diff --git a/CMakeLists.txt b/CMakeLists.txt
index 855b33e..4500831 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -72,7 +72,7 @@ if(GLOBAL)
 file(GLOB GLOBAL_SOURCES global/*.c)
 LIST (APPEND SOURCES ${GLOBAL_SOURCES})
 endif(GLOBAL)
-file(GLOB HEADERS *.h)
+file(GLOB HEADERS *.h libs/*.h)
 
 add_library(catima ${SOURCES})
 set_target_properties(catima PROPERTIES
diff --git a/calculations.cpp b/calculations.cpp
index a47c20f..bb71d0e 100644
--- a/calculations.cpp
+++ b/calculations.cpp
@@ -447,10 +447,11 @@ double sezi_dedx_e(const Projectile &p, const Material &mat, const Config &c){
     double w;
     double sum=0.0;
     bool use95 = c.low_energy == low_energy_types::srim_95;
+    double T = p.T;
     for(int i=0;i<mat.ncomponents();i++){
         auto t = mat.get_element(i);
         w = mat.weight_fraction(i);
-        sum += w*srim_dedx_e(p.Z,t.Z,p.T, use95)/t.A;
+        sum += w*srim_dedx_e(p.Z,t.Z,T, use95)/t.A;
     }
     return 100*sum*Avogadro; // returning MeV/g/cm2
 }
diff --git a/catima.cpp b/catima.cpp
index f541e4f..1044188 100644
--- a/catima.cpp
+++ b/catima.cpp
@@ -257,12 +257,25 @@ Result calculate(Projectile &p, const Material &t, const Config &c){
 
     auto fx2 = [&](double x)->double{ 
 	    double range = range_spline(T);
-            double tt = range - range_spline(x);      
-            double t0 = std::min(range, t.thickness());
+        double tt = range - range_spline(x);      
+        double t0 = std::min(range, t.thickness());
 	    return (tt-t0)*(tt-t0)*angular_variance_spline.derivative(x);
             };
-    res.sigma_x = integrator.integrate(fx2,res.Eout, res.Ein)/t.density()/t.density();
+           
+    
+    res.sigma_x = integrator_adaptive.integrate(fx2,res.Eout, res.Ein,1e-3, 1e-3,4)/t.density()/t.density();    
+    //res.sigma_x = integrator_adaptive.integrate(fx2p,0, t.thickness_cm(),1e-3, 1e-3,4)/t.density()/t.density();    
     res.sigma_x = sqrt(res.sigma_x);
+
+    auto fx1 = [&](double x)->double{ 
+	    double range = range_spline(T);
+        double tt = range - range_spline(x);      
+        double t0 = std::min(range, t.thickness());
+	    return (t0-tt)*angular_variance_spline.derivative(x);
+            };
+    
+    res.cov = integrator_adaptive.integrate(fx1,res.Eout, res.Eout, 1e-6, 1e-3,4)/t.density();
+
     #ifdef REACTIONS
     res.sp = nonreaction_rate(p,t,c);
     #endif
@@ -275,18 +288,20 @@ MultiResult calculate(Projectile &p, const Layers &layers, const Config &c){
     res.total_result.Ein = e;
     res.results.reserve(layers.num());
     double z = 0;
+    double cov = 0;
     for(auto&m:layers.get_materials()){
         z += m.thickness_cm();
         Result r = calculate(p,m,e,c);
-        e = r.Eout;
-        res.total_result.sigma_a += r.sigma_a*r.sigma_a;
+        e = r.Eout;        
         res.total_result.Eloss += r.Eloss;
         res.total_result.sigma_E += r.sigma_E*r.sigma_E; 
         res.total_result.tof += r.tof;
-        res.total_result.Eout = r.Eout;
-        double temp = r.sigma_a*(layers.thickness_cm() - z); 
-        res.total_result.sigma_x += (r.sigma_x*r.sigma_x) + (temp*temp);
-        //res.total_result.sigma_x += r.sigma_x*r.sigma_x;
+        res.total_result.Eout = r.Eout;        
+        double a2 = res.total_result.sigma_a;
+        res.total_result.sigma_x += (2*m.thickness_cm()*res.total_result.cov) + (a2*m.thickness_cm()*m.thickness_cm()) + r.sigma_x*r.sigma_x;
+        //res.total_result.sigma_x += (a2*m.thickness_cm()*m.thickness_cm()) + r.sigma_x*r.sigma_x;
+        res.total_result.cov += a2*m.thickness_cm() + r.cov;
+        res.total_result.sigma_a += r.sigma_a*r.sigma_a;
         #ifdef REACTIONS
         res.total_result.sp = (r.sp>=0.0)?res.total_result.sp*r.sp:-1;
         #endif
diff --git a/integrator.cpp b/integrator.cpp
index 20c7463..80386de 100644
--- a/integrator.cpp
+++ b/integrator.cpp
@@ -7,6 +7,8 @@
 
 namespace catima{
     integrator_type integrator;
+    integrator_adaptive_type integrator_adaptive;
+
 #ifdef GSL_INTEGRATION
     double funcwrapper3(double x, void *_c){
     std::function<double(double)> *f = (std::function<double(double)> *)_c;
diff --git a/integrator.h b/integrator.h
index 56bd398..a039055 100644
--- a/integrator.h
+++ b/integrator.h
@@ -23,11 +23,16 @@
 //#ifdef USE_THREADS
 //#include <mutex>
 //#endif
-
+#include "catima/glq_integrator.h"
+#include "catima/gkq_integrator.h"
 #ifdef GSL_INTEGRATION
 #include "gsl/gsl_integration.h"
 #endif
 
+
+using integrators::GaussLegendreIntegration;
+using integrators::GaussKronrodIntegration;
+
 namespace catima{
     
 #ifdef GSL_INTEGRATION
@@ -52,136 +57,15 @@ class IntegratorGSL{
     };
 #endif
 
-template<int order>
-struct GL_data{
-};
-
-template<int order>
-class GaussLegendreIntegration{
-public:
-    template<typename F>
-    double integrate(F f, double a, double b) const;
-    template<typename F>
-    double operator()(F f, double a, double b) const {return integrate(f, a, b);}
-    double w(int i) const {return GL_data<order>::w()[i];}
-    double x(int i) const {return GL_data<order>::x()[i];}
-    int n() const {return order;}
-    std::array<double,order> get_points(double a = -1.0, double b = 1.0)const;
-};
-
-template<int order>
-template<typename F>
-double GaussLegendreIntegration<order>::integrate(F f, double a, double b) const{
-    double res=0.0;
-    double p = 0.5*(b-a);
-    double q = 0.5*(b+a);
-
-    if(order%2){res+= w(0) * (f(p*x(0) + q));} // in case odd-order
-    for(int i=order%2;i<order/2 + order%2;i++){
-        res += w(i) * (f(p*x(i) + q) + f(-p*x(i) + q));
-    }
-    return p*res;
-}
-
-template<int order>
-std::array<double,order> GaussLegendreIntegration<order>::get_points(double a,  double b)const{
-    std::array<double,order> points;
-    double p = 0.5*(b-a);
-    double q = 0.5*(b+a);
-    
-    int num = (order/2);
-    for(int i=0;i< num;i++){
-        points[num-i-1] = -p*x(i) + q;
-        points[num+i] = p*x(i) + q;
-    }
-    return points;
-}
-
-// order = 8
-template<>
-struct GL_data<8>{
-    static const std::array<double,4>& x(){
-        static const std::array<double,4> _x = 
-            {0.1834346424956498049394761,0.5255324099163289858177390,0.7966664774136267395915539,0.9602898564975362316835609};
-        return _x;
-    }
-    static const std::array<double,4>& w(){
-        static const std::array<double,4> _w = 
-            {0.3626837833783619829651504,0.3137066458778872873379622,0.2223810344533744705443560,0.1012285362903762591525314};
-        return _w;
-    }
-};
-
-// order = 10
-template<>
-struct GL_data<10>{
-    static const std::array<double,5>& x(){
-        static const std::array<double,5> _x = 
-            {0.1488743389816312108848260,0.4333953941292471907992659,0.6794095682990244062343274,0.8650633666889845107320967,0.9739065285171717200779640};
-        return _x;
-    }
-    static const std::array<double,5>& w(){
-        static const std::array<double,5> _w = 
-            {0.2955242247147528701738930,0.2692667193099963550912269,0.2190863625159820439955349,0.1494513491505805931457763,0.0666713443086881375935688};
-        return _w;
-    }
-};
-
-// order  = 12
-template<>
-struct GL_data<12>{
-    static const std::array<double,6>& x(){
-        static const std::array<double,6> _x = 
-            {0.1252334085114689154724414,0.3678314989981801937526915,0.5873179542866174472967024,0.7699026741943046870368938,0.9041172563704748566784659,0.9815606342467192506905491};
-        return _x;
-    }
-    
-    static const std::array<double,6>& w(){
-        static const std::array<double,6> _w = 
-            {0.2491470458134027850005624,0.2334925365383548087608499,0.2031674267230659217490645,0.1600783285433462263346525,0.1069393259953184309602547,0.0471753363865118271946160};
-        return _w;
-    }
-};
-
-// order  = 14
-template<>
-struct GL_data<14>{
-    static const std::array<double,7>& x(){
-        static const std::array<double,7> _x = 
-            {0.1080549487073436620662447,0.3191123689278897604356718,0.5152486363581540919652907,0.6872929048116854701480198,0.8272013150697649931897947,0.9284348836635735173363911,0.9862838086968123388415973};
-        return _x;
-    }
-    
-    static const std::array<double,7>& w(){
-        static const std::array<double,7> _w = 
-            {0.2152638534631577901958764,0.2051984637212956039659241,0.1855383974779378137417166,0.1572031671581935345696019,0.1215185706879031846894148,0.0801580871597602098056333,0.0351194603317518630318329};
-        return _w;
-    }
-};
-
-// order = 16
-template<>
-struct GL_data<16>{
-    static const std::array<double,8>& x(){
-        static const std::array<double,8> _x = 
-           {0.0950125098376374401853193,0.2816035507792589132304605,0.4580167776572273863424194,0.6178762444026437484466718,0.7554044083550030338951012,0.8656312023878317438804679,0.9445750230732325760779884,0.9894009349916499325961542};
-        return _x;
-    }
-    
-    static const std::array<double,8>& w(){
-        static const std::array<double,8> _w = 
-           {0.1894506104550684962853967,0.1826034150449235888667637,0.1691565193950025381893121,0.1495959888165767320815017,0.1246289712555338720524763,0.0951585116824927848099251,0.0622535239386478928628438,0.0271524594117540948517806};
-        return _w;
-    }
-};
-
 #ifdef GSL_INTEGRATION
 using integrator_type = IntegratorGSL;
 #else
 using integrator_type = GaussLegendreIntegration<8>;
 #endif
+using integrator_adaptive_type = GaussKronrodIntegration<21>;
 
 extern integrator_type integrator;
+extern integrator_adaptive_type integrator_adaptive;
 }
 
 #endif
diff --git a/libs/gkq_integrator.h b/libs/gkq_integrator.h
new file mode 100644
index 0000000..51db896
--- /dev/null
+++ b/libs/gkq_integrator.h
@@ -0,0 +1,440 @@
+/*
+ *  Copyright(C) 2017, Andrej Prochazka
+ *  This program is free software: you can redistribute it and/or modify
+ *  it under the terms of the GNU Affero General Public License as published by
+ *  the Free Software Foundation, either version 3 of the License, or
+ *  (at your option) any later version.
+ *  This program is distributed in the hope that it will be useful,
+ *  but WITHOUT ANY WARRANTY; without even the implied warranty of
+ *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ *  GNU Affero General Public License for more details.
+
+ *  You should have received a copy of the GNU Affero General Public License
+ *  along with this program.  If not, see <http://www.gnu.org/licenses/>.
+ */
+
+#ifndef GKQ_INTEGRATOR_H
+#define GKQ_INTEGRATOR_H
+#include <array>
+#include <cmath>
+#include <limits>
+#include <utility>
+#include <vector>
+
+namespace integrators{
+
+template<int order>
+struct GK_data{
+};
+
+/**
+ * @brief adaptive integrator 
+ * following orders are supported: 7,15,21,31,61
+ * @tparam order Kronrod order
+ */
+template<int order>
+class GaussKronrodIntegration{
+public:
+    template<typename F>
+    static double integrate(F& f, double a, double b, double eps = 1e-3, double reps=1e-6, int N = 1);
+
+    template<typename F>
+    static double integrate_intervals(F& f, const std::vector<std::pair<double,double>>& intervals, double eps = 1e-3, double reps=1e-6);
+
+    template<typename F>
+    static std::pair<double,double> integrate_nonadaptive(F& f, double a, double b);
+
+    template<typename F>
+    static double integrate_adaptive(F& f, double a, double b, double eps = 1e-3, double reps=1e-6, int level=49);
+
+    static double w(int i) {return GK_data<order>::w()[i];}
+    static double wg(int i) {return GK_data<order>::wg()[i];}
+    static double x(int i) {return GK_data<order>::x()[i];}
+    static int n() {return order;}
+    static std::array<double,order> get_points(double a = -1.0, double b = 1.0);
+
+private:
+    static const size_t ngauss = (order-1)/2;
+    static const size_t xsize = order/2 + 1;
+    static const bool oddgauss = ((order-1)/2)&1;
+};
+
+template<int order>
+template<typename F>
+std::pair<double,double> GaussKronrodIntegration<order>::integrate_nonadaptive(F& f, double a, double b){
+    double res;
+    double gres = 0.0;
+    double val;
+    double p = 0.5*(b-a);
+    double q = 0.5*(b+a);
+    unsigned int gi = 1; //by default assume odd-order gauss
+    unsigned int ki = 2;
+
+    // 1st kronrod point
+    val = f(p*x(0) + q);
+    res = w(0) * val;
+    if(oddgauss){ // 1st gaus point if odd order gauss
+        gres = wg(0) * val;
+        gi = 2;
+        ki = 1;
+        }
+
+    for(unsigned int i=gi;i<xsize;i+=2){
+        val = f(p*x(i) + q);
+        res += w(i) * val;
+        gres += wg(i/2)*val;
+
+        val = f(-p*x(i) + q);
+        res += w(i) * val;
+        gres += wg(i/2)*val;
+    }
+
+    for(unsigned int i=ki;i<xsize;i+=2){
+        res += w(i) * (f(p*x(i) + q) + f(-p*x(i) + q));
+    }
+
+    double err = std::max( std::abs(gres-res), std::numeric_limits<double>::epsilon());
+
+    return std::make_pair(p*res, p*err);
+}
+
+template<int order>
+template<typename F>
+double GaussKronrodIntegration<order>::integrate_adaptive(F& f, double a, double b, double eps, double rprec, int level){
+    double result = 0.0;
+    double err = 0.0;
+    const double numlimit = 10*std::numeric_limits<double>::epsilon();
+
+    auto r = integrate_nonadaptive(f, a, b);
+    result = r.first;
+    err = r.second;
+    //printf("level = %d, I=%lf, e=%lf, %lf - %lf\n",level,result,err,a,b);
+    if( (std::abs(result) < numlimit) || ((b-a)<numlimit)){
+        return result;
+    }
+
+    double aeps = std::max(rprec*std::abs(result), eps);
+    if((aeps<numlimit) || (std::abs(result)<aeps)){
+	    return result;
+    }
+
+    if( level && (err > aeps)){
+	    double mid = 0.5*(a+b);
+        result  = integrate_adaptive(f, a, mid, 0.707*aeps, 0, level-1);
+        result += integrate_adaptive(f, mid, b, 0.707*aeps, 0, level-1);
+        }
+
+    return result;
+    }
+
+template<int order>
+template<typename F>
+double GaussKronrodIntegration<order>::integrate(F& f, double a, double b, double eps, double reps, int N){
+    double step = (b-a)/N;
+    double result = 0;
+    for(int i=0; i<N;i++){
+        double m =a+(i*step);
+        result+=integrate_adaptive(f,m,m+step, eps/N, reps);
+    }
+
+    return result;
+}
+
+template<int order>
+template<typename F>
+double GaussKronrodIntegration<order>::integrate_intervals(F& f, const std::vector<std::pair<double,double>>& intervals, double eps, double reps){
+    double result = 0;
+    for(auto& i:intervals){
+        result+=integrate_adaptive(f,i.first,i.second, eps/intervals.size(), reps);
+    }
+
+    return result;
+}
+
+template<int order>
+std::array<double,order> GaussKronrodIntegration<order>::get_points(double a,  double b){
+    std::array<double,order> points;
+    double p = 0.5*(b-a);
+    double q = 0.5*(b+a);
+
+    int num = (order/2);
+    for(int i=0;i< num;i++){
+        points[num-i-1] = -p*x(i) + q;
+        points[num+i] = p*x(i) + q;
+    }
+    return points;
+}
+
+
+/// weights and abscissas
+// order = 7
+template<>
+struct GK_data<7>{
+    static std::array<double,4> const & x(){
+        static const std::array<double,4> _x =
+            {0.0, 0.4342437493468025580021, 0.774596669241483377036,0.9604912687080202834235};
+        return _x;
+    }
+    static std::array<double,4> const & w(){
+        static const std::array<double,4> _w =
+            {0.4509165386584741423451, 0.4013974147759622229051, 0.2684880898683334407286, 0.1046562260264672651938};
+        return _w;
+        }
+    static std::array<double,4> const & wg(){
+        static const std::array<double,4> _wg =
+            {0.8888888888888888888889, 0.555555555555555555556};
+        return _wg;
+        }
+};
+
+//order = 15
+template<>
+struct GK_data<15>{
+    static std::array<double,8> const & x(){
+        static const std::array<double,8> _x =
+            {0.0,
+            0.207784955007898467600689403773244913,
+            0.405845151377397166906606412076961463,
+            0.586087235467691130294144838258729598,
+            0.741531185599394439863864773280788407,
+            0.864864423359769072789712788640926201,
+            0.949107912342758524526189684047851262,
+            0.991455371120812639206854697526328517};
+            return _x;
+    }
+    static std::array<double,8> const & w(){
+        static const std::array<double,8> _w =
+            {
+         0.209482141084727828012999174891714264,
+         0.204432940075298892414161999234649085,
+         0.190350578064785409913256402421013683,
+         0.169004726639267902826583426598550284,
+         0.140653259715525918745189590510237920,
+         0.104790010322250183839876322541518017,
+         0.0630920926299785532907006631892042867,
+         0.0229353220105292249637320080589695920};
+        return _w;
+        }
+    static std::array<double,4> const & wg(){
+        static const std::array<double,4> _wg =
+        { 0.417959183673469387755102040816326531,
+          0.381830050505118944950369775488975134,
+          0.279705391489276667901467771423779582,
+          0.129484966168869693270611432679082018};
+        return _wg;
+        }
+};
+
+//order = 21
+template<>
+struct GK_data<21>{
+    static std::array<double,11> const & x(){
+        static const std::array<double,11> _x = {
+            0.00000000000000000e+00,
+            1.48874338981631211e-01,
+            2.94392862701460198e-01,
+            4.33395394129247191e-01,
+            5.62757134668604683e-01,
+            6.79409568299024406e-01,
+            7.80817726586416897e-01,
+            8.65063366688984511e-01,
+            9.30157491355708226e-01,
+            9.73906528517171720e-01,
+            9.95657163025808081e-01};
+            return _x;
+    }
+    static std::array<double,11> const & w(){
+        static const std::array<double,11> _w =
+            {
+            1.49445554002916906e-01,
+            1.47739104901338491e-01,
+            1.42775938577060081e-01,
+            1.34709217311473326e-01,
+            1.23491976262065851e-01,
+            1.09387158802297642e-01,
+            9.31254545836976055e-02,
+            7.50396748109199528e-02,
+            5.47558965743519960e-02,
+            3.25581623079647275e-02,
+            1.16946388673718743e-02,
+            };
+        return _w;
+        }
+    static std::array<double,5> const & wg(){
+        static const std::array<double,5> _wg =
+        {
+            2.95524224714752870e-01,
+            2.69266719309996355e-01,
+            2.19086362515982044e-01,
+            1.49451349150580593e-01,
+            6.66713443086881376e-02,};
+        return _wg;
+        }
+};
+
+
+
+//order = 31
+template<>
+struct GK_data<31>{
+    static std::array<double,16> const & x(){
+        static const std::array<double,16> _x = {
+            0.00000000000000000e+00,
+            1.01142066918717499e-01,
+            2.01194093997434522e-01,
+            2.99180007153168812e-01,
+            3.94151347077563370e-01,
+            4.85081863640239681e-01,
+            5.70972172608538848e-01,
+            6.50996741297416971e-01,
+            7.24417731360170047e-01,
+            7.90418501442465933e-01,
+            8.48206583410427216e-01,
+            8.97264532344081901e-01,
+            9.37273392400705904e-01,
+            9.67739075679139134e-01,
+            9.87992518020485428e-01,
+            9.98002298693397060e-01    
+            };
+            return _x;
+    }
+    static std::array<double,16> const & w(){
+        static const std::array<double,16> _w =
+            {
+            1.01330007014791549e-01,
+            1.00769845523875595e-01,
+            9.91735987217919593e-02,
+            9.66427269836236785e-02,
+            9.31265981708253212e-02,
+            8.85644430562117706e-02,
+            8.30805028231330210e-02,
+            7.68496807577203789e-02,
+            6.98541213187282587e-02,
+            6.20095678006706403e-02,
+            5.34815246909280873e-02,
+            4.45897513247648766e-02,
+            3.53463607913758462e-02,
+            2.54608473267153202e-02,
+            1.50079473293161225e-02,
+            5.37747987292334899e-03
+            };
+        return _w;
+        }
+    static std::array<double,8> const & wg(){
+        static const std::array<double,8> _wg =
+        {
+        2.02578241925561273e-01,
+        1.98431485327111576e-01,
+        1.86161000015562211e-01,
+        1.66269205816993934e-01,
+        1.39570677926154314e-01,
+        1.07159220467171935e-01,
+        7.03660474881081247e-02,
+        3.07532419961172684e-02
+        };
+        return _wg;
+        }
+};
+
+//order = 61
+template<>
+struct GK_data<61>{
+    static std::array<double,31> const & x(){
+        static const std::array<double,31> _x = {
+         0.00000000000000000e+00,
+         5.14718425553176958e-02,
+         1.02806937966737030e-01,
+         1.53869913608583547e-01,
+         2.04525116682309891e-01,
+         2.54636926167889846e-01,
+         3.04073202273625077e-01,
+         3.52704725530878113e-01,
+         4.00401254830394393e-01,
+         4.47033769538089177e-01,
+         4.92480467861778575e-01,
+         5.36624148142019899e-01,
+         5.79345235826361692e-01,
+         6.20526182989242861e-01,
+         6.60061064126626961e-01,
+         6.97850494793315797e-01,
+         7.33790062453226805e-01,
+         7.67777432104826195e-01,
+         7.99727835821839083e-01,
+         8.29565762382768397e-01,
+         8.57205233546061099e-01,
+         8.82560535792052682e-01,
+         9.05573307699907799e-01,
+         9.26200047429274326e-01,
+         9.44374444748559979e-01,
+         9.60021864968307512e-01,
+         9.73116322501126268e-01,
+         9.83668123279747210e-01,
+         9.91630996870404595e-01,
+         9.96893484074649540e-01,
+         9.99484410050490638e-01
+            };
+            return _x;
+    }
+    static std::array<double,31> const & w(){
+        static const std::array<double,31> _w =
+            {
+         5.14947294294515676e-02,
+         5.14261285374590259e-02,
+         5.12215478492587722e-02,
+         5.08817958987496065e-02,
+         5.04059214027823468e-02,
+         4.97956834270742064e-02,
+         4.90554345550297789e-02,
+         4.81858617570871291e-02,
+         4.71855465692991539e-02,
+         4.60592382710069881e-02,
+         4.48148001331626632e-02,
+         4.34525397013560693e-02,
+         4.19698102151642461e-02,
+         4.03745389515359591e-02,
+         3.86789456247275930e-02,
+         3.68823646518212292e-02,
+         3.49793380280600241e-02,
+         3.29814470574837260e-02,
+         3.09072575623877625e-02,
+         2.87540487650412928e-02,
+         2.65099548823331016e-02,
+         2.41911620780806014e-02,
+         2.18280358216091923e-02,
+         1.94141411939423812e-02,
+         1.69208891890532726e-02,
+         1.43697295070458048e-02,
+         1.18230152534963417e-02,
+         9.27327965951776343e-03,
+         6.63070391593129217e-03,
+         3.89046112709988405e-03,
+         1.38901369867700762e-03
+            };
+        return _w;
+        }
+    static std::array<double,15> const & wg(){
+        static const std::array<double,15> _wg =
+        {
+         1.02852652893558840e-01,
+         1.01762389748405505e-01,
+         9.95934205867952671e-02,
+         9.63687371746442596e-02,
+         9.21225222377861287e-02,
+         8.68997872010829798e-02,
+         8.07558952294202154e-02,
+         7.37559747377052063e-02,
+         6.59742298821804951e-02,
+         5.74931562176190665e-02,
+         4.84026728305940529e-02,
+         3.87991925696270496e-02,
+         2.87847078833233693e-02,
+         1.84664683110909591e-02,
+         7.96819249616660562e-03
+        };
+        return _wg;
+        }
+};
+
+
+} // end of namespace
+#endif
diff --git a/libs/glq_integrator.h b/libs/glq_integrator.h
new file mode 100644
index 0000000..d3aaf3e
--- /dev/null
+++ b/libs/glq_integrator.h
@@ -0,0 +1,356 @@
+/*
+ *  Copyright(C) 2017, Andrej Prochazka
+ *  This program is free software: you can redistribute it and/or modify
+ *  it under the terms of the GNU Affero General Public License as published by
+ *  the Free Software Foundation, either version 3 of the License, or
+ *  (at your option) any later version.
+ *  This program is distributed in the hope that it will be useful,
+ *  but WITHOUT ANY WARRANTY; without even the implied warranty of
+ *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ *  GNU Affero General Public License for more details.
+
+ *  You should have received a copy of the GNU Affero General Public License
+ *  along with this program.  If not, see <http://www.gnu.org/licenses/>.
+ */
+#ifndef GLQ_INTEGRATOR_H
+#define GLQ_INTEGRATOR_H
+#include <array>
+
+namespace integrators{
+
+template<int order>
+struct GL_data{
+};
+
+template<int order>
+class GaussLegendreIntegration{
+public:
+    template<typename F>
+    double integrate(F& f, double a, double b) const;
+    template<typename F>
+    double operator()(F& f, double a, double b) const {return integrate(f, a, b);}
+    double w(int i) const {return GL_data<order>::w()[i];}
+    double x(int i) const {return GL_data<order>::x()[i];}
+    int n() const {return order;}
+    std::array<double,order> get_points(double a = -1.0, double b = 1.0)const;
+};
+
+template<int order>
+template<typename F>
+double GaussLegendreIntegration<order>::integrate(F& f, double a, double b) const{
+    double res=0.0;
+    double p = 0.5*(b-a);
+    double q = 0.5*(b+a);
+
+    if(order%2){res+= w(0) * (f(p*x(0) + q));} // in case odd-order
+    for(int i=order%2;i<order/2 + order%2;i++){
+        res += w(i) * (f(p*x(i) + q) + f(-p*x(i) + q));
+    }
+    return p*res;
+}
+
+template<int order>
+std::array<double,order> GaussLegendreIntegration<order>::get_points(double a,  double b)const{
+    std::array<double,order> points;
+    double p = 0.5*(b-a);
+    double q = 0.5*(b+a);
+
+    int num = (order/2);
+    for(int i=0;i< num;i++){
+        points[num-i-1] = -p*x(i) + q;
+        points[num+i] = p*x(i) + q;
+    }
+    return points;
+}
+
+
+template<int order>
+class GaussLegendreIntegration2D{
+public:
+    template<typename F>
+    double integrate(F& f, double a, double b, double c, double d) const;
+    template<typename F>
+    double operator()(F& f, double a, double b, double c, double d) const {return integrate(f, a,b,c,d);}
+private:
+    GaussLegendreIntegration<order> integrator;
+};
+
+template<int order>
+template<typename F>
+double GaussLegendreIntegration2D<order>::integrate(F& f, double a, double b, double c, double d) const{
+    double res=0.0;
+    double p = (b-a)/2.0;
+    double q = (b+a)/2.0;
+    double r = (d-c)/2.0;
+    double s = (d+c)/2.0;
+
+    double xx, yy, sum;
+    for(int i=0;i<order/2;i++){
+        xx = (p*integrator.x(i));
+        for(int j=0;j<order/2;j++){
+            yy = (r*integrator.x(j));
+            sum = (f(xx + q, yy + s) + f(xx + q, -yy+s));
+            sum += (f(-xx + q, yy + s) + f(-xx + q, -yy+s));
+            res += integrator.w(i) * integrator.w(j) * sum;
+        }
+    }
+    return p*r*res;
+}
+
+template<int order, int order2 = order>
+class GaussLegendreIntegration2DA{
+public:
+    template<typename F>
+    double integrate(F& f, double a, double b, double c, double d) const;
+    template<typename F>
+    double operator()(F& f, double a, double b, double c, double d) const {return integrate(f, a,b,c,d);}
+private:
+    GaussLegendreIntegration<order> integrator;
+    GaussLegendreIntegration<order2> integrator2;
+};
+
+template<int order, int order2>
+template<typename F>
+double GaussLegendreIntegration2DA<order, order2>::integrate(F& f, double a, double b, double c, double d) const{
+    double res=0.0;
+    double p = (b-a)/2.0;
+    double q = (b+a)/2.0;
+    double r = (d-c)/2.0;
+    double s = (d+c)/2.0;
+
+    double xx, yy, sum;
+    for(int i=0;i<order/2;i++){
+        xx = (p*integrator.x(i));
+        for(int j=0;j<order2/2;j++){
+            yy = (r*integrator2.x(j));
+            sum = (f(xx + q, yy + s) + f(xx + q, -yy+s));
+            sum += (f(-xx + q, yy + s) + f(-xx + q, -yy+s));
+            res += integrator.w(i) * integrator2.w(j) * sum;
+        }
+    }
+    return p*r*res;
+}
+
+/// weights
+//order = 3
+
+template<>
+struct GL_data<3>{
+    static const std::array<double,2>& x(){
+        static const std::array<double,2> _x = {0.0,0.7745966692414833770359};
+        return _x;
+    }
+
+    static const std::array<double,2>& w(){
+        static const std::array<double,2> _w = {0.8888888888888888888889,0.555555555555555555556};
+        return _w;
+    }
+};
+
+// order = 4
+template<>
+struct GL_data<4>{
+    static const std::array<double,2>& x(){
+        static const std::array<double,2> _x =
+            {0.3399810435848562648026658,0.8611363115940525752239465};
+        return _x;
+    }
+
+    static const std::array<double,2>& w(){
+        static const std::array<double,2> _w =
+            {0.6521451548625461426269361,0.3478548451374538573730639};
+        return _w;
+    }
+};
+
+// order = 5
+template<>
+struct GL_data<5>{
+    static const std::array<double,3>& x(){
+        static const std::array<double,3> _x =
+            {0.0, 0.5384693101056830910363, 0.9061798459386639927976};
+        return _x;
+    }
+
+    static const std::array<double,3>& w(){
+        static const std::array<double,3> _w =
+            {0.568888888888888888888, 0.4786286704993664680413, 0.2369268850561890875143};
+        return _w;
+    }
+};
+
+// order = 6
+template<>
+struct GL_data<6>{
+    static const std::array<double,3>& x(){
+        static const std::array<double,3> _x =
+            {0.2386191860831969086305017,0.6612093864662645136613996,0.9324695142031520278123016};
+        return _x;
+    }
+    static const std::array<double,3>& w(){
+        static const std::array<double,3> _w =
+            {0.4679139345726910473898703,0.3607615730481386075698335,0.1713244923791703450402961};
+        return _w;
+    }
+};
+
+// order = 7
+template<>
+struct GL_data<7>{
+    static const std::array<double,4>& x(){
+        static const std::array<double,4> _x =
+            {0.0, 0.4058451513773971669066, 0.7415311855993944398639,0.9491079123427585245262};
+        return _x;
+    }
+    static const std::array<double,4>& w(){
+        static const std::array<double,4> _w =
+            {0.417959183673469387755, 0.38183005050511894495, 0.279705391489276667901, 0.129484966168869693271};
+        return _w;
+    }
+};
+
+// order = 8
+template<>
+struct GL_data<8>{
+    static const std::array<double,4>& x(){
+        static const std::array<double,4> _x =
+            {0.1834346424956498049394761,0.5255324099163289858177390,0.7966664774136267395915539,0.9602898564975362316835609};
+        return _x;
+    }
+    static const std::array<double,4>& w(){
+        static const std::array<double,4> _w =
+            {0.3626837833783619829651504,0.3137066458778872873379622,0.2223810344533744705443560,0.1012285362903762591525314};
+        return _w;
+    }
+};
+
+// order = 10
+template<>
+struct GL_data<10>{
+    static const std::array<double,5>& x(){
+        static const std::array<double,5> _x =
+            {0.1488743389816312108848260,0.4333953941292471907992659,0.6794095682990244062343274,0.8650633666889845107320967,0.9739065285171717200779640};
+        return _x;
+    }
+    static const std::array<double,5>& w(){
+        static const std::array<double,5> _w =
+            {0.2955242247147528701738930,0.2692667193099963550912269,0.2190863625159820439955349,0.1494513491505805931457763,0.0666713443086881375935688};
+        return _w;
+    }
+};
+
+// order  = 12
+template<>
+struct GL_data<12>{
+    static const std::array<double,6>& x(){
+        static const std::array<double,6> _x =
+            {0.1252334085114689154724414,0.3678314989981801937526915,0.5873179542866174472967024,0.7699026741943046870368938,0.9041172563704748566784659,0.9815606342467192506905491};
+        return _x;
+    }
+
+    static const std::array<double,6>& w(){
+        static const std::array<double,6> _w =
+            {0.2491470458134027850005624,0.2334925365383548087608499,0.2031674267230659217490645,0.1600783285433462263346525,0.1069393259953184309602547,0.0471753363865118271946160};
+        return _w;
+    }
+};
+
+// order  = 14
+template<>
+struct GL_data<14>{
+    static const std::array<double,7>& x(){
+        static const std::array<double,7> _x =
+            {0.1080549487073436620662447,0.3191123689278897604356718,0.5152486363581540919652907,0.6872929048116854701480198,0.8272013150697649931897947,0.9284348836635735173363911,0.9862838086968123388415973};
+        return _x;
+    }
+
+    static const std::array<double,7>& w(){
+        static const std::array<double,7> _w =
+            {0.2152638534631577901958764,0.2051984637212956039659241,0.1855383974779378137417166,0.1572031671581935345696019,0.1215185706879031846894148,0.0801580871597602098056333,0.0351194603317518630318329};
+        return _w;
+    }
+};
+
+// order = 16
+template<>
+struct GL_data<16>{
+    static const std::array<double,8>& x(){
+        static const std::array<double,8> _x =
+           {0.0950125098376374401853193,0.2816035507792589132304605,0.4580167776572273863424194,0.6178762444026437484466718,0.7554044083550030338951012,0.8656312023878317438804679,0.9445750230732325760779884,0.9894009349916499325961542};
+        return _x;
+    }
+
+    static const std::array<double,8>& w(){
+        static const std::array<double,8> _w =
+           {0.1894506104550684962853967,0.1826034150449235888667637,0.1691565193950025381893121,0.1495959888165767320815017,0.1246289712555338720524763,0.0951585116824927848099251,0.0622535239386478928628438,0.0271524594117540948517806};
+        return _w;
+    }
+};
+
+// order = 20
+template<>
+struct GL_data<20>{
+    static const std::array<double,10>& x(){
+        static const std::array<double,10> _x =
+            {0.0765265211334973337546404,0.2277858511416450780804962,0.3737060887154195606725482,0.5108670019508270980043641,0.6360536807265150254528367,0.7463319064601507926143051,0.8391169718222188233945291,0.9122344282513259058677524,0.9639719272779137912676661,0.9931285991850949247861224};
+        return _x;
+    }
+
+    static const std::array<double,10>& w(){
+        static const std::array<double,10> _w =
+            {0.1527533871307258506980843,0.1491729864726037467878287,0.1420961093183820513292983,0.1316886384491766268984945,0.1181945319615184173123774,0.1019301198172404350367501,0.0832767415767047487247581,0.0626720483341090635695065,0.0406014298003869413310400,0.0176140071391521183118620};
+        return _w;
+    }
+};
+
+// order = 32
+template<>
+struct GL_data<32>{
+    static const std::array<double,16>& x(){
+        static const std::array<double,16> _x =
+            {0.0483076656877383162348126,0.1444719615827964934851864,0.2392873622521370745446032,0.3318686022821276497799168,0.4213512761306353453641194,0.5068999089322293900237475,0.5877157572407623290407455,0.6630442669302152009751152,0.7321821187402896803874267,0.7944837959679424069630973,0.8493676137325699701336930,0.8963211557660521239653072,0.9349060759377396891709191,0.9647622555875064307738119,0.9856115115452683354001750,0.9972638618494815635449811};
+        return _x;
+    }
+
+    static const std::array<double,16>& w(){
+        static const std::array<double,16> _w =
+            {0.0965400885147278005667648,0.0956387200792748594190820,0.0938443990808045656391802,0.0911738786957638847128686,0.0876520930044038111427715,0.0833119242269467552221991,0.0781938957870703064717409,0.0723457941088485062253994,0.0658222227763618468376501,0.0586840934785355471452836,0.0509980592623761761961632,0.0428358980222266806568786,0.0342738629130214331026877,0.0253920653092620594557526,0.0162743947309056706051706,0.0070186100094700966004071};
+        return _w;
+    }
+};
+
+//order = 64
+template<>
+struct GL_data<64>{
+    static const std::array<double,32>& x(){
+        static const std::array<double,32> _x =
+            {0.0243502926634244325089558,0.0729931217877990394495429,0.1214628192961205544703765,0.1696444204239928180373136,0.2174236437400070841496487,0.2646871622087674163739642,0.3113228719902109561575127,0.3572201583376681159504426,0.4022701579639916036957668,0.4463660172534640879849477,0.4894031457070529574785263,0.5312794640198945456580139,0.5718956462026340342838781,0.6111553551723932502488530,0.6489654712546573398577612,0.6852363130542332425635584,0.7198818501716108268489402,0.7528199072605318966118638,0.7839723589433414076102205,0.8132653151227975597419233,0.8406292962525803627516915,0.8659993981540928197607834,0.8893154459951141058534040,0.9105221370785028057563807,0.9295691721319395758214902,0.9464113748584028160624815,0.9610087996520537189186141,0.9733268277899109637418535,0.9833362538846259569312993,0.9910133714767443207393824,0.9963401167719552793469245,0.9993050417357721394569056};
+        return _x;
+    }
+
+    static const std::array<double,32>& w(){
+        static const std::array<double,32> _w =
+            {0.0486909570091397203833654,0.0485754674415034269347991,0.0483447622348029571697695,0.0479993885964583077281262,0.0475401657148303086622822,0.0469681828162100173253263,0.0462847965813144172959532,0.0454916279274181444797710,0.0445905581637565630601347,0.0435837245293234533768279,0.0424735151236535890073398,0.0412625632426235286101563,0.0399537411327203413866569,0.0385501531786156291289625,0.0370551285402400460404151,0.0354722132568823838106931,0.0338051618371416093915655,0.0320579283548515535854675,0.0302346570724024788679741,0.0283396726142594832275113,0.0263774697150546586716918,0.0243527025687108733381776,0.0222701738083832541592983,0.0201348231535302093723403,0.0179517157756973430850453,0.0157260304760247193219660,0.0134630478967186425980608,0.0111681394601311288185905,0.0088467598263639477230309,0.0065044579689783628561174,0.0041470332605624676352875,0.0017832807216964329472961};
+        return _w;
+    }
+};
+
+
+//order = 128
+template<>
+struct GL_data<128>{
+    static const std::array<double,64>& x(){
+        static const std::array<double,64> _x =
+            {0.0122236989606157641980521,0.0366637909687334933302153,0.0610819696041395681037870,0.0854636405045154986364980,0.1097942311276437466729747,0.1340591994611877851175753,0.1582440427142249339974755,0.1823343059853371824103826,0.2063155909020792171540580,0.2301735642266599864109866,0.2538939664226943208556180,0.2774626201779044028062316,0.3008654388776772026671541,0.3240884350244133751832523,0.3471177285976355084261628,0.3699395553498590266165917,0.3925402750332674427356482,0.4149063795522750154922739,0.4370245010371041629370429,0.4588814198335521954490891,0.4804640724041720258582757,0.5017595591361444642896063,0.5227551520511754784539479,0.5434383024128103634441936,0.5637966482266180839144308,0.5838180216287630895500389,0.6034904561585486242035732,0.6228021939105849107615396,0.6417416925623075571535249,0.6602976322726460521059468,0.6784589224477192593677557,0.6962147083695143323850866,0.7135543776835874133438599,0.7304675667419088064717369,0.7469441667970619811698824,0.7629743300440947227797691,0.7785484755064119668504941,0.7936572947621932902433329,0.8082917575079136601196422,0.8224431169556438424645942,0.8361029150609068471168753,0.8492629875779689691636001,0.8619154689395484605906323,0.8740527969580317986954180,0.8856677173453972174082924,0.8967532880491581843864474,0.9073028834017568139214859,0.9173101980809605370364836,0.9267692508789478433346245,0.9356743882779163757831268,0.9440202878302201821211114,0.9518019613412643862177963,0.9590147578536999280989185,0.9656543664319652686458290,0.9717168187471365809043384,0.9771984914639073871653744,0.9820961084357185360247656,0.9864067427245862088712355,0.9901278184917343833379303,0.9932571129002129353034372,0.9957927585349811868641612,0.9977332486255140198821574,0.9990774599773758950119878,0.9998248879471319144736081};
+        return _x;
+    }
+
+    static const std::array<double,64>& w(){
+        static const std::array<double,64> _w =
+            {0.0244461801962625182113259,0.0244315690978500450548486,0.0244023556338495820932980,0.0243585572646906258532685,0.0243002001679718653234426,0.0242273192228152481200933,0.0241399579890192849977167,0.0240381686810240526375873,0.0239220121367034556724504,0.0237915577810034006387807,0.0236468835844476151436514,0.0234880760165359131530253,0.0233152299940627601224157,0.0231284488243870278792979,0.0229278441436868469204110,0.0227135358502364613097126,0.0224856520327449668718246,0.0222443288937997651046291,0.0219897106684604914341221,0.0217219495380520753752610,0.0214412055392084601371119,0.0211476464682213485370195,0.0208414477807511491135839,0.0205227924869600694322850,0.0201918710421300411806732,0.0198488812328308622199444,0.0194940280587066028230219,0.0191275236099509454865185,0.0187495869405447086509195,0.0183604439373313432212893,0.0179603271850086859401969,0.0175494758271177046487069,0.0171281354231113768306810,0.0166965578015892045890915,0.0162550009097851870516575,0.0158037286593993468589656,0.0153430107688651440859909,0.0148731226021473142523855,0.0143943450041668461768239,0.0139069641329519852442880,0.0134112712886163323144890,0.0129075627392673472204428,0.0123961395439509229688217,0.0118773073727402795758911,0.0113513763240804166932817,0.0108186607395030762476596,0.0102794790158321571332153,0.0097341534150068058635483,0.0091830098716608743344787,0.0086263777986167497049788,0.0080645898904860579729286,0.0074979819256347286876720,0.0069268925668988135634267,0.0063516631617071887872143,0.0057726375428656985893346,0.0051901618326763302050708,0.0046045842567029551182905,0.0040162549837386423131943,0.0034255260409102157743378,0.0028327514714579910952857,0.0022382884309626187436221,0.0016425030186690295387909,0.0010458126793403487793129,0.0004493809602920903763943};
+        return _w;
+    }
+};
+
+} // end of namespace
+#endif
diff --git a/structures.h b/structures.h
index d63615d..8c46d17 100644
--- a/structures.h
+++ b/structures.h
@@ -239,6 +239,7 @@ namespace catima{
         double sigma_a=0.0;
         double sigma_r=0.0;
         double sigma_x=0.0;
+	double cov = 0.0;
         double tof=0.0;
         #ifdef REACTIONS
         double sp = 1.0;
diff --git a/tests/test_calculations.cpp b/tests/test_calculations.cpp
index cb4ffa4..60cb286 100644
--- a/tests/test_calculations.cpp
+++ b/tests/test_calculations.cpp
@@ -241,6 +241,7 @@ using namespace std;
       water.thickness_cm(7.4);      
       ll.add(water);
       res2 = catima::calculate(p,ll);
+      CHECK(ll.thickness_cm() == approx(17,0.00001));
       CHECK(res2.total_result.sigma_x == approx(0.25,0.05));
       CHECK(res2.total_result.sigma_x == approx(res17.sigma_x,0.001));
 
@@ -251,6 +252,16 @@ using namespace std;
       l.add(water);
       res2 = catima::calculate(p,l);
       CHECK(res2.total_result.sigma_x == approx(res.sigma_x).R(0.01));
+
+      catima::Layers lll;
+      water.thickness_cm(29.4/4);
+      lll.add(water);
+      lll.add(water);
+      lll.add(water);
+      lll.add(water);
+      res2 = catima::calculate(p,lll);
+      CHECK(res2.total_result.sigma_x == approx(res29.sigma_x).R(0.01));
+
     }
     TEST_CASE("result from stopped material"){
         catima::Projectile p{12,6,6,1000};
@@ -461,4 +472,4 @@ using namespace std;
         CHECK(0.1*hbar*c_light/atomic_mass_unit == approx(0.21183,0.0001));
         CHECK(16.0*dedx_constant*electron_mass*fine_structure/(atomic_mass_unit*3.0*4.0*M_PI) == approx(5.21721169334564e-7).R(1e-3));
         }
-    
\ No newline at end of file
+