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    * Licensed to the Apache Software Foundation (ASF) under one or more
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    * 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
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    *
    *      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,
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  package org.apache.commons.math4.legacy.analysis.function;
  
  import org.apache.commons.math4.legacy.analysis.UnivariateFunction;
  import org.apache.commons.math4.legacy.analysis.differentiation.DerivativeStructure;
  import org.apache.commons.math4.legacy.core.dfp.Dfp;
  import org.apache.commons.math4.legacy.core.dfp.DfpField;
  import org.apache.commons.math4.legacy.core.dfp.DfpMath;
  import org.apache.commons.math4.core.jdkmath.JdkMath;
  import org.junit.Assert;
  import org.junit.Test;
  
  public class SincTest {
  
     @Test
     public void testShortcut() {
         final Sinc s = new Sinc();
         final UnivariateFunction f = new UnivariateFunction() {
             @Override
             public double value(double x) {
                 Dfp dfpX = new DfpField(25).newDfp(x);
                 return DfpMath.sin(dfpX).divide(dfpX).toDouble();
             }
         };
  
         for (double x = 1e-30; x < 1e10; x *= 2) {
             final double fX = f.value(x);
             final double sX = s.value(x);
             Assert.assertEquals("x=" + x, fX, sX, 2.0e-16);
         }
     }
  
     @Test
     public void testCrossings() {
         final Sinc s = new Sinc(true);
         final int numCrossings = 1000;
         final double tol = 2e-16;
         for (int i = 1; i <= numCrossings; i++) {
             Assert.assertEquals("i=" + i, 0, s.value(i), tol);
         }
     }
  
     @Test
     public void testZero() {
         final Sinc s = new Sinc();
         Assert.assertEquals(1d, s.value(0), 0);
     }
  
     @Test
     public void testEuler() {
         final Sinc s = new Sinc();
         final double x = 123456.789;
         double prod = 1;
         double xOverPow2 = x / 2;
         while (xOverPow2 > 0) {
             prod *= JdkMath.cos(xOverPow2);
             xOverPow2 /= 2;
         }
         Assert.assertEquals(prod, s.value(x), 1e-13);
     }
  
     @Test
     public void testDerivativeZero() {
         final DerivativeStructure s0 = new Sinc(true).value(new DerivativeStructure(1, 1, 0, 0.0));
         Assert.assertEquals(0, s0.getPartialDerivative(1), 0);
     }
  
     @Test
     public void testDerivatives1Dot2Unnormalized() {
         DerivativeStructure s = new Sinc(false).value(new DerivativeStructure(1, 5, 0, 1.2));
         Assert.assertEquals( 0.77669923830602195806, s.getPartialDerivative(0), 1.0e-16);
         Assert.assertEquals(-0.34528456985779031701, s.getPartialDerivative(1), 1.0e-16);
         Assert.assertEquals(-0.2012249552097047631,  s.getPartialDerivative(2), 1.0e-16);
         Assert.assertEquals( 0.2010975926270339262,  s.getPartialDerivative(3), 4.0e-16);
         Assert.assertEquals( 0.106373929549242204,   s.getPartialDerivative(4), 1.0e-15);
         Assert.assertEquals(-0.1412599110579478695,  s.getPartialDerivative(5), 3.0e-15);
     }
  
     @Test
     public void testDerivatives1Dot2Normalized() {
         DerivativeStructure s = new Sinc(true).value(new DerivativeStructure(1, 5, 0, 1.2));
         Assert.assertEquals(-0.15591488063143983888, s.getPartialDerivative(0), 6.0e-17);
         Assert.assertEquals(-0.54425176145292298767, s.getPartialDerivative(1), 2.0e-16);
         Assert.assertEquals(2.4459044611635856107,   s.getPartialDerivative(2), 9.0e-16);
        Assert.assertEquals(0.5391369206235909586,   s.getPartialDerivative(3), 7.0e-16);
        Assert.assertEquals(-16.984649869728849865,  s.getPartialDerivative(4), 8.0e-15);
        Assert.assertEquals(5.0980327462666316586,   s.getPartialDerivative(5), 9.0e-15);
    }
 
    @Test
    public void testDerivativeShortcut() {
        final Sinc sinc = new Sinc();
        final UnivariateFunction f = new UnivariateFunction() {
                @Override
             public double value(double x) {
                    Dfp dfpX = new DfpField(25).newDfp(x);
                    return DfpMath.cos(dfpX).subtract(DfpMath.sin(dfpX).divide(dfpX)).divide(dfpX).toDouble();
                }
            };
 
        for (double x = 1e-30; x < 1e10; x *= 2) {
            final double fX = f.value(x);
            final DerivativeStructure sX = sinc.value(new DerivativeStructure(1, 1, 0, x));
            Assert.assertEquals("x=" + x, fX, sX.getPartialDerivative(1), 3.0e-13);
        }
    }
 }