diff --git a/src/neuron.hxx b/src/neuron.hxx
index 7ccaec0..931d230 100644
--- a/src/neuron.hxx
+++ b/src/neuron.hxx
@@ -167,6 +167,7 @@
     @page biblio Bibliography
 
      - <a href="http://briandolhansky.com/blog/2014/10/30/artificial-neural-networks-matrix-form-part-5">Artificial Neural Networks: Matrix Form (Part 5)</a>
+     - <a href="http://briandolhansky.com/blog/2013/9/27/artificial-neural-networks-backpropagation-part-4">Artificial Neural Networks: Mathematics of Backpropagation (Part 4)</a>
      - <a href="http://www.tornau.name/wp-content/uploads/2009/04/studiumsmaterialien/neuronale_netze_zusammefassung.pdf">Vorlesung Neuronale Netze - Zusammenfassung - Christoph Tornau</a>
      - <a href="http://www.neuronalesnetz.de/">Neuronale Netze — Eine Einführung</a>
      - <a href="http://alphard.ethz.ch/hafner/Vorles/Optim/ANN/Artificial%20Neural%20Network%20based%20Curve%20Prediction%20Documentation.pdf">Artificial Neural Network based Curve Prediction</a>
@@ -179,11 +180,11 @@
 namespace math {
   // tangens hyperbolicus as standard activation function
   template<typename TYPE> TYPE tanh(const TYPE& v) {
-    return ::tanh((double)v);
+    return ::tanh((long double)v);
   }
   // derivate of activation function for back propagation
   template<typename TYPE> TYPE tanh_diff(const TYPE& v) {
-    TYPE ch(::cosh((double)v));
+    TYPE ch(::cosh((long double)v));
     return 1/(ch*ch);
   }
 }
@@ -200,13 +201,19 @@ class NeuroNet {
   public:
     NeuroNet() {
     }
-    Matrix<TYPE, 1, OUTPUT_LAYERS> feed(Matrix<TYPE, 1, INPUT_LAYERS> in) {
+    Matrix<TYPE, 1, OUTPUT_LAYERS> operator()(const Matrix<TYPE, 1, INPUT_LAYERS>& in) {
       Matrix<TYPE, 1, HIDDEN_LAYER_SIZE> l((in*_wi).apply(ACTIVATION));
       for (int i(0); i<HIDDEN_LAYERS-1; ++i)
         l = (l*_wh[i]).apply(ACTIVATION);
       Matrix<TYPE, 1, OUTPUT_LAYERS> out((l*_wo).apply(ACTIVATION));
       return out;
     }
+    Matrix<TYPE, 1, OUTPUT_LAYERS> learn(const Matrix<TYPE, 1, INPUT_LAYERS>& in,
+                                         const Matrix<TYPE, 1, OUTPUT_LAYERS>& expect) {
+      Matrix<TYPE, 1, OUTPUT_LAYERS> out((*this)(in));
+      Matrix<TYPE, 1, OUTPUT_LAYERS> diff(expect-out);
+      return diff;
+    }
   private:
     Matrix<TYPE, INPUT_LAYERS, HIDDEN_LAYER_SIZE> _wi;
     Matrix<TYPE, HIDDEN_LAYER_SIZE, HIDDEN_LAYER_SIZE> _wh[HIDDEN_LAYERS-1];
diff --git a/test/neuron.cxx b/test/neuron.cxx
index 7ea2a9b..8a42bc5 100644
--- a/test/neuron.cxx
+++ b/test/neuron.cxx
@@ -31,12 +31,16 @@ class NeuroNetTest: public CppUnit::TestFixture {
                                    1,
                                    1,
                                    -1};
+      for (int step(0); step<10; ++step)
+        for (int i(0); i<sizeof(in)/sizeof(*in); ++i)
+          for (int rep(0); rep<10; ++rep)
+            auto res(neuronet.learn(in[i], out[i]));
       for (int i(0); i<sizeof(in)/sizeof(*in); ++i) {
         std::cout<<in[i]<<" → "<<out[i]<<" ~ "
-                 <<neuronet.feed(in[i]).apply([](float&v){
+                 <<neuronet(in[i]).apply([](float&v){
                      v = v<0 ? -1.0 : 1.0;
                    })<<std::endl;
-        auto res(neuronet.feed(in[i])
+        auto res(neuronet(in[i])
                  .apply([](float&v){
                      std::cout<<"v="<<v<<std::endl;
                      v = v<0 ? -1.0 : 1.0;