Fixed DerivativeStructure.pow(0.0).

x^0 is always 1.0, regardless of x (even if x is NaN in fact).

src/main/java/org/apache/commons/math4/analysis/differentiation/DSCompiler.java

@@ -886,6 +886,13 @@ public class DSCompiler {
     public void pow(final double[] operand, final int operandOffset, final double p,
                     final double[] result, final int resultOffset) {
 
+        if (p == 0) {
+            // special case, x^0 = 1 for all x
+            result[resultOffset] = 1.0;
+            Arrays.fill(result, resultOffset + 1, resultOffset + getSize(), 0);
+            return;
+        }
+
         // create the function value and derivatives
         // [x^p, px^(p-1), p(p-1)x^(p-2), ... ]
         double[] function = new double[1 + order];

src/test/java/org/apache/commons/math4/analysis/differentiation/DerivativeStructureTest.java

@@ -31,6 +31,7 @@ import org.apache.commons.math4.rng.RandomSource;
 import org.apache.commons.math4.util.ArithmeticUtils;
 import org.apache.commons.math4.util.CombinatoricsUtils;
 import org.apache.commons.math4.util.FastMath;
+import org.apache.commons.math4.util.Precision;
 import org.junit.Assert;
 import org.junit.Test;
 
@@ -323,6 +324,27 @@ public class DerivativeStructureTest extends ExtendedFieldElementAbstractTest<De
                 Assert.assertTrue(Double.isNaN(zeroZero.getPartialDerivative(1, 1, 0)));
             }
 
+            // very special case: 0^0 where the power is a primitive
+            DerivativeStructure zeroDsZeroDouble = new DerivativeStructure(3,  maxOrder, 0, 0.0).pow(0.0);
+            boolean first = true;
+            for (final double d : zeroDsZeroDouble.getAllDerivatives()) {
+                if (first) {
+                    Assert.assertEquals(1.0, d, Precision.EPSILON);
+                    first = false;
+                } else {
+                    Assert.assertEquals(0.0, d, Precision.SAFE_MIN);
+                }
+            }
+            DerivativeStructure zeroDsZeroInt = new DerivativeStructure(3,  maxOrder, 0, 0.0).pow(0);
+            first = true;
+            for (final double d : zeroDsZeroInt.getAllDerivatives()) {
+                if (first) {
+                    Assert.assertEquals(1.0, d, Precision.EPSILON);
+                    first = false;
+                } else {
+                    Assert.assertEquals(0.0, d, Precision.SAFE_MIN);
+                }
+            }
         }
 
     }