberSize {
         /** The numbers. */
         protected Complex[] numbers;

         /**
          * The type of the data.
          */
         @Param({"cis", "random", "edge"})
         private String type;

         /**
          * Gets the numbers.
          *
          * @return the numbers
          */
         public Complex[] getNumbers() {
             return numbers;
         }

         /**
          * Create the complex numbers.
          */
         @Setup
         public void setup() {
             numbers = createNumbers(new SplittableRandom());
         }

         /**
          * Creates the numbers.
          *
          * @param rng Random number generator.
          * @return the random complex number
          */
         Complex[] createNumbers(SplittableRandom rng) {
             Supplier<Complex> generator;
             if ("cis".equals(type)) {
                 generator = () -> Complex.ofCis(rng.nextDouble() * 2 * Math.PI);
             } else if ("random".equals(type)) {
                 generator = () -> Complex.ofCartesian(createRandomNumber(rng), createRandomNumber(rng));
             } else if ("edge".equals(type)) {
                 generator = () -> Complex.ofCartesian(createEdgeNumber(rng), createEdgeNumber(rng));
             } else {
                 throw new IllegalStateException("Unknown number type: " + type);
             }
             return Stream.generate(generator).limit(getSize()).toArray(Complex[]::new);
         }
     }

     /**
      * Contains two arrays of complex numbers.
      */
     @State(Scope.Benchmark)
     public static class TwoComplexNumbers extends ComplexNumbers {
         /** The numbers. */
         private Complex[] numbers2;

         /**
          * Gets the second set of numbers.
          *
          * @return the numbers
          */
         public Complex[] getNumbers2() {
             return numbers2;
         }

         /**
          * Create the complex numbers.
          */
         @Override
         @Setup
         public void setup() {
             // Do not call super.setup() so we recycle the RNG and avoid duplicates
             final SplittableRandom rng = new SplittableRandom();
             numbers = createNumbers(rng);
             numbers2 = createNumbers(rng);
         }
     }

     /**
      * Contains an array of complex numbers and an array of real numbers.
      */
     @State(Scope.Benchmark)
     public static class ComplexAndRealNumbers extends ComplexNumbers {
         /** The numbers. */
         private double[] numbers2;

         /**
          * Gets the second set of numbers.
          *
          * @return the numbers
          */
         public double[] getNumbers2() {
             return numbers2;
         }

         /**
          * Create the complex numbers.
          */
         @Override
         @Setup
         public void setup() {
             // Do not call super.setup() so we recycle the RNG and avoid duplicates
             final SplittableRandom rng = new SplittableRandom();
             numbers = createNumbers(rng);
             numbers2 = Arrays.stream(createNumbers(rng)).mapToDouble(Complex::real).toArray();
         }
     }

     /**
      * Define a function between a complex and real number.
      */
     private interface ComplexRealFunction {
         /**
          * Applies this function to the given arguments.
          *
          * @param z the complex argument
          * @param x the real argument
          * @return the function result
          */
         Complex apply(Complex z, double x);
     }

     /**
      * Creates a random double number with a random sign and mantissa and a large range for
      * the exponent. The numbers will not be uniform over the range.
      *
      * @param rng Random number generator.
      * @return the random number
      */
     private static double createRandomNumber(SplittableRandom rng) {
         // Create random doubles using random bits in the sign bit and the mantissa.
         // Then create an exponent in the range -64 to 64. Thus the sum product
         // of 4 max or min values will not over or underflow.
         final long mask = ((1L << 52) - 1) | 1L << 63;
         final long bits = rng.nextLong() & mask;
         // The exponent must be unsigned so + 1023 to the signed exponent
         final long exp = rng.nextInt(129) - 64 + 1023;
         return Double.longBitsToDouble(bits | (exp << 52));
     }

     /**
      * Creates a random double number that will be an edge case:
      * {@code +/-inf, +/-max, +/-min, +/-0, nan}.
      *
      * @param rng Random number generator.
      * @return the random number
      */
     private static double createEdgeNumber(SplittableRandom rng) {
         return EDGE_NUMBERS[rng.nextInt(EDGE_NUMBERS.length)];
     }

     /**
      * Apply the function to all the numbers.
      *
      * @param numbers Numbers.
      * @param fun Function.
      * @return the result of the function.
      */
     private static boolean[] apply(Complex[] numbers, Predicate<Complex> fun) {
         final boolean[] result = new boolean[numbers.length];
         for (int i = 0; i < numbers.length; i++) {
             result[i] = fun.test(numbers[i]);
         }
         return result;
     }

     /**
      * Apply the function to all the numbers.
      *
      * @param numbers Numbers.
      * @param fun Function.
      * @return the result of the function.
      */
     private static double[] apply(Complex[] numbers, ToDoubleFunction<Complex> fun) {
         final double[] result = new double[numbers.length];
         for (int i = 0; i < numbers.length; i++) {
             result[i] = fun.applyAsDouble(numbers[i]);
         }
         return result;
     }

     /**
      * Apply the function to all the numbers.
      *
      * @param numbers Numbers.
      * @param fun Function.
      * @return the result of the function.
      */
     private static Complex[] apply(Complex[] numbers, UnaryOperator<Complex> fun) {
         final Complex[] result = new Complex[numbers.length];
         for (int i = 0; i < numbers.length; i++) {
             result[i] = fun.apply(numbers[i]);
         }
         return result;
     }

     /**
      * Apply the function to the paired numbers.
      *
      * @param numbers First numbers of the pairs.
      * @param numbers2 Second numbers of the pairs.
      * @param fun Function.
      * @return the result of the function.
      */
     private static Complex[] apply(Complex[] numbers, Complex[] numbers2,
             BiFunction<Complex, Complex, Complex> fun) {
         final Complex[] result = new Complex[numbers.length];
         for (int i = 0; i < numbers.length; i++) {
             result[i] = fun.apply(numbers[i], numbers2[i]);
         }
         return result;
     }

     /**
      * Apply the function to the paired numbers.
      *
      * @param numbers First numbers of the pairs.
      * @param numbers2 Second numbers of the pairs.
      * @param fun Function.
      * @return the result of the function.
      */
     private static Complex[] apply(Complex[] numbers, double[] numbers2,
             ComplexRealFunction fun) {
         final Complex[] result = new Complex[numbers.length];
         for (int i = 0; i < numbers.length; i++) {
             result[i] = fun.apply(numbers[i], numbers2[i]);
         }
         return result;
     }

     /**
      * Identity function. This can be used to measure overhead of object array creation.
      *
      * @param z Complex number.
      * @return the complex number
      */
     private static Complex identity(Complex z) {
         return z;
     }

     /**
      * Copy function. This can be used to measure overhead of object array creation plus
      * new Complex creation.
      *
      * @param z Complex number.
      * @return a copy of the complex number
      */
     private static Complex copy(Complex z) {
         return Complex.ofCartesian(z.real(), z.imag());
     }

     // Benchmark methods.
     //
     // The methods are partially documented as the names are self-documenting.
     // CHECKSTYLE: stop JavadocMethod
     // CHECKSTYLE: stop DesignForExtension
     //
     // Benchmarks use function references to perform different operations on the complex numbers.
     // Tests show that explicit programming of the same benchmarks run in the same time.
     // For reference examples are provided for the fastest operations: real() and conj().

     /**
      * Explicit benchmark without using a method reference.
      * This should run in the same time as {@link #real(ComplexNumbers)}.
      * This is commented out as it exists for reference purposes.
      */
     //@Benchmark
     public double[] real2(ComplexNumbers numbers) {
         final Complex[] z = numbers.getNumbers();
         final double[] result = new double[z.length];
         for (int i = 0; i < z.length; i++) {
             result[i] = z[i].real();
         }
         return result;
     }

     /**
      * Explicit benchmark without using a method reference.
      * This should run in the same time as {@link #conj(ComplexNumbers)}.
      * This is commented out as it exists for reference purposes.
      */
     //@Benchmark
     public Complex[] conj2(ComplexNumbers numbers) {
         final Complex[] z = numbers.getNumbers();
         final Complex[] result = new Complex[z.length];
         for (int i = 0; i < z.length; i++) {
             result[i] = z[i].conj();
         }
         return result;
     }

     /**
      * Baseline the creation of the new array of numbers.
      * This contains the baseline JMH overhead for all the benchmarks that create complex numbers.
      * All other methods are expected to be slower than this.
      */
     @Benchmark
     public Complex[] baselineNewArray(ComplexNumberSize numberSize) {
         return new Complex[numberSize.getSize()];
     }

     /**
      * Baseline the creation of a copy array of numbers.
      * This is commented out as it provides no information other than to demonstrate that
      * {@link #baselineCopy(ComplexNumbers)} is not being optimised to a single array copy
      * operation.
      */
     //@Benchmark
     public Complex[] baselineCopyArray(ComplexNumbers numbers) {
         return Arrays.copyOf(numbers.getNumbers(), numbers.getNumbers().length);
     }

     /**
      * Baseline the creation of the new array of numbers with the same complex number (an identity).
      *
      * <p>Note: This runs much faster than {@link #baselineCopy(ComplexNumbers)}. This is
      * attributed to the identity function not requiring that the fields of the
      * complex are accessed unlike all other methods that do computations on the real and/or
      * imaginary parts. The method is slower than a creation of a new empty array or a
      * copy array thus contains the loop overhead of the benchmarks that create new numbers.
      *
      * @see #baselineNewArray(ComplexNumberSize)
      * @see #baselineCopyArray(ComplexNumbers)
      */
     @Benchmark
     public Complex[] baselineIdentity(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), ComplexPerformance::identity);
     }

     /**
      * Baseline the creation of the new array of numbers with a copy complex number. This
      * measures the overhead of creation of new complex numbers including field access
      * to the real and imaginary parts.
      */
     @Benchmark
     public Complex[] baselineCopy(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), ComplexPerformance::copy);
     }

     // Unary operations that return a boolean

     @Benchmark
     public boolean[] isNaN(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::isNaN);
     }

     @Benchmark
     public boolean[] isInfinite(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::isInfinite);
     }

     @Benchmark
     public boolean[] isFinite(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::isFinite);
     }

     // Unary operations that return a double

     @Benchmark
     public double[] real(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::real);
     }

     @Benchmark
     public double[] imag(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::imag);
     }

     @Benchmark
     public double[] abs(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::abs);
     }

     @Benchmark
     public double[] arg(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::arg);
     }

     @Benchmark
     public double[] norm(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::norm);
     }

     // Unary operations that return a complex number

     @Benchmark
     public Complex[] conj(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::conj);
     }

     @Benchmark
     public Complex[] negate(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::negate);
     }

     @Benchmark
     public Complex[] proj(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::proj);
     }

     @Benchmark
     public Complex[] cos(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::cos);
     }

     @Benchmark
     public Complex[] cosh(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::cosh);
     }

     @Benchmark
     public Complex[] exp(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::exp);
     }

     @Benchmark
     public Complex[] log(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::log);
     }

     @Benchmark
     public Complex[] log10(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::log10);
     }

     @Benchmark
     public Complex[] sin(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::sin);
     }

     @Benchmark
     public Complex[] sinh(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::sinh);
     }

     @Benchmark
     public Complex[] sqrt(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::sqrt);
     }

     @Benchmark
     public Complex[] tan(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::tan);
     }

     @Benchmark
     public Complex[] tanh(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::tanh);
     }

     @Benchmark
     public Complex[] acos(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::acos);
     }

     @Benchmark
     public Complex[] acosh(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::acosh);
     }

     @Benchmark
     public Complex[] asin(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::asin);
     }

     @Benchmark
     public Complex[] asinh(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::asinh);
     }

     @Benchmark
     public Complex[] atan(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::atan);
     }

     @Benchmark
     public Complex[] atanh(ComplexNumbers numbers) {
         return apply(numbers.getNumbers(), Complex::atanh);
     }

     // Binary operations on two complex numbers.

     @Benchmark
     public Complex[] pow(TwoComplexNumbers numbers) {
         return apply(numbers.getNumbers(), numbers.getNumbers2(), Complex::pow);
     }

     @Benchmark
     public Complex[] multiply(TwoComplexNumbers numbers) {
         return apply(numbers.getNumbers(), numbers.getNumbers2(), Complex::multiply);
     }

     @Benchmark
     public Complex[] divide(TwoComplexNumbers numbers) {
         return apply(numbers.getNumbers(), numbers.getNumbers2(), Complex::divide);
     }

     @Benchmark
     public Complex[] add(TwoComplexNumbers numbers) {
         return apply(numbers.getNumbers(), numbers.getNumbers2(), Complex::add);
     }

     @Benchmark
     public Complex[] subtract(TwoComplexNumbers numbers) {
         return apply(numbers.getNumbers(), numbers.getNumbers2(), Complex::subtract);
     }

     // Binary operations on a complex and a real number.
     // These only benchmark methods on the real component as the
     // following are expected to be the same speed as the real-only operations
     // given the equivalent primitive operations:
     // - multiplyImaginary
     // - divideImaginary
     // - addImaginary
     // - subtractImaginary
     // - subtractFrom
     // - subtractFromImaginary

     @Benchmark
     public Complex[] powReal(ComplexAndRealNumbers numbers) {
         return apply(numbers.getNumbers(), numbers.getNumbers2(), Complex::pow);
     }

     @Benchmark
     public Complex[] multiplyReal(ComplexAndRealNumbers numbers) {
         return apply(numbers.getNumbers(), numbers.getNumbers2(), Complex::multiply);
     }

     @Benchmark
     public Complex[] divideReal(ComplexAndRealNumbers numbers) {
         return apply(numbers.getNumbers(), numbers.getNumbers2(), Complex::divide);
     }

     @Benchmark
     public Complex[] addReal(ComplexAndRealNumbers numbers) {
         return apply(numbers.getNumbers(), numbers.getNumbers2(), Complex::add);
     }

     @Benchmark
     public Complex[] subtractReal(ComplexAndRealNumbers numbers) {
         return apply(numbers.getNumbers(), numbers.getNumbers2(), Complex::subtract);
     }
 }
	/*
	* 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.examples.jmh.complex;

	import org.apache.commons.numbers.complex.Complex;
	import org.openjdk.jmh.annotations.Benchmark;
	import org.openjdk.jmh.annotations.BenchmarkMode;
	import org.openjdk.jmh.annotations.Fork;
	import org.openjdk.jmh.annotations.Measurement;
	import org.openjdk.jmh.annotations.Mode;
	import org.openjdk.jmh.annotations.OutputTimeUnit;
	import org.openjdk.jmh.annotations.Param;
	import org.openjdk.jmh.annotations.Scope;
	import org.openjdk.jmh.annotations.Setup;
	import org.openjdk.jmh.annotations.State;
	import org.openjdk.jmh.annotations.Warmup;

	import java.util.Arrays;
	import java.util.SplittableRandom;
	import java.util.concurrent.TimeUnit;
	import java.util.function.BiFunction;
	import java.util.function.Predicate;
	import java.util.function.Supplier;
	import java.util.function.ToDoubleFunction;
	import java.util.function.UnaryOperator;
	import java.util.stream.Stream;

	/**
	* Executes a benchmark to measure the speed of operations in the {@link Complex} class.
	*/
	@BenchmarkMode(Mode.AverageTime)
	@OutputTimeUnit(TimeUnit.NANOSECONDS)
	@Warmup(iterations = 5, time = 1, timeUnit = TimeUnit.SECONDS)
	@Measurement(iterations = 5, time = 1, timeUnit = TimeUnit.SECONDS)
	@State(Scope.Benchmark)
	@Fork(value = 1, jvmArgs = {"-server", "-Xms512M", "-Xmx512M"})
	public class ComplexPerformance {
	/**
	* An array of edge numbers that will produce edge case results from functions:
	* {@code +/-inf, +/-max, +/-min, +/-0, nan}.
	*/
	private static final double[] EDGE_NUMBERS = {
	Double.POSITIVE_INFINITY, Double.NEGATIVE_INFINITY, Double.MAX_VALUE,
	-Double.MAX_VALUE, Double.MIN_VALUE, -Double.MIN_VALUE, 0.0, -0.0, Double.NaN};

	/**
	* Contains the size of numbers.
	*/
	@State(Scope.Benchmark)
	public static class ComplexNumberSize {
	/**
	* The size of the data.
	*/
	@Param({"1000"})
	private int size;

	/**
	* Gets the size.
	*
	* @return the size
	*/
	public int getSize() {
	return size;
	}
	}

	/**
	* Contains an array of complex numbers.
	*/
	@State(Scope.Benchmark)
	public static class ComplexNumbers extends ComplexNumberSize {
	/** The numbers. */
	protected Complex[] numbers;

	/**
	* The type of the data.
	*/
	@Param({"cis", "random", "edge"})
	private String type;

	/**
	* Gets the numbers.
	*
	* @return the numbers
	*/
	public Complex[] getNumbers() {
	return numbers;
	}

	/**
	* Create the complex numbers.
	*/
	@Setup
	public void setup() {
	numbers = createNumbers(new SplittableRandom());
	}

	/**
	* Creates the numbers.
	*
	* @param rng Random number generator.
	* @return the random complex number
	*/
	Complex[] createNumbers(SplittableRandom rng) {
	Supplier<Complex> generator;
	if ("cis".equals(type)) {
	generator = () -> Complex.ofCis(rng.nextDouble() * 2 * Math.PI);
	} else if ("random".equals(type)) {
	generator = () -> Complex.ofCartesian(createRandomNumber(rng), createRandomNumber(rng));
	} else if ("edge".equals(type)) {
	generator = () -> Complex.ofCartesian(createEdgeNumber(rng), createEdgeNumber(rng));
	} else {
	throw new IllegalStateException("Unknown number type: " + type);
	}
	return Stream.generate(generator).limit(getSize()).toArray(Complex[]::new);
	}
	}

	/**
	* Contains two arrays of complex numbers.
	*/
	@State(Scope.Benchmark)
	public static class TwoComplexNumbers extends ComplexNumbers {
	/** The numbers. */
	private Complex[] numbers2;

	/**
	* Gets the second set of numbers.
	*
	* @return the numbers
	*/
	public Complex[] getNumbers2() {
	return numbers2;
	}

	/**
	* Create the complex numbers.
	*/
	@Override
	@Setup
	public void setup() {
	// Do not call super.setup() so we recycle the RNG and avoid duplicates
	final SplittableRandom rng = new SplittableRandom();
	numbers = createNumbers(rng);
	numbers2 = createNumbers(rng);
	}
	}

	/**
	* Contains an array of complex numbers and an array of real numbers.
	*/
	@State(Scope.Benchmark)
	public static class ComplexAndRealNumbers extends ComplexNumbers {
	/** The numbers. */
	private double[] numbers2;

	/**
	* Gets the second set of numbers.
	*
	* @return the numbers
	*/
	public double[] getNumbers2() {
	return numbers2;
	}

	/**
	* Create the complex numbers.
	*/
	@Override
	@Setup
	public void setup() {
	// Do not call super.setup() so we recycle the RNG and avoid duplicates
	final SplittableRandom rng = new SplittableRandom();
	numbers = createNumbers(rng);
	numbers2 = Arrays.stream(createNumbers(rng)).mapToDouble(Complex::real).toArray();
	}
	}

	/**
	* Define a function between a complex and real number.
	*/
	private interface ComplexRealFunction {
	/**
	* Applies this function to the given arguments.
	*
	* @param z the complex argument
	* @param x the real argument
	* @return the function result
	*/
	Complex apply(Complex z, double x);
	}

	/**
	* Creates a random double number with a random sign and mantissa and a large range for
	* the exponent. The numbers will not be uniform over the range.
	*
	* @param rng Random number generator.
	* @return the random number
	*/
	private static double createRandomNumber(SplittableRandom rng) {
	// Create random doubles using random bits in the sign bit and the mantissa.
	// Then create an exponent in the range -64 to 64. Thus the sum product
	// of 4 max or min values will not over or underflow.
	final long mask = ((1L << 52) - 1) \| 1L << 63;
	final long bits = rng.nextLong() & mask;
	// The exponent must be unsigned so + 1023 to the signed exponent
	final long exp = rng.nextInt(129) - 64 + 1023;
	return Double.longBitsToDouble(bits \| (exp << 52));
	}

	/**
	* Creates a random double number that will be an edge case:
	* {@code +/-inf, +/-max, +/-min, +/-0, nan}.
	*
	* @param rng Random number generator.
	* @return the random number
	*/
	private static double createEdgeNumber(SplittableRandom rng) {
	return EDGE_NUMBERS[rng.nextInt(EDGE_NUMBERS.length)];
	}

	/**
	* Apply the function to all the numbers.
	*
	* @param numbers Numbers.
	* @param fun Function.
	* @return the result of the function.
	*/
	private static boolean[] apply(Complex[] numbers, Predicate<Complex> fun) {
	final boolean[] result = new boolean[numbers.length];
	for (int i = 0; i < numbers.length; i++) {
	result[i] = fun.test(numbers[i]);
	}
	return result;
	}

	/**
	* Apply the function to all the numbers.
	*
	* @param numbers Numbers.
	* @param fun Function.
	* @return the result of the function.
	*/
	private static double[] apply(Complex[] numbers, ToDoubleFunction<Complex> fun) {
	final double[] result = new double[numbers.length];
	for (int i = 0; i < numbers.length; i++) {
	result[i] = fun.applyAsDouble(numbers[i]);
	}
	return result;
	}

	/**
	* Apply the function to all the numbers.
	*
	* @param numbers Numbers.
	* @param fun Function.
	* @return the result of the function.
	*/
	private static Complex[] apply(Complex[] numbers, UnaryOperator<Complex> fun) {
	final Complex[] result = new Complex[numbers.length];
	for (int i = 0; i < numbers.length; i++) {
	result[i] = fun.apply(numbers[i]);
	}
	return result;
	}

	/**
	* Apply the function to the paired numbers.
	*
	* @param numbers First numbers of the pairs.
	* @param numbers2 Second numbers of the pairs.
	* @param fun Function.
	* @return the result of the function.
	*/
	private static Complex[] apply(Complex[] numbers, Complex[] numbers2,
	BiFunction<Complex, Complex, Complex> fun) {
	final Complex[] result = new Complex[numbers.length];
	for (int i = 0; i < numbers.length; i++) {
	result[i] = fun.apply(numbers[i], numbers2[i]);
	}
	return result;
	}

	/**
	* Apply the function to the paired numbers.
	*
	* @param numbers First numbers of the pairs.
	* @param numbers2 Second numbers of the pairs.
	* @param fun Function.
	* @return the result of the function.
	*/
	private static Complex[] apply(Complex[] numbers, double[] numbers2,
	ComplexRealFunction fun) {
	final Complex[] result = new Complex[numbers.length];
	for (int i = 0; i < numbers.length; i++) {
	result[i] = fun.apply(numbers[i], numbers2[i]);
	}
	return result;
	}

	/**
	* Identity function. This can be used to measure overhead of object array creation.
	*
	* @param z Complex number.
	* @return the complex number
	*/
	private static Complex identity(Complex z) {
	return z;
	}

	/**
	* Copy function. This can be used to measure overhead of object array creation plus
	* new Complex creation.
	*
	* @param z Complex number.
	* @return a copy of the complex number
	*/
	private static Complex copy(Complex z) {
	return Complex.ofCartesian(z.real(), z.imag());
	}

	// Benchmark methods.
	//
	// The methods are partially documented as the names are self-documenting.
	// CHECKSTYLE: stop JavadocMethod
	// CHECKSTYLE: stop DesignForExtension
	//
	// Benchmarks use function references to perform different operations on the complex numbers.
	// Tests show that explicit programming of the same benchmarks run in the same time.
	// For reference examples are provided for the fastest operations: real() and conj().

	/**
	* Explicit benchmark without using a method reference.
	* This should run in the same time as {@link #real(ComplexNumbers)}.
	* This is commented out as it exists for reference purposes.
	*/
	//@Benchmark
	public double[] real2(ComplexNumbers numbers) {
	final Complex[] z = numbers.getNumbers();
	final double[] result = new double[z.length];
	for (int i = 0; i < z.length; i++) {
	result[i] = z[i].real();
	}
	return result;
	}

	/**
	* Explicit benchmark without using a method reference.
	* This should run in the same time as {@link #conj(ComplexNumbers)}.
	* This is commented out as it exists for reference purposes.
	*/
	//@Benchmark
	public Complex[] conj2(ComplexNumbers numbers) {
	final Complex[] z = numbers.getNumbers();
	final Complex[] result = new Complex[z.length];
	for (int i = 0; i < z.length; i++) {
	result[i] = z[i].conj();
	}
	return result;
	}

	/**
	* Baseline the creation of the new array of numbers.
	* This contains the baseline JMH overhead for all the benchmarks that create complex numbers.
	* All other methods are expected to be slower than this.
	*/
	@Benchmark
	public Complex[] baselineNewArray(ComplexNumberSize numberSize) {
	return new Complex[numberSize.getSize()];
	}

	/**
	* Baseline the creation of a copy array of numbers.
	* This is commented out as it provides no information other than to demonstrate that
	* {@link #baselineCopy(ComplexNumbers)} is not being optimised to a single array copy
	* operation.
	*/
	//@Benchmark
	public Complex[] baselineCopyArray(ComplexNumbers numbers) {
	return Arrays.copyOf(numbers.getNumbers(), numbers.getNumbers().length);
	}

	/**
	* Baseline the creation of the new array of numbers with the same complex number (an identity).
	*
	* <p>Note: This runs much faster than {@link #baselineCopy(ComplexNumbers)}. This is
	* attributed to the identity function not requiring that the fields of the
	* complex are accessed unlike all other methods that do computations on the real and/or
	* imaginary parts. The method is slower than a creation of a new empty array or a
	* copy array thus contains the loop overhead of the benchmarks that create new numbers.
	*
	* @see #baselineNewArray(ComplexNumberSize)
	* @see #baselineCopyArray(ComplexNumbers)
	*/
	@Benchmark
	public Complex[] baselineIdentity(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), ComplexPerformance::identity);
	}

	/**
	* Baseline the creation of the new array of numbers with a copy complex number. This
	* measures the overhead of creation of new complex numbers including field access
	* to the real and imaginary parts.
	*/
	@Benchmark
	public Complex[] baselineCopy(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), ComplexPerformance::copy);
	}

	// Unary operations that return a boolean

	@Benchmark
	public boolean[] isNaN(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::isNaN);
	}

	@Benchmark
	public boolean[] isInfinite(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::isInfinite);
	}

	@Benchmark
	public boolean[] isFinite(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::isFinite);
	}

	// Unary operations that return a double

	@Benchmark
	public double[] real(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::real);
	}

	@Benchmark
	public double[] imag(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::imag);
	}

	@Benchmark
	public double[] abs(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::abs);
	}

	@Benchmark
	public double[] arg(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::arg);
	}

	@Benchmark
	public double[] norm(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::norm);
	}

	// Unary operations that return a complex number

	@Benchmark
	public Complex[] conj(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::conj);
	}

	@Benchmark
	public Complex[] negate(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::negate);
	}

	@Benchmark
	public Complex[] proj(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::proj);
	}

	@Benchmark
	public Complex[] cos(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::cos);
	}

	@Benchmark
	public Complex[] cosh(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::cosh);
	}

	@Benchmark
	public Complex[] exp(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::exp);
	}

	@Benchmark
	public Complex[] log(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::log);
	}

	@Benchmark
	public Complex[] log10(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::log10);
	}

	@Benchmark
	public Complex[] sin(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::sin);
	}

	@Benchmark
	public Complex[] sinh(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::sinh);
	}

	@Benchmark
	public Complex[] sqrt(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::sqrt);
	}

	@Benchmark
	public Complex[] tan(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::tan);
	}

	@Benchmark
	public Complex[] tanh(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::tanh);
	}

	@Benchmark
	public Complex[] acos(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::acos);
	}

	@Benchmark
	public Complex[] acosh(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::acosh);
	}

	@Benchmark
	public Complex[] asin(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::asin);
	}

	@Benchmark
	public Complex[] asinh(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::asinh);
	}

	@Benchmark
	public Complex[] atan(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::atan);
	}

	@Benchmark
	public Complex[] atanh(ComplexNumbers numbers) {
	return apply(numbers.getNumbers(), Complex::atanh);
	}

	// Binary operations on two complex numbers.

	@Benchmark
	public Complex[] pow(TwoComplexNumbers numbers) {
	return apply(numbers.getNumbers(), numbers.getNumbers2(), Complex::pow);
	}

	@Benchmark
	public Complex[] multiply(TwoComplexNumbers numbers) {
	return apply(numbers.getNumbers(), numbers.getNumbers2(), Complex::multiply);
	}

	@Benchmark
	public Complex[] divide(TwoComplexNumbers numbers) {
	return apply(numbers.getNumbers(), numbers.getNumbers2(), Complex::divide);
	}

	@Benchmark
	public Complex[] add(TwoComplexNumbers numbers) {
	return apply(numbers.getNumbers(), numbers.getNumbers2(), Complex::add);
	}

	@Benchmark
	public Complex[] subtract(TwoComplexNumbers numbers) {
	return apply(numbers.getNumbers(), numbers.getNumbers2(), Complex::subtract);
	}

	// Binary operations on a complex and a real number.
	// These only benchmark methods on the real component as the
	// following are expected to be the same speed as the real-only operations
	// given the equivalent primitive operations:
	// - multiplyImaginary
	// - divideImaginary
	// - addImaginary
	// - subtractImaginary
	// - subtractFrom
	// - subtractFromImaginary

	@Benchmark
	public Complex[] powReal(ComplexAndRealNumbers numbers) {
	return apply(numbers.getNumbers(), numbers.getNumbers2(), Complex::pow);
	}

	@Benchmark
	public Complex[] multiplyReal(ComplexAndRealNumbers numbers) {
	return apply(numbers.getNumbers(), numbers.getNumbers2(), Complex::multiply);
	}

	@Benchmark
	public Complex[] divideReal(ComplexAndRealNumbers numbers) {
	return apply(numbers.getNumbers(), numbers.getNumbers2(), Complex::divide);
	}

	@Benchmark
	public Complex[] addReal(ComplexAndRealNumbers numbers) {
	return apply(numbers.getNumbers(), numbers.getNumbers2(), Complex::add);
	}

	@Benchmark
	public Complex[] subtractReal(ComplexAndRealNumbers numbers) {
	return apply(numbers.getNumbers(), numbers.getNumbers2(), Complex::subtract);
	}
	}