initial implementation

include/xo/distribution/Normal.hpp

@@ -0,0 +1,51 @@
+/* @file Normal.hpp */
+
+#pragma once
+
+#include "distribution/Distribution.hpp"
+#include <cmath>
+
+namespace xo {
+    namespace distribution {
+        /* the guassian distribution,  with mean 0 and variance 1
+         */
+        class Normal : public Distribution<double> {
+        public:
+            Normal() = default;
+
+            /* normal probability density:
+             *
+             *                  x^2
+             *            -(1/2)              1/2
+             *    p(x) = e            / (2.pi)
+             */
+            static double density(double x) {
+                static double c_sqrt_2pi = ::sqrt(2 * M_PI);
+
+                return ::exp(-0.5 * x * x) / c_sqrt_2pi;
+            } /*density*/
+
+            /* cumulative distribution function for N(0,1):
+             *
+             *   / x
+             *   |
+             *   |    p(x).dx
+             *   |
+             *   / -oo
+             *
+             * where p(x) is the normal density function p(x) = e^[-x^2/2]
+             */
+            static double cdf_impl(double x) {
+                return 0.5 * std::erfc(-M_SQRT1_2 * x);
+            } /*cdf_impl*/
+
+            // ----- inherited from Distribution<double> -----
+
+            virtual double cdf(double const & x) const override {
+                return cdf_impl(x);
+            } /*cdf*/
+        }; /*Normal*/
+    } /*namespace distribution*/
+} /*namespace xo*/
+
+/* end Normal.hpp */