Javadoc link to reference.

Remark on numerical accuracy added as code comment.
Added unit tests.
Added normalized sinc function.


git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1180588 13f79535-47bb-0310-9956-ffa450edef68

src/main/java/org/apache/commons/math/analysis/function/Sinc.java

@@ -21,15 +21,51 @@ import org.apache.commons.math.analysis.UnivariateRealFunction;
 import org.apache.commons.math.util.FastMath;
 
 /**
- * The sinc function, {code sin(x)/x}.
+ * <a href="http://en.wikipedia.org/wiki/Sinc_function">Sinc</a> function.
- * Returns {code 1} if {code |x| < 1e-9}.
  *
  * @version $Id$
  * @since 3.0
  */
 public class Sinc implements UnivariateRealFunction {
+    /** For normalized sinc function. */
+    private final boolean normalized;
+
+    /**
+     * The sinc function, {@code sin(x) / x}.
+     */
+    public Sinc() {
+        this(false);
+    }
+
+    /**
+     * Instantiates the sinc function.
+     *
+     * @param normalized If {@code true}, the function is
+     * <code> sin(&pi;x) / &pi;x</code>, otherwise {@code sin(x) / x}.
+     */
+    public Sinc(boolean normalized) {
+        this.normalized = normalized;
+    }
+
     /** {@inheritDoc} */
     public double value(double x) {
+        if (normalized) {
+            final double piTimesX = Math.PI * x;
+            return sinc(piTimesX);
+        } else {
+            return sinc(x);
+        }
+    }
+
+    /**
+     * @param x Argument.
+     * @return {@code sin(x) / x}.
+     */
+    private static double sinc(double x) {
+        // The direct assignment to 1 for values below 1e-9 is an efficiency
+        // optimization on the ground that the result of the full computation
+        // is indistinguishable from 1 due to the limited accuracy of the
+        // floating point representation.
         return FastMath.abs(x) < 1e-9 ? 1 : FastMath.sin(x) / x;
     }
 }

src/test/java/org/apache/commons/math/analysis/function/SincTest.java

@@ -0,0 +1,72 @@
+/*
+ * 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.math.analysis.function;
+
+import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.util.FastMath;
+import org.apache.commons.math.util.MathUtils;
+
+import org.junit.Test;
+import org.junit.Assert;
+
+public class SincTest {
+
+   @Test
+   public void testShortcut() {
+       final Sinc s = new Sinc();
+       final UnivariateRealFunction f = new UnivariateRealFunction() {
+               public double value(double x) {
+                   return FastMath.sin(x) / x;
+               }
+           };
+
+       for (double x = 1e-30; x < 1e10; x *= 5) {
+           final double fX = f.value(x);
+           final double sX = s.value(x);
+           Assert.assertEquals("x=" + x, fX, sX, 0);
+       }
+   }
+
+   @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 *= FastMath.cos(xOverPow2);
+           xOverPow2 /= 2;
+       }
+       Assert.assertEquals(prod, s.value(x), 1e-13);
+   }
+}