Improved root finding to avoid over/underflow.

Author: jkalias

src/Numerics.Tests/RootFindingTests/RobustNewtonRaphsonTest.cs

@@ -133,6 +133,24 @@ public void InfinitelyManyRootsWithGivenAccuracy()
             Assert.AreEqual(-50, RobustNewtonRaphson.FindRoot(f1, df1, -200, 100, 1e-8), 1e-6);
         }
 
+        [Test]
+        public void BoundsNearMaxValueNoOverflow()
+        {
+            // degenerate case with infinitely many roots
+            Func<double, double> f1 = x => 0.0;
+            Func<double, double> df1 = x => 0.0;
+            Assert.AreEqual(double.MaxValue, RobustNewtonRaphson.FindRoot(f1, df1, double.MaxValue - 2, double.MaxValue - 1), 1e-6);
+        }
+
+        [Test]
+        public void BoundsNearMinValueNoUnderflow()
+        {
+            // degenerate case with infinitely many roots
+            Func<double, double> f1 = x => 0.0;
+            Func<double, double> df1 = x => 0.0;
+            Assert.AreEqual(double.MinValue, RobustNewtonRaphson.FindRoot(f1, df1, double.MinValue + 1, double.MinValue + 2), 1e-6);
+        }
+
         [Test]
         public void NoRoot()
         {

src/Numerics/RootFinding/RobustNewtonRaphson.cs

@@ -77,7 +77,7 @@ public static bool TryFindRoot(Func<double, double> f, Func<double, double> df,
             double fmin = f(lowerBound);
             double fmax = f(upperBound);
 
-            root = 0.5 * (lowerBound + upperBound);
+            root = lowerBound + 0.5 * (upperBound - lowerBound);
             double fx = f(root);
             if (Math.Abs(fx) < accuracy)
             {