Improved materials and the Kramers-Kronig solver.

dmayerich
1 parent 4198e3be
Showing 28 changed files with 7997 additions and 7851 deletions Show diff stats
CMakeLists.txt
EstimateMaterial.cpp
FileIO.cpp
GAMMA.cpp
PerformanceData.h
SimulateSpectrum.cpp
bessel.h
bessik.CPP
bessjy.cpp
cbessik.cpp
cbessjy.cpp
cudaKK.h
cudaMain.cu
etaToluene.txt
eta_TolueneK.txt
eta_TolueneN.txt
globals.h
interactivemie.cpp
interactivemie.h
interactivemie.ui
@@ -25,6 +25,9 @@ find_package(GLUT REQUIRED)
 #find GLEW
 find_package(GLEW REQUIRED)
  
+#find Qwt
+find_package(Qwt REQUIRED)
+
 #add Qt OpenGL stuff
 set(QT_USE_QTOPENGL TRUE)
  
@@ -53,9 +56,10 @@ file(GLOB SRC_CU &quot;*.cu&quot;)
 #set up copying data files
 configure_file(kPMMA.txt ${CMAKE_CURRENT_BINARY_DIR}/kPMMA.txt @ONLY)
 configure_file(eta_polystyreneK.txt ${CMAKE_CURRENT_BINARY_DIR}/eta_polystyreneK.txt @ONLY)
-configure_file(eta_TolueneK.txt ${CMAKE_CURRENT_BINARY_DIR}/eta_TolueneK.txt @ONLY)
-configure_file(eta_TolueneN.txt ${CMAKE_CURRENT_BINARY_DIR}/eta_TolueneN.txt @ONLY)
+configure_file(etaToluene.txt ${CMAKE_CURRENT_BINARY_DIR}/etaToluene.txt @ONLY)
 configure_file(source_midIR.txt ${CMAKE_CURRENT_BINARY_DIR}/source_midIR.txt @ONLY)
+configure_file(kPolyethylene.txt ${CMAKE_CURRENT_BINARY_DIR}/kPolyethylene.txt @ONLY)
+configure_file(kPTFE.txt ${CMAKE_CURRENT_BINARY_DIR}/kPTFE.txt @ONLY)
  
 #determine which source files have to be moc'd
 Qt4_wrap_cpp(UI_MOC ${SRC_H})
@@ -72,7 +76,4 @@ source_group(QtUI FILES ${SRC_UI})
 cuda_add_executable(IMie ${SRC_CPP} ${SRC_H} ${UI_H} ${UI_MOC} ${ALL_RCC} ${SRC_CU})
  
 #set the link libraries
-target_link_libraries(IMie ${QT_LIBRARIES} ${QT_QTOPENGL_LIBRARY} ${OPENGL_gl_LIBRARY} ${OPENGL_glu_LIBRARY} ${GLEW_LIBRARY})
-
-
-
+target_link_libraries(IMie ${QT_LIBRARIES} ${QT_QTOPENGL_LIBRARY} ${OPENGL_gl_LIBRARY} ${OPENGL_glu_LIBRARY} ${GLEW_LIBRARY} ${QWT_LIBRARY})
 \ No newline at end of file
-#include "globals.h"
-#include <stdlib.h>
-#define PI 3.14159
-
-double CalculateError(double* E)
-{
-	//Calculate the error between the Reference Spectrum and the Simulated Spectrum
-	double sumE = 0.0;
-	int nVals = RefSpectrum[currentSpec].size();
-	double nu;
-	for(int i=0; i<nVals; i++)
-	{
-		nu = RefSpectrum[currentSpec][i].nu;
-		E[i] = RefSpectrum[currentSpec][i].A + nu * refSlope - SimSpectrum[i].A;
-		sumE += E[i]*E[i];
-	}
-
-	return sumE/nVals;
-}
-
-void EstimateK(double* E)
-{
-	int nVals = RefSpectrum[currentSpec].size();
-	double nuStart = RefSpectrum[currentSpec].front().nu;
-	double nuEnd = RefSpectrum[currentSpec].back().nu;
-
-	double r = radius/10000.0;
-	double nu;
-	double dNu = (nuEnd - nuStart)/(nVals-1);
-	double eScale;
-	for(int i=0; i<nVals; i++)
-	{
-		nu = nuStart + i*2;
-
-		eScale = 1/(8*PI*r*nu);
-		EtaK[i].A = EtaK[i].A + eScale * E[i];
-		if(EtaK[i].A < 0.0) EtaK[i].A = 0.0;
-	}
-}
-
-void EstimateMaterial()
-{
-	/*This function estimates the material properties of a sphere based on the
-	input spectrum RefSpectrum and the optical properties of the system.
-	1) The material properties are stored in EtaK and EtaN
-	2) The best fit is stored in SimSpectrum*/
-
-	//initialize the material index of refraction
-	EtaN.clear();	
-	EtaK.clear();
-
-	//insert the default material properties
-	SpecPair temp;
-	for(int s=0; s<(int)RefSpectrum[currentSpec].size(); s++)
-	{
-		//the real part of the IR is the user-specified baseline IR
-		temp.nu = RefSpectrum[currentSpec][s].nu;
-		temp.A = baseIR;
-		EtaN.push_back(temp);
-		//the imaginary part of the IR is zero absorbance
-		temp.A = 0.0f;
-		EtaK.push_back(temp);
-	}
-
-
-	//allocate space to store the list of error values
-	double* E = (double*)malloc(sizeof(double) * RefSpectrum[currentSpec].size());
-	//copy the absorbance values into a linear array
-	double* k = (double*)malloc(sizeof(double) * EtaK.size());
-	double* n = (double*)malloc(sizeof(double) * EtaN.size());
-
-	//iterate to solve for both n and k
-	double sumE = 99999.9;
-	int j=0;
-	//clear the console
-	system("cls");
-	while(sumE > minMSE && j < maxFitIter)
-	{	
-		//simulate a spectrum based on the current IR		
-		SimulateSpectrum();
-
-		//calculate the error term
-		sumE = CalculateError(E);
-
-		//estimate the new absorbance
-		EstimateK(E);
-
-		//use Kramers-Kronig to compute n
-		
-		for(unsigned int i=0; i<EtaK.size(); i++)
-			k[i] = EtaK[i].A;
-		cudaKramersKronig(n, k, EtaK.size(), EtaK.front().nu, EtaK.back().nu, baseIR);
-
-		//copy the real part of the index of refraction into the vector
-		EtaN.clear();
-		for(int i=0; i<(int)EtaK.size(); i++)
-		{
-			temp.nu =  EtaK[i].nu;
-			temp.A = n[i];
-			EtaN.push_back(temp);
-		}
-
-		cout<<"    E = "<<sumE<<endl;
-		j++;
-		//SaveSpectrum(n, nVals, "simNj.txt");
-		//SaveSpectrum(k, nVals, "simKj.txt");
-		//SaveSpectrum(simSpec, nVals, "simSpec.txt");
-		//exit(1);
-		
-	}
-
-	free(E);
-	free(k);
-	free(n);
-
-
-
-
-}
 \ No newline at end of file
+#include "globals.h"
+#include <stdlib.h>
+#define PI 3.14159
+
+double CalculateError(double* E)
+{
+    //Calculate the error between the Reference Spectrum and the Simulated Spectrum
+    double sumE = 0.0;
+    int nVals = RefSpectrum[currentSpec].size();
+    double nu;
+    for(int i=0; i<nVals; i++)
+    {
+        nu = RefSpectrum[currentSpec][i].nu;
+        E[i] = RefSpectrum[currentSpec][i].A + nu * refSlope - SimSpectrum[i].A;
+        sumE += E[i]*E[i];
+    }
+
+    return sumE/nVals;
+}
+
+void EstimateK(double* E)
+{
+    int nVals = RefSpectrum[currentSpec].size();
+    double nuStart = RefSpectrum[currentSpec].front().nu;
+    double nuEnd = RefSpectrum[currentSpec].back().nu;
+
+    double r = radius/10000.0;
+    double nu;
+    double dNu = (nuEnd - nuStart)/(nVals-1);
+    double eScale;
+    for(int i=0; i<nVals; i++)
+    {
+        nu = nuStart + i*2;
+
+        eScale = 1/(8*PI*r*nu);
+        EtaK[i].A = EtaK[i].A + eScale * E[i];
+        if(EtaK[i].A < 0.0) EtaK[i].A = 0.0;
+    }
+}
+
+void EstimateMaterial()
+{
+    /*This function estimates the material properties of a sphere based on the
+    input spectrum RefSpectrum and the optical properties of the system.
+    1) The material properties are stored in EtaK and EtaN
+    2) The best fit is stored in SimSpectrum*/
+
+    //initialize the material index of refraction
+    EtaN.clear();
+    EtaK.clear();
+
+    //insert the default material properties
+    SpecPair temp;
+    for(int s=0; s<(int)RefSpectrum[currentSpec].size(); s++)
+    {
+        //the real part of the IR is the user-specified baseline IR
+        temp.nu = RefSpectrum[currentSpec][s].nu;
+        temp.A = baseIR;
+        EtaN.push_back(temp);
+        //the imaginary part of the IR is zero absorbance
+        temp.A = 0.0f;
+        EtaK.push_back(temp);
+    }
+
+
+    //allocate space to store the list of error values
+    double* E = (double*)malloc(sizeof(double) * RefSpectrum[currentSpec].size());
+    //copy the absorbance values into a linear array
+    double* k = (double*)malloc(sizeof(double) * EtaK.size());
+    double* n = (double*)malloc(sizeof(double) * EtaN.size());
+
+    //iterate to solve for both n and k
+    double sumE = 99999.9;
+    int j=0;
+    //clear the console
+    system("cls");
+    while(sumE > minMSE && j < maxFitIter)
+    {
+        //simulate a spectrum based on the current IR
+        SimulateSpectrum();
+
+        //calculate the error term
+        sumE = CalculateError(E);
+
+        //estimate the new absorbance
+        EstimateK(E);
+
+        //use Kramers-Kronig to compute n
+
+        for(unsigned int i=0; i<EtaK.size(); i++)
+            k[i] = EtaK[i].A;
+        cudaKramersKronig(n, k, EtaK.size(), EtaK.front().nu, EtaK.back().nu, baseIR);
+
+        //copy the real part of the index of refraction into the vector
+        EtaN.clear();
+        for(int i=0; i<(int)EtaK.size(); i++)
+        {
+            temp.nu =  EtaK[i].nu;
+            temp.A = n[i];
+            EtaN.push_back(temp);
+        }
+
+        cout<<"    E = "<<sumE<<endl;
+        j++;
+        //SaveSpectrum(n, nVals, "simNj.txt");
+        //SaveSpectrum(k, nVals, "simKj.txt");
+        //SaveSpectrum(simSpec, nVals, "simSpec.txt");
+        //exit(1);
+
+    }
+
+    free(E);
+    free(k);
+    free(n);
+
+
+
+
+}
@@ -6,191 +6,198 @@ using namespace std;
  
 vector<SpecPair> LoadSpectrum(string filename)
 {
-	//load a spectrum from a file and resample to 2wn intervals
-
-	//create the spectrum
-	vector<SpecPair> S;
-
-	//open the file
-	ifstream inFile(filename.c_str());
-
-	//read all elements of the file
-	SpecPair temp;
-	while(!inFile.eof()){
-		inFile>>temp.nu;
-		inFile>>temp.A;
-		S.push_back(temp);
-	}
-
-	//compute the minimum and maximum input wavenumbers
-	double inMin = S.front().nu;
-	double inMax = S.back().nu;
-
-	int nuMin = (int)ceil(inMin);
-	int nuMax = (int)floor(inMax);
-
-	//make sure both are either even or odd
-	if(nuMin % 2 != nuMax % 2)
-		nuMax--;
-
-	//compute the number of values in the resampled spectrum
-	int nVals = (nuMax - nuMin)/2 + 1;
-
-	//allocate space for the spectrum
-	vector<SpecPair> outSpec;
-
-	double nu, highVal, lowVal, a;
-	int j=1;
-	for(int i=0; i<nVals; i++)
-	{
-		nu = nuMin + i * 2;
-		temp.nu = nu;
-
-		//handle the boundary cases
-		if(nu < inMin || nu > inMax)
-			temp.A = 0.0;
-		else
-		{
-			//move to the correct position in the input array
-			while(j < (int)S.size()-1 && S[j].nu <= nu)
-				j++;
-
-
-			lowVal = S[j-1].nu;
-			highVal = S[j].nu;
-			a = (nu - lowVal)/(highVal - lowVal);
-			temp.A = S[j-1].A * (1.0 - a) + S[j].A * a;
-		}
-		outSpec.push_back(temp);
-	}
-
-
-
-	return outSpec;
+    //load a spectrum from a file and resample to 2wn intervals
+
+    //create the spectrum
+    vector<SpecPair> S;
+
+    //open the file
+    ifstream inFile(filename.c_str());
+    if(!inFile)
+    {
+        cout<<"Error loading spectrum: "<<inFile<<endl;
+        return S;
+    }
+
+    //read all elements of the file
+    SpecPair temp;
+    while(!inFile.eof()) {
+        inFile>>temp.nu;
+        inFile>>temp.A;
+        S.push_back(temp);
+    }
+
+    //compute the minimum and maximum input wavenumbers
+    double inMin = S.front().nu;
+    double inMax = S.back().nu;
+
+    int nuMin = (int)ceil(inMin);
+    int nuMax = (int)floor(inMax);
+
+    //make sure both are either even or odd
+    if(nuMin % 2 != nuMax % 2)
+        nuMax--;
+
+    //compute the number of values in the resampled spectrum
+    int nVals = (nuMax - nuMin)/2 + 1;
+
+    //allocate space for the spectrum
+    vector<SpecPair> outSpec;
+
+    double nu, highVal, lowVal, a;
+    int j=1;
+    for(int i=0; i<nVals; i++)
+    {
+        nu = nuMin + i * 2;
+        temp.nu = nu;
+
+        //handle the boundary cases
+        if(nu < inMin || nu > inMax)
+            temp.A = 0.0;
+        else
+        {
+            //move to the correct position in the input array
+            while(j < (int)S.size()-1 && S[j].nu <= nu)
+                j++;
+
+
+            lowVal = S[j-1].nu;
+            highVal = S[j].nu;
+            a = (nu - lowVal)/(highVal - lowVal);
+            temp.A = S[j-1].A * (1.0 - a) + S[j].A * a;
+        }
+        outSpec.push_back(temp);
+    }
+
+
+
+    return outSpec;
 }
  
 vector<SpecPair> SetReferenceSpectrum(char* text)
 {
-	stringstream inString(text);
+    stringstream inString(text);
  
-	//create the spectrum
-	vector<SpecPair> S;
+    //create the spectrum
+    vector<SpecPair> S;
  
-	SpecPair temp;
-	while(!inString.eof()){
-		inString>>temp.nu;
-		inString>>temp.A;
-		S.push_back(temp);
-	}
+    SpecPair temp;
+    while(!inString.eof()) {
+        inString>>temp.nu;
+        inString>>temp.A;
+        S.push_back(temp);
+    }
  
-	return S;
+    return S;
 }
  
-void SaveK(string fileName)
+/*void SaveK(string fileName)
 {
-	ofstream outFile(fileName.c_str());
-	for(unsigned int i=0; i<EtaK.size(); i++)
-	{
-		outFile<<EtaK[i].nu<<"          ";
-		outFile<<EtaK[i].A<<endl;
-	}
-	outFile.close();
-}
-
-void SaveN(string fileName)
+    ofstream outFile(fileName.c_str());
+    for(unsigned int i=0; i<EtaK.size(); i++)
+    {
+        outFile<<EtaK[i].nu<<"          ";
+        outFile<<EtaK[i].A<<endl;
+    }
+    outFile.close();
+}*/
+
+void SaveMaterial(string fileName)
 {
-	ofstream outFile(fileName.c_str());
-	for(unsigned int i=0; i<EtaN.size(); i++)
-	{
-		outFile<<EtaN[i].nu<<"          ";
-		outFile<<EtaN[i].A<<endl;
-	}
-	outFile.close();
+    ofstream outFile(fileName.c_str());
+    outFile<<"nu"<<'\t'<<"n"<<'\t'<<"k"<<endl;
+    for(unsigned int i=0; i<EtaN.size(); i++)
+    {
+        outFile<<EtaN[i].nu<<'\t';
+        outFile<<EtaN[i].A<<'\t';
+        outFile<<EtaK[i].A<<endl;
+    }
+    outFile.close();
 }
  
 void SaveSimulation(string fileName)
 {
-	ofstream outFile(fileName.c_str());
-	outFile.precision(10);
-	for(unsigned int i=0; i<SimSpectrum.size(); i++)
-	{
-		outFile<<SimSpectrum[i].nu<<"          ";
-		outFile<<SimSpectrum[i].A<<endl;
-	}
-	outFile.close();
+    ofstream outFile(fileName.c_str());
+    outFile.precision(10);
+    for(unsigned int i=0; i<SimSpectrum.size(); i++)
+    {
+        outFile<<SimSpectrum[i].nu<<"          ";
+        outFile<<SimSpectrum[i].A<<endl;
+    }
+    outFile.close();
 }
  
 void SaveState()
 {
-	ofstream outFile("main.prj");
-	//Window Parameters
-	outFile<<nuMin<<endl;
-	outFile<<nuMax<<endl;
-	outFile<<aMin<<endl;
-	outFile<<aMax<<endl;
-	outFile<<dNu<<endl;
-
-	//material parameters
-	outFile<<radius<<endl;
-	outFile<<baseIR<<endl;
-	outFile<<cA<<endl;
-
-	//optical parameters
-	outFile<<cNAi<<endl;
-	outFile<<cNAo<<endl;
-	outFile<<oNAi<<endl;
-	outFile<<oNAo<<endl;
-
-	outFile.close();
+    ofstream outFile("main.prj");
+    //Window Parameters
+    outFile<<nuMin<<endl;
+    outFile<<nuMax<<endl;
+    outFile<<aMin<<endl;
+    outFile<<aMax<<endl;
+    outFile<<dNu<<endl;
+
+    //material parameters
+    outFile<<radius<<endl;
+    outFile<<baseIR<<endl;
+    outFile<<cA<<endl;
+
+    //optical parameters
+    outFile<<cNAi<<endl;
+    outFile<<cNAo<<endl;
+    outFile<<oNAi<<endl;
+    outFile<<oNAo<<endl;
+
+    outFile.close();
  
 }
  
 void LoadState()
 {
-	ifstream inFile("main.prj");
-	//Window Parameters
-	inFile>>nuMin;
-	inFile>>nuMax;
-	inFile>>aMin;
-	inFile>>aMax;
-	inFile>>dNu;
-
-	//material parameters
-	inFile>>radius;
-	inFile>>baseIR;
-	inFile>>cA;
-
-	//optical parameters
-	inFile>>cNAi;
-	inFile>>cNAo;
-	inFile>>oNAi;
-	inFile>>oNAo;
-
-	inFile.close();
+    ifstream inFile("main.prj");
+    //Window Parameters
+    inFile>>nuMin;
+    inFile>>nuMax;
+    inFile>>aMin;
+    inFile>>aMax;
+    inFile>>dNu;
+
+    //material parameters
+    inFile>>radius;
+    inFile>>baseIR;
+    inFile>>cA;
+
+    //optical parameters
+    inFile>>cNAi;
+    inFile>>cNAo;
+    inFile>>oNAi;
+    inFile>>oNAo;
+
+    inFile.close();
  
 }
  
 void SetDefaults()
 {
  
-	nuMin = 800;
-	nuMax = 4000;
-	dNu = 2;
+    nuMin = 800;
+    nuMax = 4000;
+    dNu = 2;
  
-	aMin = 0;
-	aMax = 1;
+    aMin = 0;
+    aMax = 1;
  
  
-	//material parameters
-	radius = 4.0f;
-	baseIR = 1.49f;
-	cA = 1.0;
-	vector<SpecPair> KMaterial;
-	vector<SpecPair> NMaterial;
+    //material parameters
+    radius = 4.0f;
+    baseIR = 1.49f;
+    cA = 1.0;
+    vector<SpecPair> KMaterial;
+    vector<SpecPair> NMaterial;
  
-	//optical parameters
-	cNAi = 0.0;
-	cNAo = 0.6;
-	oNAi = 0.0;
-	oNAo = 0.6;
-}
 \ No newline at end of file
+    //optical parameters
+    cNAi = 0.0;
+    cNAo = 0.6;
+    oNAi = 0.0;
+    oNAo = 0.6;
+}
-//  gamma.cpp -- computation of gamma function.
-//      Algorithms and coefficient values from "Computation of Special
-//      Functions", Zhang and Jin, John Wiley and Sons, 1996.
-//
-//  (C) 2003, C. Bond. All rights reserved.
-//
-// Returns gamma function of argument 'x'.
-//
-// NOTE: Returns 1e308 if argument is a negative integer or 0,
-//      or if argument exceeds 171.
-//
-#define _USE_MATH_DEFINES
-#include <math.h>
-double gamma(double x)
-{
-    int i,k,m;
-    double ga,gr,r,z;
-
-    static double g[] = {
-        1.0,
-        0.5772156649015329,
-       -0.6558780715202538,
-       -0.420026350340952e-1,
-        0.1665386113822915,
-       -0.421977345555443e-1,
-       -0.9621971527877e-2,
-        0.7218943246663e-2,
-       -0.11651675918591e-2,
-       -0.2152416741149e-3,
-        0.1280502823882e-3,
-       -0.201348547807e-4,
-       -0.12504934821e-5,
-        0.1133027232e-5,
-       -0.2056338417e-6,
-        0.6116095e-8,
-        0.50020075e-8,
-       -0.11812746e-8,
-        0.1043427e-9,
-        0.77823e-11,
-       -0.36968e-11,
-        0.51e-12,
-       -0.206e-13,
-       -0.54e-14,
-        0.14e-14};
-
-    if (x > 171.0) return 1e308;    // This value is an overflow flag.
-    if (x == (int)x) {
-        if (x > 0.0) {
-            ga = 1.0;               // use factorial
-            for (i=2;i<x;i++) {
-               ga *= i;
-            }
-         }
-         else
-            ga = 1e308;
-     }
-     else {
-        if (fabs(x) > 1.0) {
-            z = fabs(x);
-            m = (int)z;
-            r = 1.0;
-            for (k=1;k<=m;k++) {
-                r *= (z-k);
-            }
-            z -= m;
-        }
-        else
-            z = x;
-        gr = g[24];
-        for (k=23;k>=0;k--) {
-            gr = gr*z+g[k];
-        }
-        ga = 1.0/(gr*z);
-        if (fabs(x) > 1.0) {
-            ga *= r;
-            if (x < 0.0) {
-                ga = -M_PI/(x*ga*sin(M_PI*x));
-            }
-        }
-    }
-    return ga;
-}
+//  gamma.cpp -- computation of gamma function.
+//      Algorithms and coefficient values from "Computation of Special
+//      Functions", Zhang and Jin, John Wiley and Sons, 1996.
+//
+//  (C) 2003, C. Bond. All rights reserved.
+//
+// Returns gamma function of argument 'x'.
+//
+// NOTE: Returns 1e308 if argument is a negative integer or 0,
+//      or if argument exceeds 171.
+//
+#define _USE_MATH_DEFINES
+#include <math.h>
+double gamma(double x)
+{
+    int i,k,m;
+    double ga,gr,r,z;
+
+    static double g[] = {
+        1.0,
+        0.5772156649015329,
+        -0.6558780715202538,
+        -0.420026350340952e-1,
+        0.1665386113822915,
+        -0.421977345555443e-1,
+        -0.9621971527877e-2,
+        0.7218943246663e-2,
+        -0.11651675918591e-2,
+        -0.2152416741149e-3,
+        0.1280502823882e-3,
+        -0.201348547807e-4,
+        -0.12504934821e-5,
+        0.1133027232e-5,
+        -0.2056338417e-6,
+        0.6116095e-8,
+        0.50020075e-8,
+        -0.11812746e-8,
+        0.1043427e-9,
+        0.77823e-11,
+        -0.36968e-11,
+        0.51e-12,
+        -0.206e-13,
+        -0.54e-14,
+        0.14e-14
+    };
+
+    if (x > 171.0) return 1e308;    // This value is an overflow flag.
+    if (x == (int)x) {
+        if (x > 0.0) {
+            ga = 1.0;               // use factorial
+            for (i=2; i<x; i++) {
+                ga *= i;
+            }
+        }
+        else
+            ga = 1e308;
+    }
+    else {
+        if (fabs(x) > 1.0) {
+            z = fabs(x);
+            m = (int)z;
+            r = 1.0;
+            for (k=1; k<=m; k++) {
+                r *= (z-k);
+            }
+            z -= m;
+        }
+        else
+            z = x;
+        gr = g[24];
+        for (k=23; k>=0; k--) {
+            gr = gr*z+g[k];
+        }
+        ga = 1.0/(gr*z);
+        if (fabs(x) > 1.0) {
+            ga *= r;
+            if (x < 0.0) {
+                ga = -M_PI/(x*ga*sin(M_PI*x));
+            }
+        }
+    }
+    return ga;
+}
-// add the following to a cpp file:
-// PerformanceData PD;
-
-
-#pragma once
-#include <ostream>
-using namespace std;
-
-enum PerformanceDataType
-{
-	PD_DISPLAY=0,
-	PD_SPS,
-	PD_UNUSED0,
-
-	//my stuff
-	SIMULATE_SPECTRUM,
-	SIMULATE_GPU,
-	KRAMERS_KRONIG,
-
-	
-
-	//end my stuff
-	PERFORMANCE_DATA_TYPE_COUNT
-};
-
-static char PDTypeNames[][255] = {
-		"Display            ",
-		"Simulation Total   ",
-		" ----------------- ",
-		//my stuff
-		"Simulate Spectrum  ",
-		"      GPU Portion  ",
-		"Kramers-Kronig     ",
-
-		//end my stuff
-		
-};
-#ifdef WIN32
-#include <stdio.h>
-#include <windows.h>
-#include <float.h>
-
-#include <iostream>
-#include <iomanip>
-
-//-------------------------------------------------------------------------------
-
-class PerformanceData
-{
-public:
-	PerformanceData() { ClearAll(); QueryPerformanceFrequency(&cps); }
-	~PerformanceData(){}
-
-	void ClearAll()
-	{
-		for ( int i=0; i<PERFORMANCE_DATA_TYPE_COUNT; i++ ) {
-			for ( int j=0; j<256; j++ ) times[i][j] = 0;
-			pos[i] = 0;
-			minTime[i] = 0xFFFFFFFF;
-			maxTime[i] = 0;
-			totalTime[i] = 0;
-			dataReady[i] = false;
-		}
-	}
-
-	void StartTimer( int type ) { QueryPerformanceCounter( &startTime[type] );}
-	void EndTimer( int type ) {
-		LARGE_INTEGER endTime;
-		QueryPerformanceCounter( &endTime );
-		double t = (double)(endTime.QuadPart - startTime[type].QuadPart);
-		//unsigned int t = GetTickCount() - startTime[type];
-		if ( t < minTime[type] ) minTime[type] = t;
-		if ( t > maxTime[type] ) maxTime[type] = t;
-		totalTime[type] -= times[type][ pos[type] ];
-		times[type][ pos[type] ] = t;
-		totalTime[type] += t;
-		pos[type]++;
-		if ( pos[type] == 0 ) dataReady[type] = true;
-	}
-
-	void PrintResult( ostream &os,int i=PERFORMANCE_DATA_TYPE_COUNT)
-	{
-		os.setf(ios::fixed);
-		if ((i<PERFORMANCE_DATA_TYPE_COUNT)&&(i>=0)){
-			double a = GetAvrgTime(i);
-			if ( a ) 
-				os<< PDTypeNames[i]<<" :  avrg="<<setw(8)<<setprecision(3)<<a<<"\tmin="<<setw(8)<<setprecision(3)<< GetMinTime(i) <<"\tmax="<<setw(8)<<setprecision(3)<< GetMaxTime(i) <<endl ;
-			else 
-				os<< PDTypeNames[i]<<" :  avrg=   -----\tmin=   -----\tmax=   -----"<<endl;
-		}
-	}
-
-	void PrintResults( ostream &os)
-	{
-		for ( int i=0; i<PERFORMANCE_DATA_TYPE_COUNT; i++ ) 
-			PrintResult(os,i);
-	}
-
-	double	GetLastTime( int type ) { return times[type][pos[type]]; }
-	double	GetAvrgTime( int type ) { double a = 1000.0 * totalTime[type] / (float)cps.QuadPart / ( (dataReady[type]) ? 256.0 : (double)pos[type] ); return (_finite(a))? a:0; }
-	double	GetMinTime( int type ) { return 1000.0 * minTime[type] / (float)cps.LowPart; }
-	double	GetMaxTime( int type ) { return 1000.0 * maxTime[type] / (float)cps.LowPart; }
-
-private:
-	double times[PERFORMANCE_DATA_TYPE_COUNT][256];
-	unsigned char pos[PERFORMANCE_DATA_TYPE_COUNT];
-	LARGE_INTEGER startTime[PERFORMANCE_DATA_TYPE_COUNT];
-	double minTime[ PERFORMANCE_DATA_TYPE_COUNT ];
-	double maxTime[ PERFORMANCE_DATA_TYPE_COUNT ];
-	double totalTime[ PERFORMANCE_DATA_TYPE_COUNT ];
-	bool dataReady[ PERFORMANCE_DATA_TYPE_COUNT ];
-	LARGE_INTEGER cps;
-};
-
-//-------------------------------------------------------------------------------
-#else	
-
-class PerformanceData{
-public:
-	PerformanceData() {;};
-	~PerformanceData(){;};
-	void ClearAll(){;};
-	void StartTimer( int type ) {;};
-	void EndTimer( int type ) {;};
-	void PrintResults( ostream &os){;};
-	void PrintResult( ostream &os, int i=PERFORMANCE_DATA_TYPE_COUNT){;};
-	double	GetLastTime( int type ) { return 0.0; };
-	double	GetAvrgTime( int type ) { return 0.0; };
-	double	GetMinTime( int type ) { return 0.0; };
-	double	GetMaxTime( int type ) { return 0.0; };
-};
-
-#endif
-//-------------------------------------------------------------------------------
-
-extern PerformanceData PD;
-
-//-------------------------------------------------------------------------------
+// add the following to a cpp file:
+// PerformanceData PD;
+
+
+#pragma once
+#include <ostream>
+using namespace std;
+
+enum PerformanceDataType
+{
+    PD_DISPLAY=0,
+    PD_SPS,
+    PD_UNUSED0,
+
+    //my stuff
+    SIMULATE_SPECTRUM,
+    SIMULATE_GPU,
+    KRAMERS_KRONIG,
+
+
+
+    //end my stuff
+    PERFORMANCE_DATA_TYPE_COUNT
+};
+
+static char PDTypeNames[][255] = {
+    "Display            ",
+    "Simulation Total   ",
+    " ----------------- ",
+    //my stuff
+    "Simulate Spectrum  ",
+    "      GPU Portion  ",
+    "Kramers-Kronig     ",
+
+    //end my stuff
+
+};
+#ifdef WIN32
+#include <stdio.h>
+#include <windows.h>
+#include <float.h>
+
+#include <iostream>
+#include <iomanip>
+
+//-------------------------------------------------------------------------------
+
+class PerformanceData
+{
+public:
+    PerformanceData() {
+        ClearAll();
+        QueryPerformanceFrequency(&cps);
+    }
+    ~PerformanceData() {}
+
+    void ClearAll()
+    {
+        for ( int i=0; i<PERFORMANCE_DATA_TYPE_COUNT; i++ ) {
+            for ( int j=0; j<256; j++ ) times[i][j] = 0;
+            pos[i] = 0;
+            minTime[i] = 0xFFFFFFFF;
+            maxTime[i] = 0;
+            totalTime[i] = 0;
+            dataReady[i] = false;
+        }
+    }
+
+    void StartTimer( int type ) {
+        QueryPerformanceCounter( &startTime[type] );
+    }
+    void EndTimer( int type ) {
+        LARGE_INTEGER endTime;
+        QueryPerformanceCounter( &endTime );
+        double t = (double)(endTime.QuadPart - startTime[type].QuadPart);
+        //unsigned int t = GetTickCount() - startTime[type];
+        if ( t < minTime[type] ) minTime[type] = t;
+        if ( t > maxTime[type] ) maxTime[type] = t;
+        totalTime[type] -= times[type][ pos[type] ];
+        times[type][ pos[type] ] = t;
+        totalTime[type] += t;
+        pos[type]++;
+        if ( pos[type] == 0 ) dataReady[type] = true;
+    }
+
+    void PrintResult( ostream &os,int i=PERFORMANCE_DATA_TYPE_COUNT)
+    {
+        os.setf(ios::fixed);
+        if ((i<PERFORMANCE_DATA_TYPE_COUNT)&&(i>=0)) {
+            double a = GetAvrgTime(i);
+            if ( a )
+                os<< PDTypeNames[i]<<" :  avrg="<<setw(8)<<setprecision(3)<<a<<"\tmin="<<setw(8)<<setprecision(3)<< GetMinTime(i) <<"\tmax="<<setw(8)<<setprecision(3)<< GetMaxTime(i) <<endl ;
+            else
+                os<< PDTypeNames[i]<<" :  avrg=   -----\tmin=   -----\tmax=   -----"<<endl;
+        }
+    }
+
+    void PrintResults( ostream &os)
+    {
+        for ( int i=0; i<PERFORMANCE_DATA_TYPE_COUNT; i++ )
+            PrintResult(os,i);
+    }
+
+    double	GetLastTime( int type ) {
+        return times[type][pos[type]];
+    }
+    double	GetAvrgTime( int type ) {
+        double a = 1000.0 * totalTime[type] / (float)cps.QuadPart / ( (dataReady[type]) ? 256.0 : (double)pos[type] );
+        return (_finite(a))? a:0;
+    }
+    double	GetMinTime( int type ) {
+        return 1000.0 * minTime[type] / (float)cps.LowPart;
+    }
+    double	GetMaxTime( int type ) {
+        return 1000.0 * maxTime[type] / (float)cps.LowPart;
+    }
+
+private:
+    double times[PERFORMANCE_DATA_TYPE_COUNT][256];
+    unsigned char pos[PERFORMANCE_DATA_TYPE_COUNT];
+    LARGE_INTEGER startTime[PERFORMANCE_DATA_TYPE_COUNT];
+    double minTime[ PERFORMANCE_DATA_TYPE_COUNT ];
+    double maxTime[ PERFORMANCE_DATA_TYPE_COUNT ];
+    double totalTime[ PERFORMANCE_DATA_TYPE_COUNT ];
+    bool dataReady[ PERFORMANCE_DATA_TYPE_COUNT ];
+    LARGE_INTEGER cps;
+};
+
+//-------------------------------------------------------------------------------
+#else
+
+class PerformanceData {
+public:
+    PerformanceData() {
+        ;
+    };
+    ~PerformanceData() {
+        ;
+    };
+    void ClearAll() {
+        ;
+    };
+    void StartTimer( int type ) {
+        ;
+    };
+    void EndTimer( int type ) {
+        ;
+    };
+    void PrintResults( ostream &os) {
+        ;
+    };
+    void PrintResult( ostream &os, int i=PERFORMANCE_DATA_TYPE_COUNT) {
+        ;
+    };
+    double	GetLastTime( int type ) {
+        return 0.0;
+    };
+    double	GetAvrgTime( int type ) {
+        return 0.0;
+    };
+    double	GetMinTime( int type ) {
+        return 0.0;
+    };
+    double	GetMaxTime( int type ) {
+        return 0.0;
+    };
+};
+
+#endif
+//-------------------------------------------------------------------------------
+
+extern PerformanceData PD;
+
+//-------------------------------------------------------------------------------
-#include <math.h>
-#include <complex>
-#include <iostream>
-#include <fstream>
-#include "globals.h"
-#include <QProgressDialog>
-#include <stdlib.h>
-//#include "cufft.h"
-using namespace std;
-
-#define pi 3.14159
-
-typedef complex<double> scComplex;
-
-extern int cbessjyva(double v,complex<double> z,double &vm,complex<double>*cjv,
-    complex<double>*cyv,complex<double>*cjvp,complex<double>*cyvp);
-extern int bessjyv(double v,double x,double &vm,double *jv,double *yv,
-    double *djv,double *dyv);
-
-complex<double> Jl_neg(complex<double> x)
-{
-	//this function computes the bessel function of the first kind Jl(x) for l = -0.5
-	return ( sqrt(2.0/pi) * cos(x) )/sqrt(x);
-}
-
-double Jl_neg(double x)
-{
-	//this function computes the bessel function of the first kind Jl(x) for l = -0.5
-	return ( sqrt(2.0/pi) * cos(x) )/sqrt(x);
-}
-
-double Yl_neg(double x)
-{
-	//this function computes the bessel function of the second kind Yl(x) for l = -0.5;
-	return ( sqrt(2.0/pi) * sin(x) )/sqrt(x);
-}
-
-void computeB(complex<double>* B, double radius, complex<double> refIndex, double lambda, int Nl)
-{
-	double k = (2*pi)/lambda;
-	int b = 2;
-
-	//allocate space for the real bessel functions
-	double* jv = (double*)malloc(sizeof(double)*(Nl+b));
-	double* yv = (double*)malloc(sizeof(double)*(Nl+b));
-	double* jvp = (double*)malloc(sizeof(double)*(Nl+b));
-	double* yvp = (double*)malloc(sizeof(double)*(Nl+b));
-
-	//allocate space for the complex bessel functions
-	complex<double>* cjv = (complex<double>*)malloc(sizeof(complex<double>)*(Nl+b));
-	complex<double>* cyv = (complex<double>*)malloc(sizeof(complex<double>)*(Nl+b));
-	complex<double>* cjvp = (complex<double>*)malloc(sizeof(complex<double>)*(Nl+b));
-	complex<double>* cyvp = (complex<double>*)malloc(sizeof(complex<double>)*(Nl+b));
-
-	double kr = k*radius;
-	complex<double> knr = k*refIndex*(double)radius;
-	complex<double> n = refIndex;
-
-	//compute the bessel functions for k*r
-	double vm;// = Nl - 1;
-	bessjyv((Nl)+0.5, kr, vm, jv, yv, jvp, yvp);
-	//cout<<"Nl: "<<Nl<<"  vm: "<<vm<<endl;
-	//printf("Nl: %f, vm: %f\n", (float)Nl, (float)vm);
-
-	//compute the bessel functions for k*n*r
-	cbessjyva((Nl)+0.5, knr, vm, cjv, cyv, cjvp, cyvp);
-
-	//scale factor for spherical bessel functions
-	double scale_kr = sqrt(pi/(2.0*kr));
-	complex<double> scale_knr = sqrt(pi/(2.0*knr));
-
-	complex<double> numer, denom;
-	double j_kr;
-	double y_kr;
-	complex<double> j_knr;
-	complex<double> j_d_knr;
-	double j_d_kr;
-	complex<double> h_kr;
-	complex<double> h_d_kr;
-	complex<double> h_neg;
-	complex<double> h_pos;
-
-	//cout<<"B coefficients:"<<endl;
-	for(int l=0; l<Nl; l++)
-	{
-		//compute the spherical bessel functions
-		j_kr = jv[l] * scale_kr;
-		y_kr = yv[l] * scale_kr;
-		j_knr = cjv[l] * scale_knr;
-
-		//compute the Hankel function
-		h_kr = complex<double>(j_kr, y_kr);
-
-		//compute the derivatives
-		if(l == 0)
-		{
-			//spherical bessel functions for l=0
-			j_d_kr = scale_kr * (Jl_neg(kr) - (jv[l] + kr*jv[l+1])/kr )/2.0;
-			j_d_knr = scale_knr * ( Jl_neg(knr) - (cjv[l] + knr*cjv[l+1])/knr )/2.0;
-			h_neg = complex<double>(scale_kr*Jl_neg(kr), scale_kr*Yl_neg(kr));
-			h_pos = complex<double>(scale_kr*jv[l+1], scale_kr*yv[l+1]);
-			h_d_kr = (h_neg - (h_kr + kr*h_pos)/kr)/2.0;
-		}
-		else
-		{
-			//spherical bessel functions
-			j_d_kr = scale_kr * (jv[l-1] - (jv[l] + kr*jv[l+1])/kr )/2.0;
-			j_d_knr = scale_knr * ( cjv[l-1] - (cjv[l] + knr*cjv[l+1])/knr )/2.0;
-			h_neg = complex<double>(scale_kr*jv[l-1], scale_kr*yv[l-1]);
-			h_pos = complex<double>(scale_kr*jv[l+1], scale_kr*yv[l+1]);
-			h_d_kr = (h_neg - (h_kr + kr*h_pos)/kr)/2.0;
-		}
-
-		numer = j_kr*j_d_knr*n - j_knr*j_d_kr;
-		denom = j_knr*h_d_kr - h_kr*j_d_knr*n;
-		B[l] =  numer/denom;
-
-		//B[l] = scComplex(temp.real(), temp.imag());
-		//cout<<B[l]<<endl;
-	}
-
-	free(jv);
-	free(yv);
-	free(jvp);
-	free(yvp);
-	free(cjv);
-	free(cyv);
-	free(cjvp);
-	free(cyvp);
-}
-
-void Legendre(double* P, double x, int Nl)
-{
-	//computes the legendre polynomials from orders 0 to Nl-1
-	P[0] = 1;
-	if(Nl == 1) return;
-	P[1] = x;
-	for(int l = 2; l < Nl; l++)
-	{
-		P[l] = ((2*l - 1)*x*P[l-1] - (l - 1)*P[l-2])/l;
-	}
-
-}
-
-complex<double> integrateUi(double cAngleI, double cAngleO, double oAngleI, double oAngleO, double M = 2*pi)
-{
-	/*This function integrates the incident field of magnitude M in the far zone
-	in order to evaluate the field at the central pixel of a detector.
-	cNAi = condenser inner angle
-	cNAo = condenser outer angle
-	oNAi = objective inner angle
-	oNAo = objective outer angle
-	M = field magnitude*/
-
-	double alphaIn = max(cAngleI, oAngleI);
-	double alphaOut = min(cAngleO,oAngleO);
-
-	complex<double> Ui;
-	if(alphaIn > alphaOut)
-		Ui = complex<double>(0.0, 0.0);
-	else
-		Ui = complex<double>(M * 2 * pi * (cos(alphaIn) - cos(alphaOut)), 0.0f);
-
-	return Ui;
-
-}
-
-void computeCondenserAlpha(double* alpha, int Nl, double cAngleI, double cAngleO)
-{
-	/*This function computes the condenser integral in order to build the field of incident light
-	alpha = list of Nl floating point values representing the condenser alpha as a function of l
-	Nl = number of orders in the incident field
-	cAngleI, cAngleO = inner and outer condenser angles (inner and outer NA)*/
-
-	//compute the Legendre polynomials for the condenser aperature
-	double* PcNAo = (double*)malloc(sizeof(double)*(Nl+1));
-	Legendre(PcNAo, cos(cAngleO), Nl+1);
-	double* PcNAi = (double*)malloc(sizeof(double)*(Nl+1));
-	Legendre(PcNAi, cos(cAngleI), Nl+1);
-
-	for(int l=0; l<Nl; l++)
-	{
-		//integration term
-		if(l == 0)
-			alpha[l] = -PcNAo[l+1] + PcNAo[0] + PcNAi[l+1] - PcNAi[0];
-		else
-			alpha[l] = -PcNAo[l+1] + PcNAo[l-1] + PcNAi[l+1] - PcNAi[l-1];
-
-		alpha[l] *= 2 * pi;
-	}
-
-}
-
-complex<double> integrateUs(double r, double lambda, complex<double> eta,
-						   double cAngleI, double cAngleO, double oAngleI, double oAngleO, double M = 2*pi)
-{
-	/*This function integrates the incident field of magnitude M in the far zone
-	in order to evaluate the field at the central pixel of a detector.
-	r = sphere radius
-	lambda = wavelength
-	eta = index of refraction
-	cNAi = condenser inner NA
-	cNAo = condenser outer NA
-	oNAi = objective inner NA
-	oNAo = objective outer NA
-	M = field magnitude*/
-
-	//compute the required number of orders
-	double k = 2*pi/lambda;
-	int Nl = (int)ceil( k + 4 * exp(log(k*r)/3) + 3 );
-
-	//compute the material coefficients B
-	complex<double>* B = (complex<double>*)malloc(sizeof(complex<double>)*Nl);
-	//compute the Legendre polynomials for the condenser and objective aperatures
-	double* PcNAo = (double*)malloc(sizeof(double)*(Nl+1));
-	Legendre(PcNAo, cos(cAngleO), Nl+1);
-	double* PcNAi = (double*)malloc(sizeof(double)*(Nl+1));
-	Legendre(PcNAi, cos(cAngleI), Nl+1);
-
-	double* PoNAo = (double*)malloc(sizeof(double)*(Nl+1));
-	Legendre(PoNAo, cos(oAngleO), Nl+1);
-	double* PoNAi = (double*)malloc(sizeof(double)*(Nl+1));
-	Legendre(PoNAi, cos(oAngleI), Nl+1);
-
-	//store the index of refraction;
-	complex<double> IR(eta.real(), eta.imag());
-
-	//compute the scattering coefficients
-	computeB(B, r, IR, lambda, Nl);
-
-	//aperature terms for the condenser (alpha) and objective (beta)
-	double alpha;
-	double beta;
-	double c;
-	complex<double> Us(0.0, 0.0);
-
-	for(int l=0; l<Nl; l++)
-	{
-		//integration term
-		if(l == 0)
-		{
-			alpha = -PcNAo[l+1] + PcNAo[0] + PcNAi[l+1] - PcNAi[0];
-			beta = -PoNAo[l+1] + PoNAo[0] + PoNAi[l+1] - PoNAi[0];
-		}
-		else
-		{
-			alpha = -PcNAo[l+1] + PcNAo[l-1] + PcNAi[l+1] - PcNAi[l-1];
-			beta = -PoNAo[l+1] + PoNAo[l-1] + PoNAi[l+1] - PoNAi[l-1];
-		}
-		c = (2*pi)/(2.0 * l + 1.0);
-		Us += c * alpha * beta * B[l] * M;
-
-
-	}
-	free(PcNAo);
-	free(PcNAi);
-	free(PoNAo);
-	free(PoNAi);
-	free(B);
-
-	return Us;
-
-}
-
-void pointSpectrum()
-{
-	PD.StartTimer(SIMULATE_SPECTRUM);
-	//clear the previous spectrum
-	SimSpectrum.clear();
-
-	double dNu = 2.0f;
-	double lambda;
-
-	//compute the angles based on NA
-	double cAngleI = asin(cNAi);
-	double cAngleO = asin(cNAo);
-	double oAngleI = asin(oNAi);
-	double oAngleO = asin(oNAo);
-
-	//implement a reflection-mode system if necessary
-	if(opticsMode == ReflectionOpticsType){
-
-		//set the condenser to match the objective
-		cAngleI = oAngleI;
-		cAngleO = oAngleO;
-
-		//invert the objective
-		oAngleO = pi - cAngleI;
-		oAngleI = pi - cAngleO;
-	}
-
-	//integrate the incident field at the detector position
-	complex<double> Ui = integrateUi(cAngleI, cAngleO, oAngleI, oAngleO, 2*pi);
-	double I0 = Ui.real() * Ui.real() + Ui.imag() * Ui.imag();
-	I0 *= scaleI0;
-
-
-
-	//double I;
-	SpecPair temp;
-	double nu;
-	complex<double> eta;
-	complex<double> Us, U;
-
-	double vecLen = 0.0;
-	for(unsigned int i=0; i<EtaK.size(); i++)
-	{
-		nu = EtaK[i].nu;
-		lambda = 10000.0f/nu;
-		if(applyMaterial)
-			eta = complex<double>(EtaN[i].A, EtaK[i].A);
-		else
-			eta = complex<double>(baseIR, 0.0);
-
-
-		//integrate the scattered field at the detector position
-		Us = integrateUs(radius, lambda, eta, cAngleI, cAngleO, oAngleI, oAngleO, 2*pi);
-		U = Us + Ui;
-		double I = U.real() * U.real() + U.imag() * U.imag();
-
-		temp.nu = nu;
-
-		//set the spectrum value based on the current display type
-		if(dispSimType == AbsorbanceSpecType)
-			temp.A = -log10(I/I0);
-		else
-			temp.A = I;
-
-		if(dispNormalize)
-			vecLen += temp.A * temp.A;
-
-		SimSpectrum.push_back(temp);
-	}
-	vecLen = sqrt(vecLen);
-
-	if(dispNormalize)
-		for(unsigned int i=0; i<SimSpectrum.size(); i++)
-			SimSpectrum[i].A = (SimSpectrum[i].A / vecLen) * dispNormFactor;
-
-	PD.EndTimer(SIMULATE_SPECTRUM);
-}
-
-void updateSpectrum(double* I, double I0, int n)
-{
-	SimSpectrum.clear();
-	SpecPair temp;
-
-	//update the displayed spectrum based on the computed intensity I
-	for(int i=0; i<n; i++)
-	{
-		temp.nu = EtaK[i].nu;
-
-		//set the spectrum value based on the current display type
-		if(dispSimType == AbsorbanceSpecType)
-		{
-			temp.A = -log10(I[i]/I0);
-			//cout<<temp.nu<<"    "<<I[i]<<endl;
-		}
-		else
-		{
-			temp.A = I[i];
-			if(useSourceSpectrum)
-				temp.A *= SourceResampled[i].A;
-		}
-
-		SimSpectrum.push_back(temp);
-	}
-}
-
-void computeCassegrainAngles(double& cAngleI, double& cAngleO, double& oAngleI, double& oAngleO)
-{
-	//compute the angles based on NA
-	cAngleI = asin(cNAi);
-	cAngleO = asin(cNAo);
-	oAngleI = asin(oNAi);
-	oAngleO = asin(oNAo);
-
-	//implement a reflection-mode system if necessary
-	if(opticsMode == ReflectionOpticsType){
-
-		//set the condenser to match the objective
-		cAngleI = oAngleI;
-		cAngleO = oAngleO;
-
-		//invert the objective
-		oAngleO = pi - cAngleI;
-		oAngleI = pi - cAngleO;
-	}
-
-
-}
-
-int computeNl()
-{
-	double maxNu = EtaK.back().nu;
-	double maxLambda = 10000.0f/maxNu;
-	double k = 2*pi/maxLambda;
-	int Nl = (int)ceil( k + 4 * exp(log(k*radius)/3) + 3 );
-
-	return Nl;
-}
-
-void computeBArray(complex<double>* B, int Nl, int nLambda)
-{
-	double nu;
-	complex<double> eta;
-	double* Lambda = (double*)malloc(sizeof(double) * nLambda);
-
-	//for each wavenumber nu
-	for(unsigned int i=0; i<EtaK.size(); i++)
-	{
-		//compute information based on wavelength and material
-		nu = EtaK[i].nu;
-		Lambda[i] = 10000.0f/nu;
-		if(applyMaterial)
-			eta = complex<double>(EtaN[i].A, EtaK[i].A);
-		else
-			eta = complex<double>(baseIR, 0.0);
-
-		//allocate memory for the scattering coefficients
-		//complex<float>* B = (complex<float>*)malloc(sizeof(complex<float>)*Nl);
-
-		complex<double> IR(eta.real(), eta.imag());
-		computeB(&B[i * Nl], radius, IR, Lambda[i], Nl);
-	}
-}
-
-void computeOpticalParameters(double& cAngleI, double& cAngleO, double& oAngleI, double& oAngleO, double& I0, double* alpha, int Nl)
-{
-	computeCassegrainAngles(cAngleI, cAngleO, oAngleI, oAngleO);
-
-	//evaluate the incident field intensity
-	I0 = 0.0;
-	complex<double> Ui;
-
-	Ui = integrateUi(cAngleI, cAngleO, oAngleI, oAngleO, 2*pi);
-	I0 = Ui.real()*2*pi;
-
-	//compute alpha (condenser integral)
-	computeCondenserAlpha(alpha, Nl, cAngleI, cAngleO);
-}
-
-void gpuDetectorSpectrum(int numSamples)
-{
-	//integrate across the objective aperature and calculate the resulting intensity on a detector
-	PD.StartTimer(SIMULATE_SPECTRUM);
-	//clear the previous spectrum
-	SimSpectrum.clear();
-
-	//compute Nl (maximum order of the spectrum)
-	int Nl = computeNl();
-
-	double* alpha = (double*)malloc(sizeof(double)*(Nl + 1));
-	double cAngleI, cAngleO, oAngleI, oAngleO, I0;
-	computeOpticalParameters(cAngleI, cAngleO, oAngleI, oAngleO, I0, alpha, Nl);
-
-	//allocate space for a list of wavelengths
-	int nLambda = EtaK.size();
-
-	//allocate space for the 2D array (Nl x nu) of scattering coefficients
-	complex<double>* B = (complex<double>*)malloc(sizeof(complex<double>) * Nl * nLambda);
-	computeBArray(B, Nl, nLambda);
-
-
-
-	//allocate temporary space for the spectrum
-	double* I = (double*)malloc(sizeof(double) * EtaK.size());
-
-	//compute the spectrum on the GPU
-	PD.StartTimer(SIMULATE_GPU);
-	cudaComputeSpectrum(I, (double*)B, alpha, Nl, nLambda, oAngleI, oAngleO, cAngleI, cAngleO, numSamples);
-	PD.EndTimer(SIMULATE_GPU);
-
-	updateSpectrum(I, I0, nLambda);
-
-	PD.EndTimer(SIMULATE_SPECTRUM);
-
-}
-
-void SimulateSpectrum()
-{
-	if(pointDetector)
-		pointSpectrum();
-	else
-		gpuDetectorSpectrum(objectiveSamples);
-		//detectorSpectrum(objectiveSamples);
-}
-
-double absorbanceDistortion(){
-
-	//compute the mean of the spectrum
-	double sumSim = 0.0;
-	for(unsigned int i=0; i<SimSpectrum.size(); i++)
-	{
-		sumSim += SimSpectrum[i].A;
-	}
-	double meanSim = sumSim/SimSpectrum.size();
-
-	//compute the distortion (MSE from the mean)
-	double sumSE = 0.0;
-	for(unsigned int i=0; i<SimSpectrum.size(); i++)
-	{
-		sumSE += pow(SimSpectrum[i].A - meanSim, 2);
-	}
-	double MSE = sumSE / SimSpectrum.size();
-
-	return MSE;
-}
-
-double intensityDistortion(){
-
-	//compute the mean intensity of the spectrum
-	double sumSim = 0.0;
-	for(unsigned int i=0; i<SimSpectrum.size(); i++)
-	{
-		sumSim += pow(SimSpectrum[i].A, 2);
-	}
-	double magSim = sqrt(sumSim);
-
-	//compute the distortion (MSE from the mean)
-	double proj = 0.0;
-	for(unsigned int i=0; i<SimSpectrum.size(); i++)
-	{
-		proj += (SimSpectrum[i].A/magSim) * (1.0/SimSpectrum.size());
-	}
-	double error = proj;
-
-	return error;
-}
-
-void DistortionMap(float* distortionMap, int nSteps){
-	ofstream outFile("distortion.txt");
-
-	//set the parameters for the distortion simulation
-	double range = 0.4;
-	double step = (range)/(nSteps-1);
-
-	oNAi = 0.2;
-	oNAo = 0.5;
-
-	double startNAi = 0.0;
-	double startNAo = 0.3;
-
-	//compute the optical parameters
-	//compute Nl (maximum order of the spectrum)
-	int Nl = computeNl();
-
-	double* alpha = (double*)malloc(sizeof(double)*(Nl + 1));
-	double cAngleI, cAngleO, oAngleI, oAngleO, I0;
-
-	//allocate space for a list of wavelengths
-	int nLambda = EtaK.size();
-
-	//allocate temporary space for the spectrum
-	double* I = (double*)malloc(sizeof(double) * EtaK.size());
-
-	//calculate the material parameters
-	//allocate space for the 2D array (Nl x nu) of scattering coefficients
-	complex<double>* B = (complex<double>*)malloc(sizeof(complex<double>) * Nl * nLambda);
-	computeBArray(B, Nl, nLambda);
-
-    QProgressDialog progress("Computing distortion map...", "Stop", 0, nSteps * nSteps);
-    progress.setWindowModality(Qt::WindowModal);
-
-	double D;
-	double e = 0.001;
-	int i, o;
-	for(i=0; i<nSteps; i++)
-	{
-        for(o=0; o<nSteps; o++)
-		{
-            //update the progress bar and check for an exit
-            progress.setValue(i * nSteps + o);
-            if (progress.wasCanceled())
-                break;
-
-            //set the current optical parameters
-			cNAi = startNAi + i * step;
-			cNAo = startNAo + o * step;
-			//cout<<cNAi<<"   "<<cNAo<<endl;
-
-			//set the current optical parameters
-			//cNAi = i;
-			//cNAo = o;
-
-			//compute the optical parameters
-			computeOpticalParameters(cAngleI, cAngleO, oAngleI, oAngleO, I0, alpha, Nl);
-
-			//simulate the spectrum
-			cudaComputeSpectrum(I, (double*)B, alpha, Nl, nLambda, oAngleI, oAngleO, cAngleI, cAngleO, objectiveSamples);
-			updateSpectrum(I, I0, nLambda);
-
-			if(dispSimType == AbsorbanceSpecType)
-			{
-				if(cNAi >= cNAo || cNAi >= oNAo || oNAi >= cNAo || oNAi >= oNAo)
-					D = -1.0;
-				else
-					D = absorbanceDistortion();
-			}
-			else
-			{
-				if(cNAi >= cNAo || oNAi >= oNAo)
-					D = -1.0;
-				else
-					D = intensityDistortion();
-			}
-			distortionMap[o * nSteps + i] = D;
-			outFile<<D<<"       ";
-		}
-		outFile<<endl;
-		//cout<<i<<endl;
-    }
-
-	progress.setValue(nSteps * nSteps);
-
-	outFile.close();
-}
+#include <math.h>
+#include <complex>
+#include <iostream>
+#include <fstream>
+#include "globals.h"
+#include <QProgressDialog>
+#include <stdlib.h>
+//#include "cufft.h"
+using namespace std;
+
+#define pi 3.14159
+
+typedef complex<double> scComplex;
+
+extern int cbessjyva(double v,complex<double> z,double &vm,complex<double>*cjv,
+                     complex<double>*cyv,complex<double>*cjvp,complex<double>*cyvp);
+extern int bessjyv(double v,double x,double &vm,double *jv,double *yv,
+                   double *djv,double *dyv);
+
+complex<double> Jl_neg(complex<double> x)
+{
+    //this function computes the bessel function of the first kind Jl(x) for l = -0.5
+    return ( sqrt(2.0/pi) * cos(x) )/sqrt(x);
+}
+
+double Jl_neg(double x)
+{
+    //this function computes the bessel function of the first kind Jl(x) for l = -0.5
+    return ( sqrt(2.0/pi) * cos(x) )/sqrt(x);
+}
+
+double Yl_neg(double x)
+{
+    //this function computes the bessel function of the second kind Yl(x) for l = -0.5;
+    return ( sqrt(2.0/pi) * sin(x) )/sqrt(x);
+}
+
+void computeB(complex<double>* B, double radius, complex<double> refIndex, double lambda, int Nl)
+{
+    double k = (2*pi)/lambda;
+    int b = 2;
+
+    //allocate space for the real bessel functions
+    double* jv = (double*)malloc(sizeof(double)*(Nl+b));
+    double* yv = (double*)malloc(sizeof(double)*(Nl+b));
+    double* jvp = (double*)malloc(sizeof(double)*(Nl+b));
+    double* yvp = (double*)malloc(sizeof(double)*(Nl+b));
+
+    //allocate space for the complex bessel functions
+    complex<double>* cjv = (complex<double>*)malloc(sizeof(complex<double>)*(Nl+b));
+    complex<double>* cyv = (complex<double>*)malloc(sizeof(complex<double>)*(Nl+b));
+    complex<double>* cjvp = (complex<double>*)malloc(sizeof(complex<double>)*(Nl+b));
+    complex<double>* cyvp = (complex<double>*)malloc(sizeof(complex<double>)*(Nl+b));
+
+    double kr = k*radius;
+    complex<double> knr = k*refIndex*(double)radius;
+    complex<double> n = refIndex;
+
+    //compute the bessel functions for k*r
+    double vm;// = Nl - 1;
+    bessjyv((Nl)+0.5, kr, vm, jv, yv, jvp, yvp);
+    //cout<<"Nl: "<<Nl<<"  vm: "<<vm<<endl;
+    //printf("Nl: %f, vm: %f\n", (float)Nl, (float)vm);
+
+    //compute the bessel functions for k*n*r
+    cbessjyva((Nl)+0.5, knr, vm, cjv, cyv, cjvp, cyvp);
+
+    //scale factor for spherical bessel functions
+    double scale_kr = sqrt(pi/(2.0*kr));
+    complex<double> scale_knr = sqrt(pi/(2.0*knr));
+
+    complex<double> numer, denom;
+    double j_kr;
+    double y_kr;
+    complex<double> j_knr;
+    complex<double> j_d_knr;
+    double j_d_kr;
+    complex<double> h_kr;
+    complex<double> h_d_kr;
+    complex<double> h_neg;
+    complex<double> h_pos;
+
+    //cout<<"B coefficients:"<<endl;
+    for(int l=0; l<Nl; l++)
+    {
+        //compute the spherical bessel functions
+        j_kr = jv[l] * scale_kr;
+        y_kr = yv[l] * scale_kr;
+        j_knr = cjv[l] * scale_knr;
+
+        //compute the Hankel function
+        h_kr = complex<double>(j_kr, y_kr);
+
+        //compute the derivatives
+        if(l == 0)
+        {
+            //spherical bessel functions for l=0
+            j_d_kr = scale_kr * (Jl_neg(kr) - (jv[l] + kr*jv[l+1])/kr )/2.0;
+            j_d_knr = scale_knr * ( Jl_neg(knr) - (cjv[l] + knr*cjv[l+1])/knr )/2.0;
+            h_neg = complex<double>(scale_kr*Jl_neg(kr), scale_kr*Yl_neg(kr));
+            h_pos = complex<double>(scale_kr*jv[l+1], scale_kr*yv[l+1]);
+            h_d_kr = (h_neg - (h_kr + kr*h_pos)/kr)/2.0;
+        }
+        else
+        {
+            //spherical bessel functions
+            j_d_kr = scale_kr * (jv[l-1] - (jv[l] + kr*jv[l+1])/kr )/2.0;
+            j_d_knr = scale_knr * ( cjv[l-1] - (cjv[l] + knr*cjv[l+1])/knr )/2.0;
+            h_neg = complex<double>(scale_kr*jv[l-1], scale_kr*yv[l-1]);
+            h_pos = complex<double>(scale_kr*jv[l+1], scale_kr*yv[l+1]);
+            h_d_kr = (h_neg - (h_kr + kr*h_pos)/kr)/2.0;
+        }
+
+        numer = j_kr*j_d_knr*n - j_knr*j_d_kr;
+        denom = j_knr*h_d_kr - h_kr*j_d_knr*n;
+        B[l] =  numer/denom;
+
+        //B[l] = scComplex(temp.real(), temp.imag());
+        //cout<<B[l]<<endl;
+    }
+
+    free(jv);
+    free(yv);
+    free(jvp);
+    free(yvp);
+    free(cjv);
+    free(cyv);
+    free(cjvp);
+    free(cyvp);
+}
+
+void Legendre(double* P, double x, int Nl)
+{
+    //computes the legendre polynomials from orders 0 to Nl-1
+    P[0] = 1;
+    if(Nl == 1) return;
+    P[1] = x;
+    for(int l = 2; l < Nl; l++)
+    {
+        P[l] = ((2*l - 1)*x*P[l-1] - (l - 1)*P[l-2])/l;
+    }
+
+}
+
+complex<double> integrateUi(double cAngleI, double cAngleO, double oAngleI, double oAngleO, double M = 2*pi)
+{
+    /*This function integrates the incident field of magnitude M in the far zone
+    in order to evaluate the field at the central pixel of a detector.
+    cNAi = condenser inner angle
+    cNAo = condenser outer angle
+    oNAi = objective inner angle
+    oNAo = objective outer angle
+    M = field magnitude*/
+
+    double alphaIn = max(cAngleI, oAngleI);
+    double alphaOut = min(cAngleO,oAngleO);
+
+    complex<double> Ui;
+    if(alphaIn > alphaOut)
+        Ui = complex<double>(0.0, 0.0);
+    else
+        Ui = complex<double>(M * 2 * pi * (cos(alphaIn) - cos(alphaOut)), 0.0f);
+
+    return Ui;
+
+}
+
+void computeCondenserAlpha(double* alpha, int Nl, double cAngleI, double cAngleO)
+{
+    /*This function computes the condenser integral in order to build the field of incident light
+    alpha = list of Nl floating point values representing the condenser alpha as a function of l
+    Nl = number of orders in the incident field
+    cAngleI, cAngleO = inner and outer condenser angles (inner and outer NA)*/
+
+    //compute the Legendre polynomials for the condenser aperature
+    double* PcNAo = (double*)malloc(sizeof(double)*(Nl+1));
+    Legendre(PcNAo, cos(cAngleO), Nl+1);
+    double* PcNAi = (double*)malloc(sizeof(double)*(Nl+1));
+    Legendre(PcNAi, cos(cAngleI), Nl+1);
+
+    for(int l=0; l<Nl; l++)
+    {
+        //integration term
+        if(l == 0)
+            alpha[l] = -PcNAo[l+1] + PcNAo[0] + PcNAi[l+1] - PcNAi[0];
+        else
+            alpha[l] = -PcNAo[l+1] + PcNAo[l-1] + PcNAi[l+1] - PcNAi[l-1];
+
+        alpha[l] *= 2 * pi;
+    }
+
+}
+
+complex<double> integrateUs(double r, double lambda, complex<double> eta,
+                            double cAngleI, double cAngleO, double oAngleI, double oAngleO, double M = 2*pi)
+{
+    /*This function integrates the incident field of magnitude M in the far zone
+    in order to evaluate the field at the central pixel of a detector.
+    r = sphere radius
+    lambda = wavelength
+    eta = index of refraction
+    cNAi = condenser inner NA
+    cNAo = condenser outer NA
+    oNAi = objective inner NA
+    oNAo = objective outer NA
+    M = field magnitude*/
+
+    //compute the required number of orders
+    double k = 2*pi/lambda;
+    int Nl = (int)ceil( k + 4 * exp(log(k*r)/3) + 3 );
+
+    //compute the material coefficients B
+    complex<double>* B = (complex<double>*)malloc(sizeof(complex<double>)*Nl);
+    //compute the Legendre polynomials for the condenser and objective aperatures
+    double* PcNAo = (double*)malloc(sizeof(double)*(Nl+1));
+    Legendre(PcNAo, cos(cAngleO), Nl+1);
+    double* PcNAi = (double*)malloc(sizeof(double)*(Nl+1));
+    Legendre(PcNAi, cos(cAngleI), Nl+1);
+
+    double* PoNAo = (double*)malloc(sizeof(double)*(Nl+1));
+    Legendre(PoNAo, cos(oAngleO), Nl+1);
+    double* PoNAi = (double*)malloc(sizeof(double)*(Nl+1));
+    Legendre(PoNAi, cos(oAngleI), Nl+1);
+
+    //store the index of refraction;
+    complex<double> IR(eta.real(), eta.imag());
+
+    //compute the scattering coefficients
+    computeB(B, r, IR, lambda, Nl);
+
+    //aperature terms for the condenser (alpha) and objective (beta)
+    double alpha;
+    double beta;
+    double c;
+    complex<double> Us(0.0, 0.0);
+
+    for(int l=0; l<Nl; l++)
+    {
+        //integration term
+        if(l == 0)
+        {
+            alpha = -PcNAo[l+1] + PcNAo[0] + PcNAi[l+1] - PcNAi[0];
+            beta = -PoNAo[l+1] + PoNAo[0] + PoNAi[l+1] - PoNAi[0];
+        }
+        else
+        {
+            alpha = -PcNAo[l+1] + PcNAo[l-1] + PcNAi[l+1] - PcNAi[l-1];
+            beta = -PoNAo[l+1] + PoNAo[l-1] + PoNAi[l+1] - PoNAi[l-1];
+        }
+        c = (2*pi)/(2.0 * l + 1.0);
+        Us += c * alpha * beta * B[l] * M;
+
+
+    }
+    free(PcNAo);
+    free(PcNAi);
+    free(PoNAo);
+    free(PoNAi);
+    free(B);
+
+    return Us;
+
+}
+
+void pointSpectrum()
+{
+    PD.StartTimer(SIMULATE_SPECTRUM);
+    
+    //if there is no material to simulate
+    if(EtaK.size() == 0)
+	    return;
+    //clear the previous spectrum
+    SimSpectrum.clear();
+
+    double dNu = 2.0f;
+    double lambda;
+
+    //compute the angles based on NA
+    double cAngleI = asin(cNAi);
+    double cAngleO = asin(cNAo);
+    double oAngleI = asin(oNAi);
+    double oAngleO = asin(oNAo);
+
+    //implement a reflection-mode system if necessary
+    if(opticsMode == ReflectionOpticsType) {
+
+        //set the condenser to match the objective
+        cAngleI = oAngleI;
+        cAngleO = oAngleO;
+
+        //invert the objective
+        oAngleO = pi - cAngleI;
+        oAngleI = pi - cAngleO;
+    }
+
+    //integrate the incident field at the detector position
+    complex<double> Ui = integrateUi(cAngleI, cAngleO, oAngleI, oAngleO, 2*pi);
+    double I0 = Ui.real() * Ui.real() + Ui.imag() * Ui.imag();
+    I0 *= scaleI0;
+
+
+
+    //double I;
+    SpecPair temp;
+    double nu;
+    complex<double> eta;
+    complex<double> Us, U;
+
+    double vecLen = 0.0;
+    for(unsigned int i=0; i<EtaK.size(); i++)
+    {
+        nu = EtaK[i].nu;
+        lambda = 10000.0f/nu;
+        if(applyMaterial)
+            eta = complex<double>(EtaN[i].A, EtaK[i].A);
+        else
+            eta = complex<double>(baseIR, 0.0);
+
+
+        //integrate the scattered field at the detector position
+        Us = integrateUs(radius, lambda, eta, cAngleI, cAngleO, oAngleI, oAngleO, 2*pi);
+        U = Us + Ui;
+        double I = U.real() * U.real() + U.imag() * U.imag();
+
+        temp.nu = nu;
+
+        //set the spectrum value based on the current display type
+        if(dispSimType == AbsorbanceSpecType)
+            temp.A = -log10(I/I0);
+        else
+            temp.A = I;
+
+        if(dispNormalize)
+            vecLen += temp.A * temp.A;
+
+        SimSpectrum.push_back(temp);
+    }
+    vecLen = sqrt(vecLen);
+
+    if(dispNormalize)
+        for(unsigned int i=0; i<SimSpectrum.size(); i++)
+            SimSpectrum[i].A = (SimSpectrum[i].A / vecLen) * dispNormFactor;
+
+    PD.EndTimer(SIMULATE_SPECTRUM);
+}
+
+void updateSpectrum(double* I, double I0, int n)
+{
+    SimSpectrum.clear();
+    SpecPair temp;
+
+    //update the displayed spectrum based on the computed intensity I
+    for(int i=0; i<n; i++)
+    {
+        temp.nu = EtaK[i].nu;
+
+        //set the spectrum value based on the current display type
+        if(dispSimType == AbsorbanceSpecType)
+        {
+            temp.A = -log10(I[i]/I0);
+            //cout<<temp.nu<<"    "<<I[i]<<endl;
+        }
+        else
+        {
+            temp.A = I[i];
+            if(useSourceSpectrum)
+                temp.A *= SourceResampled[i].A;
+        }
+
+        SimSpectrum.push_back(temp);
+    }
+}
+
+void computeCassegrainAngles(double& cAngleI, double& cAngleO, double& oAngleI, double& oAngleO)
+{
+    //compute the angles based on NA
+    cAngleI = asin(cNAi);
+    cAngleO = asin(cNAo);
+    oAngleI = asin(oNAi);
+    oAngleO = asin(oNAo);
+
+    //implement a reflection-mode system if necessary
+    if(opticsMode == ReflectionOpticsType) {
+
+        //set the condenser to match the objective
+        cAngleI = oAngleI;
+        cAngleO = oAngleO;
+
+        //invert the objective
+        oAngleO = pi - cAngleI;
+        oAngleI = pi - cAngleO;
+    }
+
+
+}
+
+int computeNl()
+{
+    double maxNu = EtaK.back().nu;
+    double maxLambda = 10000.0f/maxNu;
+    double k = 2*pi/maxLambda;
+    int Nl = (int)ceil( k + 4 * exp(log(k*radius)/3) + 3 );
+
+    return Nl;
+}
+
+void computeBArray(complex<double>* B, int Nl, int nLambda)
+{
+    double nu;
+    complex<double> eta;
+    double* Lambda = (double*)malloc(sizeof(double) * nLambda);
+
+    //for each wavenumber nu
+    for(unsigned int i=0; i<EtaK.size(); i++)
+    {
+        //compute information based on wavelength and material
+        nu = EtaK[i].nu;
+        Lambda[i] = 10000.0f/nu;
+        if(applyMaterial)
+            eta = complex<double>(EtaN[i].A, EtaK[i].A);
+        else
+            eta = complex<double>(baseIR, 0.0);
+
+        //allocate memory for the scattering coefficients
+        //complex<float>* B = (complex<float>*)malloc(sizeof(complex<float>)*Nl);
+
+        complex<double> IR(eta.real(), eta.imag());
+        computeB(&B[i * Nl], radius, IR, Lambda[i], Nl);
+    }
+}
+
+void computeOpticalParameters(double& cAngleI, double& cAngleO, double& oAngleI, double& oAngleO, double& I0, double* alpha, int Nl)
+{
+    computeCassegrainAngles(cAngleI, cAngleO, oAngleI, oAngleO);
+
+    //evaluate the incident field intensity
+    I0 = 0.0;
+    complex<double> Ui;
+
+    Ui = integrateUi(cAngleI, cAngleO, oAngleI, oAngleO, 2*pi);
+    I0 = Ui.real()*2*pi;
+
+    //compute alpha (condenser integral)
+    computeCondenserAlpha(alpha, Nl, cAngleI, cAngleO);
+}
+
+void gpuDetectorSpectrum(int numSamples)
+{
+     //allocate space for a list of wavelengths
+    int nLambda = EtaK.size();
+    if(nLambda == 0)
+	    return;
+    
+    //integrate across the objective aperature and calculate the resulting intensity on a detector
+    PD.StartTimer(SIMULATE_SPECTRUM);
+    //clear the previous spectrum
+    SimSpectrum.clear();
+
+    //compute Nl (maximum order of the spectrum)
+    int Nl = computeNl();
+    
+
+    double* alpha = (double*)malloc(sizeof(double)*(Nl + 1));
+    double cAngleI, cAngleO, oAngleI, oAngleO, I0;
+    computeOpticalParameters(cAngleI, cAngleO, oAngleI, oAngleO, I0, alpha, Nl);
+    
+
+   
+    
+
+    //allocate space for the 2D array (Nl x nu) of scattering coefficients
+    complex<double>* B = (complex<double>*)malloc(sizeof(complex<double>) * Nl * nLambda);
+    computeBArray(B, Nl, nLambda);
+
+
+
+    //allocate temporary space for the spectrum
+    double* I = (double*)malloc(sizeof(double) * EtaK.size());
+
+    //compute the spectrum on the GPU
+    PD.StartTimer(SIMULATE_GPU);
+    cudaComputeSpectrum(I, (double*)B, alpha, Nl, nLambda, oAngleI, oAngleO, cAngleI, cAngleO, numSamples);
+    PD.EndTimer(SIMULATE_GPU);
+
+    updateSpectrum(I, I0, nLambda);
+
+    PD.EndTimer(SIMULATE_SPECTRUM);
+
+}
+
+void SimulateSpectrum()
+{
+    if(pointDetector)
+        pointSpectrum();
+    else
+        gpuDetectorSpectrum(objectiveSamples);
+	   
+}
+
+double absorbanceDistortion() {
+
+    //compute the mean of the spectrum
+    double sumSim = 0.0;
+    for(unsigned int i=0; i<SimSpectrum.size(); i++)
+    {
+        sumSim += SimSpectrum[i].A;
+    }
+    double meanSim = sumSim/SimSpectrum.size();
+
+    //compute the distortion (MSE from the mean)
+    double sumSE = 0.0;
+    for(unsigned int i=0; i<SimSpectrum.size(); i++)
+    {
+        sumSE += pow(SimSpectrum[i].A - meanSim, 2);
+    }
+    double MSE = sumSE / SimSpectrum.size();
+
+    return MSE;
+}
+
+double intensityDistortion() {
+
+    //compute the mean intensity of the spectrum
+    double sumSim = 0.0;
+    for(unsigned int i=0; i<SimSpectrum.size(); i++)
+    {
+        sumSim += pow(SimSpectrum[i].A, 2);
+    }
+    double magSim = sqrt(sumSim);
+
+    //compute the distortion (MSE from the mean)
+    double proj = 0.0;
+    for(unsigned int i=0; i<SimSpectrum.size(); i++)
+    {
+        proj += (SimSpectrum[i].A/magSim) * (1.0/SimSpectrum.size());
+    }
+    double error = proj;
+
+    return error;
+}
+
+void DistortionMap(float* distortionMap, int nSteps) {
+    ofstream outFile("distortion.txt");
+
+    //set the parameters for the distortion simulation
+    double range = 0.4;
+    double step = (range)/(nSteps-1);
+
+    oNAi = 0.2;
+    oNAo = 0.5;
+
+    double startNAi = 0.0;
+    double startNAo = 0.3;
+
+    //compute the optical parameters
+    //compute Nl (maximum order of the spectrum)
+    int Nl = computeNl();
+
+    double* alpha = (double*)malloc(sizeof(double)*(Nl + 1));
+    double cAngleI, cAngleO, oAngleI, oAngleO, I0;
+
+    //allocate space for a list of wavelengths
+    int nLambda = EtaK.size();
+
+    //allocate temporary space for the spectrum
+    double* I = (double*)malloc(sizeof(double) * EtaK.size());
+
+    //calculate the material parameters
+    //allocate space for the 2D array (Nl x nu) of scattering coefficients
+    complex<double>* B = (complex<double>*)malloc(sizeof(complex<double>) * Nl * nLambda);
+    computeBArray(B, Nl, nLambda);
+
+    QProgressDialog progress("Computing distortion map...", "Stop", 0, nSteps * nSteps);
+    progress.setWindowModality(Qt::WindowModal);
+
+    double D;
+    double e = 0.001;
+    int i, o;
+    for(i=0; i<nSteps; i++)
+    {
+        for(o=0; o<nSteps; o++)
+        {
+            //update the progress bar and check for an exit
+            progress.setValue(i * nSteps + o);
+            if (progress.wasCanceled())
+                break;
+
+            //set the current optical parameters
+            cNAi = startNAi + i * step;
+            cNAo = startNAo + o * step;
+            //cout<<cNAi<<"   "<<cNAo<<endl;
+
+            //set the current optical parameters
+            //cNAi = i;
+            //cNAo = o;
+
+            //compute the optical parameters
+            computeOpticalParameters(cAngleI, cAngleO, oAngleI, oAngleO, I0, alpha, Nl);
+
+            //simulate the spectrum
+            cudaComputeSpectrum(I, (double*)B, alpha, Nl, nLambda, oAngleI, oAngleO, cAngleI, cAngleO, objectiveSamples);
+            updateSpectrum(I, I0, nLambda);
+
+            if(dispSimType == AbsorbanceSpecType)
+            {
+                if(cNAi >= cNAo || cNAi >= oNAo || oNAi >= cNAo || oNAi >= oNAo)
+                    D = -1.0;
+                else
+                    D = absorbanceDistortion();
+            }
+            else
+            {
+                if(cNAi >= cNAo || oNAi >= oNAo)
+                    D = -1.0;
+                else
+                    D = intensityDistortion();
+            }
+            distortionMap[o * nSteps + i] = D;
+            outFile<<D<<"       ";
+        }
+        outFile<<endl;
+        //cout<<i<<endl;
+    }
+
+    progress.setValue(nSteps * nSteps);
+
+    outFile.close();
+}
-#ifndef bessH
-#define bessH
-#define _USE_MATH_DEFINES
-#include <math.h>
-#include <complex>
-using namespace std;
-#define eps 1e-15
-#define el 0.5772156649015329
-
-int msta1(double x,int mp);
-int msta2(double x,int n,int mp);
-int bessjy01a(double x,double &j0,double &j1,double &y0,double &y1,
-    double &j0p,double &j1p,double &y0p,double &y1p);
-int bessjy01b(double x,double &j0,double &j1,double &y0,double &y1,
-    double &j0p,double &j1p,double &y0p,double &y1p);
-int bessjyna(int n,double x,int &nm,double *jn,double *yn,
-    double *jnp,double *ynp);
-int bessjynb(int n,double x,int &nm,double *jn,double *yn,
-    double *jnp,double *ynp);
-int bessjyv(double v,double x,double &vm,double *jv,double *yv,
-    double *jvp,double *yvp);
-int bessik01a(double x,double &i0,double &i1,double &k0,double &k1,
-    double &i0p,double &i1p,double &k0p,double &k1p);
-int bessik01b(double x,double &i0,double &i1,double &k0,double &k1,
-    double &i0p,double &i1p,double &k0p,double &k1p);
-int bessikna(int n,double x,int &nm,double *in,double *kn,
-    double *inp,double *knp);
-int bessiknb(int n,double x,int &nm,double *in,double *kn,
-    double *inp,double *knp);
-int bessikv(double v,double x,double &vm,double *iv,double *kv,
-    double *ivp,double *kvp);
-int cbessjy01(complex<double> z,complex<double> &cj0,complex<double> &cj1,
-    complex<double> &cy0,complex<double> &cy1,complex<double> &cj0p,
-    complex<double> &cj1p,complex<double> &cy0p,complex<double> &cy1p);
-int cbessjyna(int n,complex<double> z,int &nm,complex<double> *cj,
-    complex<double> *cy,complex<double> *cjp,complex<double> *cyp);
-int cbessjynb(int n,complex<double> z,int &nm,complex<double> *cj,
-    complex<double> *cy,complex<double> *cjp,complex<double> *cyp);
-int cbessik01(complex<double>z,complex<double>&ci0,complex<double>&ci1,
-    complex<double>&ck0,complex<double>&ck1,complex<double>&ci0p,
-    complex<double>&ci1p,complex<double>&ck0p,complex<double>&ck1p);
-int cbessikna(int n,complex<double> z,int &nm,complex<double> *ci,
-    complex<double> *ck,complex<double> *cip,complex<double> *ckp);
-int cbessiknb(int n,complex<double> z,int &nm,complex<double> *ci,
-    complex<double> *ck,complex<double> *cip,complex<double> *ckp);
-int cbessjyva(double v,complex<double> z,double &vm,complex<double>*cjv,
-    complex<double>*cyv,complex<double>*cjvp,complex<double>*cyvp);
-int cbessikv(double v,complex<double>z,double &vm,complex<double> *civ,
-    complex<double> *ckv,complex<double> *civp,complex<double> *ckvp);
-
-#endif
+#ifndef bessH
+#define bessH
+#define _USE_MATH_DEFINES
+#include <math.h>
+#include <complex>
+using namespace std;
+#define eps 1e-15
+#define el 0.5772156649015329
+
+int msta1(double x,int mp);
+int msta2(double x,int n,int mp);
+int bessjy01a(double x,double &j0,double &j1,double &y0,double &y1,
+              double &j0p,double &j1p,double &y0p,double &y1p);
+int bessjy01b(double x,double &j0,double &j1,double &y0,double &y1,
+              double &j0p,double &j1p,double &y0p,double &y1p);
+int bessjyna(int n,double x,int &nm,double *jn,double *yn,
+             double *jnp,double *ynp);
+int bessjynb(int n,double x,int &nm,double *jn,double *yn,
+             double *jnp,double *ynp);
+int bessjyv(double v,double x,double &vm,double *jv,double *yv,
+            double *jvp,double *yvp);
+int bessik01a(double x,double &i0,double &i1,double &k0,double &k1,
+              double &i0p,double &i1p,double &k0p,double &k1p);
+int bessik01b(double x,double &i0,double &i1,double &k0,double &k1,
+              double &i0p,double &i1p,double &k0p,double &k1p);
+int bessikna(int n,double x,int &nm,double *in,double *kn,
+             double *inp,double *knp);
+int bessiknb(int n,double x,int &nm,double *in,double *kn,
+             double *inp,double *knp);
+int bessikv(double v,double x,double &vm,double *iv,double *kv,
+            double *ivp,double *kvp);
+int cbessjy01(complex<double> z,complex<double> &cj0,complex<double> &cj1,
+              complex<double> &cy0,complex<double> &cy1,complex<double> &cj0p,
+              complex<double> &cj1p,complex<double> &cy0p,complex<double> &cy1p);
+int cbessjyna(int n,complex<double> z,int &nm,complex<double> *cj,
+              complex<double> *cy,complex<double> *cjp,complex<double> *cyp);
+int cbessjynb(int n,complex<double> z,int &nm,complex<double> *cj,
+              complex<double> *cy,complex<double> *cjp,complex<double> *cyp);
+int cbessik01(complex<double>z,complex<double>&ci0,complex<double>&ci1,
+              complex<double>&ck0,complex<double>&ck1,complex<double>&ci0p,
+              complex<double>&ci1p,complex<double>&ck0p,complex<double>&ck1p);
+int cbessikna(int n,complex<double> z,int &nm,complex<double> *ci,
+              complex<double> *ck,complex<double> *cip,complex<double> *ckp);
+int cbessiknb(int n,complex<double> z,int &nm,complex<double> *ci,
+              complex<double> *ck,complex<double> *cip,complex<double> *ckp);
+int cbessjyva(double v,complex<double> z,double &vm,complex<double>*cjv,
+              complex<double>*cyv,complex<double>*cjvp,complex<double>*cyvp);
+int cbessikv(double v,complex<double>z,double &vm,complex<double> *civ,
+             complex<double> *ckv,complex<double> *civp,complex<double> *ckvp);
+
+#endif
-//  bessik.cpp -- computation of modified Bessel functions In, Kn
-//      and their derivatives. Algorithms and coefficient values from
-//      "Computation of Special Functions", Zhang and Jin, John
-//      Wiley and Sons, 1996.
-//
-//  (C) 2003, C. Bond. All rights reserved.
-//
-#define _USE_MATH_DEFINES
-#include <math.h>
-#include "bessel.h"
-
-double gamma(double x);
-
-int bessik01a(double x,double &i0,double &i1,double &k0,double &k1,
-    double &i0p,double &i1p,double &k0p,double &k1p)
-{
-    double r,x2,ca,cb,ct,ww,w0,xr,xr2;
-    int k,kz;
-    static double a[] = {
-        0.125,
-        7.03125e-2,
-        7.32421875e-2,
-        1.1215209960938e-1,
-        2.2710800170898e-1,
-        5.7250142097473e-1,
-        1.7277275025845,
-        6.0740420012735,
-        2.4380529699556e1,
-        1.1001714026925e2,
-        5.5133589612202e2,
-        3.0380905109224e3};
-    static double b[] = {
-        -0.375,
-        -1.171875e-1,
-        -1.025390625e-1,
-        -1.4419555664063e-1,
-        -2.7757644653320e-1,
-        -6.7659258842468e-1,
-        -1.9935317337513,
-        -6.8839142681099,
-        -2.7248827311269e1,
-        -1.2159789187654e2,
-        -6.0384407670507e2,
-        -3.3022722944809e3};
-    static double a1[] = {
-        0.125,
-        0.2109375,
-        1.0986328125,
-        1.1775970458984e1,
-        2.1461706161499e2,
-        5.9511522710323e3,
-        2.3347645606175e5,
-        1.2312234987631e7};
-
-    if (x < 0.0) return 1;
-    if (x == 0.0) {
-        i0 = 1.0;
-        i1 = 0.0;
-        k0 = 1e308;
-        k1 = 1e308;
-        i0p = 0.0;
-        i1p = 0.5;
-        k0p = -1e308;
-        k1p = -1e308;
-        return 0;
-    }
-    x2 = x*x;
-    if (x <= 18.0) {
-        i0 = 1.0;
-        r = 1.0;
-        for (k=1;k<=50;k++) {
-            r *= 0.25*x2/(k*k);
-            i0 += r;
-            if (fabs(r/i0) < eps) break;
-        }
-        i1 = 1.0;
-        r = 1.0;
-        for (k=1;k<=50;k++) {
-            r *= 0.25*x2/(k*(k+1));
-            i1 += r;
-            if (fabs(r/i1) < eps) break;
-        }
-        i1 *= 0.5*x;
-    }
-    else {
-        if (x >= 50.0) kz = 7;
-        else if (x >= 35.0) kz = 9;
-        else kz = 12;
-        ca = exp(x)/sqrt(2.0*M_PI*x);
-        i0 = 1.0;
-        xr = 1.0/x;
-        for (k=0;k<kz;k++) {
-            i0 += a[k]*pow(xr,k+1);
-        }
-        i0 *= ca;
-        i1 = 1.0;
-        for (k=0;k<kz;k++) {
-            i1 += b[k]*pow(xr,k+1);
-        }
-        i1 *= ca;
-    }
-    if (x <= 9.0) {
-        ct = -(log(0.5*x)+el);
-        k0 = 0.0;
-        w0 = 0.0;
-        r = 1.0;
-        ww = 0.0;
-        for (k=1;k<=50;k++) {
-            w0 += 1.0/k;
-            r *= 0.25*x2/(k*k);
-            k0 += r*(w0+ct);
-            if (fabs((k0-ww)/k0) < eps) break;
-            ww = k0;
-        }
-        k0 += ct;
-    }
-    else {
-        cb = 0.5/x;
-        xr2 = 1.0/x2;
-        k0 = 1.0;
-        for (k=0;k<8;k++) {
-            k0 += a1[k]*pow(xr2,k+1);
-        }
-        k0 *= cb/i0;
-    }
-    k1 = (1.0/x - i1*k0)/i0;
-    i0p = i1;
-    i1p = i0-i1/x;
-    k0p = -k1;
-    k1p = -k0-k1/x;
-    return 0;
-}
-
-int bessik01b(double x,double &i0,double &i1,double &k0,double &k1,
-    double &i0p,double &i1p,double &k0p,double &k1p)
-{
-    double t,t2,dtmp,dtmp1;
-
-    if (x < 0.0) return 1;
-    if (x == 0.0) {
-        i0 = 1.0;
-        i1 = 0.0;
-        k0 = 1e308;
-        k1 = 1e308;
-        i0p = 0.0;
-        i1p = 0.5;
-        k0p = -1e308;
-        k1p = -1e308;
-        return 0;
-    }
-    if (x < 3.75) {
-        t = x/3.75;
-        t2 = t*t;
-        i0 = (((((0.0045813*t2+0.0360768)*t2+0.2659732)*t2+
-             1.2067492)*t2+3.0899424)*t2+3.5156229)*t2+1.0;
-        i1 = x*(((((0.00032411*t2+0.00301532)*t2+0.02658733*t2+
-             0.15084934)*t2+0.51498869)*t2+0.87890594)*t2+0.5);
-    }
-    else {
-        t = 3.75/x;
-        dtmp1 = exp(x)/sqrt(x);
-        dtmp = (((((((0.00392377*t-0.01647633)*t+0.026355537)*t-0.02057706)*t+
-          0.00916281)*t-0.00157565)*t+0.00225319)*t+0.01328592)*t+0.39894228;
-        i0 = dtmp*dtmp1;
-        dtmp = (((((((-0.00420059*t+0.01787654)*t-0.02895312)*t+0.02282967)*t-
-          0.01031555)*t+0.00163801)*t-0.00362018)*t-0.03988024)*t+0.39894228;
-        i1 = dtmp*dtmp1;
-    }
-    if (x < 2.0) {
-        t = 0.5*x;
-        t2 = t*t;       // already calculated above
-        dtmp = (((((0.0000074*t2+0.0001075)*t2+0.00262698)*t2+0.0348859)*t2+
-          0.23069756)*t2+0.4227842)*t2-0.57721566;
-        k0 = dtmp - i0*log(t);
-        dtmp = (((((-0.00004686*t2-0.00110404)*t2-0.01919402)*t2-
-          0.18156897)*t2-0.67278578)*t2+0.15443144)*t2+1.0;
-        k1 = dtmp/x + i1*log(t);
-    }
-    else {
-        t = 2.0/x;
-        dtmp1 = exp(-x)/sqrt(x);
-        dtmp = (((((0.00053208*t-0.0025154)*t+0.00587872)*t-0.01062446)*t+
-          0.02189568)*t-0.07832358)*t+1.25331414;
-        k0 = dtmp*dtmp1;
-        dtmp = (((((-0.00068245*t+0.00325614)*t-0.00780353)*t+0.01504268)*t-
-          0.0365562)*t+0.23498619)*t+1.25331414;
-        k1 = dtmp*dtmp1;
-    }
-    i0p = i1;
-    i1p = i0 - i1/x;
-    k0p = -k1;
-    k1p = -k0 - k1/x;
-    return 0;
-}
-int bessikna(int n,double x,int &nm,double *in,double *kn,
-    double *inp,double *knp)
-{
-    double bi0,bi1,bk0,bk1,g,g0,g1,f,f0,f1,h,h0,h1,s0;
-    int k,m,ecode;
-
-    if ((x < 0.0) || (n < 0)) return 1;
-    if (x < eps) {
-        for (k=0;k<=n;k++) {
-            in[k] = 0.0;
-            kn[k] = 1e308;
-            inp[k] = 0.0;
-            knp[k] = -1e308;
-        }
-        in[0] = 1.0;
-        inp[1] = 0.5;
-        return 0;
-    }
-    nm = n;
-    ecode = bessik01a(x,in[0],in[1],kn[0],kn[1],inp[0],inp[1],knp[0],knp[1]);
-    if (n < 2) return 0;
-    bi0 = in[0];
-    bi1 = in[1];
-    bk0 = kn[0];
-    bk1 = kn[1];
-    if ((x > 40.0) && (n < (int)(0.25*x))) {
-        h0 = bi0;
-        h1 = bi1;
-        for (k=2;k<=n;k++) {
-            h = -2.0*(k-1.0)*h1/x+h0;
-            in[k] = h;
-            h0 = h1;
-            h1 = h;
-        }
-    }
-    else {
-        m = msta1(x,200);
-        if (m < n) nm = m;
-        else m = msta2(x,n,15);
-        f0 = 0.0;
-        f1 = 1.0e-100;
-        for (k=m;k>=0;k--) {
-            f = 2.0*(k+1.0)*f1/x+f0;
-            if (x <= nm) in[k] = f;
-            f0 = f1;
-            f1 = f;
-        }
-        s0 = bi0/f;
-        for (k=0;k<=m;k++) {
-            in[k] *= s0;
-        }
-    }
-    g0 = bk0;
-    g1 = bk1;
-    for (k=2;k<=nm;k++) {
-        g = 2.0*(k-1.0)*g1/x+g0;
-        kn[k] = g;
-        g0 = g1;
-        g1 = g;
-    }
-    for (k=2;k<=nm;k++) {
-        inp[k] = in[k-1]-k*in[k]/x;
-        knp[k] = -kn[k-1]-k*kn[k]/x;
-    }
-    return 0;
-}
-int bessiknb(int n,double x,int &nm,double *in,double *kn,
-    double *inp,double *knp)
-{
-    double s0,bs,f,f0,f1,sk0,a0,bkl,vt,r,g,g0,g1;
-    int k,kz,m,l;
-
-    if ((x < 0.0) || (n < 0)) return 1;
-    if (x < eps) {
-        for (k=0;k<=n;k++) {
-            in[k] = 0.0;
-            kn[k] = 1e308;
-            inp[k] = 0.0;
-            knp[k] = -1e308;
-        }
-        in[0] = 1.0;
-        inp[1] = 0.5;
-        return 0;
-    }
-    nm = n;
-    if (n == 0) nm = 1;
-    m = msta1(x,200);
-    if (m < nm) nm = m;
-    else m = msta2(x,nm,15);
-    bs = 0.0;
-    sk0 = 0.0;
-    f0 = 0.0;
-    f1 = 1.0e-100;
-    for (k=m;k>=0;k--) {
-        f = 2.0*(k+1.0)*f1/x+f0;
-        if (k <= nm) in[k] = f;
-        if ((k != 0) && (k == 2*(int)(k/2))) {
-            sk0 += 4.0*f/k;
-        }
-        bs += 2.0*f;
-        f0 = f1;
-        f1 = f;
-    }
-    s0 = exp(x)/(bs-f);
-    for (k=0;k<=nm;k++) {
-        in[k] *= s0;
-    }
-    if (x <= 8.0) {
-        kn[0] = -(log(0.5*x)+el)*in[0]+s0*sk0;
-        kn[1] = (1.0/x-in[1]*kn[0])/in[0];
-    }
-    else {
-        a0 = sqrt(M_PI_2/x)*exp(-x);
-        if (x >= 200.0) kz = 6;
-        else if (x >= 80.0) kz = 8;
-        else if (x >= 25.0) kz = 10;
-        else kz = 16;
-        for (l=0;l<2;l++) {
-            bkl = 1.0;
-            vt = 4.0*l;
-            r = 1.0;
-            for (k=1;k<=kz;k++) {
-                r *= 0.125*(vt-pow(2.0*k-1.0,2))/(k*x);
-                bkl += r;
-            }
-            kn[l] = a0*bkl;
-        }
-    }
-    g0 = kn[0];
-    g1 = kn[1];
-    for (k=2;k<=nm;k++) {
-        g = 2.0*(k-1.0)*g1/x+g0;
-        kn[k] = g;
-        g0 = g1;
-        g1 = g;
-    }
-    inp[0] = in[1];
-    knp[0] = -kn[1];
-    for (k=1;k<=nm;k++) {
-        inp[k] = in[k-1]-k*in[k]/x;
-        knp[k] = -kn[k-1]-k*kn[k]/x;
-    }
-    return 0;
-}
-
-//  The following program computes the modified Bessel functions
-//  Iv(x) and Kv(x) for arbitrary positive order. For negative
-//  order use:
-//
-//          I-v(x) = Iv(x) + 2/pi sin(v pi) Kv(x)
-//          K-v(x) = Kv(x)
-//
-int bessikv(double v,double x,double &vm,double *iv,double *kv,
-    double *ivp,double *kvp)
-{
-    double x2,v0,piv,vt,a1,v0p,gap,r,bi0,ca,sum;
-    double f,f1,f2,ct,cs,wa,gan,ww,w0,v0n;
-    double r1,r2,bk0,bk1,bk2,a2,cb;
-    int n,k,kz,m;
-
-    if ((v < 0.0) || (x < 0.0)) return 1;
-    x2 = x*x;
-    n = (int)v;
-    v0 = v-n;
-    if (n == 0) n = 1;
-    if (x == 0.0) {
-        for (k=0;k<=n;k++) {
-            iv[k] = 0.0;
-            kv[k] = -1e308;
-            ivp[k] = 0.0;
-            kvp[k] = 1e308;
-        }
-        if (v0 == 0.0) {
-            iv[0] = 1.0;
-            ivp[1] = 0.5;
-        }
-        vm = v;
-        return 0;
-    }
-    piv = M_PI*v0;
-    vt = 4.0*v0*v0;
-    if (v0 == 0.0) {
-        a1 = 1.0;
-    }
-    else {
-        v0p = 1.0+v0;
-        gap = gamma(v0p);
-        a1 = pow(0.5*x,v0)/gap;
-    }
-    if (x >= 50.0) kz = 8;
-    else if (x >= 35.0) kz = 10;
-    else kz = 14;
-    if (x <= 18.0) {
-        bi0 = 1.0;
-        r = 1.0;
-        for (k=1;k<=30;k++) {
-            r *= 0.25*x2/(k*(k+v0));
-            bi0 += r;
-            if (fabs(r/bi0) < eps) break;
-        }
-        bi0 *= a1;
-    }
-    else {
-        ca = exp(x)/sqrt(2.0*M_PI*x);
-        sum = 1.0;
-        r = 1.0;
-        for (k=1;k<=kz;k++) {
-            r *= -0.125*(vt-pow(2.0*k-1.0,2.0))/(k*x);
-            sum += r;
-        }
-        bi0 = ca*sum;
-    }
-    m = msta1(x,200);
-    if (m < n) n = m;
-    else m = msta2(x,n,15);
-    f2 = 0.0;
-    f1 = 1.0e-100;
-    for (k=m;k>=0;k--) {
-        f = 2.0*(v0+k+1.0)*f1/x+f2;
-        if (k <= n) iv[k] = f;
-        f2 = f1;
-        f1 = f;
-    }
-    cs = bi0/f;
-    for (k=0;k<=n;k++) {
-        iv[k] *= cs;
-    }
-    ivp[0] = v0*iv[0]/x+iv[1];
-    for (k=1;k<=n;k++) {
-        ivp[k] = -(k+v0)*iv[k]/x+iv[k-1];
-    }
-    ww = 0.0;
-    if (x <= 9.0) {
-        if (v0 == 0.0) {
-            ct = -log(0.5*x)-el;
-            cs = 0.0;
-            w0 = 0.0;
-            r = 1.0;
-            for (k=1;k<=50;k++) {
-                w0 += 1.0/k;
-                r *= 0.25*x2/(k*k);
-                cs += r*(w0+ct);
-                wa = fabs(cs);
-                if (fabs((wa-ww)/wa) < eps) break;
-                ww = wa;
-            }
-            bk0 = ct+cs;
-        }
-        else {
-            v0n = 1.0-v0;
-            gan = gamma(v0n);
-            a2 = 1.0/(gan*pow(0.5*x,v0));
-            a1 = pow(0.5*x,v0)/gap;
-            sum = a2-a1;
-            r1 = 1.0;
-            r2 = 1.0;
-            for (k=1;k<=120;k++) {
-                r1 *= 0.25*x2/(k*(k-v0));
-                r2 *= 0.25*x2/(k*(k+v0));
-                sum += a2*r1-a1*r2;
-                wa = fabs(sum);
-                if (fabs((wa-ww)/wa) < eps) break;
-                ww = wa;
-            }
-            bk0 = M_PI_2*sum/sin(piv);
-        }
-    }
-    else {
-        cb = exp(-x)*sqrt(M_PI_2/x);
-        sum = 1.0;
-        r = 1.0;
-        for (k=1;k<=kz;k++) {
-            r *= 0.125*(vt-pow(2.0*k-1.0,2.0))/(k*x);
-            sum += r;
-        }
-        bk0 = cb*sum;
-    }
-    bk1 = (1.0/x-iv[1]*bk0)/iv[0];
-    kv[0] = bk0;
-    kv[1] = bk1;
-    for (k=2;k<=n;k++) {
-        bk2 = 2.0*(v0+k-1.0)*bk1/x+bk0;
-        kv[k] = bk2;
-        bk0 = bk1;
-        bk1 = bk2;
-    }
-    kvp[0] = v0*kv[0]/x-kv[1];
-    for (k=1;k<=n;k++) {
-        kvp[k] = -(k+v0)*kv[k]/x-kv[k-1];
-    }
-    vm = n+v0;
-    return 0;
-}
+//  bessik.cpp -- computation of modified Bessel functions In, Kn
+//      and their derivatives. Algorithms and coefficient values from
+//      "Computation of Special Functions", Zhang and Jin, John
+//      Wiley and Sons, 1996.
+//
+//  (C) 2003, C. Bond. All rights reserved.
+//
+#define _USE_MATH_DEFINES
+#include <math.h>
+#include "bessel.h"
+
+double gamma(double x);
+
+int bessik01a(double x,double &i0,double &i1,double &k0,double &k1,
+              double &i0p,double &i1p,double &k0p,double &k1p)
+{
+    double r,x2,ca,cb,ct,ww,w0,xr,xr2;
+    int k,kz;
+    static double a[] = {
+        0.125,
+        7.03125e-2,
+        7.32421875e-2,
+        1.1215209960938e-1,
+        2.2710800170898e-1,
+        5.7250142097473e-1,
+        1.7277275025845,
+        6.0740420012735,
+        2.4380529699556e1,
+        1.1001714026925e2,
+        5.5133589612202e2,
+        3.0380905109224e3
+    };
+    static double b[] = {
+        -0.375,
+        -1.171875e-1,
+        -1.025390625e-1,
+        -1.4419555664063e-1,
+        -2.7757644653320e-1,
+        -6.7659258842468e-1,
+        -1.9935317337513,
+        -6.8839142681099,
+        -2.7248827311269e1,
+        -1.2159789187654e2,
+        -6.0384407670507e2,
+        -3.3022722944809e3
+    };
+    static double a1[] = {
+        0.125,
+        0.2109375,
+        1.0986328125,
+        1.1775970458984e1,
+        2.1461706161499e2,
+        5.9511522710323e3,
+        2.3347645606175e5,
+        1.2312234987631e7
+    };
+
+    if (x < 0.0) return 1;
+    if (x == 0.0) {
+        i0 = 1.0;
+        i1 = 0.0;
+        k0 = 1e308;
+        k1 = 1e308;
+        i0p = 0.0;
+        i1p = 0.5;
+        k0p = -1e308;
+        k1p = -1e308;
+        return 0;
+    }
+    x2 = x*x;
+    if (x <= 18.0) {
+        i0 = 1.0;
+        r = 1.0;
+        for (k=1; k<=50; k++) {
+            r *= 0.25*x2/(k*k);
+            i0 += r;
+            if (fabs(r/i0) < eps) break;
+        }
+        i1 = 1.0;
+        r = 1.0;
+        for (k=1; k<=50; k++) {
+            r *= 0.25*x2/(k*(k+1));
+            i1 += r;
+            if (fabs(r/i1) < eps) break;
+        }
+        i1 *= 0.5*x;
+    }
+    else {
+        if (x >= 50.0) kz = 7;
+        else if (x >= 35.0) kz = 9;
+        else kz = 12;
+        ca = exp(x)/sqrt(2.0*M_PI*x);
+        i0 = 1.0;
+        xr = 1.0/x;
+        for (k=0; k<kz; k++) {
+            i0 += a[k]*pow(xr,k+1);
+        }
+        i0 *= ca;
+        i1 = 1.0;
+        for (k=0; k<kz; k++) {
+            i1 += b[k]*pow(xr,k+1);
+        }
+        i1 *= ca;
+    }
+    if (x <= 9.0) {
+        ct = -(log(0.5*x)+el);
+        k0 = 0.0;
+        w0 = 0.0;
+        r = 1.0;
+        ww = 0.0;
+        for (k=1; k<=50; k++) {
+            w0 += 1.0/k;
+            r *= 0.25*x2/(k*k);
+            k0 += r*(w0+ct);
+            if (fabs((k0-ww)/k0) < eps) break;
+            ww = k0;
+        }
+        k0 += ct;
+    }
+    else {
+        cb = 0.5/x;
+        xr2 = 1.0/x2;
+        k0 = 1.0;
+        for (k=0; k<8; k++) {
+            k0 += a1[k]*pow(xr2,k+1);
+        }
+        k0 *= cb/i0;
+    }
+    k1 = (1.0/x - i1*k0)/i0;
+    i0p = i1;
+    i1p = i0-i1/x;
+    k0p = -k1;
+    k1p = -k0-k1/x;
+    return 0;
+}
+
+int bessik01b(double x,double &i0,double &i1,double &k0,double &k1,
+              double &i0p,double &i1p,double &k0p,double &k1p)
+{
+    double t,t2,dtmp,dtmp1;
+
+    if (x < 0.0) return 1;
+    if (x == 0.0) {
+        i0 = 1.0;
+        i1 = 0.0;
+        k0 = 1e308;
+        k1 = 1e308;
+        i0p = 0.0;
+        i1p = 0.5;
+        k0p = -1e308;
+        k1p = -1e308;
+        return 0;
+    }
+    if (x < 3.75) {
+        t = x/3.75;
+        t2 = t*t;
+        i0 = (((((0.0045813*t2+0.0360768)*t2+0.2659732)*t2+
+                1.2067492)*t2+3.0899424)*t2+3.5156229)*t2+1.0;
+        i1 = x*(((((0.00032411*t2+0.00301532)*t2+0.02658733*t2+
+                   0.15084934)*t2+0.51498869)*t2+0.87890594)*t2+0.5);
+    }
+    else {
+        t = 3.75/x;
+        dtmp1 = exp(x)/sqrt(x);
+        dtmp = (((((((0.00392377*t-0.01647633)*t+0.026355537)*t-0.02057706)*t+
+                   0.00916281)*t-0.00157565)*t+0.00225319)*t+0.01328592)*t+0.39894228;
+        i0 = dtmp*dtmp1;
+        dtmp = (((((((-0.00420059*t+0.01787654)*t-0.02895312)*t+0.02282967)*t-
+                   0.01031555)*t+0.00163801)*t-0.00362018)*t-0.03988024)*t+0.39894228;
+        i1 = dtmp*dtmp1;
+    }
+    if (x < 2.0) {
+        t = 0.5*x;
+        t2 = t*t;       // already calculated above
+        dtmp = (((((0.0000074*t2+0.0001075)*t2+0.00262698)*t2+0.0348859)*t2+
+                 0.23069756)*t2+0.4227842)*t2-0.57721566;
+        k0 = dtmp - i0*log(t);
+        dtmp = (((((-0.00004686*t2-0.00110404)*t2-0.01919402)*t2-
+                  0.18156897)*t2-0.67278578)*t2+0.15443144)*t2+1.0;
+        k1 = dtmp/x + i1*log(t);
+    }
+    else {
+        t = 2.0/x;
+        dtmp1 = exp(-x)/sqrt(x);
+        dtmp = (((((0.00053208*t-0.0025154)*t+0.00587872)*t-0.01062446)*t+
+                 0.02189568)*t-0.07832358)*t+1.25331414;
+        k0 = dtmp*dtmp1;
+        dtmp = (((((-0.00068245*t+0.00325614)*t-0.00780353)*t+0.01504268)*t-
+                 0.0365562)*t+0.23498619)*t+1.25331414;
+        k1 = dtmp*dtmp1;
+    }
+    i0p = i1;
+    i1p = i0 - i1/x;
+    k0p = -k1;
+    k1p = -k0 - k1/x;
+    return 0;
+}
+int bessikna(int n,double x,int &nm,double *in,double *kn,
+             double *inp,double *knp)
+{
+    double bi0,bi1,bk0,bk1,g,g0,g1,f,f0,f1,h,h0,h1,s0;
+    int k,m,ecode;
+
+    if ((x < 0.0) || (n < 0)) return 1;
+    if (x < eps) {
+        for (k=0; k<=n; k++) {
+            in[k] = 0.0;
+            kn[k] = 1e308;
+            inp[k] = 0.0;
+            knp[k] = -1e308;
+        }
+        in[0] = 1.0;
+        inp[1] = 0.5;
+        return 0;
+    }
+    nm = n;
+    ecode = bessik01a(x,in[0],in[1],kn[0],kn[1],inp[0],inp[1],knp[0],knp[1]);
+    if (n < 2) return 0;
+    bi0 = in[0];
+    bi1 = in[1];
+    bk0 = kn[0];
+    bk1 = kn[1];
+    if ((x > 40.0) && (n < (int)(0.25*x))) {
+        h0 = bi0;
+        h1 = bi1;
+        for (k=2; k<=n; k++) {
+            h = -2.0*(k-1.0)*h1/x+h0;
+            in[k] = h;
+            h0 = h1;
+            h1 = h;
+        }
+    }
+    else {
+        m = msta1(x,200);
+        if (m < n) nm = m;
+        else m = msta2(x,n,15);
+        f0 = 0.0;
+        f1 = 1.0e-100;
+        for (k=m; k>=0; k--) {
+            f = 2.0*(k+1.0)*f1/x+f0;
+            if (x <= nm) in[k] = f;
+            f0 = f1;
+            f1 = f;
+        }
+        s0 = bi0/f;
+        for (k=0; k<=m; k++) {
+            in[k] *= s0;
+        }
+    }
+    g0 = bk0;
+    g1 = bk1;
+    for (k=2; k<=nm; k++) {
+        g = 2.0*(k-1.0)*g1/x+g0;
+        kn[k] = g;
+        g0 = g1;
+        g1 = g;
+    }
+    for (k=2; k<=nm; k++) {
+        inp[k] = in[k-1]-k*in[k]/x;
+        knp[k] = -kn[k-1]-k*kn[k]/x;
+    }
+    return 0;
+}
+int bessiknb(int n,double x,int &nm,double *in,double *kn,
+             double *inp,double *knp)
+{
+    double s0,bs,f,f0,f1,sk0,a0,bkl,vt,r,g,g0,g1;
+    int k,kz,m,l;
+
+    if ((x < 0.0) || (n < 0)) return 1;
+    if (x < eps) {
+        for (k=0; k<=n; k++) {
+            in[k] = 0.0;
+            kn[k] = 1e308;
+            inp[k] = 0.0;
+            knp[k] = -1e308;
+        }
+        in[0] = 1.0;
+        inp[1] = 0.5;
+        return 0;
+    }
+    nm = n;
+    if (n == 0) nm = 1;
+    m = msta1(x,200);
+    if (m < nm) nm = m;
+    else m = msta2(x,nm,15);
+    bs = 0.0;
+    sk0 = 0.0;
+    f0 = 0.0;
+    f1 = 1.0e-100;
+    for (k=m; k>=0; k--) {
+        f = 2.0*(k+1.0)*f1/x+f0;
+        if (k <= nm) in[k] = f;
+        if ((k != 0) && (k == 2*(int)(k/2))) {
+            sk0 += 4.0*f/k;
+        }
+        bs += 2.0*f;
+        f0 = f1;
+        f1 = f;
+    }
+    s0 = exp(x)/(bs-f);
+    for (k=0; k<=nm; k++) {
+        in[k] *= s0;
+    }
+    if (x <= 8.0) {
+        kn[0] = -(log(0.5*x)+el)*in[0]+s0*sk0;
+        kn[1] = (1.0/x-in[1]*kn[0])/in[0];
+    }
+    else {
+        a0 = sqrt(M_PI_2/x)*exp(-x);
+        if (x >= 200.0) kz = 6;
+        else if (x >= 80.0) kz = 8;
+        else if (x >= 25.0) kz = 10;
+        else kz = 16;
+        for (l=0; l<2; l++) {
+            bkl = 1.0;
+            vt = 4.0*l;
+            r = 1.0;
+            for (k=1; k<=kz; k++) {
+                r *= 0.125*(vt-pow(2.0*k-1.0,2))/(k*x);
+                bkl += r;
+            }
+            kn[l] = a0*bkl;
+        }
+    }
+    g0 = kn[0];
+    g1 = kn[1];
+    for (k=2; k<=nm; k++) {
+        g = 2.0*(k-1.0)*g1/x+g0;
+        kn[k] = g;
+        g0 = g1;
+        g1 = g;
+    }
+    inp[0] = in[1];
+    knp[0] = -kn[1];
+    for (k=1; k<=nm; k++) {
+        inp[k] = in[k-1]-k*in[k]/x;
+        knp[k] = -kn[k-1]-k*kn[k]/x;
+    }
+    return 0;
+}
+
+//  The following program computes the modified Bessel functions
+//  Iv(x) and Kv(x) for arbitrary positive order. For negative
+//  order use:
+//
+//          I-v(x) = Iv(x) + 2/pi sin(v pi) Kv(x)
+//          K-v(x) = Kv(x)
+//
+int bessikv(double v,double x,double &vm,double *iv,double *kv,
+            double *ivp,double *kvp)
+{
+    double x2,v0,piv,vt,a1,v0p,gap,r,bi0,ca,sum;
+    double f,f1,f2,ct,cs,wa,gan,ww,w0,v0n;
+    double r1,r2,bk0,bk1,bk2,a2,cb;
+    int n,k,kz,m;
+
+    if ((v < 0.0) || (x < 0.0)) return 1;
+    x2 = x*x;
+    n = (int)v;
+    v0 = v-n;
+    if (n == 0) n = 1;
+    if (x == 0.0) {
+        for (k=0; k<=n; k++) {
+            iv[k] = 0.0;
+            kv[k] = -1e308;
+            ivp[k] = 0.0;
+            kvp[k] = 1e308;
+        }
+        if (v0 == 0.0) {
+            iv[0] = 1.0;
+            ivp[1] = 0.5;
+        }
+        vm = v;
+        return 0;
+    }
+    piv = M_PI*v0;
+    vt = 4.0*v0*v0;
+    if (v0 == 0.0) {
+        a1 = 1.0;
+    }
+    else {
+        v0p = 1.0+v0;
+        gap = gamma(v0p);
+        a1 = pow(0.5*x,v0)/gap;
+    }
+    if (x >= 50.0) kz = 8;
+    else if (x >= 35.0) kz = 10;
+    else kz = 14;
+    if (x <= 18.0) {
+        bi0 = 1.0;
+        r = 1.0;
+        for (k=1; k<=30; k++) {
+            r *= 0.25*x2/(k*(k+v0));
+            bi0 += r;
+            if (fabs(r/bi0) < eps) break;
+        }
+        bi0 *= a1;
+    }
+    else {
+        ca = exp(x)/sqrt(2.0*M_PI*x);
+        sum = 1.0;
+        r = 1.0;
+        for (k=1; k<=kz; k++) {
+            r *= -0.125*(vt-pow(2.0*k-1.0,2.0))/(k*x);
+            sum += r;
+        }
+        bi0 = ca*sum;
+    }
+    m = msta1(x,200);
+    if (m < n) n = m;
+    else m = msta2(x,n,15);
+    f2 = 0.0;
+    f1 = 1.0e-100;
+    for (k=m; k>=0; k--) {
+        f = 2.0*(v0+k+1.0)*f1/x+f2;
+        if (k <= n) iv[k] = f;
+        f2 = f1;
+        f1 = f;
+    }
+    cs = bi0/f;
+    for (k=0; k<=n; k++) {
+        iv[k] *= cs;
+    }
+    ivp[0] = v0*iv[0]/x+iv[1];
+    for (k=1; k<=n; k++) {
+        ivp[k] = -(k+v0)*iv[k]/x+iv[k-1];
+    }
+    ww = 0.0;
+    if (x <= 9.0) {
+        if (v0 == 0.0) {
+            ct = -log(0.5*x)-el;
+            cs = 0.0;
+            w0 = 0.0;
+            r = 1.0;
+            for (k=1; k<=50; k++) {
+                w0 += 1.0/k;
+                r *= 0.25*x2/(k*k);
+                cs += r*(w0+ct);
+                wa = fabs(cs);
+                if (fabs((wa-ww)/wa) < eps) break;
+                ww = wa;
+            }
+            bk0 = ct+cs;
+        }
+        else {
+            v0n = 1.0-v0;
+            gan = gamma(v0n);
+            a2 = 1.0/(gan*pow(0.5*x,v0));
+            a1 = pow(0.5*x,v0)/gap;
+            sum = a2-a1;
+            r1 = 1.0;
+            r2 = 1.0;
+            for (k=1; k<=120; k++) {
+                r1 *= 0.25*x2/(k*(k-v0));
+                r2 *= 0.25*x2/(k*(k+v0));
+                sum += a2*r1-a1*r2;
+                wa = fabs(sum);
+                if (fabs((wa-ww)/wa) < eps) break;
+                ww = wa;
+            }
+            bk0 = M_PI_2*sum/sin(piv);
+        }
+    }
+    else {
+        cb = exp(-x)*sqrt(M_PI_2/x);
+        sum = 1.0;
+        r = 1.0;
+        for (k=1; k<=kz; k++) {
+            r *= 0.125*(vt-pow(2.0*k-1.0,2.0))/(k*x);
+            sum += r;
+        }
+        bk0 = cb*sum;
+    }
+    bk1 = (1.0/x-iv[1]*bk0)/iv[0];
+    kv[0] = bk0;
+    kv[1] = bk1;
+    for (k=2; k<=n; k++) {
+        bk2 = 2.0*(v0+k-1.0)*bk1/x+bk0;
+        kv[k] = bk2;
+        bk0 = bk1;
+        bk1 = bk2;
+    }
+    kvp[0] = v0*kv[0]/x-kv[1];
+    for (k=1; k<=n; k++) {
+        kvp[k] = -(k+v0)*kv[k]/x-kv[k-1];
+    }
+    vm = n+v0;
+    return 0;
+}
-//  bessjy.cpp -- computation of Bessel functions Jn, Yn and their
-//      derivatives. Algorithms and coefficient values from
-//      "Computation of Special Functions", Zhang and Jin, John
-//      Wiley and Sons, 1996.
-//
-//  (C) 2003, C. Bond. All rights reserved.
-//
-// Note that 'math.h' provides (or should provide) values for:
-//      pi      M_PI
-//      2/pi    M_2_PI
-//      pi/4    M_PI_4
-//      pi/2    M_PI_2
-//
-#define _USE_MATH_DEFINES
-#include <math.h>
-#include "bessel.h"
-
-double gamma(double x);
-//
-//  INPUT:
-//      double x    -- argument of Bessel function
-//
-//  OUTPUT (via address pointers):
-//      double j0   -- Bessel function of 1st kind, 0th order
-//      double j1   -- Bessel function of 1st kind, 1st order
-//      double y0   -- Bessel function of 2nd kind, 0th order
-//      double y1   -- Bessel function of 2nd kind, 1st order
-//      double j0p  -- derivative of Bessel function of 1st kind, 0th order
-//      double j1p  -- derivative of Bessel function of 1st kind, 1st order
-//      double y0p  -- derivative of Bessel function of 2nd kind, 0th order
-//      double y1p  -- derivative of Bessel function of 2nd kind, 1st order
-//
-//  RETURN:
-//      int error code: 0 = OK, 1 = error
-//
-//  This algorithm computes the above functions using series expansions.
-//
-int bessjy01a(double x,double &j0,double &j1,double &y0,double &y1,
-    double &j0p,double &j1p,double &y0p,double &y1p)
-{
-    double x2,r,ec,w0,w1,r0,r1,cs0,cs1;
-    double cu,p0,q0,p1,q1,t1,t2;
-    int k,kz;
-    static double a[] = {
-        -7.03125e-2,
-         0.112152099609375,
-        -0.5725014209747314,
-         6.074042001273483,
-        -1.100171402692467e2,
-         3.038090510922384e3,
-        -1.188384262567832e5,
-         6.252951493434797e6,
-        -4.259392165047669e8,
-         3.646840080706556e10,
-        -3.833534661393944e12,
-         4.854014686852901e14,
-        -7.286857349377656e16,
-         1.279721941975975e19};
-    static double b[] = {
-         7.32421875e-2,
-        -0.2271080017089844,
-         1.727727502584457,
-        -2.438052969955606e1,
-         5.513358961220206e2,
-        -1.825775547429318e4,
-         8.328593040162893e5,
-        -5.006958953198893e7,
-         3.836255180230433e9,
-        -3.649010818849833e11,
-         4.218971570284096e13,
-        -5.827244631566907e15,
-         9.476288099260110e17,
-        -1.792162323051699e20};
-    static double a1[] = {
-         0.1171875,
-        -0.1441955566406250,
-         0.6765925884246826,
-        -6.883914268109947,
-         1.215978918765359e2,
-        -3.302272294480852e3,
-         1.276412726461746e5,
-        -6.656367718817688e6,
-         4.502786003050393e8,
-        -3.833857520742790e10,
-         4.011838599133198e12,
-        -5.060568503314727e14,
-         7.572616461117958e16,
-        -1.326257285320556e19};
-    static double b1[] = {
-        -0.1025390625,
-         0.2775764465332031,
-        -1.993531733751297,
-         2.724882731126854e1,
-        -6.038440767050702e2,
-         1.971837591223663e4,
-        -8.902978767070678e5,
-         5.310411010968522e7,
-        -4.043620325107754e9,
-         3.827011346598605e11,
-        -4.406481417852278e13,
-         6.065091351222699e15,
-        -9.833883876590679e17,
-         1.855045211579828e20};
-
-    if (x < 0.0) return 1;
-    if (x == 0.0) {
-        j0 = 1.0;
-        j1 = 0.0;
-        y0 = -1e308;
-        y1 = -1e308;
-        j0p = 0.0;
-        j1p = 0.5;
-        y0p = 1e308;
-        y1p = 1e308;
-        return 0;
-    }
-    x2 = x*x;
-    if (x <= 12.0) {
-        j0 = 1.0;
-        r = 1.0;
-        for (k=1;k<=30;k++) {
-            r *= -0.25*x2/(k*k);
-            j0 += r;
-            if (fabs(r) < fabs(j0)*1e-15) break;
-        }
-        j1 = 1.0;
-        r = 1.0;
-        for (k=1;k<=30;k++) {
-            r *= -0.25*x2/(k*(k+1));
-            j1 += r;
-            if (fabs(r) < fabs(j1)*1e-15) break;
-        }
-        j1 *= 0.5*x;
-        ec = log(0.5*x)+el;
-        cs0 = 0.0;
-        w0 = 0.0;
-        r0 = 1.0;
-        for (k=1;k<=30;k++) {
-            w0 += 1.0/k;
-            r0 *= -0.25*x2/(k*k);
-            r = r0 * w0;
-            cs0 += r;
-            if (fabs(r) < fabs(cs0)*1e-15) break;
-        }
-        y0 = M_2_PI*(ec*j0-cs0);
-        cs1 = 1.0;
-        w1 = 0.0;
-        r1 = 1.0;
-        for (k=1;k<=30;k++) {
-            w1 += 1.0/k;
-            r1 *= -0.25*x2/(k*(k+1));
-            r = r1*(2.0*w1+1.0/(k+1));
-            cs1 += r;
-            if (fabs(r) < fabs(cs1)*1e-15) break;
-        }
-        y1 = M_2_PI * (ec*j1-1.0/x-0.25*x*cs1);
-    }
-    else {
-        if (x >= 50.0) kz = 8;          // Can be changed to 10
-        else if (x >= 35.0) kz = 10;    //  "       "        12
-        else kz = 12;                   //  "       "        14
-        t1 = x-M_PI_4;
-        p0 = 1.0;
-        q0 = -0.125/x;
-        for (k=0;k<kz;k++) {
-            p0 += a[k]*pow(x,-2*k-2);
-            q0 += b[k]*pow(x,-2*k-3);
-        }
-        cu = sqrt(M_2_PI/x);
-        j0 = cu*(p0*cos(t1)-q0*sin(t1));
-        y0 = cu*(p0*sin(t1)+q0*cos(t1));
-        t2 = x-0.75*M_PI;
-        p1 = 1.0;
-        q1 = 0.375/x;
-        for (k=0;k<kz;k++) {
-            p1 += a1[k]*pow(x,-2*k-2);
-            q1 += b1[k]*pow(x,-2*k-3);
-        }
-        j1 = cu*(p1*cos(t2)-q1*sin(t2));
-        y1 = cu*(p1*sin(t2)+q1*cos(t2));
-    }
-    j0p = -j1;
-    j1p = j0-j1/x;
-    y0p = -y1;
-    y1p = y0-y1/x;
-    return 0;
-}
-//
-//  INPUT:
-//      double x    -- argument of Bessel function
-//
-//  OUTPUT:
-//      double j0   -- Bessel function of 1st kind, 0th order
-//      double j1   -- Bessel function of 1st kind, 1st order
-//      double y0   -- Bessel function of 2nd kind, 0th order
-//      double y1   -- Bessel function of 2nd kind, 1st order
-//      double j0p  -- derivative of Bessel function of 1st kind, 0th order
-//      double j1p  -- derivative of Bessel function of 1st kind, 1st order
-//      double y0p  -- derivative of Bessel function of 2nd kind, 0th order
-//      double y1p  -- derivative of Bessel function of 2nd kind, 1st order
-//
-//  RETURN:
-//      int error code: 0 = OK, 1 = error
-//
-//  This algorithm computes the functions using polynomial approximations.
-//
-int bessjy01b(double x,double &j0,double &j1,double &y0,double &y1,
-    double &j0p,double &j1p,double &y0p,double &y1p)
-{
-    double t,t2,dtmp,a0,p0,q0,p1,q1,ta0,ta1;
-    if (x < 0.0) return 1;
-    if (x == 0.0) {
-        j0 = 1.0;
-        j1 = 0.0;
-        y0 = -1e308;
-        y1 = -1e308;
-        j0p = 0.0;
-        j1p = 0.5;
-        y0p = 1e308;
-        y1p = 1e308;
-        return 0;
-    }
-    if(x <= 4.0) {
-        t = x/4.0;
-        t2 = t*t;
-        j0 = ((((((-0.5014415e-3*t2+0.76771853e-2)*t2-0.0709253492)*t2+
-            0.4443584263)*t2-1.7777560599)*t2+3.9999973021)*t2
-            -3.9999998721)*t2+1.0;
-        j1 = t*(((((((-0.1289769e-3*t2+0.22069155e-2)*t2-0.0236616773)*t2+
-            0.1777582922)*t2-0.8888839649)*t2+2.6666660544)*t2-
-            3.999999971)*t2+1.9999999998);
-        dtmp = (((((((-0.567433e-4*t2+0.859977e-3)*t2-0.94855882e-2)*t2+
-            0.0772975809)*t2-0.4261737419)*t2+1.4216421221)*t2-
-            2.3498519931)*t2+1.0766115157)*t2+0.3674669052;
-        y0 = M_2_PI*log(0.5*x)*j0+dtmp;
-        dtmp = (((((((0.6535773e-3*t2-0.0108175626)*t2+0.107657607)*t2-
-            0.7268945577)*t2+3.1261399273)*t2-7.3980241381)*t2+
-            6.8529236342)*t2+0.3932562018)*t2-0.6366197726;
-        y1 = M_2_PI*log(0.5*x)*j1+dtmp/x;
-    }
-    else {
-        t = 4.0/x;
-        t2 = t*t;
-        a0 = sqrt(M_2_PI/x);
-        p0 = ((((-0.9285e-5*t2+0.43506e-4)*t2-0.122226e-3)*t2+
-             0.434725e-3)*t2-0.4394275e-2)*t2+0.999999997;
-        q0 = t*(((((0.8099e-5*t2-0.35614e-4)*t2+0.85844e-4)*t2-
-            0.218024e-3)*t2+0.1144106e-2)*t2-0.031249995);
-        ta0 = x-M_PI_4;
-        j0 = a0*(p0*cos(ta0)-q0*sin(ta0));
-        y0 = a0*(p0*sin(ta0)+q0*cos(ta0));
-        p1 = ((((0.10632e-4*t2-0.50363e-4)*t2+0.145575e-3)*t2
-            -0.559487e-3)*t2+0.7323931e-2)*t2+1.000000004;
-        q1 = t*(((((-0.9173e-5*t2+0.40658e-4)*t2-0.99941e-4)*t2
-            +0.266891e-3)*t2-0.1601836e-2)*t2+0.093749994);
-        ta1 = x-0.75*M_PI;
-        j1 = a0*(p1*cos(ta1)-q1*sin(ta1));
-        y1 = a0*(p1*sin(ta1)+q1*cos(ta1));
-    }
-    j0p = -j1;
-    j1p = j0-j1/x;
-    y0p = -y1;
-    y1p = y0-y1/x;
-    return 0;
-}
-int msta1(double x,int mp)
-{
-    double a0,f0,f1,f;
-    int i,n0,n1,nn;
-
-    a0 = fabs(x);
-    n0 = (int)(1.1*a0)+1;
-    f0 = 0.5*log10(6.28*n0)-n0*log10(1.36*a0/n0)-mp;
-    n1 = n0+5;
-    f1 = 0.5*log10(6.28*n1)-n1*log10(1.36*a0/n1)-mp;
-    for (i=0;i<20;i++) {
-        nn = (int)(n1-(n1-n0)/(1.0-f0/f1));
-        f = 0.5*log10(6.28*nn)-nn*log10(1.36*a0/nn)-mp;
-        if (abs(nn-n1) < 1) break;
-        n0 = n1;
-        f0 = f1;
-        n1 = nn;
-        f1 = f;
-    }
-    return nn;
-}
-int msta2(double x,int n,int mp)
-{
-    double a0,ejn,hmp,f0,f1,f,obj;
-    int i,n0,n1,nn;
-
-    a0 = fabs(x);
-    hmp = 0.5*mp;
-    ejn = 0.5*log10(6.28*n)-n*log10(1.36*a0/n);
-    if (ejn <= hmp) {
-        obj = mp;
-        n0 = (int)(1.1*a0);
-        if (n0 < 1) n0 = 1;
-    }
-    else {
-        obj = hmp+ejn;
-        n0 = n;
-    }
-    f0 = 0.5*log10(6.28*n0)-n0*log10(1.36*a0/n0)-obj;
-    n1 = n0+5;
-    f1 = 0.5*log10(6.28*n1)-n1*log10(1.36*a0/n1)-obj;
-    for (i=0;i<20;i++) {
-        nn = (int)(n1-(n1-n0)/(1.0-f0/f1));
-        f = 0.5*log10(6.28*nn)-nn*log10(1.36*a0/nn)-obj;
-        if (abs(nn-n1) < 1) break;
-        n0 = n1;
-        f0 = f1;
-        n1 = nn;
-        f1 = f;
-    }
-    return nn+10;
-}
-//
-//  INPUT:
-//  double x    -- argument of Bessel function of 1st and 2nd kind.
-//  int n       -- order
-//
-//  OUPUT:
-//
-//  int nm      -- highest order actually computed (nm <= n)
-//  double jn[] -- Bessel function of 1st kind, orders from 0 to nm
-//  double yn[] -- Bessel function of 2nd kind, orders from 0 to nm
-//  double j'n[]-- derivative of Bessel function of 1st kind,
-//                      orders from 0 to nm
-//  double y'n[]-- derivative of Bessel function of 2nd kind,
-//                      orders from 0 to nm
-//
-//  Computes Bessel functions of all order up to 'n' using recurrence
-//  relations. If 'nm' < 'n' only 'nm' orders are returned.
-//
-int bessjyna(int n,double x,int &nm,double *jn,double *yn,
-    double *jnp,double *ynp)
-{
-    double bj0,bj1,f,f0,f1,f2,cs;
-    int i,k,m,ecode;
-
-    nm = n;
-    if ((x < 0.0) || (n < 0)) return 1;
-    if (x < 1e-15) {
-        for (i=0;i<=n;i++) {
-            jn[i] = 0.0;
-            yn[i] = -1e308;
-            jnp[i] = 0.0;
-            ynp[i] = 1e308;
-        }
-        jn[0] = 1.0;
-        jnp[1] = 0.5;
-        return 0;
-    }
-    ecode = bessjy01a(x,jn[0],jn[1],yn[0],yn[1],jnp[0],jnp[1],ynp[0],ynp[1]);
-    if (n < 2) return 0;
-    bj0 = jn[0];
-    bj1 = jn[1];
-    if (n < (int)0.9*x) {
-        for (k=2;k<=n;k++) {
-            jn[k] = 2.0*(k-1.0)*bj1/x-bj0;
-            bj0 = bj1;
-            bj1 = jn[k];
-        }
-    }
-    else {
-        m = msta1(x,200);
-        if (m < n) nm = m;
-        else m = msta2(x,n,15);
-        f2 = 0.0;
-        f1 = 1.0e-100;
-        for (k=m;k>=0;k--) {
-            f = 2.0*(k+1.0)/x*f1-f2;
-            if (k <= nm) jn[k] = f;
-            f2 = f1;
-            f1 = f;
-        }
-        if (fabs(bj0) > fabs(bj1)) cs = bj0/f;
-        else cs = bj1/f2;
-        for (k=0;k<=nm;k++) {
-            jn[k] *= cs;
-        }
-    }
-    for (k=2;k<=nm;k++) {
-        jnp[k] = jn[k-1]-k*jn[k]/x;
-    }
-    f0 = yn[0];
-    f1 = yn[1];
-    for (k=2;k<=nm;k++) {
-        f = 2.0*(k-1.0)*f1/x-f0;
-        yn[k] = f;
-        f0 = f1;
-        f1 = f;
-    }
-    for (k=2;k<=nm;k++) {
-        ynp[k] = yn[k-1]-k*yn[k]/x;
-    }
-    return 0;
-}
-//
-//  Same input and output conventions as above. Different recurrence
-//  relations used for 'x' < 300.
-//
-int bessjynb(int n,double x,int &nm,double *jn,double *yn,
-    double *jnp,double *ynp)
-{
-    double t1,t2,f,f1,f2,bj0,bj1,bjk,by0,by1,cu,s0,su,sv;
-    double ec,bs,byk,p0,p1,q0,q1;
-    static double a[] = {
-        -0.7031250000000000e-1,
-         0.1121520996093750,
-        -0.5725014209747314,
-         6.074042001273483};
-    static double b[] = {
-         0.7324218750000000e-1,
-        -0.2271080017089844,
-         1.727727502584457,
-        -2.438052969955606e1};
-    static double a1[] = {
-         0.1171875,
-        -0.1441955566406250,
-         0.6765925884246826,
-        -6.883914268109947};
-    static double b1[] = {
-       -0.1025390625,
-        0.2775764465332031,
-       -1.993531733751297,
-        2.724882731126854e1};
-        
-    int i,k,m;
-    nm = n;
-    if ((x < 0.0) || (n < 0)) return 1;
-    if (x < 1e-15) {
-        for (i=0;i<=n;i++) {
-            jn[i] = 0.0;
-            yn[i] = -1e308;
-            jnp[i] = 0.0;
-            ynp[i] = 1e308;
-        }
-        jn[0] = 1.0;
-        jnp[1] = 0.5;
-        return 0;
-    }
-    if (x <= 300.0 || n > (int)(0.9*x)) {
-        if (n == 0) nm = 1;
-        m = msta1(x,200);
-        if (m < nm) nm = m;
-        else m = msta2(x,nm,15);
-        bs = 0.0;
-        su = 0.0;
-        sv = 0.0;
-        f2 = 0.0;
-        f1 = 1.0e-100;
-        for (k = m;k>=0;k--) {
-            f = 2.0*(k+1.0)/x*f1 - f2;
-            if (k <= nm) jn[k] = f;
-            if ((k == 2*(int)(k/2)) && (k != 0)) {
-                bs += 2.0*f;
-//                su += pow(-1,k>>1)*f/(double)k;
-                su += (-1)*((k & 2)-1)*f/(double)k;
-            }
-            else if (k > 1) {
-//                sv += pow(-1,k>>1)*k*f/(k*k-1.0);
-                sv += (-1)*((k & 2)-1)*(double)k*f/(k*k-1.0);
-            }
-            f2 = f1;
-            f1 = f;
-        }
-        s0 = bs+f;
-        for (k=0;k<=nm;k++) {
-            jn[k] /= s0;
-        }
-        ec = log(0.5*x) +0.5772156649015329;
-        by0 = M_2_PI*(ec*jn[0]-4.0*su/s0);
-        yn[0] = by0;
-        by1 = M_2_PI*((ec-1.0)*jn[1]-jn[0]/x-4.0*sv/s0);
-        yn[1] = by1;
-    }
-    else {
-        t1 = x-M_PI_4;
-        p0 = 1.0;
-        q0 = -0.125/x;
-        for (k=0;k<4;k++) {
-            p0 += a[k]*pow(x,-2*k-2);
-            q0 += b[k]*pow(x,-2*k-3);
-        }
-        cu = sqrt(M_2_PI/x);
-        bj0 = cu*(p0*cos(t1)-q0*sin(t1));
-        by0 = cu*(p0*sin(t1)+q0*cos(t1));
-        jn[0] = bj0;
-        yn[0] = by0;
-        t2 = x-0.75*M_PI;
-        p1 = 1.0;
-        q1 = 0.375/x;
-        for (k=0;k<4;k++) {
-            p1 += a1[k]*pow(x,-2*k-2);
-            q1 += b1[k]*pow(x,-2*k-3);
-        }
-        bj1 = cu*(p1*cos(t2)-q1*sin(t2));
-        by1 = cu*(p1*sin(t2)+q1*cos(t2));
-        jn[1] = bj1;
-        yn[1] = by1;
-        for (k=2;k<=nm;k++) {
-            bjk = 2.0*(k-1.0)*bj1/x-bj0;
-            jn[k] = bjk;
-            bj0 = bj1;
-            bj1 = bjk;
-        }
-    }
-    jnp[0] = -jn[1];
-    for (k=1;k<=nm;k++) {
-        jnp[k] = jn[k-1]-k*jn[k]/x;
-    }
-    for (k=2;k<=nm;k++) {
-        byk = 2.0*(k-1.0)*by1/x-by0;
-        yn[k] = byk;
-        by0 = by1;
-        by1 = byk;
-    }
-    ynp[0] = -yn[1];
-    for (k=1;k<=nm;k++) {
-        ynp[k] = yn[k-1]-k*yn[k]/x;
-    }
-    return 0;
-
-}
-
-//  The following routine computes Bessel Jv(x) and Yv(x) for
-//  arbitrary positive order (v). For negative order, use:
-//
-//      J-v(x) = Jv(x)cos(v pi) - Yv(x)sin(v pi)
-//      Y-v(x) = Jv(x)sin(v pi) + Yv(x)cos(v pi)
-//
-int bessjyv(double v,double x,double &vm,double *jv,double *yv,
-    double *djv,double *dyv)
-{
-    double v0,vl,vg,vv,a,a0,r,x2,bjv0,bjv1,bjvl,f,f0,f1,f2;
-    double r0,r1,ck,cs,cs0,cs1,sk,qx,px,byv0,byv1,rp,xk,rq;
-    double b,ec,w0,w1,bju0,bju1,pv0,pv1,byvk;
-    int j,k,l,m,n,kz;
-
-    x2 = x*x;
-    n = (int)v;
-    v0 = v-n;
-    if ((x < 0.0) || (v < 0.0)) return 1;
-    if (x < 1e-15) {
-        for (k=0;k<=n;k++) {
-            jv[k] = 0.0;
-            yv[k] = -1e308;
-            djv[k] = 0.0;
-            dyv[k] = 1e308;
-            if (v0 == 0.0) {
-                jv[0] = 1.0;
-                djv[1] = 0.5;
-            }
-            else djv[0] = 1e308;
-        }
-        vm = v;
-        return 0;
-    }
-    if (x <= 12.0) {
-        for (l=0;l<2;l++) {
-            vl = v0 + l;
-            bjvl = 1.0;
-            r = 1.0;
-            for (k=1;k<=40;k++) {
-                r *= -0.25*x2/(k*(k+vl));
-                bjvl += r;
-                if (fabs(r) < fabs(bjvl)*1e-15) break;
-            }
-            vg = 1.0 + vl;
-            a = pow(0.5*x,vl)/gamma(vg);
-            if (l == 0) bjv0 = bjvl*a;
-            else bjv1 = bjvl*a;
-        }
-    }
-    else {
-        if (x >= 50.0) kz = 8;
-        else if (x >= 35.0) kz = 10;
-        else kz = 11;
-        for (j=0;j<2;j++) {
-            vv = 4.0*(j+v0)*(j+v0);
-            px = 1.0;
-            rp = 1.0;
-            for (k=1;k<=kz;k++) {
-                rp *= (-0.78125e-2)*(vv-pow(4.0*k-3.0,2.0))*
-                    (vv-pow(4.0*k-1.0,2.0))/(k*(2.0*k-1.0)*x2);
-                px += rp;
-            }
-            qx = 1.0;
-            rq = 1.0;
-            for (k=1;k<=kz;k++) {
-                rq *= (-0.78125e-2)*(vv-pow(4.0*k-1.0,2.0))*
-                    (vv-pow(4.0*k+1.0,2.0))/(k*(2.0*k+1.0)*x2);
-                qx += rq;
-            }
-            qx *= 0.125*(vv-1.0)/x;
-            xk = x-(0.5*(j+v0)+0.25)*M_PI;
-            a0 = sqrt(M_2_PI/x);
-            ck = cos(xk);
-            sk = sin(xk);
-
-            if (j == 0) {
-                bjv0 = a0*(px*ck-qx*sk);
-                byv0 = a0*(px*sk+qx*ck);
-            }
-            else if (j == 1) {
-                bjv1 = a0*(px*ck-qx*sk);
-                byv1 = a0*(px*sk+qx*ck);
-            }
-        }
-    }
-    jv[0] = bjv0;
-    jv[1] = bjv1;
-    djv[0] = v0*jv[0]/x-jv[1];
-    djv[1] = -(1.0+v0)*jv[1]/x+jv[0];
-    if ((n >= 2) && (n <= (int)(0.9*x))) {
-        f0 = bjv0;
-        f1 = bjv1;
-        for (k=2;k<=n;k++) {
-            f = 2.0*(k+v0-1.0)*f1/x-f0;
-            jv[k] = f;
-            f0 = f1;
-            f1 = f;
-        }
-    }
-    else if (n >= 2) {
-        m = msta1(x,200);
-        if (m < n) n = m;
-        else m = msta2(x,n,15);
-        f2 = 0.0;
-        f1 = 1.0e-100;
-        for (k=m;k>=0;k--) {
-            f = 2.0*(v0+k+1.0)*f1/x-f2;
-            if (k <= n) jv[k] = f;
-            f2 = f1;
-            f1 = f;
-        }
-        if (fabs(bjv0) > fabs(bjv1)) cs = bjv0/f;
-        else cs = bjv1/f2;
-        for (k=0;k<=n;k++) {
-            jv[k] *= cs;
-        }
-    }
-    for (k=2;k<=n;k++) {
-        djv[k] = -(k+v0)*jv[k]/x+jv[k-1];
-    }
-    if (x <= 12.0) {
-        if (v0 != 0.0) {
-            for (l=0;l<2;l++) {
-                vl = v0 +l;
-                bjvl = 1.0;
-                r = 1.0;
-                for (k=1;k<=40;k++) {
-                    r *= -0.25*x2/(k*(k-vl));
-                    bjvl += r;
-                    if (fabs(r) < fabs(bjvl)*1e-15) break;
-                }
-                vg = 1.0-vl;
-                b = pow(2.0/x,vl)/gamma(vg);
-                if (l == 0) bju0 = bjvl*b;
-                else bju1 = bjvl*b;
-            }
-            pv0 = M_PI*v0;
-            pv1 = M_PI*(1.0+v0);
-            byv0 = (bjv0*cos(pv0)-bju0)/sin(pv0);
-            byv1 = (bjv1*cos(pv1)-bju1)/sin(pv1);
-        }
-        else {
-            ec = log(0.5*x)+el;
-            cs0 = 0.0;
-            w0 = 0.0;
-            r0 = 1.0;
-            for (k=1;k<=30;k++) {
-                w0 += 1.0/k;
-                r0 *= -0.25*x2/(k*k);
-                cs0 += r0*w0;
-            }
-            byv0 = M_2_PI*(ec*bjv0-cs0);
-            cs1 = 1.0;
-            w1 = 0.0;
-            r1 = 1.0;
-            for (k=1;k<=30;k++) {
-                w1 += 1.0/k;
-                r1 *= -0.25*x2/(k*(k+1));
-                cs1 += r1*(2.0*w1+1.0/(k+1.0));
-            }
-            byv1 = M_2_PI*(ec*bjv1-1.0/x-0.25*x*cs1);
-        }
-    }
-    yv[0] = byv0;
-    yv[1] = byv1;
-    for (k=2;k<=n;k++) {
-        byvk = 2.0*(v0+k-1.0)*byv1/x-byv0;
-        yv[k] = byvk;
-        byv0 = byv1;
-        byv1 = byvk;
-    }
-    dyv[0] = v0*yv[0]/x-yv[1];
-    for (k=1;k<=n;k++) {
-        dyv[k] = -(k+v0)*yv[k]/x+yv[k-1];
-    }
-    vm = n + v0;
-    return 0;
-}
- 
+//  bessjy.cpp -- computation of Bessel functions Jn, Yn and their
+//      derivatives. Algorithms and coefficient values from
+//      "Computation of Special Functions", Zhang and Jin, John
+//      Wiley and Sons, 1996.
+//
+//  (C) 2003, C. Bond. All rights reserved.
+//
+// Note that 'math.h' provides (or should provide) values for:
+//      pi      M_PI
+//      2/pi    M_2_PI
+//      pi/4    M_PI_4
+//      pi/2    M_PI_2
+//
+#define _USE_MATH_DEFINES
+#include <math.h>
+#include "bessel.h"
+
+double gamma(double x);
+//
+//  INPUT:
+//      double x    -- argument of Bessel function
+//
+//  OUTPUT (via address pointers):
+//      double j0   -- Bessel function of 1st kind, 0th order
+//      double j1   -- Bessel function of 1st kind, 1st order
+//      double y0   -- Bessel function of 2nd kind, 0th order
+//      double y1   -- Bessel function of 2nd kind, 1st order
+//      double j0p  -- derivative of Bessel function of 1st kind, 0th order
+//      double j1p  -- derivative of Bessel function of 1st kind, 1st order
+//      double y0p  -- derivative of Bessel function of 2nd kind, 0th order
+//      double y1p  -- derivative of Bessel function of 2nd kind, 1st order
+//
+//  RETURN:
+//      int error code: 0 = OK, 1 = error
+//
+//  This algorithm computes the above functions using series expansions.
+//
+int bessjy01a(double x,double &j0,double &j1,double &y0,double &y1,
+              double &j0p,double &j1p,double &y0p,double &y1p)
+{
+    double x2,r,ec,w0,w1,r0,r1,cs0,cs1;
+    double cu,p0,q0,p1,q1,t1,t2;
+    int k,kz;
+    static double a[] = {
+        -7.03125e-2,
+        0.112152099609375,
+        -0.5725014209747314,
+        6.074042001273483,
+        -1.100171402692467e2,
+        3.038090510922384e3,
+        -1.188384262567832e5,
+        6.252951493434797e6,
+        -4.259392165047669e8,
+        3.646840080706556e10,
+        -3.833534661393944e12,
+        4.854014686852901e14,
+        -7.286857349377656e16,
+        1.279721941975975e19
+    };
+    static double b[] = {
+        7.32421875e-2,
+        -0.2271080017089844,
+        1.727727502584457,
+        -2.438052969955606e1,
+        5.513358961220206e2,
+        -1.825775547429318e4,
+        8.328593040162893e5,
+        -5.006958953198893e7,
+        3.836255180230433e9,
+        -3.649010818849833e11,
+        4.218971570284096e13,
+        -5.827244631566907e15,
+        9.476288099260110e17,
+        -1.792162323051699e20
+    };
+    static double a1[] = {
+        0.1171875,
+        -0.1441955566406250,
+        0.6765925884246826,
+        -6.883914268109947,
+        1.215978918765359e2,
+        -3.302272294480852e3,
+        1.276412726461746e5,
+        -6.656367718817688e6,
+        4.502786003050393e8,
+        -3.833857520742790e10,
+        4.011838599133198e12,
+        -5.060568503314727e14,
+        7.572616461117958e16,
+        -1.326257285320556e19
+    };
+    static double b1[] = {
+        -0.1025390625,
+        0.2775764465332031,
+        -1.993531733751297,
+        2.724882731126854e1,
+        -6.038440767050702e2,
+        1.971837591223663e4,
+        -8.902978767070678e5,
+        5.310411010968522e7,
+        -4.043620325107754e9,
+        3.827011346598605e11,
+        -4.406481417852278e13,
+        6.065091351222699e15,
+        -9.833883876590679e17,
+        1.855045211579828e20
+    };
+
+    if (x < 0.0) return 1;
+    if (x == 0.0) {
+        j0 = 1.0;
+        j1 = 0.0;
+        y0 = -1e308;
+        y1 = -1e308;
+        j0p = 0.0;
+        j1p = 0.5;
+        y0p = 1e308;
+        y1p = 1e308;
+        return 0;
+    }
+    x2 = x*x;
+    if (x <= 12.0) {
+        j0 = 1.0;
+        r = 1.0;
+        for (k=1; k<=30; k++) {
+            r *= -0.25*x2/(k*k);
+            j0 += r;
+            if (fabs(r) < fabs(j0)*1e-15) break;
+        }
+        j1 = 1.0;
+        r = 1.0;
+        for (k=1; k<=30; k++) {
+            r *= -0.25*x2/(k*(k+1));
+            j1 += r;
+            if (fabs(r) < fabs(j1)*1e-15) break;
+        }
+        j1 *= 0.5*x;
+        ec = log(0.5*x)+el;
+        cs0 = 0.0;
+        w0 = 0.0;
+        r0 = 1.0;
+        for (k=1; k<=30; k++) {
+            w0 += 1.0/k;
+            r0 *= -0.25*x2/(k*k);
+            r = r0 * w0;
+            cs0 += r;
+            if (fabs(r) < fabs(cs0)*1e-15) break;
+        }
+        y0 = M_2_PI*(ec*j0-cs0);
+        cs1 = 1.0;
+        w1 = 0.0;
+        r1 = 1.0;
+        for (k=1; k<=30; k++) {
+            w1 += 1.0/k;
+            r1 *= -0.25*x2/(k*(k+1));
+            r = r1*(2.0*w1+1.0/(k+1));
+            cs1 += r;
+            if (fabs(r) < fabs(cs1)*1e-15) break;
+        }
+        y1 = M_2_PI * (ec*j1-1.0/x-0.25*x*cs1);
+    }
+    else {
+        if (x >= 50.0) kz = 8;          // Can be changed to 10
+        else if (x >= 35.0) kz = 10;    //  "       "        12
+        else kz = 12;                   //  "       "        14
+        t1 = x-M_PI_4;
+        p0 = 1.0;
+        q0 = -0.125/x;
+        for (k=0; k<kz; k++) {
+            p0 += a[k]*pow(x,-2*k-2);
+            q0 += b[k]*pow(x,-2*k-3);
+        }
+        cu = sqrt(M_2_PI/x);
+        j0 = cu*(p0*cos(t1)-q0*sin(t1));
+        y0 = cu*(p0*sin(t1)+q0*cos(t1));
+        t2 = x-0.75*M_PI;
+        p1 = 1.0;
+        q1 = 0.375/x;
+        for (k=0; k<kz; k++) {
+            p1 += a1[k]*pow(x,-2*k-2);
+            q1 += b1[k]*pow(x,-2*k-3);
+        }
+        j1 = cu*(p1*cos(t2)-q1*sin(t2));
+        y1 = cu*(p1*sin(t2)+q1*cos(t2));
+    }
+    j0p = -j1;
+    j1p = j0-j1/x;
+    y0p = -y1;
+    y1p = y0-y1/x;
+    return 0;
+}
+//
+//  INPUT:
+//      double x    -- argument of Bessel function
+//
+//  OUTPUT:
+//      double j0   -- Bessel function of 1st kind, 0th order
+//      double j1   -- Bessel function of 1st kind, 1st order
+//      double y0   -- Bessel function of 2nd kind, 0th order
+//      double y1   -- Bessel function of 2nd kind, 1st order
+//      double j0p  -- derivative of Bessel function of 1st kind, 0th order
+//      double j1p  -- derivative of Bessel function of 1st kind, 1st order
+//      double y0p  -- derivative of Bessel function of 2nd kind, 0th order
+//      double y1p  -- derivative of Bessel function of 2nd kind, 1st order
+//
+//  RETURN:
+//      int error code: 0 = OK, 1 = error
+//
+//  This algorithm computes the functions using polynomial approximations.
+//
+int bessjy01b(double x,double &j0,double &j1,double &y0,double &y1,
+              double &j0p,double &j1p,double &y0p,double &y1p)
+{
+    double t,t2,dtmp,a0,p0,q0,p1,q1,ta0,ta1;
+    if (x < 0.0) return 1;
+    if (x == 0.0) {
+        j0 = 1.0;
+        j1 = 0.0;
+        y0 = -1e308;
+        y1 = -1e308;
+        j0p = 0.0;
+        j1p = 0.5;
+        y0p = 1e308;
+        y1p = 1e308;
+        return 0;
+    }
+    if(x <= 4.0) {
+        t = x/4.0;
+        t2 = t*t;
+        j0 = ((((((-0.5014415e-3*t2+0.76771853e-2)*t2-0.0709253492)*t2+
+                 0.4443584263)*t2-1.7777560599)*t2+3.9999973021)*t2
+              -3.9999998721)*t2+1.0;
+        j1 = t*(((((((-0.1289769e-3*t2+0.22069155e-2)*t2-0.0236616773)*t2+
+                    0.1777582922)*t2-0.8888839649)*t2+2.6666660544)*t2-
+                 3.999999971)*t2+1.9999999998);
+        dtmp = (((((((-0.567433e-4*t2+0.859977e-3)*t2-0.94855882e-2)*t2+
+                    0.0772975809)*t2-0.4261737419)*t2+1.4216421221)*t2-
+                 2.3498519931)*t2+1.0766115157)*t2+0.3674669052;
+        y0 = M_2_PI*log(0.5*x)*j0+dtmp;
+        dtmp = (((((((0.6535773e-3*t2-0.0108175626)*t2+0.107657607)*t2-
+                    0.7268945577)*t2+3.1261399273)*t2-7.3980241381)*t2+
+                 6.8529236342)*t2+0.3932562018)*t2-0.6366197726;
+        y1 = M_2_PI*log(0.5*x)*j1+dtmp/x;
+    }
+    else {
+        t = 4.0/x;
+        t2 = t*t;
+        a0 = sqrt(M_2_PI/x);
+        p0 = ((((-0.9285e-5*t2+0.43506e-4)*t2-0.122226e-3)*t2+
+               0.434725e-3)*t2-0.4394275e-2)*t2+0.999999997;
+        q0 = t*(((((0.8099e-5*t2-0.35614e-4)*t2+0.85844e-4)*t2-
+                  0.218024e-3)*t2+0.1144106e-2)*t2-0.031249995);
+        ta0 = x-M_PI_4;
+        j0 = a0*(p0*cos(ta0)-q0*sin(ta0));
+        y0 = a0*(p0*sin(ta0)+q0*cos(ta0));
+        p1 = ((((0.10632e-4*t2-0.50363e-4)*t2+0.145575e-3)*t2
+               -0.559487e-3)*t2+0.7323931e-2)*t2+1.000000004;
+        q1 = t*(((((-0.9173e-5*t2+0.40658e-4)*t2-0.99941e-4)*t2
+                  +0.266891e-3)*t2-0.1601836e-2)*t2+0.093749994);
+        ta1 = x-0.75*M_PI;
+        j1 = a0*(p1*cos(ta1)-q1*sin(ta1));
+        y1 = a0*(p1*sin(ta1)+q1*cos(ta1));
+    }
+    j0p = -j1;
+    j1p = j0-j1/x;
+    y0p = -y1;
+    y1p = y0-y1/x;
+    return 0;
+}
+int msta1(double x,int mp)
+{
+    double a0,f0,f1,f;
+    int i,n0,n1,nn;
+
+    a0 = fabs(x);
+    n0 = (int)(1.1*a0)+1;
+    f0 = 0.5*log10(6.28*n0)-n0*log10(1.36*a0/n0)-mp;
+    n1 = n0+5;
+    f1 = 0.5*log10(6.28*n1)-n1*log10(1.36*a0/n1)-mp;
+    for (i=0; i<20; i++) {
+        nn = (int)(n1-(n1-n0)/(1.0-f0/f1));
+        f = 0.5*log10(6.28*nn)-nn*log10(1.36*a0/nn)-mp;
+        if (abs(nn-n1) < 1) break;
+        n0 = n1;
+        f0 = f1;
+        n1 = nn;
+        f1 = f;
+    }
+    return nn;
+}
+int msta2(double x,int n,int mp)
+{
+    double a0,ejn,hmp,f0,f1,f,obj;
+    int i,n0,n1,nn;
+
+    a0 = fabs(x);
+    hmp = 0.5*mp;
+    ejn = 0.5*log10(6.28*n)-n*log10(1.36*a0/n);
+    if (ejn <= hmp) {
+        obj = mp;
+        n0 = (int)(1.1*a0);
+        if (n0 < 1) n0 = 1;
+    }
+    else {
+        obj = hmp+ejn;
+        n0 = n;
+    }
+    f0 = 0.5*log10(6.28*n0)-n0*log10(1.36*a0/n0)-obj;
+    n1 = n0+5;
+    f1 = 0.5*log10(6.28*n1)-n1*log10(1.36*a0/n1)-obj;
+    for (i=0; i<20; i++) {
+        nn = (int)(n1-(n1-n0)/(1.0-f0/f1));
+        f = 0.5*log10(6.28*nn)-nn*log10(1.36*a0/nn)-obj;
+        if (abs(nn-n1) < 1) break;
+        n0 = n1;
+        f0 = f1;
+        n1 = nn;
+        f1 = f;
+    }
+    return nn+10;
+}
+//
+//  INPUT:
+//  double x    -- argument of Bessel function of 1st and 2nd kind.
+//  int n       -- order
+//
+//  OUPUT:
+//
+//  int nm      -- highest order actually computed (nm <= n)
+//  double jn[] -- Bessel function of 1st kind, orders from 0 to nm
+//  double yn[] -- Bessel function of 2nd kind, orders from 0 to nm
+//  double j'n[]-- derivative of Bessel function of 1st kind,
+//                      orders from 0 to nm
+//  double y'n[]-- derivative of Bessel function of 2nd kind,
+//                      orders from 0 to nm
+//
+//  Computes Bessel functions of all order up to 'n' using recurrence
+//  relations. If 'nm' < 'n' only 'nm' orders are returned.
+//
+int bessjyna(int n,double x,int &nm,double *jn,double *yn,
+             double *jnp,double *ynp)
+{
+    double bj0,bj1,f,f0,f1,f2,cs;
+    int i,k,m,ecode;
+
+    nm = n;
+    if ((x < 0.0) || (n < 0)) return 1;
+    if (x < 1e-15) {
+        for (i=0; i<=n; i++) {
+            jn[i] = 0.0;
+            yn[i] = -1e308;
+            jnp[i] = 0.0;
+            ynp[i] = 1e308;
+        }
+        jn[0] = 1.0;
+        jnp[1] = 0.5;
+        return 0;
+    }
+    ecode = bessjy01a(x,jn[0],jn[1],yn[0],yn[1],jnp[0],jnp[1],ynp[0],ynp[1]);
+    if (n < 2) return 0;
+    bj0 = jn[0];
+    bj1 = jn[1];
+    if (n < (int)0.9*x) {
+        for (k=2; k<=n; k++) {
+            jn[k] = 2.0*(k-1.0)*bj1/x-bj0;
+            bj0 = bj1;
+            bj1 = jn[k];
+        }
+    }
+    else {
+        m = msta1(x,200);
+        if (m < n) nm = m;
+        else m = msta2(x,n,15);
+        f2 = 0.0;
+        f1 = 1.0e-100;
+        for (k=m; k>=0; k--) {
+            f = 2.0*(k+1.0)/x*f1-f2;
+            if (k <= nm) jn[k] = f;
+            f2 = f1;
+            f1 = f;
+        }
+        if (fabs(bj0) > fabs(bj1)) cs = bj0/f;
+        else cs = bj1/f2;
+        for (k=0; k<=nm; k++) {
+            jn[k] *= cs;
+        }
+    }
+    for (k=2; k<=nm; k++) {
+        jnp[k] = jn[k-1]-k*jn[k]/x;
+    }
+    f0 = yn[0];
+    f1 = yn[1];
+    for (k=2; k<=nm; k++) {
+        f = 2.0*(k-1.0)*f1/x-f0;
+        yn[k] = f;
+        f0 = f1;
+        f1 = f;
+    }
+    for (k=2; k<=nm; k++) {
+        ynp[k] = yn[k-1]-k*yn[k]/x;
+    }
+    return 0;
+}
+//
+//  Same input and output conventions as above. Different recurrence
+//  relations used for 'x' < 300.
+//
+int bessjynb(int n,double x,int &nm,double *jn,double *yn,
+             double *jnp,double *ynp)
+{
+    double t1,t2,f,f1,f2,bj0,bj1,bjk,by0,by1,cu,s0,su,sv;
+    double ec,bs,byk,p0,p1,q0,q1;
+    static double a[] = {
+        -0.7031250000000000e-1,
+        0.1121520996093750,
+        -0.5725014209747314,
+        6.074042001273483
+    };
+    static double b[] = {
+        0.7324218750000000e-1,
+        -0.2271080017089844,
+        1.727727502584457,
+        -2.438052969955606e1
+    };
+    static double a1[] = {
+        0.1171875,
+        -0.1441955566406250,
+        0.6765925884246826,
+        -6.883914268109947
+    };
+    static double b1[] = {
+        -0.1025390625,
+        0.2775764465332031,
+        -1.993531733751297,
+        2.724882731126854e1
+    };
+
+    int i,k,m;
+    nm = n;
+    if ((x < 0.0) || (n < 0)) return 1;
+    if (x < 1e-15) {
+        for (i=0; i<=n; i++) {
+            jn[i] = 0.0;
+            yn[i] = -1e308;
+            jnp[i] = 0.0;
+            ynp[i] = 1e308;
+        }
+        jn[0] = 1.0;
+        jnp[1] = 0.5;
+        return 0;
+    }
+    if (x <= 300.0 || n > (int)(0.9*x)) {
+        if (n == 0) nm = 1;
+        m = msta1(x,200);
+        if (m < nm) nm = m;
+        else m = msta2(x,nm,15);
+        bs = 0.0;
+        su = 0.0;
+        sv = 0.0;
+        f2 = 0.0;
+        f1 = 1.0e-100;
+        for (k = m; k>=0; k--) {
+            f = 2.0*(k+1.0)/x*f1 - f2;
+            if (k <= nm) jn[k] = f;
+            if ((k == 2*(int)(k/2)) && (k != 0)) {
+                bs += 2.0*f;
+//                su += pow(-1,k>>1)*f/(double)k;
+                su += (-1)*((k & 2)-1)*f/(double)k;
+            }
+            else if (k > 1) {
+//                sv += pow(-1,k>>1)*k*f/(k*k-1.0);
+                sv += (-1)*((k & 2)-1)*(double)k*f/(k*k-1.0);
+            }
+            f2 = f1;
+            f1 = f;
+        }
+        s0 = bs+f;
+        for (k=0; k<=nm; k++) {
+            jn[k] /= s0;
+        }
+        ec = log(0.5*x) +0.5772156649015329;
+        by0 = M_2_PI*(ec*jn[0]-4.0*su/s0);
+        yn[0] = by0;
+        by1 = M_2_PI*((ec-1.0)*jn[1]-jn[0]/x-4.0*sv/s0);
+        yn[1] = by1;
+    }
+    else {
+        t1 = x-M_PI_4;
+        p0 = 1.0;
+        q0 = -0.125/x;
+        for (k=0; k<4; k++) {
+            p0 += a[k]*pow(x,-2*k-2);
+            q0 += b[k]*pow(x,-2*k-3);
+        }
+        cu = sqrt(M_2_PI/x);
+        bj0 = cu*(p0*cos(t1)-q0*sin(t1));
+        by0 = cu*(p0*sin(t1)+q0*cos(t1));
+        jn[0] = bj0;
+        yn[0] = by0;
+        t2 = x-0.75*M_PI;
+        p1 = 1.0;
+        q1 = 0.375/x;
+        for (k=0; k<4; k++) {
+            p1 += a1[k]*pow(x,-2*k-2);
+            q1 += b1[k]*pow(x,-2*k-3);
+        }
+        bj1 = cu*(p1*cos(t2)-q1*sin(t2));
+        by1 = cu*(p1*sin(t2)+q1*cos(t2));
+        jn[1] = bj1;
+        yn[1] = by1;
+        for (k=2; k<=nm; k++) {
+            bjk = 2.0*(k-1.0)*bj1/x-bj0;
+            jn[k] = bjk;
+            bj0 = bj1;
+            bj1 = bjk;
+        }
+    }
+    jnp[0] = -jn[1];
+    for (k=1; k<=nm; k++) {
+        jnp[k] = jn[k-1]-k*jn[k]/x;
+    }
+    for (k=2; k<=nm; k++) {
+        byk = 2.0*(k-1.0)*by1/x-by0;
+        yn[k] = byk;
+        by0 = by1;
+        by1 = byk;
+    }
+    ynp[0] = -yn[1];
+    for (k=1; k<=nm; k++) {
+        ynp[k] = yn[k-1]-k*yn[k]/x;
+    }
+    return 0;
+
+}
+
+//  The following routine computes Bessel Jv(x) and Yv(x) for
+//  arbitrary positive order (v). For negative order, use:
+//
+//      J-v(x) = Jv(x)cos(v pi) - Yv(x)sin(v pi)
+//      Y-v(x) = Jv(x)sin(v pi) + Yv(x)cos(v pi)
+//
+int bessjyv(double v,double x,double &vm,double *jv,double *yv,
+            double *djv,double *dyv)
+{
+    double v0,vl,vg,vv,a,a0,r,x2,bjv0,bjv1,bjvl,f,f0,f1,f2;
+    double r0,r1,ck,cs,cs0,cs1,sk,qx,px,byv0,byv1,rp,xk,rq;
+    double b,ec,w0,w1,bju0,bju1,pv0,pv1,byvk;
+    int j,k,l,m,n,kz;
+
+    x2 = x*x;
+    n = (int)v;
+    v0 = v-n;
+    if ((x < 0.0) || (v < 0.0)) return 1;
+    if (x < 1e-15) {
+        for (k=0; k<=n; k++) {
+            jv[k] = 0.0;
+            yv[k] = -1e308;
+            djv[k] = 0.0;
+            dyv[k] = 1e308;
+            if (v0 == 0.0) {
+                jv[0] = 1.0;
+                djv[1] = 0.5;
+            }
+            else djv[0] = 1e308;
+        }
+        vm = v;
+        return 0;
+    }
+    if (x <= 12.0) {
+        for (l=0; l<2; l++) {
+            vl = v0 + l;
+            bjvl = 1.0;
+            r = 1.0;
+            for (k=1; k<=40; k++) {
+                r *= -0.25*x2/(k*(k+vl));
+                bjvl += r;
+                if (fabs(r) < fabs(bjvl)*1e-15) break;
+            }
+            vg = 1.0 + vl;
+            a = pow(0.5*x,vl)/gamma(vg);
+            if (l == 0) bjv0 = bjvl*a;
+            else bjv1 = bjvl*a;
+        }
+    }
+    else {
+        if (x >= 50.0) kz = 8;
+        else if (x >= 35.0) kz = 10;
+        else kz = 11;
+        for (j=0; j<2; j++) {
+            vv = 4.0*(j+v0)*(j+v0);
+            px = 1.0;
+            rp = 1.0;
+            for (k=1; k<=kz; k++) {
+                rp *= (-0.78125e-2)*(vv-pow(4.0*k-3.0,2.0))*
+                      (vv-pow(4.0*k-1.0,2.0))/(k*(2.0*k-1.0)*x2);
+                px += rp;
+            }
+            qx = 1.0;
+            rq = 1.0;
+            for (k=1; k<=kz; k++) {
+                rq *= (-0.78125e-2)*(vv-pow(4.0*k-1.0,2.0))*
+                      (vv-pow(4.0*k+1.0,2.0))/(k*(2.0*k+1.0)*x2);
+                qx += rq;
+            }
+            qx *= 0.125*(vv-1.0)/x;
+            xk = x-(0.5*(j+v0)+0.25)*M_PI;
+            a0 = sqrt(M_2_PI/x);
+            ck = cos(xk);
+            sk = sin(xk);
+
+            if (j == 0) {
+                bjv0 = a0*(px*ck-qx*sk);
+                byv0 = a0*(px*sk+qx*ck);
+            }
+            else if (j == 1) {
+                bjv1 = a0*(px*ck-qx*sk);
+                byv1 = a0*(px*sk+qx*ck);
+            }
+        }
+    }
+    jv[0] = bjv0;
+    jv[1] = bjv1;
+    djv[0] = v0*jv[0]/x-jv[1];
+    djv[1] = -(1.0+v0)*jv[1]/x+jv[0];
+    if ((n >= 2) && (n <= (int)(0.9*x))) {
+        f0 = bjv0;
+        f1 = bjv1;
+        for (k=2; k<=n; k++) {
+            f = 2.0*(k+v0-1.0)*f1/x-f0;
+            jv[k] = f;
+            f0 = f1;
+            f1 = f;
+        }
+    }
+    else if (n >= 2) {
+        m = msta1(x,200);
+        if (m < n) n = m;
+        else m = msta2(x,n,15);
+        f2 = 0.0;
+        f1 = 1.0e-100;
+        for (k=m; k>=0; k--) {
+            f = 2.0*(v0+k+1.0)*f1/x-f2;
+            if (k <= n) jv[k] = f;
+            f2 = f1;
+            f1 = f;
+        }
+        if (fabs(bjv0) > fabs(bjv1)) cs = bjv0/f;
+        else cs = bjv1/f2;
+        for (k=0; k<=n; k++) {
+            jv[k] *= cs;
+        }
+    }
+    for (k=2; k<=n; k++) {
+        djv[k] = -(k+v0)*jv[k]/x+jv[k-1];
+    }
+    if (x <= 12.0) {
+        if (v0 != 0.0) {
+            for (l=0; l<2; l++) {
+                vl = v0 +l;
+                bjvl = 1.0;
+                r = 1.0;
+                for (k=1; k<=40; k++) {
+                    r *= -0.25*x2/(k*(k-vl));
+                    bjvl += r;
+                    if (fabs(r) < fabs(bjvl)*1e-15) break;
+                }
+                vg = 1.0-vl;
+                b = pow(2.0/x,vl)/gamma(vg);
+                if (l == 0) bju0 = bjvl*b;
+                else bju1 = bjvl*b;
+            }
+            pv0 = M_PI*v0;
+            pv1 = M_PI*(1.0+v0);
+            byv0 = (bjv0*cos(pv0)-bju0)/sin(pv0);
+            byv1 = (bjv1*cos(pv1)-bju1)/sin(pv1);
+        }
+        else {
+            ec = log(0.5*x)+el;
+            cs0 = 0.0;
+            w0 = 0.0;
+            r0 = 1.0;
+            for (k=1; k<=30; k++) {
+                w0 += 1.0/k;
+                r0 *= -0.25*x2/(k*k);
+                cs0 += r0*w0;
+            }
+            byv0 = M_2_PI*(ec*bjv0-cs0);
+            cs1 = 1.0;
+            w1 = 0.0;
+            r1 = 1.0;
+            for (k=1; k<=30; k++) {
+                w1 += 1.0/k;
+                r1 *= -0.25*x2/(k*(k+1));
+                cs1 += r1*(2.0*w1+1.0/(k+1.0));
+            }
+            byv1 = M_2_PI*(ec*bjv1-1.0/x-0.25*x*cs1);
+        }
+    }
+    yv[0] = byv0;
+    yv[1] = byv1;
+    for (k=2; k<=n; k++) {
+        byvk = 2.0*(v0+k-1.0)*byv1/x-byv0;
+        yv[k] = byvk;
+        byv0 = byv1;
+        byv1 = byvk;
+    }
+    dyv[0] = v0*yv[0]/x-yv[1];
+    for (k=1; k<=n; k++) {
+        dyv[k] = -(k+v0)*yv[k]/x+yv[k-1];
+    }
+    vm = n + v0;
+    return 0;
+}
+
-//  cbessik.cpp -- complex modified Bessel functions.
-//  Algorithms and coefficient values from "Computation of Special
-//  Functions", Zhang and Jin, John Wiley and Sons, 1996.
-//
-//  (C) 2003, C. Bond. All rights reserved.
-//
-#include <complex>
-using namespace std;
-#include "bessel.h"
-
-static complex<double> cii(0.0,1.0);
-static complex<double> czero(0.0,0.0);
-static complex<double> cone(1.0,0.0);
-
-double gamma(double x);
-
-int cbessik01(complex<double>z,complex<double>&ci0,complex<double>&ci1,
-    complex<double>&ck0,complex<double>&ck1,complex<double>&ci0p,
-    complex<double>&ci1p,complex<double>&ck0p,complex<double>&ck1p)
-{
-    complex<double> z1,z2,zr,zr2,cr,ca,cb,cs,ct,cw;
-    double a0,w0;
-    int k,kz;
-    static double a[] = {
-        0.125,
-        7.03125e-2,
-        7.32421875e-2,
-        1.1215209960938e-1,
-        2.2710800170898e-1,
-        5.7250142097473e-1,
-        1.7277275025845,
-        6.0740420012735,
-        2.4380529699556e1,
-        1.1001714026925e2,
-        5.5133589612202e2,
-        3.0380905109224e3};
-    static double b[] = {
-        -0.375,
-        -1.171875e-1,
-        -1.025390625e-1,
-        -1.4419555664063e-1,
-        -2.7757644653320e-1,
-        -6.7659258842468e-1,
-        -1.9935317337513,
-        -6.8839142681099,
-        -2.7248827311269e1,
-        -1.2159789187654e2,
-        -6.0384407670507e2,
-        -3.3022722944809e3};
-    static double a1[] = {
-        0.125,
-        0.2109375,
-        1.0986328125,
-        1.1775970458984e1,
-        2.1461706161499e2,
-        5.9511522710323e3,
-        2.3347645606175e5,
-        1.2312234987631e7,
-        8.401390346421e08,
-        7.2031420482627e10};
-
-    a0 = abs(z);
-    z2 = z*z;
-    z1 = z;
-    if (a0 == 0.0) {
-        ci0 = cone;
-        ci1 = czero;
-        ck0 = complex<double> (1e308,0);
-        ck1 = complex<double> (1e308,0);
-        ci0p = czero;
-        ci1p = complex<double>(0.5,0.0);
-        ck0p = complex<double>(-1e308,0);
-        ck1p = complex<double>(-1e308,0);
-        return 0;
-    }
-    if (real(z) < 0.0) z1 = -z;
-    if (a0 <= 18.0) {
-        ci0 = cone;
-        cr = cone;
-        for (k=1;k<=50;k++) {
-            cr *= 0.25*z2/(double)(k*k);
-            ci0 += cr;
-            if (abs(cr/ci0) < eps) break;
-        }
-        ci1 = cone;
-        cr = cone;
-        for (k=1;k<=50;k++) {
-            cr *= 0.25*z2/(double)(k*(k+1.0));
-            ci1 += cr;
-            if (abs(cr/ci1) < eps) break;
-        }
-        ci1 *= 0.5*z1;
-    }
-    else {
-        if (a0 >= 50.0) kz = 7;
-        else if (a0 >= 35.0) kz = 9;
-        else kz = 12;
-        ca = exp(z1)/sqrt(2.0*M_PI*z1);
-        ci0 = cone;
-        zr = 1.0/z1;
-        for (k=0;k<kz;k++) {
-            ci0 += a[k]*pow(zr,k+1.0);
-        }
-        ci0 *= ca;
-        ci1 = cone;
-        for (k=0;k<kz;k++) {
-            ci1 += b[k]*pow(zr,k+1.0);
-        }
-        ci1 *= ca;
-    }
-    if (a0 <= 9.0) {
-        cs = czero;
-        ct = -log(0.5*z1)-el;
-        w0 = 0.0;
-        cr = cone;
-        for (k=1;k<=50;k++) {
-            w0 += 1.0/k;
-            cr *= 0.25*z2/(double)(k*k);
-            cs += cr*(w0+ct);
-            if (abs((cs-cw)/cs) < eps) break;
-            cw = cs;
-        }
-        ck0 = ct+cs;
-    }
-    else {
-        cb = 0.5/z1;
-        zr2 = 1.0/z2;
-        ck0 = cone;
-        for (k=0;k<10;k++) {
-            ck0 += a1[k]*pow(zr2,k+1.0);
-        }
-        ck0 *= cb/ci0;
-    }
-    ck1 = (1.0/z1 - ci1*ck0)/ci0;
-    if (real(z) < 0.0) {
-        if (imag(z) < 0.0) {
-            ck0 += cii*M_PI*ci0;
-            ck1 = -ck1+cii*M_PI*ci1;
-        }
-        else if (imag(z) > 0.0) {
-            ck0 -= cii*M_PI*ci0;
-            ck1 = -ck1-cii*M_PI*ci1;
-        }
-        ci1 = -ci1;
-    }
-    ci0p = ci1;
-    ci1p = ci0-1.0*ci1/z;
-    ck0p = -ck1;
-    ck1p = -ck0-1.0*ck1/z;
-    return 0;
-}
-int cbessikna(int n,complex<double> z,int &nm,complex<double> *ci,
-    complex<double> *ck,complex<double> *cip,complex<double> *ckp)
-{
-    complex<double> ci0,ci1,ck0,ck1,ckk,cf,cf1,cf2,cs;
-    double a0;
-    int k,m,ecode;
-    a0 = abs(z);
-    nm = n;
-    if (a0 < 1.0e-100) {
-        for (k=0;k<=n;k++) {
-            ci[k] = czero;
-            ck[k] = complex<double>(-1e308,0);
-            cip[k] = czero;
-            ckp[k] = complex<double>(1e308,0);
-        }
-        ci[0] = cone;
-        cip[1] = complex<double>(0.5,0.0);
-        return 0;
-    }
-    ecode = cbessik01(z,ci[0],ci[1],ck[0],ck[1],cip[0],cip[1],ckp[0],ckp[1]);
-    if (n < 2) return 0;
-    ci0 = ci[0];
-    ci1 = ci[1];
-    ck0 = ck[0];
-    ck1 = ck[1];
-    m = msta1(a0,200);
-    if (m < n) nm = m;
-    else m = msta2(a0,n,15);
-    cf2 = czero;
-    cf1 = complex<double>(1.0e-100,0.0);
-    for (k=m;k>=0;k--) {
-        cf = 2.0*(k+1.0)*cf1/z+cf2;
-        if (k <= nm) ci[k] = cf;
-        cf2 = cf1;
-        cf1 = cf;
-    }
-    cs = ci0/cf;
-    for (k=0;k<=nm;k++) {
-        ci[k] *= cs;
-    }
-    for (k=2;k<=nm;k++) {
-        if (abs(ci[k-1]) > abs(ci[k-2])) {
-            ckk = (1.0/z-ci[k]*ck[k-1])/ci[k-1];
-        }
-        else {
-            ckk = (ci[k]*ck[k-2]+2.0*(k-1.0)/(z*z))/ci[k-2];
-        }
-        ck[k] = ckk;
-    }
-    for (k=2;k<=nm;k++) {
-        cip[k] = ci[k-1]-(double)k*ci[k]/z;
-        ckp[k] = -ck[k-1]-(double)k*ck[k]/z;
-    }
-    return 0;
-}
-int cbessiknb(int n,complex<double> z,int &nm,complex<double> *ci,
-    complex<double> *ck,complex<double> *cip,complex<double> *ckp)
-{
-    complex<double> z1,cbs,csk0,cf,cf0,cf1,ca0,cbkl;
-    complex<double> cg,cg0,cg1,cs0,cs,cr;
-    double a0,vt,fac;
-    int k,kz,l,m;
-
-    a0 = abs(z);
-    nm = n;
-    if (a0 < 1.0e-100) {
-        for (k=0;k<=n;k++) {
-            ci[k] = czero;
-            ck[k] = complex<double>(1e308,0);
-            cip[k] = czero;
-            ckp[k] = complex<double>(-1e308,0);
-        }
-        ci[0] = complex<double>(1.0,0.0);
-        cip[1] = complex<double>(0.5,0.0);
-        return 0;
-    }
-    z1 = z;
-    if (real(z) < 0.0) z1 = -z;
-    if (n == 0) nm = 1;
-    m = msta1(a0,200);
-    if (m < nm) nm = m;
-    else m = msta2(a0,nm,15);
-    cbs = czero;
-    csk0 = czero;
-    cf0 = czero;
-    cf1 = complex<double>(1.0e-100,0.0);
-    for (k=m;k>=0;k--) {
-        cf = 2.0*(k+1.0)*cf1/z1+cf0;
-        if (k <=nm) ci[k] = cf;
-        if ((k != 0) && (k == 2*(k>>1)))  csk0 += 4.0*cf/(double)k;
-        cbs += 2.0*cf;
-        cf0 = cf1;
-        cf1 = cf;
-    }
-    cs0 = exp(z1)/(cbs-cf);
-    for (k=0;k<=nm;k++) {
-        ci[k] *= cs0;
-    }
-    if (a0 <= 9.0) {
-        ck[0] = -(log(0.5*z1)+el)*ci[0]+cs0*csk0;
-        ck[1] = (1.0/z1-ci[1]*ck[0])/ci[0];
-    }
-    else {
-        ca0 = sqrt(M_PI_2/z1)*exp(-z1);
-        if (a0 >= 200.0) kz = 6;
-        else if (a0 >= 80.0) kz = 8;
-        else if (a0 >= 25.0) kz = 10;
-        else kz = 16;
-        for (l=0;l<2;l++) {
-            cbkl = cone;
-            vt = 4.0*l;
-            cr = cone;
-            for (k=1;k<=kz;k++) {
-                cr *= 0.125*(vt-pow(2.0*k-1.0,2.0))/((double)k*z1);
-                cbkl += cr;
-            }
-            ck[l] = ca0*cbkl;
-        }
-    }
-    cg0 = ck[0];    
-    cg1 = ck[1];
-    for (k=2;k<=nm;k++) {
-        cg = 2.0*(k-1.0)*cg1/z1+cg0;
-        ck[k] = cg;
-        cg0 = cg1;
-        cg1 = cg;
-    }
-    if (real(z) < 0.0) {
-        fac = 1.0;
-        for (k=0;k<=nm;k++) {
-            if (imag(z) < 0.0) {
-                ck[k] = fac*ck[k]+cii*M_PI*ci[k];
-            }
-            else {
-                ck[k] = fac*ck[k]-cii*M_PI*ci[k];
-            }
-            ci[k] *= fac;
-            fac = -fac;
-        }
-    }
-    cip[0] = ci[1];
-    ckp[0] = -ck[1];
-    for (k=1;k<=nm;k++) {
-        cip[k] = ci[k-1]-(double)k*ci[k]/z;
-        ckp[k] = -ck[k-1]-(double)k*ck[k]/z;
-    }
-    return 0;
-}
-int cbessikv(double v,complex<double>z,double &vm,complex<double> *civ,
-    complex<double> *ckv,complex<double> *civp,complex<double> *ckvp)
-{
-    complex<double> z1,z2,ca1,ca,cs,cr,ci0,cbi0,cf,cf1,cf2;
-    complex<double> ct,cp,cbk0,ca2,cr1,cr2,csu,cws,cb;
-    complex<double> cg0,cg1,cgk,cbk1,cvk;
-    double a0,v0,v0p,v0n,vt,w0,piv,gap,gan;
-    int m,n,k,kz;
-
-    a0 = abs(z);
-    z1 = z;
-    z2 = z*z;
-    n = (int)v;
-    v0 = v-n;
-    piv = M_PI*v0;
-    vt = 4.0*v0*v0;
-    if (n == 0) n = 1;
-    if (a0 < 1e-100) {
-        for (k=0;k<=n;k++) {
-            civ[k] = czero;
-            ckv[k] = complex<double>(-1e308,0);
-            civp[k] = czero;
-            ckvp[k] = complex<double>(1e308,0);
-        }
-        if (v0 == 0.0) {
-            civ[0] = cone;
-            civp[1] = complex<double> (0.5,0.0);
-        }
-        vm = v;
-        return 0;
-    }
-    if (a0 >= 50.0) kz = 8;
-    else if (a0 >= 35.0) kz = 10;
-    else kz = 14;
-    if (real(z) <= 0.0) z1 = -z;
-    if (a0 < 18.0) {
-        if (v0 == 0.0) {
-            ca1 = cone;
-        }
-        else {
-            v0p = 1.0+v0;
-            gap = gamma(v0p);
-            ca1 = pow(0.5*z1,v0)/gap;
-        }
-        ci0 = cone;
-        cr = cone;
-        for (k=1;k<=50;k++) {
-            cr *= 0.25*z2/(k*(k+v0));
-            ci0 += cr;
-            if (abs(cr/ci0) < eps) break;
-        }
-        cbi0 = ci0*ca1;
-    }
-    else {
-        ca = exp(z1)/sqrt(2.0*M_PI*z1);
-        cs = cone;
-        cr = cone;
-        for (k=1;k<=kz;k++) {
-            cr *= -0.125*(vt-pow(2.0*k-1.0,2.0))/((double)k*z1);
-            cs += cr;
-        }
-        cbi0 = ca*cs;
-    }
-    m = msta1(a0,200);
-    if (m < n) n = m;
-    else m = msta2(a0,n,15);
-    cf2 = czero;
-    cf1 = complex<double>(1.0e-100,0.0);
-    for (k=m;k>=0;k--) {
-        cf = 2.0*(v0+k+1.0)*cf1/z1+cf2;
-        if (k <= n) civ[k] = cf;
-        cf2 = cf1;
-        cf1 = cf;
-    }
-    cs = cbi0/cf;
-    for (k=0;k<=n;k++) {
-        civ[k] *= cs;
-    }
-    if (a0 <= 9.0) {
-        if (v0 == 0.0) {
-            ct = -log(0.5*z1)-el;
-            cs = czero;
-            w0 = 0.0;
-            cr = cone;
-            for (k=1;k<=50;k++) {
-                w0 += 1.0/k;
-                cr *= 0.25*z2/(double)(k*k);
-                cp = cr*(w0+ct);
-                cs += cp;
-                if ((k >= 10) && (abs(cp/cs) < eps)) break;
-            }
-            cbk0 = ct+cs;
-        }
-        else {
-            v0n = 1.0-v0;
-            gan = gamma(v0n);
-            ca2 = 1.0/(gan*pow(0.5*z1,v0));
-            ca1 = pow(0.5*z1,v0)/gap;
-            csu = ca2-ca1;
-            cr1 = cone;
-            cr2 = cone;
-            cws = czero;
-            for (k=1;k<=50;k++) {
-                cr1 *= 0.25*z2/(k*(k-v0));
-                cr2 *= 0.25*z2/(k*(k+v0));
-                csu += ca2*cr1-ca1*cr2;
-                if ((k >= 10) && (abs((cws-csu)/csu) < eps)) break;
-                cws = csu;
-            }
-            cbk0 = csu*M_PI_2/sin(piv);
-        }
-    }
-    else {
-        cb = exp(-z1)*sqrt(M_PI_2/z1);
-        cs = cone;
-        cr = cone;
-        for (k=1;k<=kz;k++) {
-            cr *= 0.125*(vt-pow(2.0*k-1.0,2.0))/((double)k*z1);
-            cs += cr;
-        }
-        cbk0 = cb*cs;
-    }
-    cbk1 = (1.0/z1-civ[1]*cbk0)/civ[0];
-    ckv[0] = cbk0;
-    ckv[1] = cbk1;
-    cg0 = cbk0;
-    cg1 = cbk1;
-    for (k=2;k<=n;k++) {
-        cgk = 2.0*(v0+k-1.0)*cg1/z1+cg0;
-        ckv[k] = cgk;
-        cg0 = cg1;
-        cg1 = cgk;
-    }
-    if (real(z) < 0.0) {
-        for (k=0;k<=n;k++) {
-            cvk = exp((k+v0)*M_PI*cii);
-            if (imag(z) < 0.0) {
-                ckv[k] = cvk*ckv[k]+M_PI*cii*civ[k];
-                civ[k] /= cvk;
-            }
-            else if (imag(z) > 0.0) {
-                ckv[k] = ckv[k]/cvk-M_PI*cii*civ[k];
-                civ[k] *= cvk;
-            }
-        }
-    }
-    civp[0] = v0*civ[0]/z+civ[1];
-    ckvp[0] = v0*ckv[0]/z-ckv[1];
-    for (k=1;k<=n;k++) {
-        civp[k] = -(k+v0)*civ[k]/z+civ[k-1];
-        ckvp[k] = -(k+v0)*ckv[k]/z-ckv[k-1];
-    }
-    vm = n+v0;
-    return 0;
-}
+//  cbessik.cpp -- complex modified Bessel functions.
+//  Algorithms and coefficient values from "Computation of Special
+//  Functions", Zhang and Jin, John Wiley and Sons, 1996.
+//
+//  (C) 2003, C. Bond. All rights reserved.
+//
+#include <complex>
+using namespace std;
+#include "bessel.h"
+
+static complex<double> cii(0.0,1.0);
+static complex<double> czero(0.0,0.0);
+static complex<double> cone(1.0,0.0);
+
+double gamma(double x);
+
+int cbessik01(complex<double>z,complex<double>&ci0,complex<double>&ci1,
+              complex<double>&ck0,complex<double>&ck1,complex<double>&ci0p,
+              complex<double>&ci1p,complex<double>&ck0p,complex<double>&ck1p)
+{
+    complex<double> z1,z2,zr,zr2,cr,ca,cb,cs,ct,cw;
+    double a0,w0;
+    int k,kz;
+    static double a[] = {
+        0.125,
+        7.03125e-2,
+        7.32421875e-2,
+        1.1215209960938e-1,
+        2.2710800170898e-1,
+        5.7250142097473e-1,
+        1.7277275025845,
+        6.0740420012735,
+        2.4380529699556e1,
+        1.1001714026925e2,
+        5.5133589612202e2,
+        3.0380905109224e3
+    };
+    static double b[] = {
+        -0.375,
+        -1.171875e-1,
+        -1.025390625e-1,
+        -1.4419555664063e-1,
+        -2.7757644653320e-1,
+        -6.7659258842468e-1,
+        -1.9935317337513,
+        -6.8839142681099,
+        -2.7248827311269e1,
+        -1.2159789187654e2,
+        -6.0384407670507e2,
+        -3.3022722944809e3
+    };
+    static double a1[] = {
+        0.125,
+        0.2109375,
+        1.0986328125,
+        1.1775970458984e1,
+        2.1461706161499e2,
+        5.9511522710323e3,
+        2.3347645606175e5,
+        1.2312234987631e7,
+        8.401390346421e08,
+        7.2031420482627e10
+    };
+
+    a0 = abs(z);
+    z2 = z*z;
+    z1 = z;
+    if (a0 == 0.0) {
+        ci0 = cone;
+        ci1 = czero;
+        ck0 = complex<double> (1e308,0);
+        ck1 = complex<double> (1e308,0);
+        ci0p = czero;
+        ci1p = complex<double>(0.5,0.0);
+        ck0p = complex<double>(-1e308,0);
+        ck1p = complex<double>(-1e308,0);
+        return 0;
+    }
+    if (real(z) < 0.0) z1 = -z;
+    if (a0 <= 18.0) {
+        ci0 = cone;
+        cr = cone;
+        for (k=1; k<=50; k++) {
+            cr *= 0.25*z2/(double)(k*k);
+            ci0 += cr;
+            if (abs(cr/ci0) < eps) break;
+        }
+        ci1 = cone;
+        cr = cone;
+        for (k=1; k<=50; k++) {
+            cr *= 0.25*z2/(double)(k*(k+1.0));
+            ci1 += cr;
+            if (abs(cr/ci1) < eps) break;
+        }
+        ci1 *= 0.5*z1;
+    }
+    else {
+        if (a0 >= 50.0) kz = 7;
+        else if (a0 >= 35.0) kz = 9;
+        else kz = 12;
+        ca = exp(z1)/sqrt(2.0*M_PI*z1);
+        ci0 = cone;
+        zr = 1.0/z1;
+        for (k=0; k<kz; k++) {
+            ci0 += a[k]*pow(zr,k+1.0);
+        }
+        ci0 *= ca;
+        ci1 = cone;
+        for (k=0; k<kz; k++) {
+            ci1 += b[k]*pow(zr,k+1.0);
+        }
+        ci1 *= ca;
+    }
+    if (a0 <= 9.0) {
+        cs = czero;
+        ct = -log(0.5*z1)-el;
+        w0 = 0.0;
+        cr = cone;
+        for (k=1; k<=50; k++) {
+            w0 += 1.0/k;
+            cr *= 0.25*z2/(double)(k*k);
+            cs += cr*(w0+ct);
+            if (abs((cs-cw)/cs) < eps) break;
+            cw = cs;
+        }
+        ck0 = ct+cs;
+    }
+    else {
+        cb = 0.5/z1;
+        zr2 = 1.0/z2;
+        ck0 = cone;
+        for (k=0; k<10; k++) {
+            ck0 += a1[k]*pow(zr2,k+1.0);
+        }
+        ck0 *= cb/ci0;
+    }
+    ck1 = (1.0/z1 - ci1*ck0)/ci0;
+    if (real(z) < 0.0) {
+        if (imag(z) < 0.0) {
+            ck0 += cii*M_PI*ci0;
+            ck1 = -ck1+cii*M_PI*ci1;
+        }
+        else if (imag(z) > 0.0) {
+            ck0 -= cii*M_PI*ci0;
+            ck1 = -ck1-cii*M_PI*ci1;
+        }
+        ci1 = -ci1;
+    }
+    ci0p = ci1;
+    ci1p = ci0-1.0*ci1/z;
+    ck0p = -ck1;
+    ck1p = -ck0-1.0*ck1/z;
+    return 0;
+}
+int cbessikna(int n,complex<double> z,int &nm,complex<double> *ci,
+              complex<double> *ck,complex<double> *cip,complex<double> *ckp)
+{
+    complex<double> ci0,ci1,ck0,ck1,ckk,cf,cf1,cf2,cs;
+    double a0;
+    int k,m,ecode;
+    a0 = abs(z);
+    nm = n;
+    if (a0 < 1.0e-100) {
+        for (k=0; k<=n; k++) {
+            ci[k] = czero;
+            ck[k] = complex<double>(-1e308,0);
+            cip[k] = czero;
+            ckp[k] = complex<double>(1e308,0);
+        }
+        ci[0] = cone;
+        cip[1] = complex<double>(0.5,0.0);
+        return 0;
+    }
+    ecode = cbessik01(z,ci[0],ci[1],ck[0],ck[1],cip[0],cip[1],ckp[0],ckp[1]);
+    if (n < 2) return 0;
+    ci0 = ci[0];
+    ci1 = ci[1];
+    ck0 = ck[0];
+    ck1 = ck[1];
+    m = msta1(a0,200);
+    if (m < n) nm = m;
+    else m = msta2(a0,n,15);
+    cf2 = czero;
+    cf1 = complex<double>(1.0e-100,0.0);
+    for (k=m; k>=0; k--) {
+        cf = 2.0*(k+1.0)*cf1/z+cf2;
+        if (k <= nm) ci[k] = cf;
+        cf2 = cf1;
+        cf1 = cf;
+    }
+    cs = ci0/cf;
+    for (k=0; k<=nm; k++) {
+        ci[k] *= cs;
+    }
+    for (k=2; k<=nm; k++) {
+        if (abs(ci[k-1]) > abs(ci[k-2])) {
+            ckk = (1.0/z-ci[k]*ck[k-1])/ci[k-1];
+        }
+        else {
+            ckk = (ci[k]*ck[k-2]+2.0*(k-1.0)/(z*z))/ci[k-2];
+        }
+        ck[k] = ckk;
+    }
+    for (k=2; k<=nm; k++) {
+        cip[k] = ci[k-1]-(double)k*ci[k]/z;
+        ckp[k] = -ck[k-1]-(double)k*ck[k]/z;
+    }
+    return 0;
+}
+int cbessiknb(int n,complex<double> z,int &nm,complex<double> *ci,
+              complex<double> *ck,complex<double> *cip,complex<double> *ckp)
+{
+    complex<double> z1,cbs,csk0,cf,cf0,cf1,ca0,cbkl;
+    complex<double> cg,cg0,cg1,cs0,cs,cr;
+    double a0,vt,fac;
+    int k,kz,l,m;
+
+    a0 = abs(z);
+    nm = n;
+    if (a0 < 1.0e-100) {
+        for (k=0; k<=n; k++) {
+            ci[k] = czero;
+            ck[k] = complex<double>(1e308,0);
+            cip[k] = czero;
+            ckp[k] = complex<double>(-1e308,0);
+        }
+        ci[0] = complex<double>(1.0,0.0);
+        cip[1] = complex<double>(0.5,0.0);
+        return 0;
+    }
+    z1 = z;
+    if (real(z) < 0.0) z1 = -z;
+    if (n == 0) nm = 1;
+    m = msta1(a0,200);
+    if (m < nm) nm = m;
+    else m = msta2(a0,nm,15);
+    cbs = czero;
+    csk0 = czero;
+    cf0 = czero;
+    cf1 = complex<double>(1.0e-100,0.0);
+    for (k=m; k>=0; k--) {
+        cf = 2.0*(k+1.0)*cf1/z1+cf0;
+        if (k <=nm) ci[k] = cf;
+        if ((k != 0) && (k == 2*(k>>1)))  csk0 += 4.0*cf/(double)k;
+        cbs += 2.0*cf;
+        cf0 = cf1;
+        cf1 = cf;
+    }
+    cs0 = exp(z1)/(cbs-cf);
+    for (k=0; k<=nm; k++) {
+        ci[k] *= cs0;
+    }
+    if (a0 <= 9.0) {
+        ck[0] = -(log(0.5*z1)+el)*ci[0]+cs0*csk0;
+        ck[1] = (1.0/z1-ci[1]*ck[0])/ci[0];
+    }
+    else {
+        ca0 = sqrt(M_PI_2/z1)*exp(-z1);
+        if (a0 >= 200.0) kz = 6;
+        else if (a0 >= 80.0) kz = 8;
+        else if (a0 >= 25.0) kz = 10;
+        else kz = 16;
+        for (l=0; l<2; l++) {
+            cbkl = cone;
+            vt = 4.0*l;
+            cr = cone;
+            for (k=1; k<=kz; k++) {
+                cr *= 0.125*(vt-pow(2.0*k-1.0,2.0))/((double)k*z1);
+                cbkl += cr;
+            }
+            ck[l] = ca0*cbkl;
+        }
+    }
+    cg0 = ck[0];
+    cg1 = ck[1];
+    for (k=2; k<=nm; k++) {
+        cg = 2.0*(k-1.0)*cg1/z1+cg0;
+        ck[k] = cg;
+        cg0 = cg1;
+        cg1 = cg;
+    }
+    if (real(z) < 0.0) {
+        fac = 1.0;
+        for (k=0; k<=nm; k++) {
+            if (imag(z) < 0.0) {
+                ck[k] = fac*ck[k]+cii*M_PI*ci[k];
+            }
+            else {
+                ck[k] = fac*ck[k]-cii*M_PI*ci[k];
+            }
+            ci[k] *= fac;
+            fac = -fac;
+        }
+    }
+    cip[0] = ci[1];
+    ckp[0] = -ck[1];
+    for (k=1; k<=nm; k++) {
+        cip[k] = ci[k-1]-(double)k*ci[k]/z;
+        ckp[k] = -ck[k-1]-(double)k*ck[k]/z;
+    }
+    return 0;
+}
+int cbessikv(double v,complex<double>z,double &vm,complex<double> *civ,
+             complex<double> *ckv,complex<double> *civp,complex<double> *ckvp)
+{
+    complex<double> z1,z2,ca1,ca,cs,cr,ci0,cbi0,cf,cf1,cf2;
+    complex<double> ct,cp,cbk0,ca2,cr1,cr2,csu,cws,cb;
+    complex<double> cg0,cg1,cgk,cbk1,cvk;
+    double a0,v0,v0p,v0n,vt,w0,piv,gap,gan;
+    int m,n,k,kz;
+
+    a0 = abs(z);
+    z1 = z;
+    z2 = z*z;
+    n = (int)v;
+    v0 = v-n;
+    piv = M_PI*v0;
+    vt = 4.0*v0*v0;
+    if (n == 0) n = 1;
+    if (a0 < 1e-100) {
+        for (k=0; k<=n; k++) {
+            civ[k] = czero;
+            ckv[k] = complex<double>(-1e308,0);
+            civp[k] = czero;
+            ckvp[k] = complex<double>(1e308,0);
+        }
+        if (v0 == 0.0) {
+            civ[0] = cone;
+            civp[1] = complex<double> (0.5,0.0);
+        }
+        vm = v;
+        return 0;
+    }
+    if (a0 >= 50.0) kz = 8;
+    else if (a0 >= 35.0) kz = 10;
+    else kz = 14;
+    if (real(z) <= 0.0) z1 = -z;
+    if (a0 < 18.0) {
+        if (v0 == 0.0) {
+            ca1 = cone;
+        }
+        else {
+            v0p = 1.0+v0;
+            gap = gamma(v0p);
+            ca1 = pow(0.5*z1,v0)/gap;
+        }
+        ci0 = cone;
+        cr = cone;
+        for (k=1; k<=50; k++) {
+            cr *= 0.25*z2/(k*(k+v0));
+            ci0 += cr;
+            if (abs(cr/ci0) < eps) break;
+        }
+        cbi0 = ci0*ca1;
+    }
+    else {
+        ca = exp(z1)/sqrt(2.0*M_PI*z1);
+        cs = cone;
+        cr = cone;
+        for (k=1; k<=kz; k++) {
+            cr *= -0.125*(vt-pow(2.0*k-1.0,2.0))/((double)k*z1);
+            cs += cr;
+        }
+        cbi0 = ca*cs;
+    }
+    m = msta1(a0,200);
+    if (m < n) n = m;
+    else m = msta2(a0,n,15);
+    cf2 = czero;
+    cf1 = complex<double>(1.0e-100,0.0);
+    for (k=m; k>=0; k--) {
+        cf = 2.0*(v0+k+1.0)*cf1/z1+cf2;
+        if (k <= n) civ[k] = cf;
+        cf2 = cf1;
+        cf1 = cf;
+    }
+    cs = cbi0/cf;
+    for (k=0; k<=n; k++) {
+        civ[k] *= cs;
+    }
+    if (a0 <= 9.0) {
+        if (v0 == 0.0) {
+            ct = -log(0.5*z1)-el;
+            cs = czero;
+            w0 = 0.0;
+            cr = cone;
+            for (k=1; k<=50; k++) {
+                w0 += 1.0/k;
+                cr *= 0.25*z2/(double)(k*k);
+                cp = cr*(w0+ct);
+                cs += cp;
+                if ((k >= 10) && (abs(cp/cs) < eps)) break;
+            }
+            cbk0 = ct+cs;
+        }
+        else {
+            v0n = 1.0-v0;
+            gan = gamma(v0n);
+            ca2 = 1.0/(gan*pow(0.5*z1,v0));
+            ca1 = pow(0.5*z1,v0)/gap;
+            csu = ca2-ca1;
+            cr1 = cone;
+            cr2 = cone;
+            cws = czero;
+            for (k=1; k<=50; k++) {
+                cr1 *= 0.25*z2/(k*(k-v0));
+                cr2 *= 0.25*z2/(k*(k+v0));
+                csu += ca2*cr1-ca1*cr2;
+                if ((k >= 10) && (abs((cws-csu)/csu) < eps)) break;
+                cws = csu;
+            }
+            cbk0 = csu*M_PI_2/sin(piv);
+        }
+    }
+    else {
+        cb = exp(-z1)*sqrt(M_PI_2/z1);
+        cs = cone;
+        cr = cone;
+        for (k=1; k<=kz; k++) {
+            cr *= 0.125*(vt-pow(2.0*k-1.0,2.0))/((double)k*z1);
+            cs += cr;
+        }
+        cbk0 = cb*cs;
+    }
+    cbk1 = (1.0/z1-civ[1]*cbk0)/civ[0];
+    ckv[0] = cbk0;
+    ckv[1] = cbk1;
+    cg0 = cbk0;
+    cg1 = cbk1;
+    for (k=2; k<=n; k++) {
+        cgk = 2.0*(v0+k-1.0)*cg1/z1+cg0;
+        ckv[k] = cgk;
+        cg0 = cg1;
+        cg1 = cgk;
+    }
+    if (real(z) < 0.0) {
+        for (k=0; k<=n; k++) {
+            cvk = exp((k+v0)*M_PI*cii);
+            if (imag(z) < 0.0) {
+                ckv[k] = cvk*ckv[k]+M_PI*cii*civ[k];
+                civ[k] /= cvk;
+            }
+            else if (imag(z) > 0.0) {
+                ckv[k] = ckv[k]/cvk-M_PI*cii*civ[k];
+                civ[k] *= cvk;
+            }
+        }
+    }
+    civp[0] = v0*civ[0]/z+civ[1];
+    ckvp[0] = v0*ckv[0]/z-ckv[1];
+    for (k=1; k<=n; k++) {
+        civp[k] = -(k+v0)*civ[k]/z+civ[k-1];
+        ckvp[k] = -(k+v0)*ckv[k]/z-ckv[k-1];
+    }
+    vm = n+v0;
+    return 0;
+}
-//  cbessjy.cpp -- complex Bessel functions.
-//  Algorithms and coefficient values from "Computation of Special
-//  Functions", Zhang and Jin, John Wiley and Sons, 1996.
-//
-//  (C) 2003, C. Bond. All rights reserved.
-//
-#include <complex>
-using namespace std;
-#include "bessel.h"
-double gamma(double);
-
-static complex<double> cii(0.0,1.0);
-static complex<double> cone(1.0,0.0);
-static complex<double> czero(0.0,0.0);
-
-int cbessjy01(complex<double> z,complex<double> &cj0,complex<double> &cj1,
-    complex<double> &cy0,complex<double> &cy1,complex<double> &cj0p,
-    complex<double> &cj1p,complex<double> &cy0p,complex<double> &cy1p)
-{
-    complex<double> z1,z2,cr,cp,cs,cp0,cq0,cp1,cq1,ct1,ct2,cu;
-    double a0,w0,w1;
-    int k,kz;
-
-    static double a[] = {
-        -7.03125e-2,
-         0.112152099609375,
-        -0.5725014209747314,
-         6.074042001273483,
-        -1.100171402692467e2,
-         3.038090510922384e3,
-        -1.188384262567832e5,
-         6.252951493434797e6,
-        -4.259392165047669e8,
-         3.646840080706556e10,
-        -3.833534661393944e12,
-         4.854014686852901e14,
-        -7.286857349377656e16,
-         1.279721941975975e19};
-    static double b[] = {
-         7.32421875e-2,
-        -0.2271080017089844,
-         1.727727502584457,
-        -2.438052969955606e1,
-         5.513358961220206e2,
-        -1.825775547429318e4,
-         8.328593040162893e5,
-        -5.006958953198893e7,
-         3.836255180230433e9,
-        -3.649010818849833e11,
-         4.218971570284096e13,
-        -5.827244631566907e15,
-         9.476288099260110e17,
-        -1.792162323051699e20};
-    static double a1[] = {
-         0.1171875,
-        -0.1441955566406250,
-         0.6765925884246826,
-        -6.883914268109947,
-         1.215978918765359e2,
-        -3.302272294480852e3,
-         1.276412726461746e5,
-        -6.656367718817688e6,
-         4.502786003050393e8,
-        -3.833857520742790e10,
-         4.011838599133198e12,
-        -5.060568503314727e14,
-         7.572616461117958e16,
-        -1.326257285320556e19};
-    static double b1[] = {
-        -0.1025390625,
-         0.2775764465332031,
-        -1.993531733751297,
-         2.724882731126854e1,
-        -6.038440767050702e2,
-         1.971837591223663e4,
-        -8.902978767070678e5,
-         5.310411010968522e7,
-        -4.043620325107754e9,
-         3.827011346598605e11,
-        -4.406481417852278e13,
-         6.065091351222699e15,
-        -9.833883876590679e17,
-         1.855045211579828e20};
-
-    a0 = abs(z);
-    z2 = z*z;
-    z1 = z;
-    if (a0 == 0.0) {
-        cj0 = cone;
-        cj1 = czero;
-        cy0 = complex<double>(-1e308,0);
-        cy1 = complex<double>(-1e308,0);
-        cj0p = czero;
-        cj1p = complex<double>(0.5,0.0);
-        cy0p = complex<double>(1e308,0);
-        cy1p = complex<double>(1e308,0);
-        return 0;
-    }
-    if (real(z) < 0.0) z1 = -z;
-    if (a0 <= 12.0) {
-        cj0 = cone;
-        cr = cone;
-        for (k=1;k<=40;k++) {
-            cr *= -0.25*z2/(double)(k*k);
-            cj0 += cr;
-            if (abs(cr) < abs(cj0)*eps) break;
-        }
-        cj1 = cone;
-        cr = cone;
-        for (k=1;k<=40;k++) {
-            cr *= -0.25*z2/(k*(k+1.0));
-            cj1 += cr;
-            if (abs(cr) < abs(cj1)*eps) break;
-        }
-        cj1 *= 0.5*z1;
-        w0 = 0.0;
-        cr = cone;
-        cs = czero;
-        for (k=1;k<=40;k++) {
-            w0 += 1.0/k;
-            cr *= -0.25*z2/(double)(k*k);
-            cp = cr*w0;
-            cs += cp;
-            if (abs(cp) < abs(cs)*eps) break;
-        }
-        cy0 = M_2_PI*((log(0.5*z1)+el)*cj0-cs);
-        w1 = 0.0;
-        cr = cone;
-        cs = cone;
-        for (k=1;k<=40;k++) {
-            w1 += 1.0/k;
-            cr *= -0.25*z2/(k*(k+1.0));
-            cp = cr*(2.0*w1+1.0/(k+1.0));
-            cs += cp;
-            if (abs(cp) < abs(cs)*eps) break;
-        }
-        cy1 = M_2_PI*((log(0.5*z1)+el)*cj1-1.0/z1-0.25*z1*cs);
-    }
-    else {
-        if (a0 >= 50.0) kz = 8;         // can be changed to 10
-        else if (a0 >= 35.0) kz = 10;   //   "      "     "  12
-        else kz = 12;                   //   "      "     "  14
-        ct1 = z1 - M_PI_4;
-        cp0 = cone;
-        for (k=0;k<kz;k++) {
-            cp0 += a[k]*pow(z1,-2.0*k-2.0);
-        }
-        cq0 = -0.125/z1;
-        for (k=0;k<kz;k++) {
-            cq0 += b[k]*pow(z1,-2.0*k-3.0);
-        }
-        cu = sqrt(M_2_PI/z1);
-        cj0 = cu*(cp0*cos(ct1)-cq0*sin(ct1));
-        cy0 = cu*(cp0*sin(ct1)+cq0*cos(ct1));
-        ct2 = z1 - 0.75*M_PI;
-        cp1 = cone;
-        for (k=0;k<kz;k++) {
-            cp1 += a1[k]*pow(z1,-2.0*k-2.0);
-        }
-        cq1 = 0.375/z1;
-        for (k=0;k<kz;k++) {
-            cq1 += b1[k]*pow(z1,-2.0*k-3.0);
-        }
-        cj1 = cu*(cp1*cos(ct2)-cq1*sin(ct2));
-        cy1 = cu*(cp1*sin(ct2)+cq1*cos(ct2));
-    }
-    if (real(z) < 0.0) {
-        if (imag(z) < 0.0) {
-            cy0 -= 2.0*cii*cj0;
-            cy1 = -(cy1-2.0*cii*cj1);
-        }
-        else if (imag(z) > 0.0) {
-            cy0 += 2.0*cii*cj0;
-            cy1 = -(cy1+2.0*cii*cj1);
-        }
-        cj1 = -cj1;
-    }
-    cj0p = -cj1;
-    cj1p = cj0-cj1/z;
-    cy0p = -cy1;
-    cy1p = cy0-cy1/z;
-    return 0;
-}
-
-int cbessjyna(int n,complex<double> z,int &nm,complex<double> *cj,
-    complex<double> *cy,complex<double> *cjp,complex<double> *cyp)
-{
-    complex<double> cbj0,cbj1,cby0,cby1,cj0,cjk,cj1,cf,cf1,cf2;
-    complex<double> cs,cg0,cg1,cyk,cyl1,cyl2,cylk,cp11,cp12,cp21,cp22;
-    complex<double> ch0,ch1,ch2;
-    double a0,yak,ya1,ya0,wa;
-    int m,k,lb,lb0;
-
-    if (n < 0) return 1;
-    a0 = abs(z);
-    nm = n;
-    if (a0 < 1.0e-100) {
-        for (k=0;k<=n;k++) {
-            cj[k] = czero;
-            cy[k] = complex<double> (-1e308,0);
-            cjp[k] = czero;
-            cyp[k] = complex<double>(1e308,0);
-        }
-        cj[0] = cone;
-        cjp[1] = complex<double>(0.5,0.0);
-        return 0;
-    }
-    cbessjy01(z,cj[0],cj[1],cy[0],cy[1],cjp[0],cjp[1],cyp[0],cyp[1]);
-    cbj0 = cj[0];
-    cbj1 = cj[1];
-    cby0 = cy[0];
-    cby1 = cy[1];
-    if (n <= 1) return 0;
-    if (n < (int)0.25*a0) {
-        cj0 = cbj0;
-        cj1 = cbj1;
-        for (k=2;k<=n;k++) {
-            cjk = 2.0*(k-1.0)*cj1/z-cj0;
-            cj[k] = cjk;
-            cj0 = cj1;
-            cj1 = cjk;
-        }
-    }
-    else {
-        m = msta1(a0,200);
-        if (m < n) nm = m;
-        else m = msta2(a0,n,15);
-        cf2 = czero;
-        cf1 = complex<double> (1.0e-100,0.0);
-        for (k=m;k>=0;k--) {
-            cf = 2.0*(k+1.0)*cf1/z-cf2;
-            if (k <=nm) cj[k] = cf;
-            cf2 = cf1;
-            cf1 = cf;
-        }
-        if (abs(cbj0) > abs(cbj1)) cs = cbj0/cf;
-        else cs = cbj1/cf2;
-        for (k=0;k<=nm;k++) {
-            cj[k] *= cs;
-        }
-    }
-    for (k=2;k<=nm;k++) {
-        cjp[k] = cj[k-1]-(double)k*cj[k]/z;
-    }
-    ya0 = abs(cby0);
-    lb = 0;
-    cg0 = cby0;
-    cg1 = cby1;
-    for (k=2;k<=nm;k++) {
-        cyk = 2.0*(k-1.0)*cg1/z-cg0;
-        yak = abs(cyk);
-        ya1 = abs(cg0);
-        if ((yak < ya0) && (yak < ya1)) lb = k;
-        cy[k] = cyk;
-        cg0 = cg1;
-        cg1 = cyk;
-    }
-    lb0 = 0;
-    if ((lb > 4) && (imag(z) != 0.0)) {
-        while (lb != lb0) {
-            ch2 = cone;
-            ch1 = czero;
-            lb0 = lb;
-            for (k=lb;k>=1;k--) {
-                ch0 = 2.0*k*ch1/z-ch2;
-                ch2 = ch1;
-                ch1 = ch0;
-            }
-            cp12 = ch0;
-            cp22 = ch2;
-            ch2 = czero;
-            ch1 = cone;
-            for (k=lb;k>=1;k--) {
-                ch0 = 2.0*k*ch1/z-ch2;
-                ch2 = ch1;
-                ch1 = ch0;
-            }
-            cp11 = ch0;
-            cp21 = ch2;
-            if (lb == nm)
-                cj[lb+1] = 2.0*lb*cj[lb]/z-cj[lb-1];
-            if (abs(cj[0]) > abs(cj[1])) {
-                cy[lb+1] = (cj[lb+1]*cby0-2.0*cp11/(M_PI*z))/cj[0];
-                cy[lb] = (cj[lb]*cby0+2.0*cp12/(M_PI*z))/cj[0];
-            }
-            else {
-                cy[lb+1] = (cj[lb+1]*cby1-2.0*cp21/(M_PI*z))/cj[1];
-                cy[lb] = (cj[lb]*cby1+2.0*cp22/(M_PI*z))/cj[1];
-            }
-            cyl2 = cy[lb+1];
-            cyl1 = cy[lb];
-            for (k=lb-1;k>=0;k--) {
-                cylk = 2.0*(k+1.0)*cyl1/z-cyl2;
-                cy[k] = cylk;
-                cyl2 = cyl1;
-                cyl1 = cylk;
-            }
-            cyl1 = cy[lb];
-            cyl2 = cy[lb+1];
-            for (k=lb+1;k<n;k++) {
-                cylk = 2.0*k*cyl2/z-cyl1;
-                cy[k+1] = cylk;
-                cyl1 = cyl2;
-                cyl2 = cylk;
-            }
-            for (k=2;k<=nm;k++) {
-                wa = abs(cy[k]);
-                if (wa < abs(cy[k-1])) lb = k;
-            }
-        }
-    }
-    for (k=2;k<=nm;k++) {
-        cyp[k] = cy[k-1]-(double)k*cy[k]/z;
-    }
-    return 0;
-}
-
-int cbessjynb(int n,complex<double> z,int &nm,complex<double> *cj,
-    complex<double> *cy,complex<double> *cjp,complex<double> *cyp)
-{
-    complex<double> cf,cf0,cf1,cf2,cbs,csu,csv,cs0,ce;
-    complex<double> ct1,cp0,cq0,cp1,cq1,cu,cbj0,cby0,cbj1,cby1;
-    complex<double> cyy,cbjk,ct2;
-    double a0,y0;
-    int k,m;
-    static double a[] = {
-        -0.7031250000000000e-1,
-         0.1121520996093750,
-        -0.5725014209747314,
-         6.074042001273483};
-    static double b[] = {
-         0.7324218750000000e-1,
-        -0.2271080017089844,
-         1.727727502584457,
-        -2.438052969955606e1};
-    static double a1[] = {
-         0.1171875,
-        -0.1441955566406250,
-         0.6765925884246826,
-        -6.883914268109947};
-    static double b1[] = {
-       -0.1025390625,
-        0.2775764465332031,
-       -1.993531733751297,
-        2.724882731126854e1};
-
-    y0 = abs(imag(z));
-    a0 = abs(z);
-    nm = n;
-    if (a0 < 1.0e-100) {
-        for (k=0;k<=n;k++) {
-            cj[k] = czero;
-            cy[k] = complex<double> (-1e308,0);
-            cjp[k] = czero;
-            cyp[k] = complex<double>(1e308,0);
-        }
-        cj[0] = cone;
-        cjp[1] = complex<double>(0.5,0.0);
-        return 0;
-    }
-    if ((a0 <= 300.0) || (n > (int)(0.25*a0))) {
-        if (n == 0) nm = 1;
-        m = msta1(a0,200);
-        if (m < nm) nm = m;
-        else m = msta2(a0,nm,15);
-        cbs = czero;
-        csu = czero;
-        csv = czero;
-        cf2 = czero;
-        cf1 = complex<double> (1.0e-100,0.0);
-        for (k=m;k>=0;k--) {
-            cf = 2.0*(k+1.0)*cf1/z-cf2;
-            if (k <= nm) cj[k] = cf;
-            if (((k & 1) == 0) && (k != 0)) {
-                if (y0 <= 1.0) {
-                    cbs += 2.0*cf;
-                }
-                else {
-                    cbs += (-1)*((k & 2)-1)*2.0*cf;
-                }
-                csu += (double)((-1)*((k & 2)-1))*cf/(double)k;
-            }
-            else if (k > 1) {
-                csv += (double)((-1)*((k & 2)-1)*k)*cf/(double)(k*k-1.0);    
-            }
-            cf2 = cf1;
-            cf1 = cf;
-        }
-        if (y0 <= 1.0) cs0 = cbs+cf;
-        else cs0 = (cbs+cf)/cos(z);
-        for (k=0;k<=nm;k++) {
-            cj[k] /= cs0;
-        }
-        ce = log(0.5*z)+el;
-        cy[0] = M_2_PI*(ce*cj[0]-4.0*csu/cs0);
-        cy[1] = M_2_PI*(-cj[0]/z+(ce-1.0)*cj[1]-4.0*csv/cs0);
-    }
-    else {
-        ct1 = z-M_PI_4;
-        cp0 = cone;
-        for (k=0;k<4;k++) {
-            cp0 += a[k]*pow(z,-2.0*k-2.0);
-        }
-        cq0 = -0.125/z;
-        for (k=0;k<4;k++) {
-            cq0 += b[k] *pow(z,-2.0*k-3.0);
-        }
-        cu = sqrt(M_2_PI/z);
-        cbj0 = cu*(cp0*cos(ct1)-cq0*sin(ct1));
-        cby0 = cu*(cp0*sin(ct1)+cq0*cos(ct1));
-        cj[0] = cbj0;
-        cy[0] = cby0;
-        ct2 = z-0.75*M_PI;
-        cp1 = cone;
-        for (k=0;k<4;k++) {
-            cp1 += a1[k]*pow(z,-2.0*k-2.0);
-        }
-        cq1 = 0.375/z;
-        for (k=0;k<4;k++) {
-            cq1 += b1[k]*pow(z,-2.0*k-3.0);
-        }
-        cbj1 = cu*(cp1*cos(ct2)-cq1*sin(ct2));
-        cby1 = cu*(cp1*sin(ct2)+cq1*cos(ct2));
-        cj[1] = cbj1;
-        cy[1] = cby1;
-        for (k=2;k<=n;k++) {
-            cbjk = 2.0*(k-1.0)*cbj1/z-cbj0;
-            cj[k] = cbjk;
-            cbj0 = cbj1;
-            cbj1 = cbjk;
-        }
-    }
-    cjp[0] = -cj[1];
-    for (k=1;k<=nm;k++) {
-        cjp[k] = cj[k-1]-(double)k*cj[k]/z;
-    }
-    if (abs(cj[0]) > 1.0)
-        cy[1] = (cj[1]*cy[0]-2.0/(M_PI*z))/cj[0];
-    for (k=2;k<=nm;k++) {
-        if (abs(cj[k-1]) >= abs(cj[k-2]))
-            cyy = (cj[k]*cy[k-1]-2.0/(M_PI*z))/cj[k-1];
-        else
-            cyy = (cj[k]*cy[k-2]-4.0*(k-1.0)/(M_PI*z*z))/cj[k-2];
-        cy[k] = cyy;
-    }
-    cyp[0] = -cy[1];
-    for (k=1;k<=nm;k++) {
-        cyp[k] = cy[k-1]-(double)k*cy[k]/z;
-    }
-
-    return 0;
-}
-
-int cbessjyva(double v,complex<double> z,double &vm,complex<double>*cjv,
-    complex<double>*cyv,complex<double>*cjvp,complex<double>*cyvp)
-{
-    complex<double> z1,z2,zk,cjvl,cr,ca,cjv0,cjv1,cpz,crp;
-    complex<double> cqz,crq,ca0,cck,csk,cyv0,cyv1,cju0,cju1,cb;
-    complex<double> cs,cs0,cr0,cs1,cr1,cec,cf,cf0,cf1,cf2;
-    complex<double> cfac0,cfac1,cg0,cg1,cyk,cp11,cp12,cp21,cp22;
-    complex<double> ch0,ch1,ch2,cyl1,cyl2,cylk;
-
-    double a0,v0,pv0,pv1,vl,ga,gb,vg,vv,w0,w1,ya0,yak,ya1,wa;
-    int j,n,k,kz,l,lb,lb0,m;
-
-    a0 = abs(z);
-    z1 = z;
-    z2 = z*z;
-    n = (int)v;
-
-
-    v0 = v-n;
-
-    pv0 = M_PI*v0;
-    pv1 = M_PI*(1.0+v0);
-    if (a0 < 1.0e-100) {
-        for (k=0;k<=n;k++) {
-            cjv[k] = czero;
-            cyv[k] = complex<double> (-1e308,0);
-            cjvp[k] = czero;
-            cyvp[k] = complex<double> (1e308,0);
-
-        }
-        if (v0 == 0.0) {
-            cjv[0] = cone;
-            cjvp[1] = complex<double> (0.5,0.0);
-        }
-        else {
-            cjvp[0] = complex<double> (1e308,0);
-        }
-        vm = v;
-        return 0;
-    }
-    if (real(z1) < 0.0) z1 = -z;
-    if (a0 <= 12.0) {
-        for (l=0;l<2;l++) {
-            vl = v0+l;
-            cjvl = cone;
-            cr = cone;
-            for (k=1;k<=40;k++) {
-                cr *= -0.25*z2/(k*(k+vl));
-                cjvl += cr;
-                if (abs(cr) < abs(cjvl)*eps) break;
-            }
-           vg = 1.0 + vl;
-           ga = gamma(vg);
-           ca = pow(0.5*z1,vl)/ga;
-           if (l == 0) cjv0 = cjvl*ca;
-           else cjv1 = cjvl*ca;
-        }
-    }
-    else {
-        if (a0 >= 50.0) kz = 8;
-        else if (a0 >= 35.0) kz = 10;
-        else kz = 11;
-        for (j=0;j<2;j++) {
-            vv = 4.0*(j+v0)*(j+v0);
-            cpz = cone;
-            crp = cone;
-            for (k=1;k<=kz;k++) {
-                crp = -0.78125e-2*crp*(vv-pow(4.0*k-3.0,2.0))*
-                    (vv-pow(4.0*k-1.0,2.0))/(k*(2.0*k-1.0)*z2);
-                cpz += crp;
-            }
-            cqz = cone;
-            crq = cone;
-            for (k=1;k<=kz;k++) {
-                crq = -0.78125e-2*crq*(vv-pow(4.0*k-1.0,2.0))*
-                    (vv-pow(4.0*k+1.0,2.0))/(k*(2.0*k+1.0)*z2);
-                cqz += crq;
-            }
-            cqz *= 0.125*(vv-1.0)/z1;
-            zk = z1-(0.5*(j+v0)+0.25)*M_PI;
-            ca0 = sqrt(M_2_PI/z1);
-            cck = cos(zk);
-            csk = sin(zk);
-            if (j == 0) {
-                cjv0 = ca0*(cpz*cck-cqz*csk);
-                cyv0 = ca0*(cpz*csk+cqz+cck);
-            }
-            else {
-                cjv1 = ca0*(cpz*cck-cqz*csk);
-                cyv1 = ca0*(cpz*csk+cqz*cck);
-            }
-        }
-    }
-    if (a0 <= 12.0) {
-        if (v0 != 0.0) {
-            for (l=0;l<2;l++) {
-                vl = v0+l;
-                cjvl = cone;
-                cr = cone;
-                for (k=1;k<=40;k++) {
-                    cr *= -0.25*z2/(k*(k-vl));
-                    cjvl += cr;
-                    if (abs(cr) < abs(cjvl)*eps) break;
-                }
-                vg = 1.0-vl;
-                gb = gamma(vg);
-                cb = pow(2.0/z1,vl)/gb;
-                if (l == 0) cju0 = cjvl*cb;
-                else cju1 = cjvl*cb;
-            }
-            cyv0 = (cjv0*cos(pv0)-cju0)/sin(pv0);
-            cyv1 = (cjv1*cos(pv1)-cju1)/sin(pv1);
-        }
-        else {
-            cec = log(0.5*z1)+el;
-            cs0 = czero;
-            w0 = 0.0;
-            cr0 = cone;
-            for (k=1;k<=30;k++) {
-                w0 += 1.0/k;
-                cr0 *= -0.25*z2/(double)(k*k);
-                cs0 += cr0*w0;
-            }
-            cyv0 = M_2_PI*(cec*cjv0-cs0);
-            cs1 = cone;
-            w1 = 0.0;
-            cr1 = cone;
-            for (k=1;k<=30;k++) {
-                w1 += 1.0/k;
-                cr1 *= -0.25*z2/(k*(k+1.0));
-                cs1 += cr1*(2.0*w1+1.0/(k+1.0));
-            }
-            cyv1 = M_2_PI*(cec*cjv1-1.0/z1-0.25*z1*cs1);
-        }
-    }
-    if (real(z) < 0.0) {
-        cfac0 = exp(pv0*cii);
-        cfac1 = exp(pv1*cii);
-        if (imag(z) < 0.0) {
-            cyv0 = cfac0*cyv0-2.0*cii*cos(pv0)*cjv0;
-            cyv1 = cfac1*cyv1-2.0*cii*cos(pv1)*cjv1;
-            cjv0 /= cfac0;
-            cjv1 /= cfac1;
-        }
-        else if (imag(z) > 0.0) {
-            cyv0 = cyv0/cfac0+2.0*cii*cos(pv0)*cjv0;
-            cyv1 = cyv1/cfac1+2.0*cii*cos(pv1)*cjv1;
-            cjv0 *= cfac0;
-            cjv1 *= cfac1;
-        }
-    }
-    cjv[0] = cjv0;
-    cjv[1] = cjv1;
-    if ((n >= 2) && (n <= (int)(0.25*a0))) {
-        cf0 = cjv0;
-        cf1 = cjv1;
-        for (k=2;k<= n;k++) {
-            cf = 2.0*(k+v0-1.0)*cf1/z-cf0;
-            cjv[k] = cf;
-            cf0 = cf1;
-            cf1 = cf;
-        }
-    }
-    else if (n >= 2) {
-        m = msta1(a0,200);
-        if (m < n) n = m;
-        else  m = msta2(a0,n,15);
-        cf2 = czero;
-        cf1 = complex<double>(1.0e-100,0.0);
-        for (k=m;k>=0;k--) {
-            cf = 2.0*(v0+k+1.0)*cf1/z-cf2;
-            if (k <= n) cjv[k] = cf;
-            cf2 = cf1;
-            cf1 = cf;
-        }
-        if (abs(cjv0) > abs(cjv1)) cs = cjv0/cf;
-        else cs = cjv1/cf2;
-        for (k=0;k<=n;k++) {
-            cjv[k] *= cs;
-        }
-    }
-    cjvp[0] = v0*cjv[0]/z-cjv[1];
-    for (k=1;k<=n;k++) {
-        cjvp[k] = -(k+v0)*cjv[k]/z+cjv[k-1];
-    }
-    cyv[0] = cyv0;
-    cyv[1] = cyv1;
-    ya0 = abs(cyv0);
-    lb = 0;
-    cg0 = cyv0;
-    cg1 = cyv1;
-    for (k=2;k<=n;k++) {
-        cyk = 2.0*(v0+k-1.0)*cg1/z-cg0;
-        yak = abs(cyk);
-        ya1 = abs(cg0);
-        if ((yak < ya0) && (yak< ya1)) lb = k;
-        cyv[k] = cyk;
-        cg0 = cg1;
-        cg1 = cyk;
-    }
-    lb0 = 0;
-    if ((lb > 4) && (imag(z) != 0.0)) {
-        while(lb != lb0) {
-            ch2 = cone;
-            ch1 = czero;
-            lb0 = lb;
-            for (k=lb;k>=1;k--) {
-                ch0 = 2.0*(k+v0)*ch1/z-ch2;
-                ch2 = ch1;
-                ch1 = ch0;
-            }
-            cp12 = ch0;
-            cp22 = ch2;
-            ch2 = czero;
-            ch1 = cone;
-            for (k=lb;k>=1;k--) {
-                ch0 = 2.0*(k+v0)*ch1/z-ch2;
-                ch2 = ch1;
-                ch1 = ch0;
-            }
-            cp11 = ch0;
-            cp21 = ch2;
-            if (lb == n)
-                cjv[lb+1] = 2.0*(lb+v0)*cjv[lb]/z-cjv[lb-1];
-            if (abs(cjv[0]) > abs(cjv[1])) {
-                cyv[lb+1] = (cjv[lb+1]*cyv0-2.0*cp11/(M_PI*z))/cjv[0];
-                cyv[lb] = (cjv[lb]*cyv0+2.0*cp12/(M_PI*z))/cjv[0];
-            }
-            else {
-                cyv[lb+1] = (cjv[lb+1]*cyv1-2.0*cp21/(M_PI*z))/cjv[1];
-                cyv[lb] = (cjv[lb]*cyv1+2.0*cp22/(M_PI*z))/cjv[1];
-            }
-            cyl2 = cyv[lb+1];
-            cyl1 = cyv[lb];
-            for (k=lb-1;k>=0;k--) {
-                cylk = 2.0*(k+v0+1.0)*cyl1/z-cyl2;
-                cyv[k] = cylk;
-                cyl2 = cyl1;
-                cyl1 = cylk;
-            }
-            cyl1 = cyv[lb];
-            cyl2 = cyv[lb+1];
-            for (k=lb+1;k<n;k++) {
-                cylk = 2.0*(k+v0)*cyl2/z-cyl1;
-                cyv[k+1] = cylk;
-                cyl1 = cyl2;
-                cyl2 = cylk;
-            }
-            for (k=2;k<=n;k++) {
-                wa = abs(cyv[k]);
-                if (wa < abs(cyv[k-1])) lb = k;
-            }
-        }
-    }
-    cyvp[0] = v0*cyv[0]/z-cyv[1];
-    for (k=1;k<=n;k++) {
-        cyvp[k] = cyv[k-1]-(k+v0)*cyv[k]/z;
-    }
-    vm = n+v0;
-    return 0;
-}
-
-
+//  cbessjy.cpp -- complex Bessel functions.
+//  Algorithms and coefficient values from "Computation of Special
+//  Functions", Zhang and Jin, John Wiley and Sons, 1996.
+//
+//  (C) 2003, C. Bond. All rights reserved.
+//
+#include <complex>
+using namespace std;
+#include "bessel.h"
+double gamma(double);
+
+static complex<double> cii(0.0,1.0);
+static complex<double> cone(1.0,0.0);
+static complex<double> czero(0.0,0.0);
+
+int cbessjy01(complex<double> z,complex<double> &cj0,complex<double> &cj1,
+              complex<double> &cy0,complex<double> &cy1,complex<double> &cj0p,
+              complex<double> &cj1p,complex<double> &cy0p,complex<double> &cy1p)
+{
+    complex<double> z1,z2,cr,cp,cs,cp0,cq0,cp1,cq1,ct1,ct2,cu;
+    double a0,w0,w1;
+    int k,kz;
+
+    static double a[] = {
+        -7.03125e-2,
+        0.112152099609375,
+        -0.5725014209747314,
+        6.074042001273483,
+        -1.100171402692467e2,
+        3.038090510922384e3,
+        -1.188384262567832e5,
+        6.252951493434797e6,
+        -4.259392165047669e8,
+        3.646840080706556e10,
+        -3.833534661393944e12,
+        4.854014686852901e14,
+        -7.286857349377656e16,
+        1.279721941975975e19
+    };
+    static double b[] = {
+        7.32421875e-2,
+        -0.2271080017089844,
+        1.727727502584457,
+        -2.438052969955606e1,
+        5.513358961220206e2,
+        -1.825775547429318e4,
+        8.328593040162893e5,
+        -5.006958953198893e7,
+        3.836255180230433e9,
+        -3.649010818849833e11,
+        4.218971570284096e13,
+        -5.827244631566907e15,
+        9.476288099260110e17,
+        -1.792162323051699e20
+    };
+    static double a1[] = {
+        0.1171875,
+        -0.1441955566406250,
+        0.6765925884246826,
+        -6.883914268109947,
+        1.215978918765359e2,
+        -3.302272294480852e3,
+        1.276412726461746e5,
+        -6.656367718817688e6,
+        4.502786003050393e8,
+        -3.833857520742790e10,
+        4.011838599133198e12,
+        -5.060568503314727e14,
+        7.572616461117958e16,
+        -1.326257285320556e19
+    };
+    static double b1[] = {
+        -0.1025390625,
+        0.2775764465332031,
+        -1.993531733751297,
+        2.724882731126854e1,
+        -6.038440767050702e2,
+        1.971837591223663e4,
+        -8.902978767070678e5,
+        5.310411010968522e7,
+        -4.043620325107754e9,
+        3.827011346598605e11,
+        -4.406481417852278e13,
+        6.065091351222699e15,
+        -9.833883876590679e17,
+        1.855045211579828e20
+    };
+
+    a0 = abs(z);
+    z2 = z*z;
+    z1 = z;
+    if (a0 == 0.0) {
+        cj0 = cone;
+        cj1 = czero;
+        cy0 = complex<double>(-1e308,0);
+        cy1 = complex<double>(-1e308,0);
+        cj0p = czero;
+        cj1p = complex<double>(0.5,0.0);
+        cy0p = complex<double>(1e308,0);
+        cy1p = complex<double>(1e308,0);
+        return 0;
+    }
+    if (real(z) < 0.0) z1 = -z;
+    if (a0 <= 12.0) {
+        cj0 = cone;
+        cr = cone;
+        for (k=1; k<=40; k++) {
+            cr *= -0.25*z2/(double)(k*k);
+            cj0 += cr;
+            if (abs(cr) < abs(cj0)*eps) break;
+        }
+        cj1 = cone;
+        cr = cone;
+        for (k=1; k<=40; k++) {
+            cr *= -0.25*z2/(k*(k+1.0));
+            cj1 += cr;
+            if (abs(cr) < abs(cj1)*eps) break;
+        }
+        cj1 *= 0.5*z1;
+        w0 = 0.0;
+        cr = cone;
+        cs = czero;
+        for (k=1; k<=40; k++) {
+            w0 += 1.0/k;
+            cr *= -0.25*z2/(double)(k*k);
+            cp = cr*w0;
+            cs += cp;
+            if (abs(cp) < abs(cs)*eps) break;
+        }
+        cy0 = M_2_PI*((log(0.5*z1)+el)*cj0-cs);
+        w1 = 0.0;
+        cr = cone;
+        cs = cone;
+        for (k=1; k<=40; k++) {
+            w1 += 1.0/k;
+            cr *= -0.25*z2/(k*(k+1.0));
+            cp = cr*(2.0*w1+1.0/(k+1.0));
+            cs += cp;
+            if (abs(cp) < abs(cs)*eps) break;
+        }
+        cy1 = M_2_PI*((log(0.5*z1)+el)*cj1-1.0/z1-0.25*z1*cs);
+    }
+    else {
+        if (a0 >= 50.0) kz = 8;         // can be changed to 10
+        else if (a0 >= 35.0) kz = 10;   //   "      "     "  12
+        else kz = 12;                   //   "      "     "  14
+        ct1 = z1 - M_PI_4;
+        cp0 = cone;
+        for (k=0; k<kz; k++) {
+            cp0 += a[k]*pow(z1,-2.0*k-2.0);
+        }
+        cq0 = -0.125/z1;
+        for (k=0; k<kz; k++) {
+            cq0 += b[k]*pow(z1,-2.0*k-3.0);
+        }
+        cu = sqrt(M_2_PI/z1);
+        cj0 = cu*(cp0*cos(ct1)-cq0*sin(ct1));
+        cy0 = cu*(cp0*sin(ct1)+cq0*cos(ct1));
+        ct2 = z1 - 0.75*M_PI;
+        cp1 = cone;
+        for (k=0; k<kz; k++) {
+            cp1 += a1[k]*pow(z1,-2.0*k-2.0);
+        }
+        cq1 = 0.375/z1;
+        for (k=0; k<kz; k++) {
+            cq1 += b1[k]*pow(z1,-2.0*k-3.0);
+        }
+        cj1 = cu*(cp1*cos(ct2)-cq1*sin(ct2));
+        cy1 = cu*(cp1*sin(ct2)+cq1*cos(ct2));
+    }
+    if (real(z) < 0.0) {
+        if (imag(z) < 0.0) {
+            cy0 -= 2.0*cii*cj0;
+            cy1 = -(cy1-2.0*cii*cj1);
+        }
+        else if (imag(z) > 0.0) {
+            cy0 += 2.0*cii*cj0;
+            cy1 = -(cy1+2.0*cii*cj1);
+        }
+        cj1 = -cj1;
+    }
+    cj0p = -cj1;
+    cj1p = cj0-cj1/z;
+    cy0p = -cy1;
+    cy1p = cy0-cy1/z;
+    return 0;
+}
+
+int cbessjyna(int n,complex<double> z,int &nm,complex<double> *cj,
+              complex<double> *cy,complex<double> *cjp,complex<double> *cyp)
+{
+    complex<double> cbj0,cbj1,cby0,cby1,cj0,cjk,cj1,cf,cf1,cf2;
+    complex<double> cs,cg0,cg1,cyk,cyl1,cyl2,cylk,cp11,cp12,cp21,cp22;
+    complex<double> ch0,ch1,ch2;
+    double a0,yak,ya1,ya0,wa;
+    int m,k,lb,lb0;
+
+    if (n < 0) return 1;
+    a0 = abs(z);
+    nm = n;
+    if (a0 < 1.0e-100) {
+        for (k=0; k<=n; k++) {
+            cj[k] = czero;
+            cy[k] = complex<double> (-1e308,0);
+            cjp[k] = czero;
+            cyp[k] = complex<double>(1e308,0);
+        }
+        cj[0] = cone;
+        cjp[1] = complex<double>(0.5,0.0);
+        return 0;
+    }
+    cbessjy01(z,cj[0],cj[1],cy[0],cy[1],cjp[0],cjp[1],cyp[0],cyp[1]);
+    cbj0 = cj[0];
+    cbj1 = cj[1];
+    cby0 = cy[0];
+    cby1 = cy[1];
+    if (n <= 1) return 0;
+    if (n < (int)0.25*a0) {
+        cj0 = cbj0;
+        cj1 = cbj1;
+        for (k=2; k<=n; k++) {
+            cjk = 2.0*(k-1.0)*cj1/z-cj0;
+            cj[k] = cjk;
+            cj0 = cj1;
+            cj1 = cjk;
+        }
+    }
+    else {
+        m = msta1(a0,200);
+        if (m < n) nm = m;
+        else m = msta2(a0,n,15);
+        cf2 = czero;
+        cf1 = complex<double> (1.0e-100,0.0);
+        for (k=m; k>=0; k--) {
+            cf = 2.0*(k+1.0)*cf1/z-cf2;
+            if (k <=nm) cj[k] = cf;
+            cf2 = cf1;
+            cf1 = cf;
+        }
+        if (abs(cbj0) > abs(cbj1)) cs = cbj0/cf;
+        else cs = cbj1/cf2;
+        for (k=0; k<=nm; k++) {
+            cj[k] *= cs;
+        }
+    }
+    for (k=2; k<=nm; k++) {
+        cjp[k] = cj[k-1]-(double)k*cj[k]/z;
+    }
+    ya0 = abs(cby0);
+    lb = 0;
+    cg0 = cby0;
+    cg1 = cby1;
+    for (k=2; k<=nm; k++) {
+        cyk = 2.0*(k-1.0)*cg1/z-cg0;
+        yak = abs(cyk);
+        ya1 = abs(cg0);
+        if ((yak < ya0) && (yak < ya1)) lb = k;
+        cy[k] = cyk;
+        cg0 = cg1;
+        cg1 = cyk;
+    }
+    lb0 = 0;
+    if ((lb > 4) && (imag(z) != 0.0)) {
+        while (lb != lb0) {
+            ch2 = cone;
+            ch1 = czero;
+            lb0 = lb;
+            for (k=lb; k>=1; k--) {
+                ch0 = 2.0*k*ch1/z-ch2;
+                ch2 = ch1;
+                ch1 = ch0;
+            }
+            cp12 = ch0;
+            cp22 = ch2;
+            ch2 = czero;
+            ch1 = cone;
+            for (k=lb; k>=1; k--) {
+                ch0 = 2.0*k*ch1/z-ch2;
+                ch2 = ch1;
+                ch1 = ch0;
+            }
+            cp11 = ch0;
+            cp21 = ch2;
+            if (lb == nm)
+                cj[lb+1] = 2.0*lb*cj[lb]/z-cj[lb-1];
+            if (abs(cj[0]) > abs(cj[1])) {
+                cy[lb+1] = (cj[lb+1]*cby0-2.0*cp11/(M_PI*z))/cj[0];
+                cy[lb] = (cj[lb]*cby0+2.0*cp12/(M_PI*z))/cj[0];
+            }
+            else {
+                cy[lb+1] = (cj[lb+1]*cby1-2.0*cp21/(M_PI*z))/cj[1];
+                cy[lb] = (cj[lb]*cby1+2.0*cp22/(M_PI*z))/cj[1];
+            }
+            cyl2 = cy[lb+1];
+            cyl1 = cy[lb];
+            for (k=lb-1; k>=0; k--) {
+                cylk = 2.0*(k+1.0)*cyl1/z-cyl2;
+                cy[k] = cylk;
+                cyl2 = cyl1;
+                cyl1 = cylk;
+            }
+            cyl1 = cy[lb];
+            cyl2 = cy[lb+1];
+            for (k=lb+1; k<n; k++) {
+                cylk = 2.0*k*cyl2/z-cyl1;
+                cy[k+1] = cylk;
+                cyl1 = cyl2;
+                cyl2 = cylk;
+            }
+            for (k=2; k<=nm; k++) {
+                wa = abs(cy[k]);
+                if (wa < abs(cy[k-1])) lb = k;
+            }
+        }
+    }
+    for (k=2; k<=nm; k++) {
+        cyp[k] = cy[k-1]-(double)k*cy[k]/z;
+    }
+    return 0;
+}
+
+int cbessjynb(int n,complex<double> z,int &nm,complex<double> *cj,
+              complex<double> *cy,complex<double> *cjp,complex<double> *cyp)
+{
+    complex<double> cf,cf0,cf1,cf2,cbs,csu,csv,cs0,ce;
+    complex<double> ct1,cp0,cq0,cp1,cq1,cu,cbj0,cby0,cbj1,cby1;
+    complex<double> cyy,cbjk,ct2;
+    double a0,y0;
+    int k,m;
+    static double a[] = {
+        -0.7031250000000000e-1,
+        0.1121520996093750,
+        -0.5725014209747314,
+        6.074042001273483
+    };
+    static double b[] = {
+        0.7324218750000000e-1,
+        -0.2271080017089844,
+        1.727727502584457,
+        -2.438052969955606e1
+    };
+    static double a1[] = {
+        0.1171875,
+        -0.1441955566406250,
+        0.6765925884246826,
+        -6.883914268109947
+    };
+    static double b1[] = {
+        -0.1025390625,
+        0.2775764465332031,
+        -1.993531733751297,
+        2.724882731126854e1
+    };
+
+    y0 = abs(imag(z));
+    a0 = abs(z);
+    nm = n;
+    if (a0 < 1.0e-100) {
+        for (k=0; k<=n; k++) {
+            cj[k] = czero;
+            cy[k] = complex<double> (-1e308,0);
+            cjp[k] = czero;
+            cyp[k] = complex<double>(1e308,0);
+        }
+        cj[0] = cone;
+        cjp[1] = complex<double>(0.5,0.0);
+        return 0;
+    }
+    if ((a0 <= 300.0) || (n > (int)(0.25*a0))) {
+        if (n == 0) nm = 1;
+        m = msta1(a0,200);
+        if (m < nm) nm = m;
+        else m = msta2(a0,nm,15);
+        cbs = czero;
+        csu = czero;
+        csv = czero;
+        cf2 = czero;
+        cf1 = complex<double> (1.0e-100,0.0);
+        for (k=m; k>=0; k--) {
+            cf = 2.0*(k+1.0)*cf1/z-cf2;
+            if (k <= nm) cj[k] = cf;
+            if (((k & 1) == 0) && (k != 0)) {
+                if (y0 <= 1.0) {
+                    cbs += 2.0*cf;
+                }
+                else {
+                    cbs += (-1)*((k & 2)-1)*2.0*cf;
+                }
+                csu += (double)((-1)*((k & 2)-1))*cf/(double)k;
+            }
+            else if (k > 1) {
+                csv += (double)((-1)*((k & 2)-1)*k)*cf/(double)(k*k-1.0);
+            }
+            cf2 = cf1;
+            cf1 = cf;
+        }
+        if (y0 <= 1.0) cs0 = cbs+cf;
+        else cs0 = (cbs+cf)/cos(z);
+        for (k=0; k<=nm; k++) {
+            cj[k] /= cs0;
+        }
+        ce = log(0.5*z)+el;
+        cy[0] = M_2_PI*(ce*cj[0]-4.0*csu/cs0);
+        cy[1] = M_2_PI*(-cj[0]/z+(ce-1.0)*cj[1]-4.0*csv/cs0);
+    }
+    else {
+        ct1 = z-M_PI_4;
+        cp0 = cone;
+        for (k=0; k<4; k++) {
+            cp0 += a[k]*pow(z,-2.0*k-2.0);
+        }
+        cq0 = -0.125/z;
+        for (k=0; k<4; k++) {
+            cq0 += b[k] *pow(z,-2.0*k-3.0);
+        }
+        cu = sqrt(M_2_PI/z);
+        cbj0 = cu*(cp0*cos(ct1)-cq0*sin(ct1));
+        cby0 = cu*(cp0*sin(ct1)+cq0*cos(ct1));
+        cj[0] = cbj0;
+        cy[0] = cby0;
+        ct2 = z-0.75*M_PI;
+        cp1 = cone;
+        for (k=0; k<4; k++) {
+            cp1 += a1[k]*pow(z,-2.0*k-2.0);
+        }
+        cq1 = 0.375/z;
+        for (k=0; k<4; k++) {
+            cq1 += b1[k]*pow(z,-2.0*k-3.0);
+        }
+        cbj1 = cu*(cp1*cos(ct2)-cq1*sin(ct2));
+        cby1 = cu*(cp1*sin(ct2)+cq1*cos(ct2));
+        cj[1] = cbj1;
+        cy[1] = cby1;
+        for (k=2; k<=n; k++) {
+            cbjk = 2.0*(k-1.0)*cbj1/z-cbj0;
+            cj[k] = cbjk;
+            cbj0 = cbj1;
+            cbj1 = cbjk;
+        }
+    }
+    cjp[0] = -cj[1];
+    for (k=1; k<=nm; k++) {
+        cjp[k] = cj[k-1]-(double)k*cj[k]/z;
+    }
+    if (abs(cj[0]) > 1.0)
+        cy[1] = (cj[1]*cy[0]-2.0/(M_PI*z))/cj[0];
+    for (k=2; k<=nm; k++) {
+        if (abs(cj[k-1]) >= abs(cj[k-2]))
+            cyy = (cj[k]*cy[k-1]-2.0/(M_PI*z))/cj[k-1];
+        else
+            cyy = (cj[k]*cy[k-2]-4.0*(k-1.0)/(M_PI*z*z))/cj[k-2];
+        cy[k] = cyy;
+    }
+    cyp[0] = -cy[1];
+    for (k=1; k<=nm; k++) {
+        cyp[k] = cy[k-1]-(double)k*cy[k]/z;
+    }
+
+    return 0;
+}
+
+int cbessjyva(double v,complex<double> z,double &vm,complex<double>*cjv,
+              complex<double>*cyv,complex<double>*cjvp,complex<double>*cyvp)
+{
+    complex<double> z1,z2,zk,cjvl,cr,ca,cjv0,cjv1,cpz,crp;
+    complex<double> cqz,crq,ca0,cck,csk,cyv0,cyv1,cju0,cju1,cb;
+    complex<double> cs,cs0,cr0,cs1,cr1,cec,cf,cf0,cf1,cf2;
+    complex<double> cfac0,cfac1,cg0,cg1,cyk,cp11,cp12,cp21,cp22;
+    complex<double> ch0,ch1,ch2,cyl1,cyl2,cylk;
+
+    double a0,v0,pv0,pv1,vl,ga,gb,vg,vv,w0,w1,ya0,yak,ya1,wa;
+    int j,n,k,kz,l,lb,lb0,m;
+
+    a0 = abs(z);
+    z1 = z;
+    z2 = z*z;
+    n = (int)v;
+
+
+    v0 = v-n;
+
+    pv0 = M_PI*v0;
+    pv1 = M_PI*(1.0+v0);
+    if (a0 < 1.0e-100) {
+        for (k=0; k<=n; k++) {
+            cjv[k] = czero;
+            cyv[k] = complex<double> (-1e308,0);
+            cjvp[k] = czero;
+            cyvp[k] = complex<double> (1e308,0);
+
+        }
+        if (v0 == 0.0) {
+            cjv[0] = cone;
+            cjvp[1] = complex<double> (0.5,0.0);
+        }
+        else {
+            cjvp[0] = complex<double> (1e308,0);
+        }
+        vm = v;
+        return 0;
+    }
+    if (real(z1) < 0.0) z1 = -z;
+    if (a0 <= 12.0) {
+        for (l=0; l<2; l++) {
+            vl = v0+l;
+            cjvl = cone;
+            cr = cone;
+            for (k=1; k<=40; k++) {
+                cr *= -0.25*z2/(k*(k+vl));
+                cjvl += cr;
+                if (abs(cr) < abs(cjvl)*eps) break;
+            }
+            vg = 1.0 + vl;
+            ga = gamma(vg);
+            ca = pow(0.5*z1,vl)/ga;
+            if (l == 0) cjv0 = cjvl*ca;
+            else cjv1 = cjvl*ca;
+        }
+    }
+    else {
+        if (a0 >= 50.0) kz = 8;
+        else if (a0 >= 35.0) kz = 10;
+        else kz = 11;
+        for (j=0; j<2; j++) {
+            vv = 4.0*(j+v0)*(j+v0);
+            cpz = cone;
+            crp = cone;
+            for (k=1; k<=kz; k++) {
+                crp = -0.78125e-2*crp*(vv-pow(4.0*k-3.0,2.0))*
+                      (vv-pow(4.0*k-1.0,2.0))/(k*(2.0*k-1.0)*z2);
+                cpz += crp;
+            }
+            cqz = cone;
+            crq = cone;
+            for (k=1; k<=kz; k++) {
+                crq = -0.78125e-2*crq*(vv-pow(4.0*k-1.0,2.0))*
+                      (vv-pow(4.0*k+1.0,2.0))/(k*(2.0*k+1.0)*z2);
+                cqz += crq;
+            }
+            cqz *= 0.125*(vv-1.0)/z1;
+            zk = z1-(0.5*(j+v0)+0.25)*M_PI;
+            ca0 = sqrt(M_2_PI/z1);
+            cck = cos(zk);
+            csk = sin(zk);
+            if (j == 0) {
+                cjv0 = ca0*(cpz*cck-cqz*csk);
+                cyv0 = ca0*(cpz*csk+cqz+cck);
+            }
+            else {
+                cjv1 = ca0*(cpz*cck-cqz*csk);
+                cyv1 = ca0*(cpz*csk+cqz*cck);
+            }
+        }
+    }
+    if (a0 <= 12.0) {
+        if (v0 != 0.0) {
+            for (l=0; l<2; l++) {
+                vl = v0+l;
+                cjvl = cone;
+                cr = cone;
+                for (k=1; k<=40; k++) {
+                    cr *= -0.25*z2/(k*(k-vl));
+                    cjvl += cr;
+                    if (abs(cr) < abs(cjvl)*eps) break;
+                }
+                vg = 1.0-vl;
+                gb = gamma(vg);
+                cb = pow(2.0/z1,vl)/gb;
+                if (l == 0) cju0 = cjvl*cb;
+                else cju1 = cjvl*cb;
+            }
+            cyv0 = (cjv0*cos(pv0)-cju0)/sin(pv0);
+            cyv1 = (cjv1*cos(pv1)-cju1)/sin(pv1);
+        }
+        else {
+            cec = log(0.5*z1)+el;
+            cs0 = czero;
+            w0 = 0.0;
+            cr0 = cone;
+            for (k=1; k<=30; k++) {
+                w0 += 1.0/k;
+                cr0 *= -0.25*z2/(double)(k*k);
+                cs0 += cr0*w0;
+            }
+            cyv0 = M_2_PI*(cec*cjv0-cs0);
+            cs1 = cone;
+            w1 = 0.0;
+            cr1 = cone;
+            for (k=1; k<=30; k++) {
+                w1 += 1.0/k;
+                cr1 *= -0.25*z2/(k*(k+1.0));
+                cs1 += cr1*(2.0*w1+1.0/(k+1.0));
+            }
+            cyv1 = M_2_PI*(cec*cjv1-1.0/z1-0.25*z1*cs1);
+        }
+    }
+    if (real(z) < 0.0) {
+        cfac0 = exp(pv0*cii);
+        cfac1 = exp(pv1*cii);
+        if (imag(z) < 0.0) {
+            cyv0 = cfac0*cyv0-2.0*cii*cos(pv0)*cjv0;
+            cyv1 = cfac1*cyv1-2.0*cii*cos(pv1)*cjv1;
+            cjv0 /= cfac0;
+            cjv1 /= cfac1;
+        }
+        else if (imag(z) > 0.0) {
+            cyv0 = cyv0/cfac0+2.0*cii*cos(pv0)*cjv0;
+            cyv1 = cyv1/cfac1+2.0*cii*cos(pv1)*cjv1;
+            cjv0 *= cfac0;
+            cjv1 *= cfac1;
+        }
+    }
+    cjv[0] = cjv0;
+    cjv[1] = cjv1;
+    if ((n >= 2) && (n <= (int)(0.25*a0))) {
+        cf0 = cjv0;
+        cf1 = cjv1;
+        for (k=2; k<= n; k++) {
+            cf = 2.0*(k+v0-1.0)*cf1/z-cf0;
+            cjv[k] = cf;
+            cf0 = cf1;
+            cf1 = cf;
+        }
+    }
+    else if (n >= 2) {
+        m = msta1(a0,200);
+        if (m < n) n = m;
+        else  m = msta2(a0,n,15);
+        cf2 = czero;
+        cf1 = complex<double>(1.0e-100,0.0);
+        for (k=m; k>=0; k--) {
+            cf = 2.0*(v0+k+1.0)*cf1/z-cf2;
+            if (k <= n) cjv[k] = cf;
+            cf2 = cf1;
+            cf1 = cf;
+        }
+        if (abs(cjv0) > abs(cjv1)) cs = cjv0/cf;
+        else cs = cjv1/cf2;
+        for (k=0; k<=n; k++) {
+            cjv[k] *= cs;
+        }
+    }
+    cjvp[0] = v0*cjv[0]/z-cjv[1];
+    for (k=1; k<=n; k++) {
+        cjvp[k] = -(k+v0)*cjv[k]/z+cjv[k-1];
+    }
+    cyv[0] = cyv0;
+    cyv[1] = cyv1;
+    ya0 = abs(cyv0);
+    lb = 0;
+    cg0 = cyv0;
+    cg1 = cyv1;
+    for (k=2; k<=n; k++) {
+        cyk = 2.0*(v0+k-1.0)*cg1/z-cg0;
+        yak = abs(cyk);
+        ya1 = abs(cg0);
+        if ((yak < ya0) && (yak< ya1)) lb = k;
+        cyv[k] = cyk;
+        cg0 = cg1;
+        cg1 = cyk;
+    }
+    lb0 = 0;
+    if ((lb > 4) && (imag(z) != 0.0)) {
+        while(lb != lb0) {
+            ch2 = cone;
+            ch1 = czero;
+            lb0 = lb;
+            for (k=lb; k>=1; k--) {
+                ch0 = 2.0*(k+v0)*ch1/z-ch2;
+                ch2 = ch1;
+                ch1 = ch0;
+            }
+            cp12 = ch0;
+            cp22 = ch2;
+            ch2 = czero;
+            ch1 = cone;
+            for (k=lb; k>=1; k--) {
+                ch0 = 2.0*(k+v0)*ch1/z-ch2;
+                ch2 = ch1;
+                ch1 = ch0;
+            }
+            cp11 = ch0;
+            cp21 = ch2;
+            if (lb == n)
+                cjv[lb+1] = 2.0*(lb+v0)*cjv[lb]/z-cjv[lb-1];
+            if (abs(cjv[0]) > abs(cjv[1])) {
+                cyv[lb+1] = (cjv[lb+1]*cyv0-2.0*cp11/(M_PI*z))/cjv[0];
+                cyv[lb] = (cjv[lb]*cyv0+2.0*cp12/(M_PI*z))/cjv[0];
+            }
+            else {
+                cyv[lb+1] = (cjv[lb+1]*cyv1-2.0*cp21/(M_PI*z))/cjv[1];
+                cyv[lb] = (cjv[lb]*cyv1+2.0*cp22/(M_PI*z))/cjv[1];
+            }
+            cyl2 = cyv[lb+1];
+            cyl1 = cyv[lb];
+            for (k=lb-1; k>=0; k--) {
+                cylk = 2.0*(k+v0+1.0)*cyl1/z-cyl2;
+                cyv[k] = cylk;
+                cyl2 = cyl1;
+                cyl1 = cylk;
+            }
+            cyl1 = cyv[lb];
+            cyl2 = cyv[lb+1];
+            for (k=lb+1; k<n; k++) {
+                cylk = 2.0*(k+v0)*cyl2/z-cyl1;
+                cyv[k+1] = cylk;
+                cyl1 = cyl2;
+                cyl2 = cylk;
+            }
+            for (k=2; k<=n; k++) {
+                wa = abs(cyv[k]);
+                if (wa < abs(cyv[k-1])) lb = k;
+            }
+        }
+    }
+    cyvp[0] = v0*cyv[0]/z-cyv[1];
+    for (k=1; k<=n; k++) {
+        cyvp[k] = cyv[k-1]-(k+v0)*cyv[k]/z;
+    }
+    vm = n+v0;
+    return 0;
+}
+
+
-__device__ double g(double v0, double v1)
-{
-	return (v0 + v1)*log(abs(v0+v1)) + (v0-v1)*log(abs(v0-v1));
-}
-
-__device__ double hfin(double v0, double v1, double dv)
-{
-	double e = 0.001;
-	double t0 = g(v0+e, v1-dv)/dv;
-	double t1 = 2*g(v0+e, v1)/dv;
-	double t2 = g(v0+e, v1+dv)/dv;
-
-	return -1.0/PI * (t0 - t1 + t2);
-}
-
-__global__ void devKramersKronig(double* gpuN, double* gpuK, int numVals, double nuStart, double nuEnd, double nOffset)
-{
-	int i = blockIdx.x * blockDim.x + threadIdx.x;
-
-	if(i >= numVals) return;
-	double nuDelta = (nuEnd - nuStart)/(numVals - 1);
-
-	double nu = nuStart + i*nuDelta;
-	double n = 0.0;
-	double jNu;
-	double jK;
-	for(int j=1; j<numVals-1; j++)
-	{
-		jNu = nuStart + j*nuDelta;
-		jK = gpuK[j];
-		n += hfin(nu, jNu, nuDelta) * jK;
-	}
-	gpuN[i] = n + nOffset;
-
-
-}
-
-void cudaKramersKronig(double* cpuN, double* cpuK, int nVals, double nuStart, double nuEnd, double nOffset)
-{
-	double* gpuK;
-	HANDLE_ERROR(cudaMalloc(&gpuK, sizeof(double)*nVals));
-	HANDLE_ERROR(cudaMemcpy(gpuK, cpuK, sizeof(double)*nVals, cudaMemcpyHostToDevice));
-	double* gpuN;
-	HANDLE_ERROR(cudaMalloc(&gpuN, sizeof(double)*nVals));
-
-	dim3 block(BLOCK_SIZE*BLOCK_SIZE);
-	dim3 grid(nVals/block.x + 1);
-	devKramersKronig<<<grid, block>>>(gpuN, gpuK, nVals, nuStart, nuEnd, nOffset);
-
-	HANDLE_ERROR(cudaMemcpy(cpuN, gpuN, sizeof(double)*nVals, cudaMemcpyDeviceToHost));
-
-	//free resources
-	HANDLE_ERROR(cudaFree(gpuK));
-	HANDLE_ERROR(cudaFree(gpuN));
-}
-
-__global__ void devComputeSpectrum(double* I, double2* B, double* alpha, int Nl,
-								   int nSamples, int nLambda, double oThetaI, double oThetaO, double cThetaI, double cThetaO)
-{
-	int i = blockIdx.x * blockDim.x + threadIdx.x;
-	if(i >= nLambda)
-        return;
-
-	//compute the delta-theta value
-	double dTheta = (oThetaO - oThetaI)/nSamples;
-
-	//allocate space for the Legendre polynomials
-	double Ptheta[2];
-
-	double cosTheta, theta;
-	cuDoubleComplex Us;
-	cuDoubleComplex UsSample;
-	cuDoubleComplex U;
-	//cuComplex Ui;
-	//Ui.x = 2*PI;
-	//Ui.y = 0.0;
-	cuDoubleComplex numer;
-	numer.x = 0.0;
-	cuDoubleComplex exp_numer;
-	cuDoubleComplex iL;
-	cuDoubleComplex imag;
-	imag.x = 0.0; imag.y = 1.0;
-	double realFac;
-	cuDoubleComplex complexFac;
-	double PlTheta;
-	double Isum = 0.0;
-	//float maxVal = 0;
-	//float val;
-	for(int iTheta = 0; iTheta < nSamples; iTheta++)
-	{
-		//calculate theta
-		theta = iTheta * dTheta + oThetaI;
-		cosTheta = cos(theta);
-
-		//initialize the theta Legendre polynomial
-		Ptheta[0] = 1.0;
-		Ptheta[1] = cosTheta;
-
-		//initialize the scattered field
-		Us.x = Us.y = 0.0;
-		iL.x = 1.0;
-		iL.y = 0.0;
-		for(int l = 0; l<Nl; l++)
-		{
-			//compute the theta legendre polynomial
-			if(l == 0)
-				PlTheta = Ptheta[0];
-			else if(l == 1)
-				PlTheta = Ptheta[1];
-			else
-			{
-				PlTheta = ((2*l - 1)*cosTheta*Ptheta[1] - (l - 1)*Ptheta[0])/l;
-				Ptheta[0] = Ptheta[1];
-				Ptheta[1] = PlTheta;
-			}
-
-			//compute the real components of the scattered field
-			realFac = alpha[l] * PlTheta;
-
-			//compute the complex components of the scattered field
-			numer.x = 0.0;
-			numer.y = -(l*PI)/2.0;
-			exp_numer = cExp(numer);
-
-			complexFac = cMult(B[Nl * i + l], exp_numer);
-			complexFac = cMult(complexFac, iL);
-
-
-			//combine the real and complex components
-			UsSample = cMult(complexFac, realFac);
-			Us = cAdd(Us, UsSample);
-
-			//increment the imaginary exponent i^l
-			iL = cMult(iL, imag);
-
-
-		}
-
-		//sum the scattered and incident fields
-		if(theta >= cThetaI && theta <= cThetaO)
-			U = cAdd(Us, 2*PI);
-		else
-			U = Us;
-		Isum += (U.x*U.x + U.y*U.y) * sin(theta) * 2 * PI * dTheta;
-	}
-
-	I[i] = Isum;
-}
-
-void cudaComputeSpectrum(double* cpuI, double* cpuB, double* cpuAlpha,
-						 int Nl, int nLambda, double oThetaI, double oThetaO, double cThetaI, double cThetaO, int nSamples)
-{
-	//copy everything to the GPU
-	double2* gpuB;
-	HANDLE_ERROR(cudaMalloc(&gpuB, sizeof(double2) * nLambda * Nl));
-	HANDLE_ERROR(cudaMemcpy(gpuB, cpuB, sizeof(double2) * nLambda * Nl, cudaMemcpyHostToDevice));
-
-
-	double* gpuAlpha;
-	HANDLE_ERROR(cudaMalloc(&gpuAlpha, sizeof(double) * Nl));
-	HANDLE_ERROR(cudaMemcpy(gpuAlpha, cpuAlpha, sizeof(double) * Nl, cudaMemcpyHostToDevice));
-
-	double* gpuI;
-	HANDLE_ERROR(cudaMalloc(&gpuI, sizeof(double) * nLambda));
-	HANDLE_ERROR(cudaMemset(gpuI, 0, sizeof(double) * nLambda));
-
-
-	//call the kernel to compute the spectrum
-	dim3 block(BLOCK_SIZE*BLOCK_SIZE);
-	dim3 grid(nLambda/block.x + 1);
-
-	//devComputeSpectrum
-	devComputeSpectrum<<<grid, block>>>(gpuI, (double2*)gpuB, gpuAlpha, Nl,
-										nSamples, nLambda, oThetaI, oThetaO, cThetaI, cThetaO);
-
-	HANDLE_ERROR(cudaMemcpy(cpuI, gpuI, sizeof(double) * nLambda, cudaMemcpyDeviceToHost));
-
-	//printf("Final array value: %f\n", cpuI[nLambda-1]);
-
-	HANDLE_ERROR(cudaFree(gpuB));
-	HANDLE_ERROR(cudaFree(gpuAlpha));
-	HANDLE_ERROR(cudaFree(gpuI));
-
-
-
-
+#include <iostream>
+using namespace std;
+
+__device__ double g(double v0, double v1)
+{
+    return (v0 + v1)*log(abs(v0+v1)) + (v0-v1)*log(abs(v0-v1));
+}
+
+__device__ double hfin(double v0, double v1, double dv)
+{
+    double e = 0.001;
+    double t0 = g(v0+e, v1-dv)/dv;
+    double t1 = 2*g(v0+e, v1)/dv;
+    double t2 = g(v0+e, v1+dv)/dv;
+
+    return -1.0/PI * (t0 - t1 + t2);
+}
+
+__global__ void devKramersKronig(double* gpuN, double* gpuK, int numVals, double nuStart, double nuEnd, double nOffset)
+{
+    int i = blockIdx.x * blockDim.x + threadIdx.x;
+
+    if(i >= numVals) return;
+    double nuDelta = (nuEnd - nuStart)/(numVals - 1);
+
+    double nu = nuStart + i*nuDelta;
+    double n = 0.0;
+    double jNu;
+    double jK;
+    for(int j=1; j<numVals-1; j++)
+    {
+        jNu = nuStart + j*nuDelta;
+        jK = gpuK[j];
+        n += hfin(nu, jNu, nuDelta) * jK;
+    }
+    gpuN[i] = n + nOffset;
+
+
+}
+
+void cudaKramersKronig(double* cpuN, double* cpuK, int nVals, double nuStart, double nuEnd, double nOffset)
+{
+    cout<<"Computing Kramers Kronig."<<endl;
+    //This function computes n given k
+
+    double* gpuK;
+    HANDLE_ERROR(cudaMalloc(&gpuK, sizeof(double)*nVals));
+    HANDLE_ERROR(cudaMemcpy(gpuK, cpuK, sizeof(double)*nVals, cudaMemcpyHostToDevice));
+    double* gpuN;
+    HANDLE_ERROR(cudaMalloc(&gpuN, sizeof(double)*nVals));
+
+    dim3 block(BLOCK_SIZE*BLOCK_SIZE);
+    dim3 grid(nVals/block.x + 1);
+    devKramersKronig<<<grid, block>>>(gpuN, gpuK, nVals, nuStart, nuEnd, nOffset);
+
+    HANDLE_ERROR(cudaMemcpy(cpuN, gpuN, sizeof(double)*nVals, cudaMemcpyDeviceToHost));
+
+    //free resources
+    HANDLE_ERROR(cudaFree(gpuK));
+    HANDLE_ERROR(cudaFree(gpuN));
+}
+
+__global__ void devComputeSpectrum(double* I, double2* B, double* alpha, int Nl,
+                                   int nSamples, int nLambda, double oThetaI, double oThetaO, double cThetaI, double cThetaO)
+{
+    int i = blockIdx.x * blockDim.x + threadIdx.x;
+    if(i >= nLambda)
+        return;
+
+    //compute the delta-theta value
+    double dTheta = (oThetaO - oThetaI)/nSamples;
+
+    //allocate space for the Legendre polynomials
+    double Ptheta[2];
+
+    double cosTheta, theta;
+    cuDoubleComplex Us;
+    cuDoubleComplex UsSample;
+    cuDoubleComplex U;
+    //cuComplex Ui;
+    //Ui.x = 2*PI;
+    //Ui.y = 0.0;
+    cuDoubleComplex numer;
+    numer.x = 0.0;
+    cuDoubleComplex exp_numer;
+    cuDoubleComplex iL;
+    cuDoubleComplex imag;
+    imag.x = 0.0;
+    imag.y = 1.0;
+    double realFac;
+    cuDoubleComplex complexFac;
+    double PlTheta;
+    double Isum = 0.0;
+    //float maxVal = 0;
+    //float val;
+    for(int iTheta = 0; iTheta < nSamples; iTheta++)
+    {
+        //calculate theta
+        theta = iTheta * dTheta + oThetaI;
+        cosTheta = cos(theta);
+
+        //initialize the theta Legendre polynomial
+        Ptheta[0] = 1.0;
+        Ptheta[1] = cosTheta;
+
+        //initialize the scattered field
+        Us.x = Us.y = 0.0;
+        iL.x = 1.0;
+        iL.y = 0.0;
+        for(int l = 0; l<Nl; l++)
+        {
+            //compute the theta legendre polynomial
+            if(l == 0)
+                PlTheta = Ptheta[0];
+            else if(l == 1)
+                PlTheta = Ptheta[1];
+            else
+            {
+                PlTheta = ((2*l - 1)*cosTheta*Ptheta[1] - (l - 1)*Ptheta[0])/l;
+                Ptheta[0] = Ptheta[1];
+                Ptheta[1] = PlTheta;
+            }
+
+            //compute the real components of the scattered field
+            realFac = alpha[l] * PlTheta;
+
+            //compute the complex components of the scattered field
+            numer.x = 0.0;
+            numer.y = -(l*PI)/2.0;
+            exp_numer = cExp(numer);
+
+            complexFac = cMult(B[Nl * i + l], exp_numer);
+            complexFac = cMult(complexFac, iL);
+
+
+            //combine the real and complex components
+            UsSample = cMult(complexFac, realFac);
+            Us = cAdd(Us, UsSample);
+
+            //increment the imaginary exponent i^l
+            iL = cMult(iL, imag);
+
+
+        }
+
+        //sum the scattered and incident fields
+        if(theta >= cThetaI && theta <= cThetaO)
+            U = cAdd(Us, 2*PI);
+        else
+            U = Us;
+        Isum += (U.x*U.x + U.y*U.y) * sin(theta) * 2 * PI * dTheta;
+    }
+
+    I[i] = Isum;
+}
+
+void cudaComputeSpectrum(double* cpuI, double* cpuB, double* cpuAlpha,
+                         int Nl, int nLambda, double oThetaI, double oThetaO, double cThetaI, double cThetaO, int nSamples)
+{
+    //copy everything to the GPU
+    double2* gpuB;
+    HANDLE_ERROR(cudaMalloc(&gpuB, sizeof(double2) * nLambda * Nl));
+    HANDLE_ERROR(cudaMemcpy(gpuB, cpuB, sizeof(double2) * nLambda * Nl, cudaMemcpyHostToDevice));
+
+
+    double* gpuAlpha;
+    HANDLE_ERROR(cudaMalloc(&gpuAlpha, sizeof(double) * Nl));
+    HANDLE_ERROR(cudaMemcpy(gpuAlpha, cpuAlpha, sizeof(double) * Nl, cudaMemcpyHostToDevice));
+
+    double* gpuI;
+    HANDLE_ERROR(cudaMalloc(&gpuI, sizeof(double) * nLambda));
+    HANDLE_ERROR(cudaMemset(gpuI, 0, sizeof(double) * nLambda));
+
+
+    //call the kernel to compute the spectrum
+    dim3 block(BLOCK_SIZE*BLOCK_SIZE);
+    dim3 grid(nLambda/block.x + 1);
+
+    //devComputeSpectrum
+    devComputeSpectrum<<<grid, block>>>(gpuI, (double2*)gpuB, gpuAlpha, Nl,
+                                        nSamples, nLambda, oThetaI, oThetaO, cThetaI, cThetaO);
+
+    HANDLE_ERROR(cudaMemcpy(cpuI, gpuI, sizeof(double) * nLambda, cudaMemcpyDeviceToHost));
+
+    //printf("Final array value: %f\n", cpuI[nLambda-1]);
+
+    HANDLE_ERROR(cudaFree(gpuB));
+    HANDLE_ERROR(cudaFree(gpuAlpha));
+    HANDLE_ERROR(cudaFree(gpuI));
+
+
+
+
 }
-#include "cuComplex.h"
-#include "cudaHandleError.h"
-
-
-#define PI 3.14159
-#define BLOCK_SIZE 16
-
-__device__ cuDoubleComplex cMult(cuDoubleComplex a, cuDoubleComplex b)
-{
-	cuDoubleComplex result;
-	result.x = a.x * b.x - a.y * b.y;
-	result.y = a.x * b.y + a.y * b.x;
-
-	return result;
-}
-
-__device__ cuDoubleComplex cMult(cuDoubleComplex a, float b)
-{
-	cuDoubleComplex result;
-	result.x = a.x * b;
-	result.y = a.y * b;
-
-	return result;
-}
-
-__device__ cuDoubleComplex cAdd(cuDoubleComplex a, cuDoubleComplex b)
-{
-	cuDoubleComplex r;
-	r.x = a.x + b.x;
-	r.y = a.y + b.y;
-
-	return r;
-}
-
-__device__ cuDoubleComplex cAdd(cuDoubleComplex a, float b)
-{
-	cuDoubleComplex r;
-	r.x = a.x + b;
-	r.y = a.y;
-
-	return r;
-}
-
-__device__ cuDoubleComplex cExp(cuDoubleComplex a)
-{
-	cuDoubleComplex r;
-
-	r.x = exp(a.x) * cos(a.y);
-	r.y = exp(a.x) * sin(a.y);
-
-	return r;
-}
-
-__device__ double cMag(cuDoubleComplex a)
-{
-	double r = sqrt(a.x * a.x + a.y * a.y);
-	return r;
-}
-
-#include "cudaKK.h"
-
+#include "cuComplex.h"
+#include "cudaHandleError.h"
+
+
+#define PI 3.14159
+#define BLOCK_SIZE 16
+
+__device__ cuDoubleComplex cMult(cuDoubleComplex a, cuDoubleComplex b)
+{
+    cuDoubleComplex result;
+    result.x = a.x * b.x - a.y * b.y;
+    result.y = a.x * b.y + a.y * b.x;
+
+    return result;
+}
+
+__device__ cuDoubleComplex cMult(cuDoubleComplex a, float b)
+{
+    cuDoubleComplex result;
+    result.x = a.x * b;
+    result.y = a.y * b;
+
+    return result;
+}
+
+__device__ cuDoubleComplex cAdd(cuDoubleComplex a, cuDoubleComplex b)
+{
+    cuDoubleComplex r;
+    r.x = a.x + b.x;
+    r.y = a.y + b.y;
+
+    return r;
+}
+
+__device__ cuDoubleComplex cAdd(cuDoubleComplex a, float b)
+{
+    cuDoubleComplex r;
+    r.x = a.x + b;
+    r.y = a.y;
+
+    return r;
+}
+
+__device__ cuDoubleComplex cExp(cuDoubleComplex a)
+{
+    cuDoubleComplex r;
+
+    r.x = exp(a.x) * cos(a.y);
+    r.y = exp(a.x) * sin(a.y);
+
+    return r;
+}
+
+__device__ double cMag(cuDoubleComplex a)
+{
+    double r = sqrt(a.x * a.x + a.y * a.y);
+    return r;
+}
+
+#include "cudaKK.h"
+
+nu	n	k
+800	1.441201025	0.002370971
+802	1.442449524	0.002279499
+804	1.443622415	0.002218164
+806	1.444731575	0.00217471
+808	1.445769313	0.002154818
+810	1.446735153	0.002133884
+812	1.447631537	0.002093632
+814	1.448499976	0.002020828
+816	1.449371594	0.001935851
+818	1.450245111	0.001882509
+820	1.451098381	0.001845384
+822	1.451931801	0.001835367
+824	1.452743077	0.001859742
+826	1.453538627	0.001906472
+828	1.454316144	0.001993264
+830	1.455057831	0.002134999
+832	1.455752574	0.002332258
+834	1.456373935	0.00257594
+836	1.45689904	0.00287502
+838	1.457307689	0.003187541
+840	1.457541056	0.00349171
+842	1.457622779	0.003661082
+844	1.45763705	0.003626834
+846	1.457709742	0.003400597
+848	1.457929984	0.003056081
+850	1.458311946	0.002701293
+852	1.458792141	0.002396757
+854	1.459332546	0.002178644
+856	1.459889834	0.002030216
+858	1.460439885	0.001936861
+860	1.460982928	0.001877498
+862	1.461517236	0.00185772
+864	1.462038725	0.001889109
+866	1.462531922	0.001950935
+868	1.462978568	0.00204692
+870	1.463376438	0.002155221
+872	1.463691463	0.002260164
+874	1.463946436	0.002246045
+876	1.46431344	0.002102302
+878	1.464835949	0.001997437
+880	1.465438552	0.001992183
+882	1.46608463	0.002084809
+884	1.466770232	0.002282701
+886	1.467508982	0.002620306
+888	1.468317634	0.00319353
+890	1.469128024	0.004219724
+892	1.46954514	0.006023859
+894	1.468393318	0.00840405
+896	1.465223625	0.009006755
+898	1.463241024	0.006966132
+900	1.463248052	0.004995548
+902	1.463894773	0.003838499
+904	1.464602858	0.003205237
+906	1.465241891	0.00285555
+908	1.465786159	0.002664765
+910	1.466248706	0.002546277
+912	1.466651178	0.002453415
+914	1.467032669	0.002364593
+916	1.467407655	0.002292823
+918	1.46779669	0.00223036
+920	1.468201898	0.002212279
+922	1.468611417	0.002242387
+924	1.469017595	0.002350077
+926	1.469359926	0.002567263
+928	1.469513165	0.00284644
+930	1.469451982	0.00294228
+932	1.469507737	0.002759167
+934	1.469802525	0.00258731
+936	1.47016397	0.002557196
+938	1.470505278	0.002621533
+940	1.470798022	0.002738964
+942	1.471029562	0.002875389
+944	1.471215597	0.002997329
+946	1.471371939	0.003096987
+948	1.471520088	0.003166052
+950	1.471676729	0.003204709
+952	1.471870413	0.003234913
+954	1.472084483	0.003296926
+956	1.472297379	0.003385829
+958	1.472502688	0.003503316
+960	1.472670115	0.003659948
+962	1.472776059	0.00382798
+964	1.472810962	0.003950488
+966	1.472833778	0.003999093
+968	1.472885211	0.003977479
+970	1.473006806	0.003933385
+972	1.473183366	0.003915274
+974	1.473380818	0.003937115
+976	1.473579696	0.004020582
+978	1.47371821	0.004148016
+980	1.473755273	0.004260284
+982	1.473742435	0.004243433
+984	1.473813229	0.004119949
+986	1.473984876	0.003998672
+988	1.474206293	0.003886511
+990	1.474481309	0.003799505
+992	1.474815078	0.00373978
+994	1.475182296	0.003738812
+996	1.475570232	0.003799565
+998	1.475963266	0.003936431
+1000	1.476300807	0.004184267
+1002	1.476368232	0.004483668
+1004	1.476369967	0.004213951
+1006	1.476895249	0.004008063
+1008	1.477500322	0.003959639
+1010	1.478191588	0.003995866
+1012	1.478975059	0.004124533
+1014	1.479861671	0.004356501
+1016	1.480895138	0.004708233
+1018	1.482142712	0.005256522
+1020	1.48362439	0.006200346
+1022	1.48502768	0.007610747
+1024	1.48723564	0.009048626
+1026	1.490922897	0.012842061
+1028	1.49396376	0.023205465
+1030	1.478739354	0.040107032
+1032	1.461784885	0.023766251
+1034	1.466147284	0.015090077
+1036	1.469449728	0.01362093
+1038	1.470761398	0.01407228
+1040	1.470518602	0.014852004
+1042	1.469251081	0.015041876
+1044	1.467778886	0.01427413
+1046	1.466770622	0.01279836
+1048	1.466441044	0.011102025
+1050	1.466660858	0.009538868
+1052	1.467249956	0.008235735
+1054	1.46804819	0.007220159
+1056	1.468976816	0.006471992
+1058	1.469955855	0.005954506
+1060	1.470985909	0.00562082
+1062	1.472067145	0.005471556
+1064	1.47321735	0.005511631
+1066	1.474451756	0.005773786
+1068	1.475791945	0.006332171
+1070	1.477216814	0.007315265
+1072	1.478635789	0.008889418
+1074	1.479890364	0.011193667
+1076	1.480860176	0.014562718
+1078	1.480694748	0.019882054
+1080	1.476167315	0.027210144
+1082	1.463907719	0.0294764
+1084	1.455702239	0.02070909
+1086	1.455979715	0.012765529
+1088	1.458369419	0.008540043
+1090	1.460662356	0.006355266
+1092	1.462558732	0.005181408
+1094	1.464110518	0.00455405
+1096	1.465407938	0.00426269
+1098	1.466512044	0.004235102
+1100	1.46743002	0.00446506
+1102	1.468108911	0.004966537
+1104	1.468358263	0.005807079
+1106	1.467623162	0.006667401
+1108	1.466185738	0.006247327
+1110	1.465723585	0.004799082
+1112	1.466149203	0.003611219
+1114	1.466844726	0.002879426
+1116	1.467543668	0.002461487
+1118	1.468167662	0.002227789
+1120	1.468718605	0.002096505
+1122	1.469207707	0.002021218
+1124	1.469650731	0.00199324
+1126	1.4700526	0.002007979
+1128	1.470402126	0.002048125
+1130	1.470687738	0.002094174
+1132	1.470960018	0.002098497
+1134	1.471252614	0.00210954
+1136	1.471548918	0.002149273
+1138	1.471836992	0.002217813
+1140	1.47209801	0.002316543
+1142	1.472334568	0.002417003
+1144	1.472575735	0.002520905
+1146	1.472833567	0.002659262
+1148	1.473072594	0.002866525
+1150	1.473263818	0.003136477
+1152	1.473369962	0.003474161
+1154	1.473307105	0.003876619
+1156	1.472935095	0.004100433
+1158	1.472665948	0.003948862
+1160	1.472597073	0.003731488
+1162	1.472679826	0.003504946
+1164	1.47288582	0.003340222
+1166	1.473175646	0.003240538
+1168	1.473557613	0.003237282
+1170	1.474022096	0.003370304
+1172	1.474591972	0.003703318
+1174	1.475290735	0.004468614
+1176	1.47579202	0.006270984
+1178	1.473894528	0.009310786
+1180	1.46944889	0.007950277
+1182	1.46919538	0.005056482
+1184	1.469937066	0.003777164
+1186	1.47058585	0.003191365
+1188	1.47109418	0.002901376
+1190	1.47148385	0.002757916
+1192	1.471773562	0.002692267
+1194	1.47196611	0.00266088
+1196	1.472077286	0.002588178
+1198	1.472200969	0.002417009
+1200	1.472450427	0.00221559
+1202	1.472836622	0.002112174
+1204	1.473304311	0.002201829
+1206	1.473753424	0.002612947
+1208	1.47385318	0.003479745
+1210	1.472800275	0.004379301
+1212	1.47140252	0.003426489
+1214	1.471594891	0.002272601
+1216	1.472055163	0.001782587
+1218	1.4724316	0.001543926
+1220	1.472739169	0.001396985
+1222	1.47301273	0.001292807
+1224	1.473263934	0.001219469
+1226	1.473498895	0.001171845
+1228	1.473716592	0.00113723
+1230	1.473930592	0.001119123
+1232	1.474133787	0.00111391
+1234	1.4743347	0.001124438
+1236	1.474530392	0.001156601
+1238	1.474716479	0.001210456
+1240	1.47488492	0.001292746
+1242	1.475028515	0.001403963
+1244	1.475124956	0.001544106
+1246	1.475144089	0.001698604
+1248	1.475058922	0.001808401
+1250	1.474899721	0.00177689
+1252	1.474841067	0.001576011
+1254	1.474939237	0.001381063
+1256	1.475098463	0.001256209
+1258	1.475265678	0.001187172
+1260	1.475420572	0.001144965
+1262	1.475574395	0.001114299
+1264	1.47572117	0.001097405
+1266	1.475867451	0.001089675
+1268	1.476011473	0.001093157
+1270	1.476147019	0.001107013
+1272	1.476270154	0.001125473
+1274	1.47638091	0.001144171
+1276	1.476483619	0.001155498
+1278	1.476581834	0.001158617
+1280	1.476683135	0.001145768
+1282	1.476799599	0.001123074
+1284	1.476932611	0.001108033
+1286	1.477072975	0.001097907
+1288	1.477222834	0.001097104
+1290	1.477380706	0.001106987
+1292	1.477543374	0.001132459
+1294	1.477707163	0.001175521
+1296	1.477860282	0.001242672
+1298	1.477988876	0.001322776
+1300	1.478089342	0.00139218
+1302	1.478182431	0.001429737
+1304	1.478308272	0.001441882
+1306	1.478493641	0.001475415
+1308	1.478712211	0.001599567
+1310	1.478858087	0.001868439
+1312	1.478730102	0.002164861
+1314	1.478458036	0.002117289
+1316	1.478449306	0.001875076
+1318	1.478611792	0.001716774
+1320	1.478814603	0.001648375
+1322	1.479022917	0.001638998
+1324	1.479220666	0.001664106
+1326	1.479414128	0.001717646
+1328	1.479592108	0.001804795
+1330	1.479731678	0.001942749
+1332	1.479726919	0.002060225
+1334	1.479751059	0.001962173
+1336	1.479935123	0.001884928
+1338	1.480148376	0.001871222
+1340	1.480373607	0.001889214
+1342	1.480600388	0.001937007
+1344	1.480827533	0.002003134
+1346	1.481049681	0.002087781
+1348	1.481265532	0.002180662
+1350	1.481487164	0.002265881
+1352	1.481736476	0.002362769
+1354	1.482004468	0.002489159
+1356	1.482275995	0.002655474
+1358	1.48252792	0.002848203
+1360	1.482763249	0.003032115
+1362	1.483034583	0.003195386
+1364	1.483382233	0.003380113
+1366	1.483799025	0.003639964
+1368	1.484272236	0.004002658
+1370	1.484829603	0.00448977
+1372	1.48552802	0.005257737
+1374	1.486275464	0.006620297
+1376	1.486517001	0.009083761
+1378	1.484325992	0.012303151
+1380	1.47977969	0.012167198
+1382	1.478003551	0.009400075
+1384	1.478053165	0.007543182
+1386	1.478421432	0.006403564
+1388	1.478900248	0.005632571
+1390	1.479406516	0.005110109
+1392	1.479917129	0.004757894
+1394	1.480417549	0.004528335
+1396	1.480897509	0.004401862
+1398	1.481351587	0.004336878
+1400	1.481797711	0.004323178
+1402	1.482240699	0.004361754
+1404	1.482665796	0.004446542
+1406	1.483059442	0.004580452
+1408	1.483422987	0.004720702
+1410	1.483790308	0.004847301
+1412	1.484190359	0.004991696
+1414	1.484613428	0.005175265
+1416	1.485051641	0.005408562
+1418	1.485480056	0.00569302
+1420	1.485885882	0.006036094
+1422	1.486260365	0.006398155
+1424	1.486596633	0.006767043
+1426	1.486908375	0.007097025
+1428	1.487267526	0.007352865
+1430	1.487756499	0.007589461
+1432	1.488416197	0.007867817
+1434	1.489247587	0.00830203
+1436	1.49022965	0.00898232
+1438	1.491261092	0.010019784
+1440	1.492201579	0.011509506
+1442	1.492747862	0.013398599
+1444	1.492754368	0.015376887
+1446	1.492440408	0.017176535
+1448	1.492035068	0.01893611
+1450	1.49142868	0.020824529
+1452	1.490404699	0.022803925
+1454	1.488886984	0.024681051
+1456	1.486877843	0.026261841
+1458	1.484428504	0.027360806
+1460	1.481747232	0.027793093
+1462	1.479066932	0.027470624
+1464	1.476679553	0.026421119
+1466	1.47482397	0.024798079
+1468	1.473644256	0.022829656
+1470	1.473199283	0.020783461
+1472	1.473390477	0.018872465
+1474	1.474116298	0.017180199
+1476	1.475333747	0.015792075
+1478	1.47696196	0.014728301
+1480	1.479085272	0.014003049
+1482	1.481808665	0.013756925
+1484	1.48531764	0.01418798
+1486	1.489949287	0.015922624
+1488	1.494990654	0.020194058
+1490	1.501195156	0.026083679
+1492	1.509903786	0.040120276
+1494	1.511966946	0.076178677
+1496	1.445607958	0.108223079
+1498	1.414560032	0.052724926
+1500	1.425687258	0.027163552
+1502	1.435092428	0.017332219
+1504	1.441798717	0.012488921
+1506	1.446695961	0.009921313
+1508	1.450331767	0.008397527
+1510	1.453186827	0.007451763
+1512	1.45545228	0.006880209
+1514	1.457319215	0.006485335
+1516	1.458949324	0.006281002
+1518	1.460412276	0.006293795
+1520	1.461761735	0.006700333
+1522	1.462443847	0.007864531
+1524	1.461222896	0.008610001
+1526	1.460432858	0.006970267
+1528	1.461281615	0.005652274
+1530	1.462269708	0.00510003
+1532	1.463067013	0.004873301
+1534	1.463664	0.004776434
+1536	1.464094179	0.004671773
+1538	1.464441095	0.004490224
+1540	1.464777048	0.004239347
+1542	1.465191657	0.00393426
+1544	1.465688526	0.003656601
+1546	1.466238893	0.003489234
+1548	1.46677633	0.003427108
+1550	1.467191673	0.003468987
+1552	1.467477728	0.003382955
+1554	1.467919322	0.003213785
+1556	1.468447563	0.003134306
+1558	1.468982556	0.003169074
+1560	1.46952197	0.003304817
+1562	1.469996105	0.00356172
+1564	1.470387926	0.003888984
+1566	1.470664197	0.004296389
+1568	1.47075697	0.004721133
+1570	1.470675807	0.005049292
+1572	1.470472242	0.005192861
+1574	1.470309764	0.005092022
+1576	1.470330922	0.004817698
+1578	1.470574897	0.004555438
+1580	1.470999073	0.00435936
+1582	1.471583642	0.004339902
+1584	1.4721379	0.004607263
+1586	1.472404549	0.004920037
+1588	1.472734555	0.00490704
+1590	1.473437241	0.004927535
+1592	1.474460918	0.005185889
+1594	1.475741944	0.005925432
+1596	1.477051732	0.00720758
+1598	1.478673359	0.009128905
+1600	1.480620288	0.013029368
+1602	1.480361683	0.020680995
+1604	1.471342992	0.029995359
+1606	1.455082768	0.024815734
+1608	1.45359592	0.012735845
+1610	1.456936261	0.007467836
+1612	1.459649264	0.005372098
+1614	1.461565353	0.004451296
+1616	1.462944851	0.004053293
+1618	1.463933847	0.003991463
+1620	1.464541591	0.004096596
+1622	1.464785362	0.004250861
+1624	1.464675723	0.004253062
+1626	1.464436751	0.003880135
+1628	1.464428733	0.003227653
+1630	1.464682454	0.002598051
+1632	1.46507305	0.002086572
+1634	1.465510023	0.001698439
+1636	1.465976195	0.001417854
+1638	1.46639465	0.00123235
+1640	1.466777147	0.001097643
+1642	1.467133507	0.000997096
+1644	1.467460665	0.000923944
+1646	1.467776889	0.000867695
+1648	1.468072302	0.00085799
+1650	1.468323132	0.000876926
+1652	1.468535355	0.000900484
+1654	1.468711262	0.000924599
+1656	1.46886442	0.000943403
+1658	1.468977178	0.00095719
+1660	1.469060193	0.000919302
+1662	1.469173361	0.000829981
+1664	1.46933993	0.00074192
+1666	1.469532185	0.000684455
+1668	1.469734587	0.000660487
+1670	1.46993137	0.00067733
+1672	1.47010973	0.000733664
+1674	1.470235927	0.000829672
+1676	1.470261895	0.000923202
+1678	1.470230428	0.000900896
+1680	1.470268242	0.000787132
+1682	1.470391952	0.000676996
+1684	1.470558163	0.000611701
+1686	1.47072223	0.000595044
+1688	1.470881225	0.000601913
+1690	1.471020294	0.000631185
+1692	1.471140847	0.000675094
+1694	1.4712396	0.000731422
+1696	1.471287792	0.000808376
+1698	1.471263994	0.00079428
+1700	1.471328964	0.000709355
+1702	1.471436818	0.000657251
+1704	1.471559458	0.000631084
+1706	1.471675566	0.00062063
+1708	1.471789402	0.000614805
+1710	1.471906048	0.000610379
+1712	1.472029443	0.000608366
+1714	1.472165687	0.000610178
+1716	1.472315399	0.000628061
+1718	1.472483869	0.000671391
+1720	1.472654475	0.000748671
+1722	1.472817311	0.000874314
+1724	1.472950429	0.001041238
+1726	1.473046007	0.001237492
+1728	1.473093759	0.001471848
+1730	1.473059395	0.001732234
+1732	1.472917418	0.001975823
+1734	1.47267689	0.002155434
+1736	1.472355338	0.002204526
+1738	1.472048818	0.002091193
+1740	1.47183344	0.001857001
+1742	1.471742434	0.00156446
+1744	1.471768805	0.001278243
+1746	1.471881629	0.001038306
+1748	1.472046322	0.000858083
+1750	1.472232414	0.000736721
+1752	1.47242316	0.000665836
+1754	1.472608674	0.000633015
+1756	1.472783278	0.000636204
+1758	1.472932588	0.000664561
+1760	1.473060858	0.000700854
+1762	1.47317848	0.00073825
+1764	1.473290453	0.000779473
+1766	1.473395502	0.000831333
+1768	1.473491455	0.000887484
+1770	1.473578175	0.000943101
+1772	1.473667126	0.00100856
+1774	1.473739298	0.001088156
+1776	1.473785511	0.001173368
+1778	1.47379002	0.001227206
+1780	1.473813896	0.001208673
+1782	1.473923549	0.001173465
+1784	1.4740917	0.001193719
+1786	1.474271982	0.001285337
+1788	1.474426157	0.001425909
+1790	1.474572919	0.001580549
+1792	1.474748784	0.001798508
+1794	1.474893485	0.002133319
+1796	1.474934899	0.002583712
+1798	1.474781105	0.003106518
+1800	1.474370814	0.003584561
+1802	1.473736221	0.003845351
+1804	1.473045883	0.003772087
+1806	1.472512227	0.003409507
+1808	1.472234727	0.002925899
+1810	1.472178211	0.002462305
+1812	1.472272365	0.002095033
+1814	1.4724386	0.001852627
+1816	1.472597486	0.001717021
+1818	1.472717182	0.001638864
+1820	1.472795358	0.001577308
+1822	1.472849206	0.001496792
+1824	1.472912356	0.001388637
+1826	1.473013974	0.001277435
+1828	1.47314853	0.001184564
+1830	1.473293302	0.001129054
+1832	1.473425437	0.001086064
+1834	1.473570566	0.001030861
+1836	1.473758736	0.00098496
+1838	1.473981581	0.000979289
+1840	1.474224453	0.001022886
+1842	1.474480777	0.001120679
+1844	1.474745868	0.001283946
+1846	1.475006131	0.001527239
+1848	1.475247239	0.001888266
+1850	1.475396699	0.002392276
+1852	1.475351258	0.003009719
+1854	1.475042175	0.003640594
+1856	1.474423945	0.004145277
+1858	1.473584937	0.004284184
+1860	1.47284787	0.003973418
+1862	1.4724611	0.003434379
+1864	1.472411327	0.002946984
+1866	1.472536164	0.002656852
+1868	1.472665029	0.002575548
+1870	1.472679666	0.002623622
+1872	1.472529231	0.002673206
+1874	1.472271964	0.002596706
+1876	1.472035096	0.002353418
+1878	1.471921073	0.002013524
+1880	1.471942987	0.001671625
+1882	1.472053638	0.001387567
+1884	1.472207083	0.00117033
+1886	1.472370953	0.001011206
+1888	1.472530627	0.000892343
+1890	1.472681675	0.000799798
+1892	1.472830389	0.000722584
+1894	1.472985008	0.000668206
+1896	1.473131098	0.000645564
+1898	1.473247692	0.000645768
+1900	1.473331292	0.000633984
+1902	1.473415571	0.000588098
+1904	1.473530879	0.000535949
+1906	1.473665341	0.00050098
+1908	1.47380841	0.000480504
+1910	1.473958285	0.000475813
+1912	1.474113403	0.000486824
+1914	1.474274	0.000515196
+1916	1.47443781	0.000562568
+1918	1.474605934	0.000630428
+1920	1.474775821	0.00072361
+1922	1.474938799	0.000847642
+1924	1.475084387	0.00099279
+1926	1.475226982	0.001144293
+1928	1.475392648	0.001317285
+1930	1.475582607	0.001558937
+1932	1.475762194	0.001903731
+1934	1.475876407	0.002375566
+1936	1.475839086	0.002980401
+1938	1.475530609	0.003642932
+1940	1.474891504	0.004165896
+1942	1.474095429	0.004339444
+1944	1.47334202	0.004204135
+1946	1.472750025	0.003801614
+1948	1.472449258	0.003277199
+1950	1.472399446	0.002825764
+1952	1.472475793	0.002533488
+1954	1.472554597	0.002394375
+1956	1.472561971	0.002346038
+1958	1.472465217	0.002325749
+1960	1.472281353	0.002200395
+1962	1.472125511	0.001994452
+1964	1.472020751	0.001704955
+1966	1.472027616	0.001378758
+1968	1.472134206	0.001096906
+1970	1.472290432	0.000878129
+1972	1.472468078	0.000721601
+1974	1.472650017	0.00061742
+1976	1.472826436	0.000562113
+1978	1.472982261	0.000551026
+1980	1.473106514	0.000575712
+1982	1.473179497	0.000615371
+1984	1.473216719	0.000626639
+1986	1.473270062	0.000619345
+1988	1.473326863	0.000644973
+1990	1.473329296	0.000691942
+1992	1.473278226	0.000694255
+1994	1.473221507	0.000622443
+1996	1.473236186	0.0004952
+1998	1.473318243	0.00040262
+2000	1.473411355	0.00035752
+2002	1.473494127	0.000340716
+2004	1.473561544	0.000340726
+2006	1.473612248	0.000349588
+2008	1.473641865	0.00035789
+2010	1.47365636	0.000352783
+2012	1.473673369	0.000327905
+2014	1.473702337	0.0002987
+2016	1.473734437	0.000271842
+2018	1.473772058	0.000242333
+2020	1.473816484	0.000218337
+2022	1.473861113	0.000199195
+2024	1.47390578	0.000183912
+2026	1.473950288	0.000171888
+2028	1.473995645	0.000164785
+2030	1.474036603	0.000164392
+2032	1.474065198	0.000169012
+2034	1.47408331	0.000154128
+2036	1.47412047	0.000133851
+2038	1.474160982	0.000121768
+2040	1.474201156	0.000114542
+2042	1.47423947	0.000109961
+2044	1.474276129	0.000107325
+2046	1.474312184	0.00010532
+2048	1.474346481	0.0001044
+2050	1.474380714	0.000104561
+2052	1.474412784	0.000105683
+2054	1.474445206	0.000107138
+2056	1.47447627	0.000109851
+2058	1.474506759	0.000113964
+2060	1.474535887	0.00011916
+2062	1.474563867	0.000125394
+2064	1.474590735	0.000135383
+2066	1.474612054	0.000150829
+2068	1.474618173	0.000163896
+2070	1.474618403	0.000158539
+2072	1.474632772	0.000143857
+2074	1.474654279	0.000133839
+2076	1.474677092	0.000126083
+2078	1.47470099	0.000119111
+2080	1.474725901	0.000113979
+2082	1.474750651	0.000110908
+2084	1.474774681	0.000108575
+2086	1.474797765	0.00010575
+2088	1.474821422	0.000102758
+2090	1.474846336	0.000100315
+2092	1.474871219	9.89E-05
+2094	1.474896096	9.85E-05
+2096	1.474919997	9.87E-05
+2098	1.474944347	9.87E-05
+2100	1.474969806	9.95E-05
+2102	1.474995643	0.000102501
+2104	1.47502159	0.000108578
+2106	1.475044176	0.000117599
+2108	1.475062645	0.00012881
+2110	1.475073954	0.000138078
+2112	1.475083937	0.000139895
+2114	1.47510043	0.000140372
+2116	1.475111984	0.000147184
+2118	1.475112146	0.000142581
+2120	1.475127628	0.000126124
+2122	1.475152113	0.000119111
+2124	1.475171824	0.000117762
+2126	1.475187748	0.000110386
+2128	1.475213108	0.000100586
+2130	1.475241165	9.65E-05
+2132	1.475270052	9.72E-05
+2134	1.475295905	0.000100589
+2136	1.47531935	0.000104482
+2138	1.475342091	0.000107041
+2140	1.475365546	0.000108872
+2142	1.47539141	0.00011149
+2144	1.475417352	0.000115452
+2146	1.475444492	0.000120558
+2148	1.475473425	0.000126538
+2150	1.475506197	0.000134734
+2152	1.475541784	0.000148644
+2154	1.475582035	0.000172041
+2156	1.475621601	0.000210049
+2158	1.475652538	0.000268126
+2160	1.475661516	0.000351069
+2162	1.475612259	0.000450345
+2164	1.475480686	0.000489939
+2166	1.475372967	0.000409493
+2168	1.475362114	0.000304388
+2170	1.475398909	0.000235891
+2172	1.475446566	0.000200519
+2174	1.475491977	0.000185711
+2176	1.475532032	0.000182425
+2178	1.475568644	0.000187449
+2180	1.475602158	0.000203021
+2182	1.475624645	0.000231533
+2184	1.475620856	0.000266979
+2186	1.475589805	0.00027467
+2188	1.47557481	0.000249531
+2190	1.475580335	0.000224075
+2192	1.475592327	0.000200277
+2194	1.475614571	0.000177273
+2196	1.475644341	0.000160286
+2198	1.475678575	0.000150581
+2200	1.475716178	0.000148631
+2202	1.475757268	0.000159419
+2204	1.475793377	0.000190928
+2206	1.475797468	0.000246686
+2208	1.475741896	0.000270255
+2210	1.475711949	0.000222823
+2212	1.47572957	0.0001833
+2214	1.47575472	0.000159208
+2216	1.475786212	0.000141368
+2218	1.475819421	0.000133886
+2220	1.475850887	0.000133378
+2222	1.475878972	0.000136687
+2224	1.475902989	0.000141595
+2226	1.4759247	0.000145519
+2228	1.475947794	0.000148459
+2230	1.475972651	0.000153317
+2232	1.475997487	0.000163254
+2234	1.476018072	0.000178923
+2236	1.476026891	0.000194257
+2238	1.476030055	0.00019645
+2240	1.476042817	0.000188282
+2242	1.476067262	0.000182547
+2244	1.476097849	0.000184193
+2246	1.47612902	0.000192794
+2248	1.476159494	0.000207469
+2250	1.476188521	0.000228636
+2252	1.476214462	0.000256822
+2254	1.476234897	0.000293238
+2256	1.47624408	0.000339844
+2258	1.476230185	0.000394697
+2260	1.476177424	0.000433842
+2262	1.476112288	0.000418808
+2264	1.47608501	0.000365652
+2266	1.476098678	0.000317993
+2268	1.476129099	0.000289252
+2270	1.476164765	0.000276323
+2272	1.476199474	0.000276008
+2274	1.476232531	0.000285195
+2276	1.476263196	0.00030584
+2278	1.476282004	0.000341615
+2280	1.476266804	0.000378324
+2282	1.476243764	0.000375183
+2284	1.476247144	0.000372499
+2286	1.476239393	0.00037913
+2288	1.476222636	0.000369071
+2290	1.476217012	0.000344203
+2292	1.476224148	0.000313724
+2294	1.476246398	0.00028318
+2296	1.476282306	0.000260398
+2298	1.476326374	0.000248364
+2300	1.476373566	0.000246962
+2302	1.476425239	0.000257337
+2304	1.476478147	0.000282117
+2306	1.476529967	0.000327012
+2308	1.476570593	0.000402901
+2310	1.476566051	0.000515679
+2312	1.476464512	0.000613222
+2314	1.476321398	0.000587317
+2316	1.476264349	0.000479704
+2318	1.47628667	0.000387543
+2320	1.476341784	0.000331936
+2322	1.476406262	0.000305882
+2324	1.47647368	0.000301743
+2326	1.476544201	0.000318022
+2328	1.476616937	0.000360763
+2330	1.476682206	0.000442865
+2332	1.476708974	0.000580146
+2334	1.47661953	0.000746878
+2336	1.476406995	0.000778906
+2338	1.476289181	0.000655879
+2340	1.476279224	0.00054986
+2342	1.476296106	0.00047431
+2344	1.476337757	0.000414797
+2346	1.476396689	0.000384139
+2348	1.476454641	0.000382158
+2350	1.476502523	0.000402158
+2352	1.476533968	0.000435516
+2354	1.476551882	0.000472183
+2356	1.476566258	0.000515961
+2358	1.476563425	0.000592576
+2360	1.476468418	0.000693207
+2362	1.476279886	0.000643638
+2364	1.47623361	0.000478342
+2366	1.476283496	0.000369914
+2368	1.476347141	0.000314093
+2370	1.476405794	0.000287309
+2372	1.476456738	0.000274524
+2374	1.476503293	0.000270062
+2376	1.476544739	0.00027183
+2378	1.476585198	0.000279195
+2380	1.476623607	0.000294905
+2382	1.476655091	0.000319348
+2384	1.476679399	0.000350241
+2386	1.476689994	0.000391786
+2388	1.476668323	0.000432288
+2390	1.47662552	0.000431895
+2392	1.476612276	0.000400307
+2394	1.476623269	0.000373781
+2396	1.476645385	0.000355411
+2398	1.47667621	0.000347152
+2400	1.476708403	0.000350924
+2402	1.476737324	0.000365707
+2404	1.476760801	0.000389705
+2406	1.476775668	0.000421335
+2408	1.476777474	0.000459934
+2410	1.47675773	0.000500617
+2412	1.476711765	0.000525703
+2414	1.476658988	0.000513224
+2416	1.476628886	0.000478248
+2418	1.476616099	0.000439596
+2420	1.476618049	0.000399407
+2422	1.476633611	0.000365632
+2424	1.476656153	0.000342099
+2426	1.476679897	0.000327643
+2428	1.476701679	0.000319852
+2430	1.476718893	0.00031809
+2432	1.4767266	0.000318227
+2434	1.476725819	0.000307018
+2436	1.476735887	0.000284561
+2438	1.476756253	0.000265983
+2440	1.476778115	0.000252938
+2442	1.476802013	0.000242679
+2444	1.476826903	0.000236093
+2446	1.476851343	0.000233131
+2448	1.476874688	0.000233167
+2450	1.476895779	0.000235416
+2452	1.476914612	0.000239364
+2454	1.476931215	0.000244209
+2456	1.476944837	0.000248579
+2458	1.476957066	0.000251145
+2460	1.476968412	0.000252431
+2462	1.47698093	0.000253692
+2464	1.476991653	0.000255788
+2466	1.476998922	0.000256434
+2468	1.477005189	0.000251073
+2470	1.477016819	0.000241598
+2472	1.477033711	0.000234162
+2474	1.477051728	0.000229677
+2476	1.477069632	0.000227592
+2478	1.47708839	0.000226834
+2480	1.477105952	0.000227169
+2482	1.47712353	0.000228589
+2484	1.477140454	0.000231746
+2486	1.477155269	0.000236824
+2488	1.477167859	0.0002416
+2490	1.477177464	0.000244394
+2492	1.477187741	0.000244248
+2494	1.477201081	0.000245128
+2496	1.477211169	0.000251435
+2498	1.477209088	0.000247994
+2500	1.477219752	0.000232736
+2502	1.477241531	0.000222498
+2504	1.477268421	0.000221589
+2506	1.477291641	0.00023258
+2508	1.477297932	0.000250427
+2510	1.477287517	0.000252498
+2512	1.47728596	0.00023219
+2514	1.477303462	0.00021105
+2516	1.477328662	0.000198391
+2518	1.477354807	0.000193636
+2520	1.477377783	0.000193342
+2522	1.477396405	0.000193372
+2524	1.477413887	0.000189643
+2526	1.477436743	0.000181795
+2528	1.477466867	0.000178838
+2530	1.477498595	0.000183502
+2532	1.477527981	0.000194837
+2534	1.47755197	0.000211328
+2536	1.477570595	0.000231394
+2538	1.477580089	0.000255837
+2540	1.47756989	0.00027571
+2542	1.477554275	0.000266055
+2544	1.477563613	0.00024386
+2546	1.477586393	0.000235285
+2548	1.477602107	0.000236305
+2550	1.477611366	0.000232544
+2552	1.477623597	0.000218806
+2554	1.477646777	0.000204744
+2556	1.477674747	0.000196655
+2558	1.477702465	0.000191976
+2560	1.477730428	0.000186393
+2562	1.477763616	0.000182465
+2564	1.477799985	0.000182342
+2566	1.477838217	0.000186623
+2568	1.477878061	0.000194772
+2570	1.477920641	0.000207509
+2572	1.477964885	0.000227537
+2574	1.478009562	0.000256126
+2576	1.478053148	0.000293784
+2578	1.478098835	0.000344607
+2580	1.47814186	0.000421001
+2582	1.478159973	0.00053994
+2584	1.478093604	0.000691325
+2586	1.477908663	0.000768064
+2588	1.477734	0.000684349
+2590	1.477674804	0.000536496
+2592	1.477703642	0.000418108
+2594	1.477766627	0.000348163
+2596	1.47783459	0.000316562
+2598	1.477897132	0.000311606
+2600	1.477950764	0.000329719
+2602	1.47798212	0.000370011
+2604	1.477968395	0.000412185
+2606	1.477930226	0.000402482
+2608	1.477933844	0.00036847
+2610	1.477945647	0.000353398
+2612	1.477950473	0.000328282
+2614	1.477975395	0.000295401
+2616	1.478012745	0.000275903
+2618	1.478051085	0.000268299
+2620	1.47808604	0.000267512
+2622	1.478116632	0.000270974
+2624	1.478145774	0.000277238
+2626	1.478171009	0.000286764
+2628	1.478191857	0.000300107
+2630	1.478202008	0.000316525
+2632	1.478195093	0.000327263
+2634	1.478180696	0.000305877
+2636	1.478199378	0.000269148
+2638	1.478235352	0.000248173
+2640	1.478270816	0.000239824
+2642	1.478304044	0.000238746
+2644	1.478329954	0.000239869
+2646	1.478352433	0.000237698
+2648	1.478376736	0.000231659
+2650	1.478404223	0.00022456
+2652	1.478435039	0.000220155
+2654	1.478465258	0.000220025
+2656	1.478492298	0.000220822
+2658	1.478516192	0.000219097
+2660	1.478542286	0.000213669
+2662	1.478571831	0.000206552
+2664	1.478606758	0.000200133
+2666	1.478645026	0.000198263
+2668	1.478684425	0.000204157
+2670	1.478716452	0.000219582
+2672	1.478728447	0.000228529
+2674	1.47874645	0.000212671
+2676	1.478783675	0.000198554
+2678	1.478825771	0.000193734
+2680	1.478867341	0.000194427
+2682	1.47890576	0.000197546
+2684	1.478944105	0.000200582
+2686	1.478982467	0.000203985
+2688	1.479020786	0.000208935
+2690	1.479056977	0.000213886
+2692	1.479093486	0.000215781
+2694	1.479132532	0.000215167
+2696	1.479177137	0.000214896
+2698	1.479224944	0.00021736
+2700	1.479273702	0.000222624
+2702	1.479323501	0.000229951
+2704	1.479374778	0.00023778
+2706	1.47942978	0.000247271
+2708	1.47948663	0.000260084
+2710	1.479545725	0.000275286
+2712	1.479609	0.000293138
+2714	1.479675821	0.000315099
+2716	1.479747834	0.00034214
+2718	1.479826864	0.000376356
+2720	1.479914349	0.000422619
+2722	1.480011619	0.000488803
+2724	1.48011529	0.000585387
+2726	1.480217436	0.000728319
+2728	1.48029271	0.000938827
+2730	1.480284699	0.001230376
+2732	1.480093337	0.001552296
+2734	1.479686045	0.00172267
+2736	1.479260698	0.001584292
+2738	1.479043822	0.001262354
+2740	1.479031373	0.00095422
+2742	1.479122344	0.000733284
+2744	1.479244752	0.000590574
+2746	1.479368961	0.000500914
+2748	1.479485477	0.000444284
+2750	1.479593467	0.000408552
+2752	1.479693914	0.000386443
+2754	1.479786963	0.000373264
+2756	1.479874783	0.00036667
+2758	1.479957584	0.000363877
+2760	1.480037273	0.000361533
+2762	1.480119242	0.000363675
+2764	1.480199134	0.000366719
+2766	1.480279226	0.000373488
+2768	1.480357698	0.000385907
+2770	1.480433858	0.000398462
+2772	1.480507254	0.000413801
+2774	1.480575671	0.00042566
+2776	1.480651059	0.000436402
+2778	1.480722663	0.000446663
+2780	1.480799774	0.000455121
+2782	1.480880532	0.000464084
+2784	1.480966873	0.000471838
+2786	1.481055122	0.000485997
+2788	1.481149376	0.000502173
+2790	1.481244667	0.00052283
+2792	1.481341189	0.000548289
+2794	1.481440145	0.000579634
+2796	1.481533085	0.000611379
+2798	1.481628758	0.000641159
+2800	1.481730232	0.000672247
+2802	1.481835672	0.000711616
+2804	1.481937644	0.000756204
+2806	1.482037722	0.000806513
+2808	1.482133328	0.000854384
+2810	1.48221893	0.000899046
+2812	1.482301281	0.000920533
+2814	1.482415432	0.000922946
+2816	1.482561883	0.000938823
+2818	1.482721464	0.000975854
+2820	1.482885937	0.001037948
+2822	1.483031462	0.001114411
+2824	1.483165355	0.001171243
+2826	1.48333288	0.001205841
+2828	1.483538865	0.001261413
+2830	1.483762339	0.001347783
+2832	1.483993724	0.001461997
+2834	1.484228597	0.001597189
+2836	1.484469148	0.001753303
+2838	1.48472336	0.001935236
+2840	1.484988918	0.002148293
+2842	1.48526979	0.002396939
+2844	1.485562444	0.002709475
+2846	1.485850301	0.00308962
+2848	1.486116357	0.003559406
+2850	1.486317037	0.004122104
+2852	1.486426168	0.004768919
+2854	1.486389319	0.005472141
+2856	1.486172881	0.006174092
+2858	1.485780553	0.006787228
+2860	1.485282546	0.007238079
+2862	1.484774737	0.007520489
+2864	1.484313069	0.007694051
+2866	1.483902949	0.007806724
+2868	1.483527587	0.007892118
+2870	1.483159233	0.007959358
+2872	1.482763173	0.007997332
+2874	1.482330362	0.007959348
+2876	1.481900332	0.007786842
+2878	1.481569899	0.007485135
+2880	1.481358298	0.007127825
+2882	1.481270464	0.006747168
+2884	1.481292247	0.006365591
+2886	1.48142276	0.006002528
+2888	1.481661524	0.005680035
+2890	1.481994694	0.005418693
+2892	1.482412863	0.005231499
+2894	1.482906156	0.005138593
+2896	1.483461748	0.005149122
+2898	1.484060687	0.005282986
+2900	1.484697491	0.005548465
+2902	1.485349018	0.005966707
+2904	1.486004513	0.006560259
+2906	1.486633305	0.007373091
+2908	1.487160493	0.008443431
+2910	1.487494274	0.009807836
+2912	1.48745635	0.011436182
+2914	1.486879188	0.013204372
+2916	1.485646477	0.01486394
+2918	1.483781384	0.016032264
+2920	1.481608423	0.01638484
+2922	1.479639022	0.01593156
+2924	1.478175633	0.014971222
+2926	1.477253662	0.01381792
+2928	1.476800099	0.012683
+2930	1.476706003	0.011705176
+2932	1.476835929	0.010945412
+2934	1.477078489	0.010409493
+2936	1.47736368	0.010077746
+2938	1.477619988	0.009915762
+2940	1.47780992	0.009890928
+2942	1.477906166	0.009952539
+2944	1.477893522	0.010055844
+2946	1.47776643	0.010146665
+2948	1.477553036	0.010170091
+2950	1.477320986	0.010097042
+2952	1.477109823	0.009954455
+2954	1.476926564	0.009771848
+2956	1.476778657	0.009560314
+2958	1.476643898	0.009316728
+2960	1.4765395	0.009008413
+2962	1.476523809	0.008604525
+2964	1.476711438	0.008191732
+2966	1.477065906	0.007931884
+2968	1.477426843	0.00787857
+2970	1.477700092	0.007954067
+2972	1.477862473	0.008070214
+2974	1.477947414	0.00817434
+2976	1.477978994	0.008250035
+2978	1.477982236	0.008288556
+2980	1.47795004	0.008283863
+2982	1.477901474	0.00816951
+2984	1.477957354	0.007951471
+2986	1.478144969	0.007718758
+2988	1.478446924	0.007521776
+2990	1.478849187	0.00739483
+2992	1.479323443	0.007354951
+2994	1.479863068	0.007424008
+2996	1.48043188	0.007629477
+2998	1.480975377	0.008003502
+3000	1.481385171	0.008498811
+3002	1.481623564	0.008966242
+3004	1.48185212	0.009250402
+3006	1.482284404	0.009454556
+3008	1.482971786	0.009765818
+3010	1.48385674	0.010315072
+3012	1.484879935	0.011209164
+3014	1.485956652	0.012566574
+3016	1.48695938	0.014492031
+3018	1.487674683	0.017152331
+3020	1.487655241	0.020658807
+3022	1.486181326	0.024792757
+3024	1.48268462	0.028533826
+3026	1.477620824	0.030573743
+3028	1.472327275	0.030419773
+3030	1.467764639	0.028528571
+3032	1.464408789	0.025462618
+3034	1.462471976	0.021841785
+3036	1.461967693	0.018321478
+3038	1.462539472	0.015436726
+3040	1.463673822	0.013417427
+3042	1.464914177	0.012181431
+3044	1.466015631	0.011480242
+3046	1.466976865	0.011108233
+3048	1.467814648	0.011036495
+3050	1.468474029	0.011234121
+3052	1.468878533	0.01165214
+3054	1.468956751	0.012167935
+3056	1.468753239	0.012649209
+3058	1.468343027	0.013064024
+3060	1.467712827	0.013421784
+3062	1.466753005	0.013602735
+3064	1.465537036	0.013356676
+3066	1.464357344	0.012495783
+3068	1.463643333	0.01111858
+3070	1.463619676	0.009623122
+3072	1.464162707	0.00840019
+3074	1.465005896	0.00762786
+3076	1.46593266	0.007314317
+3078	1.466814971	0.007427694
+3080	1.467541081	0.008001699
+3082	1.467856909	0.009099248
+3084	1.467267609	0.010561298
+3086	1.465332472	0.011595346
+3088	1.462682921	0.010891552
+3090	1.461203035	0.008553483
+3092	1.461344785	0.006257663
+3094	1.462213698	0.00474251
+3096	1.463212479	0.00389488
+3098	1.464116618	0.003502421
+3100	1.464823693	0.003425661
+3102	1.465256367	0.003542455
+3104	1.465335815	0.0036633
+3106	1.465190984	0.003512557
+3108	1.465169074	0.003071606
+3110	1.465380607	0.002623191
+3112	1.465682768	0.002302389
+3114	1.465969313	0.002083306
+3116	1.466197395	0.00190296
+3118	1.46639102	0.001701246
+3120	1.466610549	0.001472218
+3122	1.466870492	0.001266802
+3124	1.467139097	0.001102215
+3126	1.467402517	0.000972843
+3128	1.467659659	0.000865976
+3130	1.467905953	0.000787123
+3132	1.468134489	0.00072557
+3134	1.468347231	0.00067862
+3136	1.468545536	0.000643376
+3138	1.46872579	0.000613508
+3140	1.468896068	0.000585754
+3142	1.469053617	0.000561171
+3144	1.469207884	0.000538802
+3146	1.469351559	0.000520081
+3148	1.469489266	0.000505697
+3150	1.46961712	0.000493471
+3152	1.469739323	0.000480268
+3154	1.469857715	0.000470385
+3156	1.469970841	0.00045922
+3158	1.470081254	0.000450945
+3160	1.470188345	0.000450827
+3162	1.470287492	0.000455121
+3164	1.470375616	0.000465884
+3166	1.470447337	0.000478799
+3168	1.470495236	0.000482832
+3170	1.470532879	0.000455626
+3172	1.47059397	0.000403339
+3174	1.470680289	0.000360438
+3176	1.470771001	0.000332521
+3178	1.470858344	0.000313939
+3180	1.47094238	0.000300706
+3182	1.471021271	0.000290666
+3184	1.471096912	0.000282478
+3186	1.471168154	0.000275747
+3188	1.471236186	0.000269274
+3190	1.471301847	0.000262631
+3192	1.471365114	0.000255445
+3194	1.471427348	0.000248378
+3196	1.471488517	0.000241978
+3198	1.47154755	0.000236252
+3200	1.47160533	0.000230923
+3202	1.471660128	0.000226049
+3204	1.47171225	0.000221226
+3206	1.471763155	0.000214716
+3208	1.471813951	0.000206518
+3210	1.471864668	0.000198105
+3212	1.471916616	0.000190353
+3214	1.471967385	0.000183842
+3216	1.472017079	0.000178537
+3218	1.472065889	0.000173733
+3220	1.472113652	0.000169366
+3222	1.472159365	0.0001653
+3224	1.472205007	0.000161253
+3226	1.472250332	0.00015755
+3228	1.472294241	0.000154291
+3230	1.472337337	0.000151403
+3232	1.472379806	0.000148762
+3234	1.472421223	0.000146609
+3236	1.472461738	0.000144929
+3238	1.472500905	0.000143621
+3240	1.472539331	0.000142424
+3242	1.472576666	0.000141225
+3244	1.472612894	0.00013988
+3246	1.472649422	0.00013812
+3248	1.47268468	0.000136558
+3250	1.472718966	0.00013503
+3252	1.472753298	0.000133891
+3254	1.472787238	0.000133096
+3256	1.472819576	0.000132369
+3258	1.472850861	0.000131179
+3260	1.472881925	0.000129611
+3262	1.472913	0.000128051
+3264	1.472943992	0.000126497
+3266	1.4729752	0.000125487
+3268	1.473004566	0.000124918
+3270	1.473033069	0.000124283
+3272	1.473062298	0.000123525
+3274	1.473090298	0.000122442
+3276	1.473117251	0.000121444
+3278	1.473145192	0.00012076
+3280	1.473171918	0.000120133
+3282	1.473199048	0.000119423
+3284	1.473224805	0.000118787
+3286	1.47325068	0.00011805
+3288	1.473275587	0.000117491
+3290	1.473301496	0.000116941
+3292	1.473325233	0.000116412
+3294	1.473350252	0.000116041
+3296	1.47337511	0.000115835
+3298	1.47339906	0.000116086
+3300	1.47342297	0.000116987
+3302	1.473445822	0.000118268
+3304	1.473466581	0.000119505
+3306	1.473487385	0.000120364
+3308	1.473507032	0.000119983
+3310	1.473526836	0.000118961
+3312	1.47354755	0.000117874
+3314	1.473568295	0.000117091
+3316	1.473589032	0.000116576
+3318	1.473608805	0.000116631
+3320	1.473628554	0.000116649
+3322	1.473647349	0.00011664
+3324	1.473665478	0.000116602
+3326	1.47368305	0.000116254
+3328	1.4736996	0.000115188
+3330	1.473717184	0.000113812
+3332	1.473733781	0.000111681
+3334	1.473750687	0.000108818
+3336	1.473768449	0.000105958
+3338	1.473786661	0.000103152
+3340	1.473804046	0.000100395
+3342	1.473822765	9.80E-05
+3344	1.47384041	9.54E-05
+3346	1.473859047	9.25E-05
+3348	1.473878582	9.01E-05
+3350	1.473897523	8.83E-05
+3352	1.473917523	8.72E-05
+3354	1.473936067	8.64E-05
+3356	1.473954889	8.61E-05
+3358	1.47397354	8.62E-05
+3360	1.473992346	8.70E-05
+3362	1.474010557	8.83E-05
+3364	1.47402827	9.00E-05
+3366	1.474045082	9.23E-05
+3368	1.474061418	9.51E-05
+3370	1.474077043	9.79E-05
+3372	1.474090591	0.000100096
+3374	1.47410503	0.000102179
+3376	1.474117827	0.00010375
+3378	1.474130815	0.000105213
+3380	1.474143266	0.000106689
+3382	1.474155712	0.000107854
+3384	1.474167173	0.000108504
+3386	1.474178416	0.000108466
+3388	1.47418915	0.000107522
+3390	1.474199987	0.000105586
+3392	1.474211901	0.000103099
+3394	1.474224434	0.000100324
+3396	1.474236835	9.74E-05
+3398	1.474250335	9.52E-05
+3400	1.474264805	9.35E-05
+3402	1.474278267	9.21E-05
+3404	1.474291704	9.07E-05
+3406	1.474304771	8.91E-05
+3408	1.474318355	8.75E-05
+3410	1.474331936	8.57E-05
+3412	1.474346421	8.44E-05
+3414	1.474360879	8.35E-05
+3416	1.474375326	8.28E-05
+3418	1.474390181	8.26E-05
+3420	1.474405156	8.35E-05
+3422	1.474420443	8.51E-05
+3424	1.474436061	8.77E-05
+3426	1.474449644	9.19E-05
+3428	1.474462948	9.73E-05
+3430	1.474474391	0.000103498
+3432	1.474484169	0.000110175
+3434	1.47449072	0.000116489
+3436	1.474495914	0.000121652
+3438	1.474499038	0.0001252
+3440	1.474499934	0.000126017
+3442	1.474501355	0.000123364
+3444	1.474504588	0.000118359
+3446	1.474508751	0.000111284
+3448	1.474514459	0.000102049
+3450	1.474524843	9.29E-05
+3452	1.474538272	8.57E-05
+3454	1.474551723	8.04E-05
+3456	1.474565172	7.65E-05
+3458	1.474578602	7.35E-05
+3460	1.474591921	7.16E-05
+3462	1.474604503	7.00E-05
+3464	1.474616965	6.87E-05
+3466	1.474628399	6.77E-05
+3468	1.474639874	6.66E-05
+3470	1.474651882	6.58E-05
+3472	1.474662664	6.49E-05
+3474	1.474674097	6.42E-05
+3476	1.474684737	6.34E-05
+3478	1.474696083	6.21E-05
+3480	1.47470752	6.08E-05
+3482	1.474718859	6.00E-05
+3484	1.474731411	5.95E-05
+3486	1.474743217	5.98E-05
+3488	1.474755405	6.07E-05
+3490	1.474765776	6.21E-05
+3492	1.474775177	6.36E-05
+3494	1.474784377	6.40E-05
+3496	1.474793753	6.37E-05
+3498	1.474803528	6.27E-05
+3500	1.474813865	6.17E-05
+3502	1.474825403	6.13E-05
+3504	1.474836865	6.13E-05
+3506	1.47484923	6.25E-05
+3508	1.474860542	6.44E-05
+3510	1.474871181	6.71E-05
+3512	1.474881618	7.04E-05
+3514	1.474891556	7.48E-05
+3516	1.474897792	7.96E-05
+3518	1.474901998	8.35E-05
+3520	1.474905152	8.40E-05
+3522	1.474908586	8.07E-05
+3524	1.474915894	7.56E-05
+3526	1.474925638	7.11E-05
+3528	1.474937218	6.82E-05
+3530	1.474949652	6.64E-05
+3532	1.474962095	6.58E-05
+3534	1.474975481	6.67E-05
+3536	1.47498901	6.95E-05
+3538	1.475002501	7.44E-05
+3540	1.475013344	8.17E-05
+3542	1.47502156	9.03E-05
+3544	1.475025909	9.86E-05
+3546	1.475027988	0.000104547
+3548	1.475029087	0.000107434
+3550	1.475030131	0.000108038
+3552	1.475031521	0.000107167
+3554	1.47503369	0.000105179
+3556	1.475035962	0.000101095
+3558	1.475039944	9.51E-05
+3560	1.475047208	8.82E-05
+3562	1.475057577	8.18E-05
+3564	1.475069218	7.69E-05
+3566	1.475082228	7.39E-05
+3568	1.475095836	7.28E-05
+3570	1.475109436	7.34E-05
+3572	1.475122992	7.57E-05
+3574	1.475135442	7.97E-05
+3576	1.475147886	8.51E-05
+3578	1.475158773	9.29E-05
+3580	1.4751683	0.000102526
+3582	1.475173011	0.000114877
+3584	1.475167301	0.000126191
+3586	1.475160988	0.000124628
+3588	1.475159999	0.000119416
+3590	1.47516345	0.000112007
+3592	1.475169959	0.000105579
+3594	1.475178935	0.000100692
+3596	1.475189495	9.80E-05
+3598	1.47519987	9.79E-05
+3600	1.475208153	9.77E-05
+3602	1.475216397	9.63E-05
+3604	1.475226778	9.48E-05
+3606	1.475237563	9.41E-05
+3608	1.475249058	9.39E-05
+3610	1.475262354	9.47E-05
+3612	1.475276891	9.80E-05
+3614	1.475292415	0.000104631
+3616	1.475305776	0.000115783
+3618	1.475315507	0.000130667
+3620	1.475318072	0.000146477
+3622	1.475313309	0.000158531
+3624	1.475305207	0.000162319
+3626	1.475300997	0.000158126
+3628	1.475304196	0.000150672
+3630	1.475312923	0.00014455
+3632	1.47532683	0.000142051
+3634	1.475342302	0.00014553
+3636	1.475358179	0.000153343
+3638	1.475372708	0.000167576
+3640	1.475383066	0.000187306
+3642	1.47538491	0.000211282
+3644	1.475378084	0.000235521
+3646	1.475361528	0.000255526
+3648	1.475338298	0.000267309
+3650	1.475311272	0.00026762
+3652	1.475288315	0.000257282
+3654	1.475271733	0.000238427
+3656	1.475264007	0.00021591
+3658	1.47526538	0.000194199
+3660	1.475271965	0.000175916
+3662	1.475283325	0.000162335
+3664	1.475295472	0.000152841
+3666	1.47530792	0.000146982
+3668	1.475319403	0.000143998
+3670	1.475329509	0.000143648
+3672	1.475337525	0.000144734
+3674	1.475342646	0.000145901
+3676	1.475344937	0.000145536
+3678	1.475347938	0.000142791
+3680	1.47535101	0.000138713
+3682	1.475355127	0.000133855
+3684	1.47536061	0.000128953
+3686	1.475366775	0.000123725
+3688	1.475374222	0.000118054
+3690	1.475383491	0.000112539
+3692	1.475394668	0.000108763
+3694	1.475406148	0.000106869
+3696	1.475417668	0.000106179
+3698	1.475431036	0.000108026
+3700	1.475443093	0.000113499
+3702	1.475451689	0.000122346
+3704	1.475453966	0.000132017
+3706	1.475452075	0.000138205
+3708	1.475447975	0.000137813
+3710	1.475447048	0.000131957
+3712	1.475451897	0.000124912
+3714	1.475459959	0.000120086
+3716	1.475470951	0.000119369
+3718	1.475480666	0.000123023
+3720	1.475486979	0.000129682
+3722	1.47548796	0.000136686
+3724	1.475484782	0.000140356
+3726	1.475479476	0.000137643
+3728	1.475478633	0.000130059
+3730	1.475481745	0.000121898
+3732	1.475487781	0.000115279
+3734	1.475494036	0.000109786
+3736	1.475501254	0.0001053
+3738	1.475509342	0.000101063
+3740	1.475516832	9.69E-05
+3742	1.475526886	9.32E-05
+3744	1.475537291	9.10E-05
+3746	1.475546782	8.98E-05
+3748	1.475557133	8.93E-05
+3750	1.475566593	8.96E-05
+3752	1.475576695	9.07E-05
+3754	1.475586473	9.23E-05
+3756	1.475595298	9.52E-05
+3758	1.4756036	9.88E-05
+3760	1.475610915	0.000102898
+3762	1.475616097	0.000106542
+3764	1.475620291	0.000108639
+3766	1.475624418	0.000107126
+3768	1.475633066	0.000104745
+3770	1.475644052	0.000104907
+3772	1.475655523	0.000107524
+3774	1.475666948	0.000112566
+3776	1.475678309	0.000120129
+3778	1.475687551	0.000130378
+3780	1.475694636	0.000143388
+3782	1.475695475	0.000157828
+3784	1.475689514	0.000171337
+3786	1.475678359	0.000178286
+3788	1.475665939	0.000174781
+3790	1.47566102	0.000164121
+3792	1.47566355	0.00015261
+3794	1.475671857	0.000144163
+3796	1.475683213	0.000139239
+3798	1.475695293	0.000137793
+3800	1.475707725	0.000140105
+3802	1.4757181	0.000145422
+3804	1.475726484	0.000152835
+3806	1.475731342	0.000161128
+3808	1.47573352	0.000168582
+3810	1.475732924	0.00017333
+3812	1.475732993	0.000175196
+3814	1.475733987	0.000174404
+3816	1.475738176	0.000172977
+3818	1.475745275	0.000172633
+3820	1.475752771	0.000174761
+3822	1.475759674	0.000179016
+3824	1.475764703	0.000183475
+3826	1.475769755	0.00018761
+3828	1.475776986	0.000192418
+3830	1.475783098	0.000199639
+3832	1.475788297	0.000209346
+3834	1.475790958	0.000221078
+3836	1.475788399	0.000233277
+3838	1.475781539	0.000243302
+3840	1.475773258	0.00024822
+3842	1.475766957	0.000249319
+3844	1.475761815	0.000250161
+3846	1.47575639	0.000251131
+3848	1.475748935	0.000250954
+3850	1.475740677	0.000247448
+3852	1.47573419	0.000239298
+3854	1.475732013	0.00022763
+3856	1.475736094	0.000215807
+3858	1.475743401	0.000207047
+3860	1.475754065	0.000202158
+3862	1.475765096	0.000202101
+3864	1.475773442	0.000206089
+3866	1.475777823	0.000212973
+3868	1.475777044	0.00022007
+3870	1.475769788	0.000223161
+3872	1.475761679	0.000217701
+3874	1.475759835	0.00020568
+3876	1.475766159	0.000194071
+3878	1.475776036	0.000186624
+3880	1.475787496	0.000183261
+3882	1.47579899	0.000183371
+3884	1.475808298	0.000186003
+3886	1.475815532	0.000190704
+3888	1.475820446	0.000195753
+3890	1.475823615	0.000199899
+3892	1.475824887	0.000202665
+3894	1.475826912	0.000204321
+3896	1.475827988	0.000204971
+3898	1.475830058	0.000204185
+3900	1.475833336	0.00020288
+3902	1.475837981	0.000202091
+3904	1.475843498	0.000203201
+3906	1.475848785	0.000206778
+3908	1.475851041	0.00021273
+3910	1.475847864	0.000215759
+3912	1.475845039	0.000211571
+3914	1.475847728	0.000205958
+3916	1.47585513	0.000202886
+3918	1.475861612	0.00020386
+3920	1.475866801	0.000208044
+3922	1.475868017	0.000213749
+3924	1.475862852	0.000216258
+3926	1.47585769	0.000210993
+3928	1.475857257	0.000200361
+3930	1.475865029	0.000190404
+3932	1.475876388	0.000185295
+3934	1.475887586	0.000184723
+3936	1.475896004	0.000186124
+3938	1.475903314	0.000187275
+3940	1.475910608	0.000189149
+3942	1.475917896	0.000191266
+3944	1.475924571	0.000194824
+3946	1.475930811	0.000199963
+3948	1.475933986	0.000206118
+3950	1.475932956	0.000211965
+3952	1.475928783	0.000211772
+3954	1.475926843	0.00020721
+3956	1.475929862	0.000200358
+3958	1.475936289	0.000194987
+3960	1.475943518	0.00019141
+3962	1.475951862	0.000188811
+3964	1.475959113	0.000186954
+3966	1.47596855	0.000184972
+3968	1.475977129	0.000183219
+3970	1.47598747	0.000181797
+3972	1.476000044	0.000181759
+3974	1.476013374	0.000184824
+3976	1.476026922	0.000192623
+3978	1.476034056	0.000205577
+3980	1.476028174	0.000216734
+3982	1.476018745	0.000209197
+3984	1.476025637	0.000193026
+3986	1.476043674	0.000183363
+3988	1.476063276	0.000180229
+3990	1.476083041	0.000181566
+3992	1.476102695	0.000186255
+3994	1.476122622	0.000193691
+3996	1.476140785	0.000204149
+3998	1.476157521	0.000217163
+4000	1.476171336	0.000231948
 \ No newline at end of file
-800	0.00237097091817457
-802	0.00227949941219620
-804	0.00221816388191892
-806	0.00217471041775780
-808	0.00215481795727275
-810	0.00213388387011066
-812	0.00209363211698535
-814	0.00202082763908315
-816	0.00193585066178408
-818	0.00188250850160370
-820	0.00184538369212481
-822	0.00183536653704965
-824	0.00185974183080381
-826	0.00190647188683237
-828	0.00199326404385590
-830	0.00213499888469032
-832	0.00233225842027966
-834	0.00257593995310952
-836	0.00287502014227382
-838	0.00318754088914534
-840	0.00349170996961850
-842	0.00366108155160527
-844	0.00362683356184450
-846	0.00340059748640139
-848	0.00305608088262669
-850	0.00270129337895778
-852	0.00239675724637807
-854	0.00217864428240924
-856	0.00203021645685105
-858	0.00193686140678899
-860	0.00187749764181973
-862	0.00185772044069943
-864	0.00188910883086452
-866	0.00195093483930895
-868	0.00204692017755064
-870	0.00215522059478817
-872	0.00226016367314688
-874	0.00224604514385606
-876	0.00210230179408609
-878	0.00199743674523776
-880	0.00199218269491360
-882	0.00208480862951801
-884	0.00228270137034088
-886	0.00262030644370857
-888	0.00319352984551477
-890	0.00421972378192706
-892	0.00602385856914103
-894	0.00840405009274333
-896	0.00900675480510885
-898	0.00696613165618276
-900	0.00499554830114596
-902	0.00383849939561442
-904	0.00320523678732641
-906	0.00285555041538049
-908	0.00266476454212409
-910	0.00254627716354120
-912	0.00245341529587653
-914	0.00236459307673934
-916	0.00229282344387905
-918	0.00223035979386559
-920	0.00221227947671869
-922	0.00224238729804433
-924	0.00235007654381494
-926	0.00256726325953723
-928	0.00284644035247116
-930	0.00294228033320561
-932	0.00275916688965430
-934	0.00258731026217053
-936	0.00255719587176405
-938	0.00262153336828821
-940	0.00273896371051358
-942	0.00287538936255749
-944	0.00299732885131251
-946	0.00309698674175826
-948	0.00316605202547143
-950	0.00320470876397792
-952	0.00323491311445059
-954	0.00329692599734166
-956	0.00338582912769461
-958	0.00350331602393855
-960	0.00365994789379712
-962	0.00382797968742639
-964	0.00395048819829240
-966	0.00399909330987952
-968	0.00397747867047571
-970	0.00393338530466517
-972	0.00391527408455760
-974	0.00393711464406835
-976	0.00402058186620085
-978	0.00414801626311813
-980	0.00426028437517640
-982	0.00424343298749414
-984	0.00411994903649494
-986	0.00399867235513141
-988	0.00388651104937391
-990	0.00379950457370988
-992	0.00373977952014182
-994	0.00373881240280082
-996	0.00379956481032446
-998	0.00393643103780800
-1000	0.00418426742600855
-1002	0.00448366832068703
-1004	0.00421395149528264
-1006	0.00400806256602511
-1008	0.00395963930728052
-1010	0.00399586579501438
-1012	0.00412453345420230
-1014	0.00435650139468447
-1016	0.00470823294497344
-1018	0.00525652222711324
-1020	0.00620034607293144
-1022	0.00761074657742514
-1024	0.00904862587038915
-1026	0.0128420613454482
-1028	0.0232054647758307
-1030	0.0401070318402723
-1032	0.0237662509507289
-1034	0.0150900768702586
-1036	0.0136209302389719
-1038	0.0140722804433677
-1040	0.0148520038780156
-1042	0.0150418759020717
-1044	0.0142741299011939
-1046	0.0127983598294137
-1048	0.0111020250322553
-1050	0.00953886802849649
-1052	0.00823573530792714
-1054	0.00722015941851439
-1056	0.00647199198407014
-1058	0.00595450625097980
-1060	0.00562081994003704
-1062	0.00547155564647798
-1064	0.00551163119086301
-1066	0.00577378575211103
-1068	0.00633217061275026
-1070	0.00731526451760166
-1072	0.00888941764012196
-1074	0.0111936669094970
-1076	0.0145627178352916
-1078	0.0198820542781815
-1080	0.0272101442099741
-1082	0.0294763996691438
-1084	0.0207090896497001
-1086	0.0127655286195192
-1088	0.00854004269533275
-1090	0.00635526613490286
-1092	0.00518140755178082
-1094	0.00455405026737381
-1096	0.00426268956025233
-1098	0.00423510235887238
-1100	0.00446505970250814
-1102	0.00496653746864136
-1104	0.00580707926483870
-1106	0.00666740083564581
-1108	0.00624732665593806
-1110	0.00479908163793379
-1112	0.00361121925654796
-1114	0.00287942570706319
-1116	0.00246148742161380
-1118	0.00222778888171568
-1120	0.00209650525411750
-1122	0.00202121838132918
-1124	0.00199323955812561
-1126	0.00200797851417853
-1128	0.00204812470413808
-1130	0.00209417368698948
-1132	0.00209849682757402
-1134	0.00210954008712956
-1136	0.00214927272221614
-1138	0.00221781253558492
-1140	0.00231654284254776
-1142	0.00241700276584513
-1144	0.00252090482583751
-1146	0.00265926205183231
-1148	0.00286652526484237
-1150	0.00313647720191737
-1152	0.00347416081610501
-1154	0.00387661923259805
-1156	0.00410043342018308
-1158	0.00394886198110498
-1160	0.00373148843650175
-1162	0.00350494607394550
-1164	0.00334022215869222
-1166	0.00324053812759405
-1168	0.00323728249115084
-1170	0.00337030363472976
-1172	0.00370331752537631
-1174	0.00446861428672600
-1176	0.00627098368325835
-1178	0.00931078620410600
-1180	0.00795027706068620
-1182	0.00505648215885331
-1184	0.00377716421438011
-1186	0.00319136495849046
-1188	0.00290137589052677
-1190	0.00275791558623964
-1192	0.00269226681474014
-1194	0.00266088014296474
-1196	0.00258817828799466
-1198	0.00241700923017517
-1200	0.00221558969693162
-1202	0.00211217407863773
-1204	0.00220182940076526
-1206	0.00261294695511882
-1208	0.00347974535374746
-1210	0.00437930056728570
-1212	0.00342648851242818
-1214	0.00227260060290268
-1216	0.00178258728885112
-1218	0.00154392622881232
-1220	0.00139698451678244
-1222	0.00129280677379398
-1224	0.00121946854787068
-1226	0.00117184455170345
-1228	0.00113722984861070
-1230	0.00111912311009601
-1232	0.00111390956612134
-1234	0.00112443805885795
-1236	0.00115660063219376
-1238	0.00121045559427169
-1240	0.00129274578774778
-1242	0.00140396276384137
-1244	0.00154410614148823
-1246	0.00169860381220359
-1248	0.00180840115780576
-1250	0.00177688982988028
-1252	0.00157601125295148
-1254	0.00138106340282942
-1256	0.00125620905206826
-1258	0.00118717226425611
-1260	0.00114496451549449
-1262	0.00111429933337465
-1264	0.00109740533980092
-1266	0.00108967549075875
-1268	0.00109315730663637
-1270	0.00110701272913057
-1272	0.00112547293050748
-1274	0.00114417070376777
-1276	0.00115549769406343
-1278	0.00115861723477586
-1280	0.00114576824540165
-1282	0.00112307423917382
-1284	0.00110803299150391
-1286	0.00109790695605719
-1288	0.00109710433202375
-1290	0.00110698710171340
-1292	0.00113245942678089
-1294	0.00117552067320688
-1296	0.00124267198974583
-1298	0.00132277561158489
-1300	0.00139217958266282
-1302	0.00142973694885209
-1304	0.00144188181676038
-1306	0.00147541483276765
-1308	0.00159956692209740
-1310	0.00186843894759088
-1312	0.00216486082449073
-1314	0.00211728875491887
-1316	0.00187507564071290
-1318	0.00171677440706927
-1320	0.00164837511625716
-1322	0.00163899782669962
-1324	0.00166410609076352
-1326	0.00171764577889364
-1328	0.00180479473401823
-1330	0.00194274885535529
-1332	0.00206022538770732
-1334	0.00196217286057273
-1336	0.00188492778401013
-1338	0.00187122231048589
-1340	0.00188921428962955
-1342	0.00193700700412885
-1344	0.00200313353323991
-1346	0.00208778115174581
-1348	0.00218066174704292
-1350	0.00226588109762249
-1352	0.00236276913468593
-1354	0.00248915903884931
-1356	0.00265547420500685
-1358	0.00284820286383517
-1360	0.00303211548157874
-1362	0.00319538643027851
-1364	0.00338011260813816
-1366	0.00363996415682390
-1368	0.00400265764738686
-1370	0.00448976968523854
-1372	0.00525773678870123
-1374	0.00662029687278425
-1376	0.00908376119233617
-1378	0.0123031513241818
-1380	0.0121671979448086
-1382	0.00940007546463800
-1384	0.00754318150864360
-1386	0.00640356392721685
-1388	0.00563257119321882
-1390	0.00511010869784208
-1392	0.00475789415695825
-1394	0.00452833517370964
-1396	0.00440186171426137
-1398	0.00433687786700866
-1400	0.00432317844214779
-1402	0.00436175400856741
-1404	0.00444654158141412
-1406	0.00458045165701961
-1408	0.00472070193080689
-1410	0.00484730108752061
-1412	0.00499169569971829
-1414	0.00517526500052341
-1416	0.00540856165680758
-1418	0.00569301961826355
-1420	0.00603609386579061
-1422	0.00639815529754280
-1424	0.00676704333943306
-1426	0.00709702523848474
-1428	0.00735286473751553
-1430	0.00758946104003622
-1432	0.00786781701959305
-1434	0.00830202970708910
-1436	0.00898232020613486
-1438	0.0100197835148382
-1440	0.0115095063570045
-1442	0.0133985990853930
-1444	0.0153768866835411
-1446	0.0171765347348967
-1448	0.0189361099169456
-1450	0.0208245294344141
-1452	0.0228039247538198
-1454	0.0246810508004892
-1456	0.0262618411626106
-1458	0.0273608063623162
-1460	0.0277930934742346
-1462	0.0274706237226478
-1464	0.0264211185824187
-1466	0.0247980788620200
-1468	0.0228296555480849
-1470	0.0207834609064780
-1472	0.0188724652439656
-1474	0.0171801988754876
-1476	0.0157920753997752
-1478	0.0147283011159520
-1480	0.0140030494767984
-1482	0.0137569248084170
-1484	0.0141879797029108
-1486	0.0159226244331294
-1488	0.0201940578220826
-1490	0.0260836787125339
-1492	0.0401202763896059
-1494	0.0761786772950870
-1496	0.108223079178941
-1498	0.0527249260725011
-1500	0.0271635520581988
-1502	0.0173322191403291
-1504	0.0124889207648925
-1506	0.00992131298532918
-1508	0.00839752655521901
-1510	0.00745176347821015
-1512	0.00688020881374870
-1514	0.00648533490268327
-1516	0.00628100243994201
-1518	0.00629379543847072
-1520	0.00670033315002658
-1522	0.00786453088070098
-1524	0.00861000109877936
-1526	0.00697026673858113
-1528	0.00565227380276001
-1530	0.00510003019871344
-1532	0.00487330093915990
-1534	0.00477643425469498
-1536	0.00467177280329912
-1538	0.00449022432901730
-1540	0.00423934685882746
-1542	0.00393426018189818
-1544	0.00365660104528498
-1546	0.00348923385240243
-1548	0.00342710802865492
-1550	0.00346898664460405
-1552	0.00338295466527580
-1554	0.00321378452613121
-1556	0.00313430635529189
-1558	0.00316907431392649
-1560	0.00330481737182376
-1562	0.00356172011440931
-1564	0.00388898354936485
-1566	0.00429638887941885
-1568	0.00472113284868973
-1570	0.00504929184964361
-1572	0.00519286093716334
-1574	0.00509202242388202
-1576	0.00481769783190026
-1578	0.00455543799934706
-1580	0.00435935962171553
-1582	0.00433990247775519
-1584	0.00460726311748136
-1586	0.00492003737038605
-1588	0.00490704034351103
-1590	0.00492753522146188
-1592	0.00518588888004375
-1594	0.00592543183304241
-1596	0.00720757954725413
-1598	0.00912890526935344
-1600	0.0130293680056744
-1602	0.0206809953186127
-1604	0.0299953585748135
-1606	0.0248157340286292
-1608	0.0127358449020555
-1610	0.00746783575970784
-1612	0.00537209761858949
-1614	0.00445129559785390
-1616	0.00405329276394375
-1618	0.00399146289131384
-1620	0.00409659649670941
-1622	0.00425086095548363
-1624	0.00425306230534309
-1626	0.00388013491422351
-1628	0.00322765310314340
-1630	0.00259805094537761
-1632	0.00208657181154715
-1634	0.00169843933990688
-1636	0.00141785441008406
-1638	0.00123234974672297
-1640	0.00109764310439106
-1642	0.000997096490971439
-1644	0.000923943814992787
-1646	0.000867694719207358
-1648	0.000857989573211860
-1650	0.000876925837508371
-1652	0.000900483600662835
-1654	0.000924599031590994
-1656	0.000943402878947833
-1658	0.000957189946759812
-1660	0.000919301596934912
-1662	0.000829980699381760
-1664	0.000741920416434289
-1666	0.000684454640853614
-1668	0.000660487010052916
-1670	0.000677329699540855
-1672	0.000733663772686657
-1674	0.000829672252398670
-1676	0.000923202402787059
-1678	0.000900896424649981
-1680	0.000787132461270056
-1682	0.000676995955481515
-1684	0.000611701232515841
-1686	0.000595044263899243
-1688	0.000601913444772076
-1690	0.000631185451917075
-1692	0.000675093910401457
-1694	0.000731422393886708
-1696	0.000808376337564176
-1698	0.000794279618925047
-1700	0.000709354504802398
-1702	0.000657251178127169
-1704	0.000631084077034609
-1706	0.000620630016846374
-1708	0.000614804872029308
-1710	0.000610379344278778
-1712	0.000608365704329393
-1714	0.000610177708447017
-1716	0.000628060629349526
-1718	0.000671390695691186
-1720	0.000748670745348075
-1722	0.000874314265691752
-1724	0.00104123844277088
-1726	0.00123749183518020
-1728	0.00147184752955714
-1730	0.00173223404858593
-1732	0.00197582318555127
-1734	0.00215543372945357
-1736	0.00220452603076912
-1738	0.00209119301342784
-1740	0.00185700091397871
-1742	0.00156445999707629
-1744	0.00127824303920924
-1746	0.00103830550711541
-1748	0.000858082809524967
-1750	0.000736720622233361
-1752	0.000665836151632355
-1754	0.000633014507978860
-1756	0.000636204186868655
-1758	0.000664560791933513
-1760	0.000700854142871225
-1762	0.000738249770728404
-1764	0.000779473476320026
-1766	0.000831332837575542
-1768	0.000887483745995595
-1770	0.000943100942235622
-1772	0.00100855983483948
-1774	0.00108815587341361
-1776	0.00117336763806935
-1778	0.00122720647155439
-1780	0.00120867298099444
-1782	0.00117346527655232
-1784	0.00119371865588136
-1786	0.00128533671400934
-1788	0.00142590894789679
-1790	0.00158054902116715
-1792	0.00179850758319075
-1794	0.00213331852757031
-1796	0.00258371206804431
-1798	0.00310651819625664
-1800	0.00358456135015573
-1802	0.00384535056234718
-1804	0.00377208677963125
-1806	0.00340950704775298
-1808	0.00292589878928829
-1810	0.00246230467854199
-1812	0.00209503276430901
-1814	0.00185262669472132
-1816	0.00171702079169156
-1818	0.00163886439352206
-1820	0.00157730777183400
-1822	0.00149679229624579
-1824	0.00138863730310920
-1826	0.00127743508882463
-1828	0.00118456389012839
-1830	0.00112905353317808
-1832	0.00108606377735617
-1834	0.00103086061641581
-1836	0.000984959950309749
-1838	0.000979289058512249
-1840	0.00102288594610930
-1842	0.00112067935890798
-1844	0.00128394592127716
-1846	0.00152723861251123
-1848	0.00188826636609761
-1850	0.00239227576491655
-1852	0.00300971905084921
-1854	0.00364059420885185
-1856	0.00414527688649222
-1858	0.00428418417776257
-1860	0.00397341781363892
-1862	0.00343437915842565
-1864	0.00294698351848267
-1866	0.00265685216170442
-1868	0.00257554798807387
-1870	0.00262362192114651
-1872	0.00267320615475132
-1874	0.00259670566832300
-1876	0.00235341832549094
-1878	0.00201352392982882
-1880	0.00167162491751218
-1882	0.00138756730843950
-1884	0.00117032979189392
-1886	0.00101120581308014
-1888	0.000892343360827370
-1890	0.000799797724248844
-1892	0.000722584304592367
-1894	0.000668205830350704
-1896	0.000645563701038960
-1898	0.000645767881929762
-1900	0.000633984361915526
-1902	0.000588098076669510
-1904	0.000535948959936282
-1906	0.000500979831672727
-1908	0.000480503614669823
-1910	0.000475812984522745
-1912	0.000486823903968232
-1914	0.000515195500000000
-1916	0.000562568109473544
-1918	0.000630427523781356
-1920	0.000723610116430462
-1922	0.000847642176098185
-1924	0.000992789644339751
-1926	0.00114429259972093
-1928	0.00131728542788928
-1930	0.00155893716312052
-1932	0.00190373075161683
-1934	0.00237556565013185
-1936	0.00298040121387223
-1938	0.00364293200808332
-1940	0.00416589638649938
-1942	0.00433944387091247
-1944	0.00420413532397440
-1946	0.00380161374653215
-1948	0.00327719918178656
-1950	0.00282576366330091
-1952	0.00253348765310892
-1954	0.00239437526824859
-1956	0.00234603768444204
-1958	0.00232574864667046
-1960	0.00220039532483667
-1962	0.00199445232375287
-1964	0.00170495488495039
-1966	0.00137875775323702
-1968	0.00109690552229723
-1970	0.000878128994624433
-1972	0.000721601368959039
-1974	0.000617419916987627
-1976	0.000562113218832075
-1978	0.000551026292591773
-1980	0.000575711660935202
-1982	0.000615370850112472
-1984	0.000626638864213787
-1986	0.000619344762051612
-1988	0.000644972987040071
-1990	0.000691941782910493
-1992	0.000694254646432683
-1994	0.000622443290799324
-1996	0.000495200120138662
-1998	0.000402620427801543
-2000	0.000357520428000267
-2002	0.000340715817783006
-2004	0.000340725563484929
-2006	0.000349587604938024
-2008	0.000357889528657337
-2010	0.000352782837535485
-2012	0.000327904929253038
-2014	0.000298699882098499
-2016	0.000271842376811093
-2018	0.000242333037716520
-2020	0.000218337240170542
-2022	0.000199194821720737
-2024	0.000183911806628813
-2026	0.000171888258235563
-2028	0.000164785282634461
-2030	0.000164391739593814
-2032	0.000169011600820695
-2034	0.000154127618321273
-2036	0.000133850562902313
-2038	0.000121768011512588
-2040	0.000114542173977814
-2042	0.000109960714942027
-2044	0.000107324747708015
-2046	0.000105319938271901
-2048	0.000104400109927128
-2050	0.000104560803595480
-2052	0.000105682984195988
-2054	0.000107138188290709
-2056	0.000109850938702712
-2058	0.000113964387835913
-2060	0.000119159665067584
-2062	0.000125394011284327
-2064	0.000135383120416356
-2066	0.000150829077064515
-2068	0.000163896208951784
-2070	0.000158538657020860
-2072	0.000143857048326539
-2074	0.000133838990991728
-2076	0.000126082674541763
-2078	0.000119111322229434
-2080	0.000113978504701401
-2082	0.000110907574969952
-2084	0.000108574694668308
-2086	0.000105750311657561
-2088	0.000102757884920459
-2090	0.000100315348970678
-2092	9.88998809699028e-05
-2094	9.84636051990861e-05
-2096	9.86736776470892e-05
-2098	9.86832304001427e-05
-2100	9.94847029581411e-05
-2102	0.000102501492433386
-2104	0.000108578252528750
-2106	0.000117598982731806
-2108	0.000128810423312497
-2110	0.000138078130156183
-2112	0.000139894738408702
-2114	0.000140372347283306
-2116	0.000147183990385426
-2118	0.000142580842940779
-2120	0.000126124302551768
-2122	0.000119111147897455
-2124	0.000117761941379516
-2126	0.000110386213471180
-2128	0.000100586367430428
-2130	9.65127771567695e-05
-2132	9.71593180254151e-05
-2134	0.000100588542105452
-2136	0.000104481772978239
-2138	0.000107041125533866
-2140	0.000108872498221666
-2142	0.000111489568147590
-2144	0.000115451529322482
-2146	0.000120558240114413
-2148	0.000126537781071288
-2150	0.000134733619506300
-2152	0.000148643632029954
-2154	0.000172040859828778
-2156	0.000210048660817435
-2158	0.000268125741557685
-2160	0.000351069215958102
-2162	0.000450344598032358
-2164	0.000489938528699291
-2166	0.000409492796412179
-2168	0.000304387639702614
-2170	0.000235891130206754
-2172	0.000200519075056806
-2174	0.000185710828669175
-2176	0.000182424899321747
-2178	0.000187448554282292
-2180	0.000203021437757415
-2182	0.000231533383222207
-2184	0.000266979354976650
-2186	0.000274670338797065
-2188	0.000249531305296574
-2190	0.000224075465024111
-2192	0.000200276630934979
-2194	0.000177273244376758
-2196	0.000160285923199765
-2198	0.000150581068702164
-2200	0.000148630566016007
-2202	0.000159418644068291
-2204	0.000190928483551684
-2206	0.000246685640401459
-2208	0.000270254541506430
-2210	0.000222823187679136
-2212	0.000183299674920404
-2214	0.000159208446689860
-2216	0.000141367831176120
-2218	0.000133886240444937
-2220	0.000133377867922854
-2222	0.000136687110101880
-2224	0.000141595068371183
-2226	0.000145519316291541
-2228	0.000148458736825531
-2230	0.000153316938474443
-2232	0.000163253960273079
-2234	0.000178923069609914
-2236	0.000194257120755014
-2238	0.000196450490452201
-2240	0.000188281502894665
-2242	0.000182547056123856
-2244	0.000184193400303698
-2246	0.000192794200162931
-2248	0.000207468879582850
-2250	0.000228635659533982
-2252	0.000256821954754517
-2254	0.000293238050530334
-2256	0.000339843587945316
-2258	0.000394697192716897
-2260	0.000433841600455809
-2262	0.000418808222045475
-2264	0.000365652480977041
-2266	0.000317992842743265
-2268	0.000289251978678528
-2270	0.000276323460348606
-2272	0.000276007776761593
-2274	0.000285194711508216
-2276	0.000305840459677383
-2278	0.000341614672459952
-2280	0.000378323694871339
-2282	0.000375183465200990
-2284	0.000372499291886178
-2286	0.000379130457959152
-2288	0.000369071052928138
-2290	0.000344203099796142
-2292	0.000313724278864159
-2294	0.000283180068926335
-2296	0.000260398235921227
-2298	0.000248364444837745
-2300	0.000246962256014277
-2302	0.000257337196851115
-2304	0.000282117167464228
-2306	0.000327011660272884
-2308	0.000402901410624785
-2310	0.000515678907419335
-2312	0.000613221545587734
-2314	0.000587317319167494
-2316	0.000479703817387008
-2318	0.000387543339108333
-2320	0.000331935579008350
-2322	0.000305882244139694
-2324	0.000301743073919341
-2326	0.000318021837096887
-2328	0.000360763254301904
-2330	0.000442864766710211
-2332	0.000580146273004247
-2334	0.000746878008138738
-2336	0.000778905767997363
-2338	0.000655878707879373
-2340	0.000549860316308082
-2342	0.000474310426764780
-2344	0.000414796574428013
-2346	0.000384139069758195
-2348	0.000382158356339707
-2350	0.000402158338733409
-2352	0.000435516153586227
-2354	0.000472182760873504
-2356	0.000515961034751272
-2358	0.000592576004516974
-2360	0.000693206523120231
-2362	0.000643638218785556
-2364	0.000478341631402279
-2366	0.000369914098808752
-2368	0.000314093467617302
-2370	0.000287309303030045
-2372	0.000274524402561852
-2374	0.000270061869985669
-2376	0.000271829601590763
-2378	0.000279194809335497
-2380	0.000294905061876556
-2382	0.000319347534507768
-2384	0.000350241467027989
-2386	0.000391786089197638
-2388	0.000432288381112108
-2390	0.000431894838874137
-2392	0.000400306861211915
-2394	0.000373780803138032
-2396	0.000355410966982535
-2398	0.000347151739593354
-2400	0.000350924151462325
-2402	0.000365706536144189
-2404	0.000389705426960732
-2406	0.000421334803876133
-2408	0.000459934423654906
-2410	0.000500616815279102
-2412	0.000525702627325844
-2414	0.000513223543953278
-2416	0.000478247500654749
-2418	0.000439595749420076
-2420	0.000399407179067621
-2422	0.000365631853681067
-2424	0.000342099304419797
-2426	0.000327643185447820
-2428	0.000319852482413628
-2430	0.000318090248146717
-2432	0.000318226888962093
-2434	0.000307017564256603
-2436	0.000284561022911212
-2438	0.000265983112770141
-2440	0.000252937611403322
-2442	0.000242679401171322
-2444	0.000236093051616947
-2446	0.000233130690914760
-2448	0.000233167378896135
-2450	0.000235415965609999
-2452	0.000239364304311204
-2454	0.000244209499641596
-2456	0.000248579466181052
-2458	0.000251144773278908
-2460	0.000252431049719579
-2462	0.000253691712617762
-2464	0.000255788005476147
-2466	0.000256434321853842
-2468	0.000251072591655402
-2470	0.000241597521259849
-2472	0.000234162117014666
-2474	0.000229676856991507
-2476	0.000227592143774873
-2478	0.000226834091088810
-2480	0.000227168703547583
-2482	0.000228588584217583
-2484	0.000231746296813716
-2486	0.000236823965966075
-2488	0.000241600139160114
-2490	0.000244394482975018
-2492	0.000244248137929474
-2494	0.000245127828260994
-2496	0.000251434891521320
-2498	0.000247993851620619
-2500	0.000232735996433491
-2502	0.000222497793867323
-2504	0.000221589422451279
-2506	0.000232579945681551
-2508	0.000250427153657126
-2510	0.000252498000507853
-2512	0.000232189718802120
-2514	0.000211050185590214
-2516	0.000198391157226399
-2518	0.000193635707688150
-2520	0.000193341820452081
-2522	0.000193371593068733
-2524	0.000189643081211288
-2526	0.000181794690676754
-2528	0.000178838464388285
-2530	0.000183501803348288
-2532	0.000194837096053966
-2534	0.000211327514566071
-2536	0.000231393834808824
-2538	0.000255837394665623
-2540	0.000275709996672117
-2542	0.000266055047783776
-2544	0.000243859757637041
-2546	0.000235285437161138
-2548	0.000236304976186297
-2550	0.000232544359689715
-2552	0.000218806075082454
-2554	0.000204743746363893
-2556	0.000196655427865349
-2558	0.000191976123078746
-2560	0.000186392842736032
-2562	0.000182465243677096
-2564	0.000182341770175991
-2566	0.000186622668096877
-2568	0.000194771585308041
-2570	0.000207509200230819
-2572	0.000227536779149540
-2574	0.000256126025913237
-2576	0.000293783533966409
-2578	0.000344606705405512
-2580	0.000421000900491490
-2582	0.000539940417278290
-2584	0.000691325137774485
-2586	0.000768064347900480
-2588	0.000684349300000000
-2590	0.000536495643153772
-2592	0.000418107936641488
-2594	0.000348162932430616
-2596	0.000316562063243598
-2598	0.000311605992448936
-2600	0.000329718943031756
-2602	0.000370011429187919
-2604	0.000412184734144213
-2606	0.000402481978671523
-2608	0.000368470211663778
-2610	0.000353398410510846
-2612	0.000328281593188018
-2614	0.000295400882956194
-2616	0.000275902521470556
-2618	0.000268299167514448
-2620	0.000267511791747167
-2622	0.000270974116559811
-2624	0.000277238419508473
-2626	0.000286763887252883
-2628	0.000300107477286003
-2630	0.000316524811935304
-2632	0.000327263381122722
-2634	0.000305877054698251
-2636	0.000269148133708810
-2638	0.000248172907618610
-2640	0.000239823700606054
-2642	0.000238746030638882
-2644	0.000239868631298371
-2646	0.000237697572301885
-2648	0.000231658620506580
-2650	0.000224559727594560
-2652	0.000220154792342943
-2654	0.000220025182909045
-2656	0.000220821585838385
-2658	0.000219097069889182
-2660	0.000213668868513552
-2662	0.000206551642880241
-2664	0.000200132874030954
-2666	0.000198263371264169
-2668	0.000204157476079366
-2670	0.000219581959345431
-2672	0.000228529275997830
-2674	0.000212671171569940
-2676	0.000198554340066309
-2678	0.000193733620852842
-2680	0.000194427317307389
-2682	0.000197546011671515
-2684	0.000200581527813713
-2686	0.000203985348880727
-2688	0.000208935024070450
-2690	0.000213885837983080
-2692	0.000215780646355564
-2694	0.000215167439140776
-2696	0.000214895725221701
-2698	0.000217360387387823
-2700	0.000222623944199778
-2702	0.000229950531867105
-2704	0.000237779651458241
-2706	0.000247270953949545
-2708	0.000260083526905394
-2710	0.000275286056335416
-2712	0.000293138008774478
-2714	0.000315098638979930
-2716	0.000342140022611386
-2718	0.000376355762584957
-2720	0.000422618703820090
-2722	0.000488803228667163
-2724	0.000585387059813060
-2726	0.000728318801443707
-2728	0.000938827018235910
-2730	0.00123037571269695
-2732	0.00155229568740433
-2734	0.00172266995984292
-2736	0.00158429227183195
-2738	0.00126235409603059
-2740	0.000954219558161654
-2742	0.000733284051680574
-2744	0.000590574186925838
-2746	0.000500913503228797
-2748	0.000444283569806984
-2750	0.000408552058896459
-2752	0.000386442879562956
-2754	0.000373264157615818
-2756	0.000366670327661857
-2758	0.000363876514149830
-2760	0.000361532536949891
-2762	0.000363675314741141
-2764	0.000366718711717702
-2766	0.000373487709343178
-2768	0.000385907143020104
-2770	0.000398462101615587
-2772	0.000413801469177668
-2774	0.000425659990486031
-2776	0.000436402382617843
-2778	0.000446662734946199
-2780	0.000455121187378285
-2782	0.000464083631949392
-2784	0.000471837814603525
-2786	0.000485996560282024
-2788	0.000502172804216709
-2790	0.000522830212064553
-2792	0.000548289451554969
-2794	0.000579634288120943
-2796	0.000611379237870225
-2798	0.000641158616950349
-2800	0.000672247209660977
-2802	0.000711615716417748
-2804	0.000756204442404881
-2806	0.000806513382136127
-2808	0.000854383801707436
-2810	0.000899046135928726
-2812	0.000920533253907859
-2814	0.000922946174823163
-2816	0.000938823165339874
-2818	0.000975854382639431
-2820	0.00103794809306155
-2822	0.00111441105526966
-2824	0.00117124310275486
-2826	0.00120584112843460
-2828	0.00126141309789025
-2830	0.00134778284367920
-2832	0.00146199663837007
-2834	0.00159718851386329
-2836	0.00175330338362696
-2838	0.00193523559724759
-2840	0.00214829304268432
-2842	0.00239693861672905
-2844	0.00270947510257679
-2846	0.00308962037090872
-2848	0.00355940585209848
-2850	0.00412210422108316
-2852	0.00476891854151234
-2854	0.00547214050611261
-2856	0.00617409172881556
-2858	0.00678722786702444
-2860	0.00723807939551757
-2862	0.00752048939258356
-2864	0.00769405118384194
-2866	0.00780672387589873
-2868	0.00789211778455793
-2870	0.00795935754077555
-2872	0.00799733164350610
-2874	0.00795934759033912
-2876	0.00778684233057949
-2878	0.00748513477927108
-2880	0.00712782450019760
-2882	0.00674716793892496
-2884	0.00636559086703165
-2886	0.00600252759803496
-2888	0.00568003469443299
-2890	0.00541869257628554
-2892	0.00523149924308805
-2894	0.00513859281992941
-2896	0.00514912231818864
-2898	0.00528298553786387
-2900	0.00554846488279469
-2902	0.00596670745150011
-2904	0.00656025912947429
-2906	0.00737309118502326
-2908	0.00844343143196328
-2910	0.00980783562233305
-2912	0.0114361820721680
-2914	0.0132043723140582
-2916	0.0148639399258050
-2918	0.0160322637171387
-2920	0.0163848402191419
-2922	0.0159315596024990
-2924	0.0149712224125917
-2926	0.0138179195741240
-2928	0.0126830001717222
-2930	0.0117051760061400
-2932	0.0109454119425227
-2934	0.0104094926683649
-2936	0.0100777464854532
-2938	0.00991576239015874
-2940	0.00989092758914217
-2942	0.00995253861794336
-2944	0.0100558436016283
-2946	0.0101466649820268
-2948	0.0101700911447294
-2950	0.0100970420129300
-2952	0.00995445488065370
-2954	0.00977184847019253
-2956	0.00956031409076577
-2958	0.00931672833064324
-2960	0.00900841342025127
-2962	0.00860452512496009
-2964	0.00819173199579369
-2966	0.00793188379052879
-2968	0.00787856977180025
-2970	0.00795406658370171
-2972	0.00807021356855313
-2974	0.00817433984043233
-2976	0.00825003493744345
-2978	0.00828855603001654
-2980	0.00828386290179407
-2982	0.00816950979044141
-2984	0.00795147116279175
-2986	0.00771875813248752
-2988	0.00752177579743462
-2990	0.00739482968641806
-2992	0.00735495102785436
-2994	0.00742400805444368
-2996	0.00762947734762659
-2998	0.00800350176450487
-3000	0.00849881078288103
-3002	0.00896624168638865
-3004	0.00925040248900867
-3006	0.00945455630611128
-3008	0.00976581762927042
-3010	0.0103150719126273
-3012	0.0112091641279662
-3014	0.0125665741882334
-3016	0.0144920310150755
-3018	0.0171523311364697
-3020	0.0206588071576588
-3022	0.0247927573582982
-3024	0.0285338257471566
-3026	0.0305737428191527
-3028	0.0304197730378849
-3030	0.0285285708945381
-3032	0.0254626182993726
-3034	0.0218417847555673
-3036	0.0183214780469989
-3038	0.0154367262434714
-3040	0.0134174271105468
-3042	0.0121814306436623
-3044	0.0114802419869786
-3046	0.0111082334096508
-3048	0.0110364952795097
-3050	0.0112341213861221
-3052	0.0116521403194674
-3054	0.0121679353995795
-3056	0.0126492093791370
-3058	0.0130640240273400
-3060	0.0134217837485980
-3062	0.0136027351521215
-3064	0.0133566760196114
-3066	0.0124957830807641
-3068	0.0111185801076637
-3070	0.00962312187980008
-3072	0.00840019013916095
-3074	0.00762785975903174
-3076	0.00731431659052294
-3078	0.00742769361429674
-3080	0.00800169947155848
-3082	0.00909924810606661
-3084	0.0105612984915747
-3086	0.0115953458981882
-3088	0.0108915516715014
-3090	0.00855348266587572
-3092	0.00625766310903960
-3094	0.00474250996240750
-3096	0.00389487972553113
-3098	0.00350242093033435
-3100	0.00342566123955596
-3102	0.00354245491578370
-3104	0.00366329979669444
-3106	0.00351255659174282
-3108	0.00307160622386024
-3110	0.00262319086310484
-3112	0.00230238895472291
-3114	0.00208330628877116
-3116	0.00190296000440166
-3118	0.00170124594674715
-3120	0.00147221774746264
-3122	0.00126680203340060
-3124	0.00110221512874358
-3126	0.000972843085744223
-3128	0.000865976217229730
-3130	0.000787123046176519
-3132	0.000725569824317256
-3134	0.000678619961272403
-3136	0.000643376054198741
-3138	0.000613508276940799
-3140	0.000585754400051242
-3142	0.000561171104171409
-3144	0.000538801514536514
-3146	0.000520080512301793
-3148	0.000505696831504068
-3150	0.000493470880103411
-3152	0.000480268222246598
-3154	0.000470385004364871
-3156	0.000459220112914975
-3158	0.000450945450269378
-3160	0.000450827328828143
-3162	0.000455120896574839
-3164	0.000465883832863404
-3166	0.000478798660924222
-3168	0.000482832083650923
-3170	0.000455625596338195
-3172	0.000403338720059331
-3174	0.000360438306588196
-3176	0.000332520864586029
-3178	0.000313938694862586
-3180	0.000300705768353348
-3182	0.000290665831960273
-3184	0.000282478444260369
-3186	0.000275747274780963
-3188	0.000269274452306063
-3190	0.000262630704721266
-3192	0.000255445037852355
-3194	0.000248377973867383
-3196	0.000241977580841794
-3198	0.000236251689540068
-3200	0.000230923454004864
-3202	0.000226049100105626
-3204	0.000221226160126354
-3206	0.000214716060376866
-3208	0.000206517982920749
-3210	0.000198104526951019
-3212	0.000190353242003341
-3214	0.000183841618071712
-3216	0.000178536526886377
-3218	0.000173732996508941
-3220	0.000169365792718528
-3222	0.000165299675350027
-3224	0.000161252739783070
-3226	0.000157550287906591
-3228	0.000154290860671044
-3230	0.000151403187559336
-3232	0.000148762116611554
-3234	0.000146608972658800
-3236	0.000144929084687115
-3238	0.000143621190469325
-3240	0.000142423755040669
-3242	0.000141225309365069
-3244	0.000139879705280103
-3246	0.000138120388481842
-3248	0.000136557609027687
-3250	0.000135029965649156
-3252	0.000133891483928728
-3254	0.000133096425324259
-3256	0.000132368577771128
-3258	0.000131178881840028
-3260	0.000129611032335659
-3262	0.000128050800000000
-3264	0.000126496752229370
-3266	0.000125487476864466
-3268	0.000124918363511663
-3270	0.000124282902673504
-3272	0.000123524889665480
-3274	0.000122442491776109
-3276	0.000121443655497364
-3278	0.000120760252331750
-3280	0.000120133235127335
-3282	0.000119422774440518
-3284	0.000118787091342885
-3286	0.000118050006014353
-3288	0.000117490615311207
-3290	0.000116940876538515
-3292	0.000116411722780357
-3294	0.000116040811167173
-3296	0.000115834700717885
-3298	0.000116085966839459
-3300	0.000116986523436758
-3302	0.000118267730379294
-3304	0.000119505403103670
-3306	0.000120364280297837
-3308	0.000119982615737227
-3310	0.000118961448074642
-3312	0.000117873723711904
-3314	0.000117091085003690
-3316	0.000116576391297391
-3318	0.000116630812029799
-3320	0.000116648622872189
-3322	0.000116640410140475
-3324	0.000116601640984688
-3326	0.000116254038453171
-3328	0.000115188264691018
-3330	0.000113811841076524
-3332	0.000111681446514179
-3334	0.000108818040972509
-3336	0.000105958252604406
-3338	0.000103151741537451
-3340	0.000100395217441575
-3342	9.80332064093372e-05
-3344	9.53544349575209e-05
-3346	9.25223256784850e-05
-3348	9.00829101787277e-05
-3350	8.83163531062304e-05
-3352	8.72118771260860e-05
-3354	8.64440098119140e-05
-3356	8.60520504254794e-05
-3358	8.61965597139509e-05
-3360	8.70019144324470e-05
-3362	8.83318478317726e-05
-3364	9.00079714359512e-05
-3366	9.23139048671722e-05
-3368	9.50882502511675e-05
-3370	9.78832163580005e-05
-3372	0.000100096171211192
-3374	0.000102179086616863
-3376	0.000103749608742208
-3378	0.000105213237160669
-3380	0.000106688938713341
-3382	0.000107853667399164
-3384	0.000108503663896066
-3386	0.000108465998629706
-3388	0.000107522134166390
-3390	0.000105586354148376
-3392	0.000103099282581304
-3394	0.000100324257650923
-3396	9.74485799284953e-05
-3398	9.51596059704078e-05
-3400	9.35013107298140e-05
-3402	9.21170196430098e-05
-3404	9.07360614712649e-05
-3406	8.91138931604199e-05
-3408	8.74505590276362e-05
-3410	8.56664975562433e-05
-3412	8.43848055968202e-05
-3414	8.35095737363273e-05
-3416	8.28173663218536e-05
-3418	8.25803390851867e-05
-3420	8.34887031217918e-05
-3422	8.50941717249168e-05
-3424	8.76826565386191e-05
-3426	9.18893425240818e-05
-3428	9.72727573628125e-05
-3430	0.000103498414055259
-3432	0.000110175431772886
-3434	0.000116489353052258
-3436	0.000121652113320222
-3438	0.000125199891677689
-3440	0.000126017012084730
-3442	0.000123363542579961
-3444	0.000118359425974797
-3446	0.000111284305442118
-3448	0.000102049297013716
-3450	9.29060570294263e-05
-3452	8.56830126047782e-05
-3454	8.03943044406067e-05
-3456	7.64946805035534e-05
-3458	7.35384095568400e-05
-3460	7.15607792666279e-05
-3462	7.00113147312602e-05
-3464	6.86840886320734e-05
-3466	6.76516046709459e-05
-3468	6.66317002099573e-05
-3470	6.58163245627029e-05
-3472	6.48526803819241e-05
-3474	6.41769150098627e-05
-3476	6.33519637219242e-05
-3478	6.21036964756407e-05
-3480	6.07594134549892e-05
-3482	5.99888706228529e-05
-3484	5.95355056229478e-05
-3486	5.98196476615315e-05
-3488	6.07067305157839e-05
-3490	6.20707024404776e-05
-3492	6.35630004076309e-05
-3494	6.39802692410745e-05
-3496	6.36894878745265e-05
-3498	6.27365377476382e-05
-3500	6.17431130904710e-05
-3502	6.13279727787810e-05
-3504	6.13193515749704e-05
-3506	6.24903413403870e-05
-3508	6.43864144265415e-05
-3510	6.71410924962580e-05
-3512	7.03539058487688e-05
-3514	7.47946182109209e-05
-3516	7.95754496113107e-05
-3518	8.34700851824913e-05
-3520	8.39873348467991e-05
-3522	8.07272560865977e-05
-3524	7.56312308938946e-05
-3526	7.10894728276635e-05
-3528	6.81632208726418e-05
-3530	6.64216930115337e-05
-3532	6.58132280866232e-05
-3534	6.67321753128692e-05
-3536	6.94647085013537e-05
-3538	7.44308734240544e-05
-3540	8.16543395123198e-05
-3542	9.03200858171377e-05
-3544	9.85535954298993e-05
-3546	0.000104547035052111
-3548	0.000107433770750519
-3550	0.000108038450708995
-3552	0.000107166592996916
-3554	0.000105178798896553
-3556	0.000101095184756009
-3558	9.50814999627662e-05
-3560	8.82058228394490e-05
-3562	8.18208514354733e-05
-3564	7.68850700845907e-05
-3566	7.38744666163043e-05
-3568	7.27642291486909e-05
-3570	7.33994731408140e-05
-3572	7.56627166220080e-05
-3574	7.96660140607364e-05
-3576	8.51090055206606e-05
-3578	9.29167699145132e-05
-3580	0.000102526366929820
-3582	0.000114877275226176
-3584	0.000126190559302250
-3586	0.000124628073841470
-3588	0.000119415520864134
-3590	0.000112006712936662
-3592	0.000105579072932928
-3594	0.000100691596209911
-3596	9.80454508807073e-05
-3598	9.79289585249404e-05
-3600	9.76517090509766e-05
-3602	9.63252158538093e-05
-3604	9.47873503300014e-05
-3606	9.40807594813255e-05
-3608	9.38724750866359e-05
-3610	9.46504942395723e-05
-3612	9.80150733458878e-05
-3614	0.000104630751802908
-3616	0.000115783489148453
-3618	0.000130667214647273
-3620	0.000146477404898454
-3622	0.000158530547818508
-3624	0.000162318596543099
-3626	0.000158125871191841
-3628	0.000150672245587412
-3630	0.000144549679683140
-3632	0.000142051097385185
-3634	0.000145529942933542
-3636	0.000153343488815115
-3638	0.000167576397035396
-3640	0.000187305749491179
-3642	0.000211282337261951
-3644	0.000235521019158824
-3646	0.000255526042383438
-3648	0.000267309387292886
-3650	0.000267620489558132
-3652	0.000257281965913234
-3654	0.000238427431722088
-3656	0.000215910141107563
-3658	0.000194198641163347
-3660	0.000175915805990763
-3662	0.000162335012119966
-3664	0.000152841199834750
-3666	0.000146981907091703
-3668	0.000143997827610619
-3670	0.000143648436802218
-3672	0.000144734329787788
-3674	0.000145900823579283
-3676	0.000145536357339105
-3678	0.000142791335633658
-3680	0.000138712508096908
-3682	0.000133854756804407
-3684	0.000128953007630511
-3686	0.000123724720918296
-3688	0.000118053544364748
-3690	0.000112538647366327
-3692	0.000108762709162428
-3694	0.000106869096858975
-3696	0.000106178550226360
-3698	0.000108026299705946
-3700	0.000113499289845608
-3702	0.000122346067036449
-3704	0.000132017367154307
-3706	0.000138204981263169
-3708	0.000137812952692201
-3710	0.000131957371338105
-3712	0.000124911657013813
-3714	0.000120086480186131
-3716	0.000119368867384451
-3718	0.000123023160227338
-3720	0.000129681526292498
-3722	0.000136685573712829
-3724	0.000140355687154432
-3726	0.000137643004943763
-3728	0.000130059156127694
-3730	0.000121898190215580
-3732	0.000115279209639364
-3734	0.000109785664308487
-3736	0.000105299764060944
-3738	0.000101063203615323
-3740	9.68651180755000e-05
-3742	9.31808749176699e-05
-3744	9.10149507453584e-05
-3746	8.98056206735940e-05
-3748	8.93161375554986e-05
-3750	8.95680290795053e-05
-3752	9.07085327291721e-05
-3754	9.23144122730348e-05
-3756	9.51698234276085e-05
-3758	9.88200437936328e-05
-3760	0.000102897737658181
-3762	0.000106541912714358
-3764	0.000108638955977754
-3766	0.000107125969211894
-3768	0.000104745321090008
-3770	0.000104907149891996
-3772	0.000107524035997495
-3774	0.000112565658169961
-3776	0.000120128967951347
-3778	0.000130377699611365
-3780	0.000143388258757916
-3782	0.000157827987118552
-3784	0.000171336843948261
-3786	0.000178285748324712
-3788	0.000174781489954516
-3790	0.000164121439128089
-3792	0.000152610210570708
-3794	0.000144162759638053
-3796	0.000139239462639203
-3798	0.000137792736182703
-3800	0.000140104567703810
-3802	0.000145422058851258
-3804	0.000152835113748305
-3806	0.000161127793420174
-3808	0.000168581867788859
-3810	0.000173330279437380
-3812	0.000175195783104517
-3814	0.000174404180004515
-3816	0.000172977411115116
-3818	0.000172632535041757
-3820	0.000174761333878933
-3822	0.000179015946250825
-3824	0.000183474569007118
-3826	0.000187609784690581
-3828	0.000192418303544244
-3830	0.000199638672160316
-3832	0.000209346193913544
-3834	0.000221078085152779
-3836	0.000233276912915708
-3838	0.000243302212259793
-3840	0.000248219562860653
-3842	0.000249318750764567
-3844	0.000250161224209589
-3846	0.000251130509086889
-3848	0.000250954031996911
-3850	0.000247448125111366
-3852	0.000239298068537633
-3854	0.000227630000846504
-3856	0.000215807191993378
-3858	0.000207046517196079
-3860	0.000202157638401237
-3862	0.000202101096220524
-3864	0.000206089427126992
-3866	0.000212972794266054
-3868	0.000220069608188463
-3870	0.000223160954785535
-3872	0.000217701230702324
-3874	0.000205680240569784
-3876	0.000194071196201460
-3878	0.000186624022776833
-3880	0.000183260750499541
-3882	0.000183370917787493
-3884	0.000186002682616268
-3886	0.000190704000843751
-3888	0.000195753159488382
-3890	0.000199899173040718
-3892	0.000202664798143917
-3894	0.000204320562044854
-3896	0.000204971280265517
-3898	0.000204184602522533
-3900	0.000202879694728580
-3902	0.000202091110448804
-3904	0.000203200507821011
-3906	0.000206777694070363
-3908	0.000212730193424292
-3910	0.000215758904170297
-3912	0.000211571330269805
-3914	0.000205958146733392
-3916	0.000202885902366098
-3918	0.000203859899346076
-3920	0.000208043821414469
-3922	0.000213749060271441
-3924	0.000216258022232613
-3926	0.000210993095532934
-3928	0.000200360509814737
-3930	0.000190403984953153
-3932	0.000185294952858894
-3934	0.000184723195717293
-3936	0.000186124269760876
-3938	0.000187274520079713
-3940	0.000189148765118607
-3942	0.000191266181204903
-3944	0.000194823747520104
-3946	0.000199962536960736
-3948	0.000206117700447747
-3950	0.000211964821297933
-3952	0.000211771907916455
-3954	0.000207210064931517
-3956	0.000200358454677226
-3958	0.000194986979879340
-3960	0.000191410166101308
-3962	0.000188811490516811
-3964	0.000186954388139908
-3966	0.000184972375095875
-3968	0.000183218705269115
-3970	0.000181796902747989
-3972	0.000181759132648531
-3974	0.000184824282283672
-3976	0.000192623374739583
-3978	0.000205576802325497
-3980	0.000216734030830589
-3982	0.000209196916619900
-3984	0.000193026471982283
-3986	0.000183362654697217
-3988	0.000180228706844783
-3990	0.000181565573496817
-3992	0.000186254988451223
-3994	0.000193691373041908
-3996	0.000204148918879724
-3998	0.000217163156382698
-4000	0.000231947733021415
 \ No newline at end of file
-800	1.44120102496924
-802	1.44244952355793
-804	1.44362241452370
-806	1.44473157548162
-808	1.44576931343185
-810	1.44673515341541
-812	1.44763153740528
-814	1.44849997645288
-816	1.44937159368323
-818	1.45024511061741
-820	1.45109838059394
-822	1.45193180052550
-824	1.45274307737647
-826	1.45353862658166
-828	1.45431614422343
-830	1.45505783090997
-832	1.45575257351567
-834	1.45637393495922
-836	1.45689903981153
-838	1.45730768949019
-840	1.45754105585989
-842	1.45762277914234
-844	1.45763704972226
-846	1.45770974157519
-848	1.45792998369439
-850	1.45831194599516
-852	1.45879214084464
-854	1.45933254646700
-856	1.45988983429307
-858	1.46043988459777
-860	1.46098292821135
-862	1.46151723624776
-864	1.46203872496248
-866	1.46253192223325
-868	1.46297856786196
-870	1.46337643775072
-872	1.46369146339390
-874	1.46394643585616
-876	1.46431343981134
-878	1.46483594897202
-880	1.46543855156632
-882	1.46608462990801
-884	1.46677023178158
-886	1.46750898169590
-888	1.46831763414834
-890	1.46912802427779
-892	1.46954514029358
-894	1.46839331789610
-896	1.46522362501208
-898	1.46324102369024
-900	1.46324805165743
-902	1.46389477313103
-904	1.46460285834673
-906	1.46524189063531
-908	1.46578615865865
-910	1.46624870624222
-912	1.46665117759441
-914	1.46703266934571
-916	1.46740765502925
-918	1.46779668973951
-920	1.46820189802559
-922	1.46861141696830
-924	1.46901759517687
-926	1.46935992609941
-928	1.46951316452951
-930	1.46945198189589
-932	1.46950773718789
-934	1.46980252488385
-936	1.47016397014931
-938	1.47050527825284
-940	1.47079802225791
-942	1.47102956241248
-944	1.47121559715866
-946	1.47137193902005
-948	1.47152008803324
-950	1.47167672882319
-952	1.47187041329055
-954	1.47208448275609
-956	1.47229737949647
-958	1.47250268786501
-960	1.47267011513556
-962	1.47277605897765
-964	1.47281096169045
-966	1.47283377833869
-968	1.47288521062562
-970	1.47300680592029
-972	1.47318336590741
-974	1.47338081764773
-976	1.47357969584368
-978	1.47371821017195
-980	1.47375527316737
-982	1.47374243519460
-984	1.47381322933363
-986	1.47398487555170
-988	1.47420629302573
-990	1.47448130861459
-992	1.47481507770761
-994	1.47518229617302
-996	1.47557023171639
-998	1.47596326572828
-1000	1.47630080652934
-1002	1.47636823234471
-1004	1.47636996678396
-1006	1.47689524896944
-1008	1.47750032220134
-1010	1.47819158796836
-1012	1.47897505869564
-1014	1.47986167058547
-1016	1.48089513800264
-1018	1.48214271193312
-1020	1.48362438976875
-1022	1.48502767979268
-1024	1.48723564000764
-1026	1.49092289691198
-1028	1.49396375951509
-1030	1.47873935405011
-1032	1.46178488502145
-1034	1.46614728364263
-1036	1.46944972756204
-1038	1.47076139801307
-1040	1.47051860247504
-1042	1.46925108082617
-1044	1.46777888639623
-1046	1.46677062217283
-1048	1.46644104430282
-1050	1.46666085838594
-1052	1.46724995592262
-1054	1.46804818971542
-1056	1.46897681608261
-1058	1.46995585496974
-1060	1.47098590895262
-1062	1.47206714530921
-1064	1.47321734998274
-1066	1.47445175619764
-1068	1.47579194531028
-1070	1.47721681438477
-1072	1.47863578920406
-1074	1.47989036409651
-1076	1.48086017571181
-1078	1.48069474784801
-1080	1.47616731467815
-1082	1.46390771869497
-1084	1.45570223896581
-1086	1.45597971475891
-1088	1.45836941934247
-1090	1.46066235559752
-1092	1.46255873201846
-1094	1.46411051824312
-1096	1.46540793776881
-1098	1.46651204425965
-1100	1.46743001960627
-1102	1.46810891059625
-1104	1.46835826348699
-1106	1.46762316195694
-1108	1.46618573784309
-1110	1.46572358542781
-1112	1.46614920302751
-1114	1.46684472613418
-1116	1.46754366818093
-1118	1.46816766240122
-1120	1.46871860517754
-1122	1.46920770699094
-1124	1.46965073082635
-1126	1.47005259957817
-1128	1.47040212564529
-1130	1.47068773768668
-1132	1.47096001810126
-1134	1.47125261448772
-1136	1.47154891832636
-1138	1.47183699189280
-1140	1.47209800955853
-1142	1.47233456778191
-1144	1.47257573473017
-1146	1.47283356711807
-1148	1.47307259446091
-1150	1.47326381831914
-1152	1.47336996150258
-1154	1.47330710459724
-1156	1.47293509477181
-1158	1.47266594765858
-1160	1.47259707273045
-1162	1.47267982619196
-1164	1.47288581951866
-1166	1.47317564562733
-1168	1.47355761342796
-1170	1.47402209612147
-1172	1.47459197223784
-1174	1.47529073492465
-1176	1.47579201984062
-1178	1.47389452829121
-1180	1.46944888964386
-1182	1.46919538008765
-1184	1.46993706618235
-1186	1.47058584953654
-1188	1.47109418040909
-1190	1.47148385016616
-1192	1.47177356227783
-1194	1.47196611004565
-1196	1.47207728619391
-1198	1.47220096862104
-1200	1.47245042725556
-1202	1.47283662225685
-1204	1.47330431122777
-1206	1.47375342391676
-1208	1.47385318037376
-1210	1.47280027515132
-1212	1.47140252001622
-1214	1.47159489093342
-1216	1.47205516262945
-1218	1.47243159969193
-1220	1.47273916940180
-1222	1.47301272972689
-1224	1.47326393439881
-1226	1.47349889542765
-1228	1.47371659199003
-1230	1.47393059180901
-1232	1.47413378656172
-1234	1.47433469964923
-1236	1.47453039235071
-1238	1.47471647903353
-1240	1.47488491964895
-1242	1.47502851521336
-1244	1.47512495593972
-1246	1.47514408931247
-1248	1.47505892212860
-1250	1.47489972136187
-1252	1.47484106680061
-1254	1.47493923662727
-1256	1.47509846252746
-1258	1.47526567770392
-1260	1.47542057167793
-1262	1.47557439533574
-1264	1.47572116951863
-1266	1.47586745130108
-1268	1.47601147334394
-1270	1.47614701936603
-1272	1.47627015399601
-1274	1.47638091039797
-1276	1.47648361938200
-1278	1.47658183373250
-1280	1.47668313548634
-1282	1.47679959880658
-1284	1.47693261142928
-1286	1.47707297484201
-1288	1.47722283448259
-1290	1.47738070554226
-1292	1.47754337420682
-1294	1.47770716341215
-1296	1.47786028165421
-1298	1.47798887584323
-1300	1.47808934206014
-1302	1.47818243145329
-1304	1.47830827158180
-1306	1.47849364056186
-1308	1.47871221118251
-1310	1.47885808674696
-1312	1.47873010242650
-1314	1.47845803582890
-1316	1.47844930632483
-1318	1.47861179184706
-1320	1.47881460317012
-1322	1.47902291732804
-1324	1.47922066571969
-1326	1.47941412833592
-1328	1.47959210849367
-1330	1.47973167816960
-1332	1.47972691925884
-1334	1.47975105896865
-1336	1.47993512250321
-1338	1.48014837613309
-1340	1.48037360725078
-1342	1.48060038757184
-1344	1.48082753333001
-1346	1.48104968129957
-1348	1.48126553234897
-1350	1.48148716441519
-1352	1.48173647624861
-1354	1.48200446828695
-1356	1.48227599517218
-1358	1.48252791950314
-1360	1.48276324869435
-1362	1.48303458306896
-1364	1.48338223264961
-1366	1.48379902481358
-1368	1.48427223592360
-1370	1.48482960284728
-1372	1.48552801978829
-1374	1.48627546417750
-1376	1.48651700069497
-1378	1.48432599213190
-1380	1.47977968972337
-1382	1.47800355097223
-1384	1.47805316502072
-1386	1.47842143243600
-1388	1.47890024839336
-1390	1.47940651645865
-1392	1.47991712903019
-1394	1.48041754934745
-1396	1.48089750917415
-1398	1.48135158724828
-1400	1.48179771126525
-1402	1.48224069922095
-1404	1.48266579602562
-1406	1.48305944158359
-1408	1.48342298716122
-1410	1.48379030750588
-1412	1.48419035949659
-1414	1.48461342812701
-1416	1.48505164072948
-1418	1.48548005566484
-1420	1.48588588173361
-1422	1.48626036521862
-1424	1.48659663343317
-1426	1.48690837523274
-1428	1.48726752634633
-1430	1.48775649947673
-1432	1.48841619746365
-1434	1.48924758721438
-1436	1.49022965011215
-1438	1.49126109208233
-1440	1.49220157896289
-1442	1.49274786168208
-1444	1.49275436842747
-1446	1.49244040803637
-1448	1.49203506779732
-1450	1.49142867984501
-1452	1.49040469923150
-1454	1.48888698396754
-1456	1.48687784303199
-1458	1.48442850436533
-1460	1.48174723159373
-1462	1.47906693249971
-1464	1.47667955286596
-1466	1.47482397028080
-1468	1.47364425598396
-1470	1.47319928261846
-1472	1.47339047699181
-1474	1.47411629804730
-1476	1.47533374680842
-1478	1.47696195971213
-1480	1.47908527215456
-1482	1.48180866451580
-1484	1.48531763958917
-1486	1.48994928684771
-1488	1.49499065429219
-1490	1.50119515596543
-1492	1.50990378628749
-1494	1.51196694565470
-1496	1.44560795826024
-1498	1.41456003179507
-1500	1.42568725767340
-1502	1.43509242814603
-1504	1.44179871660811
-1506	1.44669596130319
-1508	1.45033176716821
-1510	1.45318682655572
-1512	1.45545228048253
-1514	1.45731921509841
-1516	1.45894932377219
-1518	1.46041227592838
-1520	1.46176173499470
-1522	1.46244384736929
-1524	1.46122289585454
-1526	1.46043285810887
-1528	1.46128161485975
-1530	1.46226970833946
-1532	1.46306701307330
-1534	1.46366399954379
-1536	1.46409417910494
-1538	1.46444109535269
-1540	1.46477704752644
-1542	1.46519165698743
-1544	1.46568852566980
-1546	1.46623889292729
-1548	1.46677632998672
-1550	1.46719167293357
-1552	1.46747772804745
-1554	1.46791932189599
-1556	1.46844756268659
-1558	1.46898255634672
-1560	1.46952197034328
-1562	1.46999610489784
-1564	1.47038792635287
-1566	1.47066419723057
-1568	1.47075696992025
-1570	1.47067580679212
-1572	1.47047224204500
-1574	1.47030976437525
-1576	1.47033092176687
-1578	1.47057489703138
-1580	1.47099907306615
-1582	1.47158364170880
-1584	1.47213789972489
-1586	1.47240454856960
-1588	1.47273455527947
-1590	1.47343724065447
-1592	1.47446091811145
-1594	1.47574194447918
-1596	1.47705173230297
-1598	1.47867335885708
-1600	1.48062028756105
-1602	1.48036168324124
-1604	1.47134299168096
-1606	1.45508276794757
-1608	1.45359592019623
-1610	1.45693626090464
-1612	1.45964926448336
-1614	1.46156535264851
-1616	1.46294485069237
-1618	1.46393384687173
-1620	1.46454159062356
-1622	1.46478536173497
-1624	1.46467572345167
-1626	1.46443675069875
-1628	1.46442873304410
-1630	1.46468245393626
-1632	1.46507304958839
-1634	1.46551002264583
-1636	1.46597619450157
-1638	1.46639465048447
-1640	1.46677714745798
-1642	1.46713350654907
-1644	1.46746066478520
-1646	1.46777688897226
-1648	1.46807230212257
-1650	1.46832313178042
-1652	1.46853535477890
-1654	1.46871126235072
-1656	1.46886441952877
-1658	1.46897717842913
-1660	1.46906019325977
-1662	1.46917336129198
-1664	1.46933992968848
-1666	1.46953218537231
-1668	1.46973458666196
-1670	1.46993137012353
-1672	1.47010972990258
-1674	1.47023592719105
-1676	1.47026189453436
-1678	1.47023042790416
-1680	1.47026824213020
-1682	1.47039195163007
-1684	1.47055816296083
-1686	1.47072223030395
-1688	1.47088122473311
-1690	1.47102029360098
-1692	1.47114084717626
-1694	1.47123960018069
-1696	1.47128779153643
-1698	1.47126399416326
-1700	1.47132896383171
-1702	1.47143681802407
-1704	1.47155945773850
-1706	1.47167556592223
-1708	1.47178940246904
-1710	1.47190604771198
-1712	1.47202944260493
-1714	1.47216568678700
-1716	1.47231539851653
-1718	1.47248386890388
-1720	1.47265447525274
-1722	1.47281731074269
-1724	1.47295042900518
-1726	1.47304600716400
-1728	1.47309375883840
-1730	1.47305939547434
-1732	1.47291741773166
-1734	1.47267688996611
-1736	1.47235533806185
-1738	1.47204881790723
-1740	1.47183343980199
-1742	1.47174243401936
-1744	1.47176880507034
-1746	1.47188162854264
-1748	1.47204632190602
-1750	1.47223241396135
-1752	1.47242316015794
-1754	1.47260867420886
-1756	1.47278327809895
-1758	1.47293258838400
-1760	1.47306085751883
-1762	1.47317848011178
-1764	1.47329045336641
-1766	1.47339550159425
-1768	1.47349145470639
-1770	1.47357817480071
-1772	1.47366712599018
-1774	1.47373929846121
-1776	1.47378551120112
-1778	1.47379002011073
-1780	1.47381389620918
-1782	1.47392354891587
-1784	1.47409170003533
-1786	1.47427198188798
-1788	1.47442615650942
-1790	1.47457291909648
-1792	1.47474878427437
-1794	1.47489348470272
-1796	1.47493489892040
-1798	1.47478110512949
-1800	1.47437081445076
-1802	1.47373622085690
-1804	1.47304588258769
-1806	1.47251222749590
-1808	1.47223472657190
-1810	1.47217821063195
-1812	1.47227236503443
-1814	1.47243859996067
-1816	1.47259748640805
-1818	1.47271718154483
-1820	1.47279535803734
-1822	1.47284920630461
-1824	1.47291235631300
-1826	1.47301397376823
-1828	1.47314852957960
-1830	1.47329330162724
-1832	1.47342543709755
-1834	1.47357056562475
-1836	1.47375873628681
-1838	1.47398158101288
-1840	1.47422445263378
-1842	1.47448077748417
-1844	1.47474586805163
-1846	1.47500613122839
-1848	1.47524723874056
-1850	1.47539669943437
-1852	1.47535125830335
-1854	1.47504217493076
-1856	1.47442394463698
-1858	1.47358493716912
-1860	1.47284787021825
-1862	1.47246109965773
-1864	1.47241132718491
-1866	1.47253616431924
-1868	1.47266502935955
-1870	1.47267966566327
-1872	1.47252923128383
-1874	1.47227196419049
-1876	1.47203509622402
-1878	1.47192107290153
-1880	1.47194298711947
-1882	1.47205363793314
-1884	1.47220708298649
-1886	1.47237095289447
-1888	1.47253062677600
-1890	1.47268167466003
-1892	1.47283038859118
-1894	1.47298500841240
-1896	1.47313109785186
-1898	1.47324769232051
-1900	1.47333129201763
-1902	1.47341557098201
-1904	1.47353087942641
-1906	1.47366534069078
-1908	1.47380841038952
-1910	1.47395828541387
-1912	1.47411340271346
-1914	1.47427400000000
-1916	1.47443781042483
-1918	1.47460593444462
-1920	1.47477582054714
-1922	1.47493879861924
-1924	1.47508438695513
-1926	1.47522698209875
-1928	1.47539264822422
-1930	1.47558260671450
-1932	1.47576219402042
-1934	1.47587640732885
-1936	1.47583908582835
-1938	1.47553060901904
-1940	1.47489150443496
-1942	1.47409542930774
-1944	1.47334201979217
-1946	1.47275002485068
-1948	1.47244925775411
-1950	1.47239944627947
-1952	1.47247579265655
-1954	1.47255459735783
-1956	1.47256197135638
-1958	1.47246521668706
-1960	1.47228135320174
-1962	1.47212551111344
-1964	1.47202075140180
-1966	1.47202761573580
-1968	1.47213420575515
-1970	1.47229043240161
-1972	1.47246807810995
-1974	1.47265001716927
-1976	1.47282643638217
-1978	1.47298226071844
-1980	1.47310651432274
-1982	1.47317949653548
-1984	1.47321671851061
-1986	1.47327006170979
-1988	1.47332686296001
-1990	1.47332929557274
-1992	1.47327822607353
-1994	1.47322150680404
-1996	1.47323618581223
-1998	1.47331824302286
-2000	1.47341135456857
-2002	1.47349412728021
-2004	1.47356154386820
-2006	1.47361224775319
-2008	1.47364186456648
-2010	1.47365636042820
-2012	1.47367336928224
-2014	1.47370233665225
-2016	1.47373443692998
-2018	1.47377205797454
-2020	1.47381648358614
-2022	1.47386111301432
-2024	1.47390577969427
-2026	1.47395028817579
-2028	1.47399564538301
-2030	1.47403660265942
-2032	1.47406519767252
-2034	1.47408330994744
-2036	1.47412047010970
-2038	1.47416098226622
-2040	1.47420115643528
-2042	1.47423947043298
-2044	1.47427612941305
-2046	1.47431218419212
-2048	1.47434648116260
-2050	1.47438071427926
-2052	1.47441278409228
-2054	1.47444520616084
-2056	1.47447627049456
-2058	1.47450675882064
-2060	1.47453588733404
-2062	1.47456386702353
-2064	1.47459073458299
-2066	1.47461205370700
-2068	1.47461817299827
-2070	1.47461840283149
-2072	1.47463277175523
-2074	1.47465427880758
-2076	1.47467709152152
-2078	1.47470098997954
-2080	1.47472590140090
-2082	1.47475065118331
-2084	1.47477468067538
-2086	1.47479776494193
-2088	1.47482142195457
-2090	1.47484633615274
-2092	1.47487121877337
-2094	1.47489609572630
-2096	1.47491999718268
-2098	1.47494434691905
-2100	1.47496980619050
-2102	1.47499564254391
-2104	1.47502159030193
-2106	1.47504417582923
-2108	1.47506264533273
-2110	1.47507395400220
-2112	1.47508393678745
-2114	1.47510043049552
-2116	1.47511198378437
-2118	1.47511214568773
-2120	1.47512762848859
-2122	1.47515211305019
-2124	1.47517182375646
-2126	1.47518774789092
-2128	1.47521310826668
-2130	1.47524116489652
-2132	1.47527005212030
-2134	1.47529590535418
-2136	1.47531935031383
-2138	1.47534209120029
-2140	1.47536554624085
-2142	1.47539141048574
-2144	1.47541735186985
-2146	1.47544449187503
-2148	1.47547342544397
-2150	1.47550619668115
-2152	1.47554178363426
-2154	1.47558203516447
-2156	1.47562160093130
-2158	1.47565253763469
-2160	1.47566151568534
-2162	1.47561225894049
-2164	1.47548068559088
-2166	1.47537296738995
-2168	1.47536211403117
-2170	1.47539890926361
-2172	1.47544656614673
-2174	1.47549197749543
-2176	1.47553203213436
-2178	1.47556864358705
-2180	1.47560215753198
-2182	1.47562464470162
-2184	1.47562085582639
-2186	1.47558980476200
-2188	1.47557480988891
-2190	1.47558033450347
-2192	1.47559232749770
-2194	1.47561457143455
-2196	1.47564434139990
-2198	1.47567857523082
-2200	1.47571617803152
-2202	1.47575726786490
-2204	1.47579337721307
-2206	1.47579746772491
-2208	1.47574189594736
-2210	1.47571194854898
-2212	1.47572956986763
-2214	1.47575472007504
-2216	1.47578621163266
-2218	1.47581942101129
-2220	1.47585088742314
-2222	1.47587897173469
-2224	1.47590298856875
-2226	1.47592470046514
-2228	1.47594779372938
-2230	1.47597265137572
-2232	1.47599748726300
-2234	1.47601807246604
-2236	1.47602689076481
-2238	1.47603005518190
-2240	1.47604281703214
-2242	1.47606726159445
-2244	1.47609784881235
-2246	1.47612902016881
-2248	1.47615949406397
-2250	1.47618852095385
-2252	1.47621446243625
-2254	1.47623489680521
-2256	1.47624408046323
-2258	1.47623018458297
-2260	1.47617742404058
-2262	1.47611228816094
-2264	1.47608500995198
-2266	1.47609867784140
-2268	1.47612909924113
-2270	1.47616476482454
-2272	1.47619947439469
-2274	1.47623253066542
-2276	1.47626319551276
-2278	1.47628200368923
-2280	1.47626680426481
-2282	1.47624376410414
-2284	1.47624714378783
-2286	1.47623939342228
-2288	1.47622263640102
-2290	1.47621701248520
-2292	1.47622414847935
-2294	1.47624639786310
-2296	1.47628230617739
-2298	1.47632637399547
-2300	1.47637356620751
-2302	1.47642523943489
-2304	1.47647814675017
-2306	1.47652996718143
-2308	1.47657059295077
-2310	1.47656605147736
-2312	1.47646451238365
-2314	1.47632139830172
-2316	1.47626434895975
-2318	1.47628666976549
-2320	1.47634178441866
-2322	1.47640626197946
-2324	1.47647367980355
-2326	1.47654420112269
-2328	1.47661693748934
-2330	1.47668220577778
-2332	1.47670897421522
-2334	1.47661953024202
-2336	1.47640699456743
-2338	1.47628918090598
-2340	1.47627922381635
-2342	1.47629610568572
-2344	1.47633775742674
-2346	1.47639668853055
-2348	1.47645464076621
-2350	1.47650252320800
-2352	1.47653396769864
-2354	1.47655188224605
-2356	1.47656625779288
-2358	1.47656342537266
-2360	1.47646841808416
-2362	1.47627988649258
-2364	1.47623361007945
-2366	1.47628349602868
-2368	1.47634714131595
-2370	1.47640579435613
-2372	1.47645673781608
-2374	1.47650329311272
-2376	1.47654473856361
-2378	1.47658519751564
-2380	1.47662360662062
-2382	1.47665509133976
-2384	1.47667939867421
-2386	1.47668999377568
-2388	1.47666832266751
-2390	1.47662551968266
-2392	1.47661227607686
-2394	1.47662326945870
-2396	1.47664538468599
-2398	1.47667621017793
-2400	1.47670840326370
-2402	1.47673732384369
-2404	1.47676080113293
-2406	1.47677566835384
-2408	1.47677747426079
-2410	1.47675773033081
-2412	1.47671176533526
-2414	1.47665898774225
-2416	1.47662888566870
-2418	1.47661609885311
-2420	1.47661804906686
-2422	1.47663361079607
-2424	1.47665615258179
-2426	1.47667989702189
-2428	1.47670167875450
-2430	1.47671889251986
-2432	1.47672660033007
-2434	1.47672581905542
-2436	1.47673588691547
-2438	1.47675625346807
-2440	1.47677811479011
-2442	1.47680201299431
-2444	1.47682690323960
-2446	1.47685134280847
-2448	1.47687468838441
-2450	1.47689577948214
-2452	1.47691461221252
-2454	1.47693121483650
-2456	1.47694483659804
-2458	1.47695706614166
-2460	1.47696841245298
-2462	1.47698092980728
-2464	1.47699165258073
-2466	1.47699892231642
-2468	1.47700518850467
-2470	1.47701681917772
-2472	1.47703371133993
-2474	1.47705172804537
-2476	1.47706963205611
-2478	1.47708839046513
-2480	1.47710595182822
-2482	1.47712353018048
-2484	1.47714045399508
-2486	1.47715526898974
-2488	1.47716785931325
-2490	1.47717746351979
-2492	1.47718774105152
-2494	1.47720108087222
-2496	1.47721116876733
-2498	1.47720908793559
-2500	1.47721975153658
-2502	1.47724153102797
-2504	1.47726842063502
-2506	1.47729164115863
-2508	1.47729793164711
-2510	1.47728751673010
-2512	1.47728595976167
-2514	1.47730346177822
-2516	1.47732866245654
-2518	1.47735480680865
-2520	1.47737778321487
-2522	1.47739640465051
-2524	1.47741388745850
-2526	1.47743674344455
-2528	1.47746686662636
-2530	1.47749859543051
-2532	1.47752798101785
-2534	1.47755196992726
-2536	1.47757059463727
-2538	1.47758008928483
-2540	1.47756988987874
-2542	1.47755427512999
-2544	1.47756361259663
-2546	1.47758639316885
-2548	1.47760210701986
-2550	1.47761136589934
-2552	1.47762359682751
-2554	1.47764677677048
-2556	1.47767474710701
-2558	1.47770246497527
-2560	1.47773042785198
-2562	1.47776361629940
-2564	1.47779998470837
-2566	1.47783821733131
-2568	1.47787806111451
-2570	1.47792064098960
-2572	1.47796488547863
-2574	1.47800956216730
-2576	1.47805314833494
-2578	1.47809883475004
-2580	1.47814186001493
-2582	1.47815997256423
-2584	1.47809360441189
-2586	1.47790866325303
-2588	1.47773400000000
-2590	1.47767480433235
-2592	1.47770364229106
-2594	1.47776662663767
-2596	1.47783459041379
-2598	1.47789713249225
-2600	1.47795076443856
-2602	1.47798212010995
-2604	1.47796839500240
-2606	1.47793022585363
-2608	1.47793384355028
-2610	1.47794564701586
-2612	1.47795047312967
-2614	1.47797539539217
-2616	1.47801274460181
-2618	1.47805108460942
-2620	1.47808604011951
-2622	1.47811663248782
-2624	1.47814577420760
-2626	1.47817100891022
-2628	1.47819185746701
-2630	1.47820200756835
-2632	1.47819509341812
-2634	1.47818069648523
-2636	1.47819937787229
-2638	1.47823535219485
-2640	1.47827081637876
-2642	1.47830404351228
-2644	1.47832995386373
-2646	1.47835243329009
-2648	1.47837673632241
-2650	1.47840422324866
-2652	1.47843503880664
-2654	1.47846525754672
-2656	1.47849229804531
-2658	1.47851619218461
-2660	1.47854228554823
-2662	1.47857183053155
-2664	1.47860675830984
-2666	1.47864502580642
-2668	1.47868442524625
-2670	1.47871645234617
-2672	1.47872844710197
-2674	1.47874644966096
-2676	1.47878367512841
-2678	1.47882577091271
-2680	1.47886734102623
-2682	1.47890576030499
-2684	1.47894410487476
-2686	1.47898246676081
-2688	1.47902078634990
-2690	1.47905697663379
-2692	1.47909348635787
-2694	1.47913253241860
-2696	1.47917713682535
-2698	1.47922494363690
-2700	1.47927370219512
-2702	1.47932350132184
-2704	1.47937477829841
-2706	1.47942977955203
-2708	1.47948662996503
-2710	1.47954572465315
-2712	1.47960899951982
-2714	1.47967582145469
-2716	1.47974783424700
-2718	1.47982686383801
-2720	1.47991434869689
-2722	1.48001161889876
-2724	1.48011529035864
-2726	1.48021743640732
-2728	1.48029271013490
-2730	1.48028469924544
-2732	1.48009333694647
-2734	1.47968604519118
-2736	1.47926069770098
-2738	1.47904382199068
-2740	1.47903137276969
-2742	1.47912234371550
-2744	1.47924475242006
-2746	1.47936896123536
-2748	1.47948547683776
-2750	1.47959346670195
-2752	1.47969391424782
-2754	1.47978696270901
-2756	1.47987478298896
-2758	1.47995758449142
-2760	1.48003727324589
-2762	1.48011924219933
-2764	1.48019913384442
-2766	1.48027922637338
-2768	1.48035769798330
-2770	1.48043385800477
-2772	1.48050725415469
-2774	1.48057567058368
-2776	1.48065105935983
-2778	1.48072266299449
-2780	1.48079977415031
-2782	1.48088053164822
-2784	1.48096687278145
-2786	1.48105512159158
-2788	1.48114937559786
-2790	1.48124466747644
-2792	1.48134118881539
-2794	1.48144014454067
-2796	1.48153308521599
-2798	1.48162875830237
-2800	1.48173023207917
-2802	1.48183567152155
-2804	1.48193764434860
-2806	1.48203772197889
-2808	1.48213332822876
-2810	1.48221893030834
-2812	1.48230128068059
-2814	1.48241543210576
-2816	1.48256188329700
-2818	1.48272146386266
-2820	1.48288593713105
-2822	1.48303146156846
-2824	1.48316535466125
-2826	1.48333287967432
-2828	1.48353886468435
-2830	1.48376233940652
-2832	1.48399372362724
-2834	1.48422859660869
-2836	1.48446914811588
-2838	1.48472335986644
-2840	1.48498891752954
-2842	1.48526978967144
-2844	1.48556244410920
-2846	1.48585030113417
-2848	1.48611635747129
-2850	1.48631703683473
-2852	1.48642616794096
-2854	1.48638931900690
-2856	1.48617288132870
-2858	1.48578055258264
-2860	1.48528254616381
-2862	1.48477473720320
-2864	1.48431306898547
-2866	1.48390294869478
-2868	1.48352758708888
-2870	1.48315923324289
-2872	1.48276317318322
-2874	1.48233036174381
-2876	1.48190033197863
-2878	1.48156989857095
-2880	1.48135829837939
-2882	1.48127046426508
-2884	1.48129224687463
-2886	1.48142276034719
-2888	1.48166152381514
-2890	1.48199469355260
-2892	1.48241286263108
-2894	1.48290615618025
-2896	1.48346174779728
-2898	1.48406068695481
-2900	1.48469749104873
-2902	1.48534901849277
-2904	1.48600451268347
-2906	1.48663330502903
-2908	1.48716049340272
-2910	1.48749427432860
-2912	1.48745634999468
-2914	1.48687918789111
-2916	1.48564647709805
-2918	1.48378138421067
-2920	1.48160842259702
-2922	1.47963902212310
-2924	1.47817563267450
-2926	1.47725366173650
-2928	1.47680009878321
-2930	1.47670600337876
-2932	1.47683592850229
-2934	1.47707848906770
-2936	1.47736368012666
-2938	1.47761998820843
-2940	1.47780991969196
-2942	1.47790616610153
-2944	1.47789352215007
-2946	1.47776642994662
-2948	1.47755303644224
-2950	1.47732098571495
-2952	1.47710982305520
-2954	1.47692656410946
-2956	1.47677865708199
-2958	1.47664389769752
-2960	1.47653950030308
-2962	1.47652380859929
-2964	1.47671143784641
-2966	1.47706590558488
-2968	1.47742684312635
-2970	1.47770009243870
-2972	1.47786247321149
-2974	1.47794741384886
-2976	1.47797899370123
-2978	1.47798223648454
-2980	1.47795004028588
-2982	1.47790147416153
-2984	1.47795735389707
-2986	1.47814496927765
-2988	1.47844692443850
-2990	1.47884918651108
-2992	1.47932344250011
-2994	1.47986306802417
-2996	1.48043188046815
-2998	1.48097537656156
-3000	1.48138517100778
-3002	1.48162356419426
-3004	1.48185212024737
-3006	1.48228440440630
-3008	1.48297178567222
-3010	1.48385673952528
-3012	1.48487993544870
-3014	1.48595665242293
-3016	1.48695938009756
-3018	1.48767468298278
-3020	1.48765524108674
-3022	1.48618132554454
-3024	1.48268461964750
-3026	1.47762082421352
-3028	1.47232727506644
-3030	1.46776463943145
-3032	1.46440878935946
-3034	1.46247197560802
-3036	1.46196769309556
-3038	1.46253947223186
-3040	1.46367382189299
-3042	1.46491417717244
-3044	1.46601563099238
-3046	1.46697686500990
-3048	1.46781464802766
-3050	1.46847402904648
-3052	1.46887853308036
-3054	1.46895675121188
-3056	1.46875323941201
-3058	1.46834302704055
-3060	1.46771282666113
-3062	1.46675300487368
-3064	1.46553703632205
-3066	1.46435734374414
-3068	1.46364333274111
-3070	1.46361967631567
-3072	1.46416270683630
-3074	1.46500589551713
-3076	1.46593266001109
-3078	1.46681497080407
-3080	1.46754108115619
-3082	1.46785690887919
-3084	1.46726760945338
-3086	1.46533247163430
-3088	1.46268292062625
-3090	1.46120303549580
-3092	1.46134478479294
-3094	1.46221369798373
-3096	1.46321247938499
-3098	1.46411661764251
-3100	1.46482369285261
-3102	1.46525636685728
-3104	1.46533581524600
-3106	1.46519098442260
-3108	1.46516907412280
-3110	1.46538060689336
-3112	1.46568276755924
-3114	1.46596931336371
-3116	1.46619739482536
-3118	1.46639101964608
-3120	1.46661054944789
-3122	1.46687049156442
-3124	1.46713909721892
-3126	1.46740251735782
-3128	1.46765965900548
-3130	1.46790595336806
-3132	1.46813448944673
-3134	1.46834723054744
-3136	1.46854553575727
-3138	1.46872578997706
-3140	1.46889606787041
-3142	1.46905361684206
-3144	1.46920788445114
-3146	1.46935155893370
-3148	1.46948926642375
-3150	1.46961711994727
-3152	1.46973932284344
-3154	1.46985771524525
-3156	1.46997084147302
-3158	1.47008125375275
-3160	1.47018834504960
-3162	1.47028749194193
-3164	1.47037561555632
-3166	1.47044733671974
-3168	1.47049523638823
-3170	1.47053287904761
-3172	1.47059397007388
-3174	1.47068028883230
-3176	1.47077100092966
-3178	1.47085834352883
-3180	1.47094237966502
-3182	1.47102127140257
-3184	1.47109691171596
-3186	1.47116815404231
-3188	1.47123618567128
-3190	1.47130184743484
-3192	1.47136511381017
-3194	1.47142734846007
-3196	1.47148851688128
-3198	1.47154755038698
-3200	1.47160533014890
-3202	1.47166012795457
-3204	1.47171224992608
-3206	1.47176315489772
-3208	1.47181395071669
-3210	1.47186466789480
-3212	1.47191661577937
-3214	1.47196738520913
-3216	1.47201707857991
-3218	1.47206588870145
-3220	1.47211365240659
-3222	1.47215936522226
-3224	1.47220500735251
-3226	1.47225033231421
-3228	1.47229424065224
-3230	1.47233733691715
-3232	1.47237980638024
-3234	1.47242122252104
-3236	1.47246173766460
-3238	1.47250090500984
-3240	1.47253933121953
-3242	1.47257666559418
-3244	1.47261289353408
-3246	1.47264942225475
-3248	1.47268468000033
-3250	1.47271896562139
-3252	1.47275329822459
-3254	1.47278723826016
-3256	1.47281957643892
-3258	1.47285086138010
-3260	1.47288192451579
-3262	1.47291300000000
-3264	1.47294399234620
-3266	1.47297519999867
-3268	1.47300456597122
-3270	1.47303306949960
-3272	1.47306229798834
-3274	1.47309029819990
-3276	1.47311725100397
-3278	1.47314519229524
-3280	1.47317191831342
-3282	1.47319904835607
-3284	1.47322480511295
-3286	1.47325068033533
-3288	1.47327558727819
-3290	1.47330149637565
-3292	1.47332523279087
-3294	1.47335025198767
-3296	1.47337510971327
-3298	1.47339905996618
-3300	1.47342296954304
-3302	1.47344582202335
-3304	1.47346658074592
-3306	1.47348738493031
-3308	1.47350703202034
-3310	1.47352683574489
-3312	1.47354755048152
-3314	1.47356829450234
-3316	1.47358903215508
-3318	1.47360880465673
-3320	1.47362855417648
-3322	1.47364734936801
-3324	1.47366547803442
-3326	1.47368305009043
-3328	1.47369959979993
-3330	1.47371718446385
-3332	1.47373378124277
-3334	1.47375068696817
-3336	1.47376844875514
-3338	1.47378666053286
-3340	1.47380404591194
-3342	1.47382276516742
-3344	1.47384040963255
-3346	1.47385904663877
-3348	1.47387858239480
-3350	1.47389752320424
-3352	1.47391752328576
-3354	1.47393606713734
-3356	1.47395488874822
-3358	1.47397353990369
-3360	1.47399234620080
-3362	1.47401055721405
-3364	1.47402826981442
-3366	1.47404508175359
-3368	1.47406141829832
-3370	1.47407704342040
-3372	1.47409059132764
-3374	1.47410503032631
-3376	1.47411782704824
-3378	1.47413081528590
-3380	1.47414326557675
-3382	1.47415571156753
-3384	1.47416717298263
-3386	1.47417841575972
-3388	1.47418915024028
-3390	1.47419998707473
-3392	1.47421190062571
-3394	1.47422443429139
-3396	1.47423683452363
-3398	1.47425033505022
-3400	1.47426480528893
-3402	1.47427826680738
-3404	1.47429170418534
-3406	1.47430477066294
-3408	1.47431835512023
-3410	1.47433193595530
-3412	1.47434642118416
-3414	1.47436087920127
-3416	1.47437532634686
-3418	1.47439018109776
-3420	1.47440515622779
-3422	1.47442044328205
-3424	1.47443606103306
-3426	1.47444964436527
-3428	1.47446294847254
-3430	1.47447439134230
-3432	1.47448416869267
-3434	1.47449072019392
-3436	1.47449591374259
-3438	1.47449903792179
-3440	1.47449993449953
-3442	1.47450135456237
-3444	1.47450458795612
-3446	1.47450875108451
-3448	1.47451445884208
-3450	1.47452484258401
-3452	1.47453827241797
-3454	1.47455172262247
-3456	1.47456517206426
-3458	1.47457860151852
-3460	1.47459192059468
-3462	1.47460450298261
-3464	1.47461696547474
-3466	1.47462839859281
-3468	1.47463987388367
-3470	1.47465188200346
-3472	1.47466266389847
-3474	1.47467409691578
-3476	1.47468473670609
-3478	1.47469608306209
-3480	1.47470752002888
-3482	1.47471885889080
-3484	1.47473141107054
-3486	1.47474321664113
-3488	1.47475540477105
-3490	1.47476577603289
-3492	1.47477517654069
-3494	1.47478437686762
-3496	1.47479375265910
-3498	1.47480352784050
-3500	1.47481386454326
-3502	1.47482540254891
-3504	1.47483686546170
-3506	1.47484922964243
-3508	1.47486054239155
-3510	1.47487118057395
-3512	1.47488161773392
-3514	1.47489155648764
-3516	1.47489779215940
-3518	1.47490199751604
-3520	1.47490515212000
-3522	1.47490858576642
-3524	1.47491589352572
-3526	1.47492563809847
-3528	1.47493721829251
-3530	1.47494965183138
-3532	1.47496209482301
-3534	1.47497548127118
-3536	1.47498901026331
-3538	1.47500250064110
-3540	1.47501334375007
-3542	1.47502155988466
-3544	1.47502590855583
-3546	1.47502798788122
-3548	1.47502908741446
-3550	1.47503013111600
-3552	1.47503152066431
-3554	1.47503369017078
-3556	1.47503596161309
-3558	1.47503994401260
-3560	1.47504720780187
-3562	1.47505757685400
-3564	1.47506921753979
-3566	1.47508222835820
-3568	1.47509583612677
-3570	1.47510943592653
-3572	1.47512299244722
-3574	1.47513544229862
-3576	1.47514788646150
-3578	1.47515877336465
-3580	1.47516830010454
-3582	1.47517301097796
-3584	1.47516730096467
-3586	1.47516098788624
-3588	1.47515999912529
-3590	1.47516344979552
-3592	1.47516995891151
-3594	1.47517893497533
-3596	1.47518949533554
-3598	1.47519986950803
-3600	1.47520815315630
-3602	1.47521639684906
-3604	1.47522677803691
-3606	1.47523756307109
-3608	1.47524905817071
-3610	1.47526235394740
-3612	1.47527689090454
-3614	1.47529241512157
-3616	1.47530577596310
-3618	1.47531550675526
-3620	1.47531807217956
-3622	1.47531330897623
-3624	1.47530520668685
-3626	1.47530099713781
-3628	1.47530419555884
-3630	1.47531292297539
-3632	1.47532682994681
-3634	1.47534230166646
-3636	1.47535817866622
-3638	1.47537270802382
-3640	1.47538306617453
-3642	1.47538491013479
-3644	1.47537808441815
-3646	1.47536152773521
-3648	1.47533829820411
-3650	1.47531127187157
-3652	1.47528831452931
-3654	1.47527173292062
-3656	1.47526400688559
-3658	1.47526538002071
-3660	1.47527196497124
-3662	1.47528332467912
-3664	1.47529547167214
-3666	1.47530792033597
-3668	1.47531940264238
-3670	1.47532950934428
-3672	1.47533752543273
-3674	1.47534264633859
-3676	1.47534493660391
-3678	1.47534793834948
-3680	1.47535101048592
-3682	1.47535512741537
-3684	1.47536061029192
-3686	1.47536677517540
-3688	1.47537422152313
-3690	1.47538349069671
-3692	1.47539466802181
-3694	1.47540614815786
-3696	1.47541766757740
-3698	1.47543103564364
-3700	1.47544309274752
-3702	1.47545168948545
-3704	1.47545396563826
-3706	1.47545207507319
-3708	1.47544797484465
-3710	1.47544704753668
-3712	1.47545189667326
-3714	1.47545995926878
-3716	1.47547095072698
-3718	1.47548066602429
-3720	1.47548697893292
-3722	1.47548796009613
-3724	1.47548478177503
-3726	1.47547947641639
-3728	1.47547863259801
-3730	1.47548174475524
-3732	1.47548778078125
-3734	1.47549403635331
-3736	1.47550125363908
-3738	1.47550934180435
-3740	1.47551683167599
-3742	1.47552688594006
-3744	1.47553729090548
-3746	1.47554678198008
-3748	1.47555713325216
-3750	1.47556659302775
-3752	1.47557669459374
-3754	1.47558647315562
-3756	1.47559529768016
-3758	1.47560360009648
-3760	1.47561091508282
-3762	1.47561609735508
-3764	1.47562029070796
-3766	1.47562441780911
-3768	1.47563306550754
-3770	1.47564405166112
-3772	1.47565552291783
-3774	1.47566694809298
-3776	1.47567830857219
-3778	1.47568755133462
-3780	1.47569463620025
-3782	1.47569547492168
-3784	1.47568951387041
-3786	1.47567835935080
-3788	1.47566593929693
-3790	1.47566101977927
-3792	1.47566354952827
-3794	1.47567185732029
-3796	1.47568321348889
-3798	1.47569529254648
-3800	1.47570772530959
-3802	1.47571809962768
-3804	1.47572648401529
-3806	1.47573134192597
-3808	1.47573352027040
-3810	1.47573292361008
-3812	1.47573299326894
-3814	1.47573398673360
-3816	1.47573817632205
-3818	1.47574527524272
-3820	1.47575277086820
-3822	1.47575967350287
-3824	1.47576470303911
-3826	1.47576975528735
-3828	1.47577698612879
-3830	1.47578309783396
-3832	1.47578829704916
-3834	1.47579095824278
-3836	1.47578839924332
-3838	1.47578153880935
-3840	1.47577325828602
-3842	1.47576695658169
-3844	1.47576181472562
-3846	1.47575638975092
-3848	1.47574893511221
-3850	1.47574067656252
-3852	1.47573418960490
-3854	1.47573201348304
-3856	1.47573609448654
-3858	1.47574340076582
-3860	1.47575406506568
-3862	1.47576509594980
-3864	1.47577344240290
-3866	1.47577782298125
-3868	1.47577704417063
-3870	1.47576978782061
-3872	1.47576167888626
-3874	1.47575983530599
-3876	1.47576615931522
-3878	1.47577603616264
-3880	1.47578749602566
-3882	1.47579899049744
-3884	1.47580829754193
-3886	1.47581553191111
-3888	1.47582044576450
-3890	1.47582361486597
-3892	1.47582488670530
-3894	1.47582691190401
-3896	1.47582798767520
-3898	1.47583005776107
-3900	1.47583333559154
-3902	1.47583798052018
-3904	1.47584349792097
-3906	1.47584878503057
-3908	1.47585104104660
-3910	1.47584786442429
-3912	1.47584503864650
-3914	1.47584772763597
-3916	1.47585513011730
-3918	1.47586161194681
-3920	1.47586680114244
-3922	1.47586801742881
-3924	1.47586285228063
-3926	1.47585768990955
-3928	1.47585725672200
-3930	1.47586502926929
-3932	1.47587638834149
-3934	1.47588758559686
-3936	1.47589600406114
-3938	1.47590331354213
-3940	1.47591060804636
-3942	1.47591789591720
-3944	1.47592457142526
-3946	1.47593081059303
-3948	1.47593398581283
-3950	1.47593295565452
-3952	1.47592878275285
-3954	1.47592684349640
-3956	1.47592986168501
-3958	1.47593628896516
-3960	1.47594351825970
-3962	1.47595186222678
-3964	1.47595911320580
-3966	1.47596854991323
-3968	1.47597712871599
-3970	1.47598746992252
-3972	1.47600004422535
-3974	1.47601337421929
-3976	1.47602692154134
-3978	1.47603405627977
-3980	1.47602817354059
-3982	1.47601874488156
-3984	1.47602563707167
-3986	1.47604367443527
-3988	1.47606327560645
-3990	1.47608304122308
-3992	1.47610269526207
-3994	1.47612262206064
-3996	1.47614078459134
-3998	1.47615752083133
-4000	1.47617133599432
 \ No newline at end of file
-#ifndef GLOBALS_H
-#define GLOBALS_H
-
-#include <vector>
-#include <string>
-#include <iostream>
-#include "PerformanceData.h"
-#include <complex>
-using namespace std;
-
-typedef float rtsFloat;
-
-struct SpecPair{
-	double nu;
-	double A;
-};
-
-struct Material{
-	vector<double> nu;
-	vector<complex<double> > eta;
-	string name;
-};
-
-enum SpecType {AbsorbanceSpecType, IntensitySpecType};
-enum OpticsType {TransmissionOpticsType, ReflectionOpticsType};
-
-extern PerformanceData PD;
-
-
-extern vector<vector<SpecPair> > RefSpectrum;
-extern int currentSpec;
-extern vector<SpecPair> SimSpectrum;
-
-//IO Functions
-vector<SpecPair> LoadSpectrum(string filename);
-vector<SpecPair> SetReferenceSpectrum(char* text);
-void SaveState();
-void LoadState();
-void SetDefaults();
-void SaveSimulation(string fileName);
-void SaveK(string fileName);
-void SaveN(string fileName);
-void LoadMaterial(string fileNameK, string fileNameN, string materialName);
-void LoadMaterial(string fileNameK, string materialName);
-
-//Display Functions
-void FitDisplay();
-
-//Update Functions
-void UpdateDisplay();
-void SimulateSpectrum();
-void cudaKramersKronig(double* cpuN, double* cpuK, int nVals, double nuStart, double nuEnd, double nOffset);
-void cudaComputeSpectrum(double* cpuI, double* cpuB, double* alpha,
-						 int Nl, int nLambda, double oThetaI, double oThetaO, double cThetaI, double cThetaO, int nSamples);
-
-//Window Parameters
-extern double nuMin;
-extern double nuMax;
-extern double aMin;
-extern double aMax;
-extern double dNu;
-extern bool dispRefSpec;
-extern bool dispSimSpec;
-extern bool dispSimK;
-extern bool dispMatK;
-extern bool dispSimN;
-extern bool dispMatN;
-extern SpecType dispSimType;
-extern bool dispNormalize;
-extern double dispNormFactor;
-
-
-extern double dispScaleK;
-extern double dispScaleN;
-
-//material parameters
-extern double radius;
-extern double baseIR;
-extern double cA;
-extern vector<SpecPair> EtaK;
-extern vector<SpecPair> EtaN;
-extern bool applyMaterial;
-extern vector<Material> MaterialList;
-extern int currentMaterial;
-void ChangeAbsorbance();
-void SetMaterial();
-
-//source parameters
-extern vector<SpecPair> SourceSpectrum;
-extern vector<SpecPair> SourceResampled;
-void ResampleSource();	//resample a source profile to match the sample points of the current material
-extern bool useSourceSpectrum;
-
-//optical parameters
-extern double cNAi;
-extern double cNAo;
-extern double oNAi;
-extern double oNAo;
-extern OpticsType opticsMode;
-extern bool pointDetector;
-extern int objectiveSamples;
-
-//fitting parameters
-extern double minMSE;
-extern int maxFitIter;
-void EstimateMaterial();
-extern double scaleI0;
-extern double refSlope;
-
-
-//distortion maps
-double ComputeDistortion();
-void DistortionMap(float* distortionMap, int nSteps);
-
-
-
-
-#endif
+#ifndef GLOBALS_H
+#define GLOBALS_H
+
+#include <vector>
+#include <string>
+#include <iostream>
+#include "PerformanceData.h"
+#include <complex>
+using namespace std;
+
+typedef float rtsFloat;
+
+struct SpecPair {
+    double nu;
+    double A;
+};
+
+struct Material {
+    vector<double> nu;
+    vector<complex<double> > eta;
+    bool validN;
+    bool validK;
+    string name;
+};
+
+enum SpecType {AbsorbanceSpecType, IntensitySpecType};
+enum OpticsType {TransmissionOpticsType, ReflectionOpticsType};
+
+extern PerformanceData PD;
+
+
+extern vector<vector<SpecPair> > RefSpectrum;
+extern int currentSpec;
+extern vector<SpecPair> SimSpectrum;
+
+//IO Functions
+vector<SpecPair> LoadSpectrum(string filename);
+vector<SpecPair> SetReferenceSpectrum(char* text);
+void SaveState();
+void LoadState();
+void SetDefaults();
+void SaveSimulation(string fileName);
+//void SaveK(string fileName);
+void SaveMaterial(string fileName);
+//void LoadMaterial(string fileNameK, string fileNameN, string materialName);
+void LoadMaterial(string fileName, string materialName);
+
+//Display Functions
+void FitDisplay();
+
+//Update Functions
+void UpdateDisplay();
+void SimulateSpectrum();
+void cudaKramersKronig(double* cpuN, double* cpuK, int nVals, double nuStart, double nuEnd, double nOffset);
+void cudaComputeSpectrum(double* cpuI, double* cpuB, double* alpha,
+                         int Nl, int nLambda, double oThetaI, double oThetaO, double cThetaI, double cThetaO, int nSamples);
+
+//Window Parameters
+extern double nuMin;	//wavenumbers
+extern double nuMax;
+extern double aMin;		//absorbance
+extern double aMax;
+extern double dNu;
+extern double nMag;		//largest magnitude for n
+extern double kMax;			//highest extinction coefficient
+extern bool dispRefSpec;
+extern bool dispSimSpec;
+extern bool dispSimK;
+extern bool dispMatK;
+extern bool dispSimN;
+extern bool dispMatN;
+extern SpecType dispSimType;
+extern bool dispNormalize;
+extern double dispNormFactor;
+
+
+extern double dispScaleK;
+extern double dispScaleN;
+
+//material parameters
+extern double radius;
+extern double baseIR;
+extern double cA;
+extern vector<SpecPair> EtaK;
+extern vector<SpecPair> EtaN;
+extern bool applyMaterial;
+extern vector<Material> MaterialList;
+extern int currentMaterial;
+void ChangeAbsorbance();
+void SetMaterial();
+
+//source parameters
+extern vector<SpecPair> SourceSpectrum;
+extern vector<SpecPair> SourceResampled;
+void ResampleSource();	//resample a source profile to match the sample points of the current material
+extern bool useSourceSpectrum;
+
+//optical parameters
+extern double cNAi;
+extern double cNAo;
+extern double oNAi;
+extern double oNAo;
+extern OpticsType opticsMode;
+extern bool pointDetector;
+extern int objectiveSamples;
+
+//fitting parameters
+extern double minMSE;
+extern int maxFitIter;
+void EstimateMaterial();
+extern double scaleI0;
+extern double refSlope;
+
+
+//distortion maps
+double ComputeDistortion();
+void DistortionMap(float* distortionMap, int nSteps);
+
+
+
+
+#endif
-#include "interactivemie.h"
-#include <stdlib.h>
+#include "interactivemie.h"
+#include <stdlib.h>
  
 qtDistortionDialog* distortionDialog;
-
-InteractiveMie::InteractiveMie(QWidget *parent, Qt::WFlags flags)
-	: QMainWindow(parent, flags)
-{
-	ui.setupUi(this);
-}
-
-InteractiveMie::~InteractiveMie()
-{
-	updating = false;
+
+InteractiveMie::InteractiveMie(QWidget *parent, Qt::WFlags flags)
+    : QMainWindow(parent, flags)
+{
+    ui.setupUi(this);
+}
+
+InteractiveMie::~InteractiveMie()
+{
+    updating = false;
 }
  
 void InteractiveMie::closeEvent(QCloseEvent *event)
 {
-	cout<<"Exiting"<<endl;
+    cout<<"Exiting"<<endl;
     exit(0);
  
-}
+}
-#ifndef INTERACTIVEMIE_H
-#define INTERACTIVEMIE_H
-
-#include <QtGui/QMainWindow>
-#include <QDragEnterEvent>
-#include <qfiledialog.h>
-#include <qinputdialog.h>
-#include "ui_interactivemie.h"
-#include "qtDistortionDialog.h"
-#include "globals.h"
-
-extern qtDistortionDialog* distortionDialog;
-
-class InteractiveMie : public QMainWindow
-{
-	Q_OBJECT
-
-public:
-	InteractiveMie(QWidget *parent = 0, Qt::WFlags flags = 0);
-	~InteractiveMie();
-	void closeEvent(QCloseEvent *event);
-	bool updating;
-
-	void refreshUI()
-	{
-		updating = true;
-
-		ui.spinNuMin->setValue(nuMin);
-		ui.spinNuMax->setValue(nuMax);
-		ui.spinAMin->setValue(aMin);
-		ui.spinAMax->setValue(aMax);
-		ui.spinRadius->setValue(radius);
-		ui.spinBaseIR->setValue(baseIR);
-		ui.spinScaleK->setValue(cA);
-		ui.spinObjNAi->setValue(oNAi);
-		ui.spinObjNAo->setValue(oNAo);
-		ui.spinCondNAi->setValue(cNAi);
-		ui.spinCondNAo->setValue(cNAo);
-		ui.spinError->setValue(minMSE);
-		ui.spinMaxIter->setValue(maxFitIter);
-		ui.spinI0Scale->setValue(scaleI0);
-
-		//display spectra values
-		ui.chkDisplaySimSpec->setChecked(dispSimSpec);
-		ui.chkDisplayRefSpec->setChecked(dispRefSpec);
-		ui.chkDisplaySimK->setChecked(dispSimK);
-		ui.chkDisplayMatK->setChecked(dispMatK);
-		ui.chkDisplaySimN->setChecked(dispSimN);
-		ui.chkDisplayMatN->setChecked(dispMatN);
-		ui.spinDispScaleK->setValue(dispScaleK);
-		ui.spinDispScaleN->setValue(dispScaleN);
-
-		//material selection combo box
-		ui.cmbMaterial->clear();
-		for(unsigned int i=0; i<MaterialList.size(); i++)
-			ui.cmbMaterial->addItem(MaterialList[i].name.c_str(), i);
-		ui.cmbMaterial->setCurrentIndex(currentMaterial);
-
-		updating = false;
-	}
-
-	void dragEnterEvent(QDragEnterEvent *event)
-	{
-		cout<<"This is a test."<<endl;
-		QStringList s = event->mimeData()->formats();
-		if (event->mimeData()->hasFormat("application/x-qt-windows-mime;value=\"FileName\"") ||
-			event->mimeData()->hasFormat("text/plain"))
-		{
-			event->acceptProposedAction();
-
-		}
-	}
-
-	void dropEvent(QDropEvent *event)
-	{
-		//cout<<"Challenge Accepted."<<endl;
-		RefSpectrum.clear();
-		RefSpectrum.push_back(SetReferenceSpectrum(event->mimeData()->text().toAscii().data()));
-		UpdateDisplay();
-	}
-
-private:
-	Ui::InteractiveMieClass ui;
-
-public slots:
-	//display parameters
-	void on_spinNuMin_valueChanged(int i){
-		nuMin = (float)i;
-		UpdateDisplay();
-	}
-	void on_spinNuMax_valueChanged(int i){
-		nuMax = (float)i;
-		UpdateDisplay();
-	}
-	void on_spinAMin_valueChanged(double d){
-		aMin = d;
-		UpdateDisplay();
-	}
-	void on_spinAMax_valueChanged(double d){
-		aMax = d;
-		UpdateDisplay();
-	}
-	void on_chkDisplaySimSpec_clicked(bool b){
-		dispSimSpec = b;
-		UpdateDisplay();
-	}
-	void on_chkDisplayRefSpec_clicked(bool b){
-		dispRefSpec = b;
-		UpdateDisplay();
-	}
-	void on_chkDisplaySimK_clicked(bool b){
-		dispSimK = b;
-		UpdateDisplay();
-	}
-	void on_chkDisplayMatK_clicked(bool b){
-		dispMatK = b;
-		UpdateDisplay();
-	}
-	void on_chkDisplaySimN_clicked(bool b){
-		dispSimN = b;
-		UpdateDisplay();
-	}
-	void on_chkDisplayMatN_clicked(bool b){
-		dispMatN = b;
-		UpdateDisplay();
-	}
-	void on_spinDispScaleK_valueChanged(double d){
-		dispScaleK = d;
-		UpdateDisplay();
-	}
-	void on_spinDispScaleN_valueChanged(double d){
-		dispScaleN = d;
-		UpdateDisplay();
-	}
-	void on_radDisplayAbsorbance_clicked(bool b){
-		dispSimType = AbsorbanceSpecType;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_radDisplayIntensity_toggled(bool b){
-		dispSimType = IntensitySpecType;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_chkNormalize_clicked(bool b){
-		dispNormalize = b;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_spinNormFactor_valueChanged(double d){
-		dispNormFactor = d;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-
-	//material parameters
-	void on_spinRadius_valueChanged(double d){
-		radius = d;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_spinBaseIR_valueChanged(double d){
-		baseIR = d;
-		ChangeAbsorbance();
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_spinScaleK_valueChanged(double d){
-		cA = d;
-		ChangeAbsorbance();
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_chkApplyMaterial_clicked(bool b){
-		applyMaterial = b;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_cmbMaterial_currentIndexChanged(int i){
-		if(updating) return;
-
-		currentMaterial = i;
-		SetMaterial();
-		SimulateSpectrum();
-		UpdateDisplay();
-		refreshUI();
-	}
-
-	//optical parameters
-	void on_spinCondNAi_valueChanged(double d){
-		cNAi = d;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_spinCondNAo_valueChanged(double d){
-		cNAo = d;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_spinObjNAi_valueChanged(double d){
-		oNAi = d;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_spinObjNAo_valueChanged(double d){
-		oNAo = d;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_radTransmissionOptics_clicked(bool d){
-		ui.spinCondNAi->setEnabled(true);
-		ui.spinCondNAo->setEnabled(true);
-		opticsMode = TransmissionOpticsType;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_radReflectionOptics_clicked(bool d){
-		ui.spinCondNAi->setEnabled(false);
-		ui.spinCondNAo->setEnabled(false);
-		ui.radDisplayAbsorbance->setEnabled(false);
-		ui.radDisplayIntensity->setChecked(true);
-		opticsMode = ReflectionOpticsType;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_chkPointDetector_clicked(bool b){
-		if(b)
-		{
-			pointDetector = true;
-			ui.spinObjectiveSamples->setEnabled(false);
-		}
-		else
-		{
-			pointDetector = false;
-			ui.spinObjectiveSamples->setEnabled(true);
-		}
-
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-
-	void on_spinObjectiveSamples_valueChanged(int i){
-		objectiveSamples = i;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-
-	//Fitting
-	void on_spinMaxIter_valueChanged(int i){
-		maxFitIter = i;
-	}
-	void on_spinError_valueChanged(double d){
-		minMSE = d;
-	}
-	void on_spinI0Scale_valueChanged(double d){
-		scaleI0 = d;
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_spinRefSlope_valueChanged(double d){
-		refSlope = d;
-		UpdateDisplay();
-	}
-
-	//display settings
-
-	//Buttons
-	void on_btnFit_clicked(){
-		FitDisplay();
-		refreshUI();
-	}
-	void on_btnSave_clicked(){
-		SaveState();
-	}
-	void on_btnReset_clicked(){
-		SetDefaults();
-		SimulateSpectrum();
-		UpdateDisplay();
-		refreshUI();
-	}
-	void on_btnResetK_clicked(){
-		ChangeAbsorbance();
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_btnEstimateK_clicked(){
-		EstimateMaterial();
-		SimulateSpectrum();
-		UpdateDisplay();
-	}
-	void on_btnDistortion_clicked(){
-		//ComputeDistortion();
-		//DistortionMap();
-		cout<<"Distortion"<<endl;
-		distortionDialog->show();
-	}
-	void on_btnTimings_clicked(){
-		PD.PrintResults(cout);
-	}
-
-	//menu items
-	void on_mnuLoadReference_triggered(){
-		QString fileName = QFileDialog::getOpenFileName(this, tr("Open Reference Spectrum"));
-
-		if(fileName != QString::null){
-			RefSpectrum.clear();
-			RefSpectrum.push_back(LoadSpectrum(fileName.toAscii().data()));
-		}
-		UpdateDisplay();
-	}
-
-	void on_mnuLoadMaterial_triggered(){
-
-		//first load the imaginary part
-		QString kFileName = QFileDialog::getOpenFileName(this, tr("Open Imaginary (k) Spectrum"));
-
-		//exit if no file was selected
-		if(kFileName == QString::null)
-			return;
-
-		QString nFileName = QFileDialog::getOpenFileName(this, tr("Open Imaginary (n) Spectrum"));
-
-		//request the material name
-		QString matName = QInputDialog::getText(this, tr("Material Name"), tr("Enter material name:"));
-
-		//if a real part was given, load both
-		if(nFileName != QString::null)
-			LoadMaterial(kFileName.toAscii().data(), nFileName.toAscii().data(), matName.toAscii().data());
-		else
-			LoadMaterial(kFileName.toAscii().data(), matName.toAscii().data());
-
-		//add the new material to the combo box
-		refreshUI();
-	}
-	void on_mnuLoadSource_triggered(){
-		cout<<"Load source."<<endl;
-	}
-	void on_chkSourceSpectrum_clicked(bool b){
-		
-		useSourceSpectrum = b;
-		SimulateSpectrum();
-		UpdateDisplay();
-		
-	}
-
-	void on_mnuSaveSim_triggered(){
-		//first load the imaginary part
-		QString fileName = QFileDialog::getSaveFileName(this, tr("Save Simulated Spectrum"));
-		SaveSimulation(fileName.toAscii().data());
-	}
-
-	void on_mnuSaveK_triggered(){
-		//first load the imaginary part
-		QString fileName = QFileDialog::getSaveFileName(this, tr("Save Imaginary Index of Refraction (k)"));
-		SaveK(fileName.toAscii().data());
-	}
-
-	void on_mnuSaveN_triggered(){
-		//first load the imaginary part
-		QString fileName = QFileDialog::getSaveFileName(this, tr("Save Real Index of Refraction (n)"));
-		SaveN(fileName.toAscii().data());
-	}
-
-
-
-};
-
-#endif // INTERACTIVEMIE_H
+#ifndef INTERACTIVEMIE_H
+#define INTERACTIVEMIE_H
+
+#include <QtGui/QMainWindow>
+#include <QDragEnterEvent>
+#include <qfiledialog.h>
+#include <qinputdialog.h>
+#include "ui_interactivemie.h"
+#include "qtDistortionDialog.h"
+#include "globals.h"
+
+extern qtDistortionDialog* distortionDialog;
+
+class InteractiveMie : public QMainWindow
+{
+Q_OBJECT
+
+public:
+InteractiveMie(QWidget *parent = 0, Qt::WFlags flags = 0);
+~InteractiveMie();
+void closeEvent(QCloseEvent *event);
+bool updating;
+
+void refreshUI()
+{
+	updating = true;
+
+	ui.spinNuMin->setValue(nuMin);
+	ui.spinNuMax->setValue(nuMax);
+	ui.spinAMin->setValue(aMin);
+	ui.spinAMax->setValue(aMax);
+	ui.spinRadius->setValue(radius);
+	ui.spinBaseIR->setValue(baseIR);
+	ui.spinScaleK->setValue(cA);
+	ui.spinObjNAi->setValue(oNAi);
+	ui.spinObjNAo->setValue(oNAo);
+	ui.spinCondNAi->setValue(cNAi);
+	ui.spinCondNAo->setValue(cNAo);
+	ui.spinError->setValue(minMSE);
+	ui.spinMaxIter->setValue(maxFitIter);
+	ui.spinI0Scale->setValue(scaleI0);
+
+	//display spectra values
+	ui.chkDisplaySimSpec->setChecked(dispSimSpec);
+	ui.chkDisplayRefSpec->setChecked(dispRefSpec);
+	ui.chkDisplaySimK->setChecked(dispSimK);
+	ui.chkDisplayMatK->setChecked(dispMatK);
+	ui.chkDisplaySimN->setChecked(dispSimN);
+	ui.chkDisplayMatN->setChecked(dispMatN);
+	ui.spinDispScaleK->setValue(kMax);
+	ui.spinDispScaleN->setValue(nMag);
+
+	//material selection combo box
+	ui.cmbMaterial->clear();
+	for(unsigned int i=0; i<MaterialList.size(); i++)
+		ui.cmbMaterial->addItem(MaterialList[i].name.c_str(), i);
+	ui.cmbMaterial->setCurrentIndex(currentMaterial);
+
+	updating = false;
+}
+
+void dragEnterEvent(QDragEnterEvent *event)
+{
+	cout<<"This is a test."<<endl;
+	QStringList s = event->mimeData()->formats();
+	if (event->mimeData()->hasFormat("application/x-qt-windows-mime;value=\"FileName\"") ||
+			event->mimeData()->hasFormat("text/plain"))
+	{
+		event->acceptProposedAction();
+
+	}
+}
+
+void dropEvent(QDropEvent *event)
+{
+	//cout<<"Challenge Accepted."<<endl;
+	RefSpectrum.clear();
+	RefSpectrum.push_back(SetReferenceSpectrum(event->mimeData()->text().toAscii().data()));
+	UpdateDisplay();
+}
+
+private:
+Ui::InteractiveMieClass ui;
+
+public slots:
+//display parameters
+void on_spinNuMin_valueChanged(int i) {
+	if(updating) return;
+	nuMin = (float)i;
+	UpdateDisplay();
+}
+void on_spinNuMax_valueChanged(int i) {
+	if(updating) return;
+	nuMax = (float)i;
+	UpdateDisplay();
+}
+void on_spinAMin_valueChanged(double d) {
+	if(updating) return;
+	aMin = d;
+	UpdateDisplay();
+}
+void on_spinAMax_valueChanged(double d) {
+	if(updating) return;
+	aMax = d;
+	UpdateDisplay();
+}
+void on_chkDisplaySimSpec_clicked(bool b) {
+	if(updating) return;
+	dispSimSpec = b;
+	UpdateDisplay();
+}
+void on_chkDisplayRefSpec_clicked(bool b) {
+	if(updating) return;
+	dispRefSpec = b;
+	UpdateDisplay();
+}
+void on_chkDisplaySimK_clicked(bool b) {
+	if(updating) return;
+	dispSimK = b;
+	UpdateDisplay();
+}
+void on_chkDisplayMatK_clicked(bool b) {
+	if(updating) return;
+	dispMatK = b;
+	UpdateDisplay();
+}
+void on_chkDisplaySimN_clicked(bool b) {
+	if(updating) return;
+	dispSimN = b;
+	UpdateDisplay();
+}
+void on_chkDisplayMatN_clicked(bool b) {
+	if(updating) return;
+	dispMatN = b;
+	UpdateDisplay();
+}
+void on_spinDispScaleK_valueChanged(double d) {
+	if(updating) return;
+	kMax = d;
+	UpdateDisplay();
+}
+void on_spinDispScaleN_valueChanged(double d) {
+	if(updating) return;
+	nMag = d;
+	UpdateDisplay();
+}
+void on_radDisplayAbsorbance_clicked(bool b) {
+	if(updating) return;
+	dispSimType = AbsorbanceSpecType;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_radDisplayIntensity_toggled(bool b) {
+	if(updating) return;
+	dispSimType = IntensitySpecType;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_chkNormalize_clicked(bool b) {
+	if(updating) return;
+	dispNormalize = b;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_spinNormFactor_valueChanged(double d) {
+	if(updating) return;
+	dispNormFactor = d;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+
+//material parameters
+void on_spinRadius_valueChanged(double d) {
+	if(updating) return;
+	radius = d;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_chkAdjustIR_clicked(bool b) {
+	if(updating) return;
+	//allow the user to change the mean n and k values
+	ui.spinBaseIR->setEnabled(b);
+	ui.spinScaleK->setEnabled(b);
+	
+}
+void on_spinBaseIR_valueChanged(double d) {
+	if(updating) return;
+	baseIR = d;
+	ChangeAbsorbance();
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_spinScaleK_valueChanged(double d) {
+	if(updating) return;
+	cA = d;
+	ChangeAbsorbance();
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_chkApplyMaterial_clicked(bool b) {
+	if(updating) return;
+	applyMaterial = b;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_cmbMaterial_currentIndexChanged(int i) {
+	if(updating) return;
+
+	currentMaterial = i;
+	SetMaterial();
+	SimulateSpectrum();
+	UpdateDisplay();
+	refreshUI();
+}
+
+//optical parameters
+void on_spinCondNAi_valueChanged(double d) {
+	cNAi = d;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_spinCondNAo_valueChanged(double d) {
+	cNAo = d;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_spinObjNAi_valueChanged(double d) {
+	oNAi = d;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_spinObjNAo_valueChanged(double d) {
+	oNAo = d;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_radTransmissionOptics_clicked(bool d) {
+	ui.spinCondNAi->setEnabled(true);
+	ui.spinCondNAo->setEnabled(true);
+	opticsMode = TransmissionOpticsType;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_radReflectionOptics_clicked(bool d) {
+	ui.spinCondNAi->setEnabled(false);
+	ui.spinCondNAo->setEnabled(false);
+	ui.radDisplayAbsorbance->setEnabled(false);
+	ui.radDisplayIntensity->setChecked(true);
+	opticsMode = ReflectionOpticsType;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_chkPointDetector_clicked(bool b) {
+	if(b)
+	{
+		pointDetector = true;
+		ui.spinObjectiveSamples->setEnabled(false);
+	}
+	else
+	{
+		pointDetector = false;
+		ui.spinObjectiveSamples->setEnabled(true);
+	}
+
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+
+void on_spinObjectiveSamples_valueChanged(int i) {
+	objectiveSamples = i;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+
+//Fitting
+void on_spinMaxIter_valueChanged(int i) {
+	maxFitIter = i;
+}
+void on_spinError_valueChanged(double d) {
+	minMSE = d;
+}
+void on_spinI0Scale_valueChanged(double d) {
+	scaleI0 = d;
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_spinRefSlope_valueChanged(double d) {
+	refSlope = d;
+	UpdateDisplay();
+}
+
+//display settings
+
+//Buttons
+void on_btnFit_clicked() {
+	FitDisplay();
+	refreshUI();
+}
+void on_btnSave_clicked() {
+	SaveState();
+}
+void on_btnReset_clicked() {
+	SetDefaults();
+	SimulateSpectrum();
+	UpdateDisplay();
+	refreshUI();
+}
+void on_btnResetK_clicked() {
+	ChangeAbsorbance();
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_btnEstimateK_clicked() {
+	EstimateMaterial();
+	SimulateSpectrum();
+	UpdateDisplay();
+}
+void on_btnDistortion_clicked() {
+	//ComputeDistortion();
+	//DistortionMap();
+	cout<<"Distortion"<<endl;
+	distortionDialog->show();
+}
+void on_btnTimings_clicked() {
+	PD.PrintResults(cout);
+}
+
+//menu items
+void on_mnuLoadReference_triggered() {
+	QString fileName = QFileDialog::getOpenFileName(this, tr("Open Reference Spectrum"));
+
+	if(fileName != QString::null) {
+		RefSpectrum.clear();
+		RefSpectrum.push_back(LoadSpectrum(fileName.toAscii().data()));
+	}
+	UpdateDisplay();
+}
+
+void on_mnuLoadMaterial_triggered() {
+
+	//first load the imaginary part
+	QString fileName = QFileDialog::getOpenFileName(this, tr("Open Material Spectrum"));
+
+	//exit if no file was selected
+	/*if(kFileName == QString::null)
+		return;
+
+	QString nFileName = QFileDialog::getOpenFileName(this, tr("Open Imaginary (n) Spectrum"));*/
+
+	//request the material name
+	QString matName = QInputDialog::getText(this, tr("Material Name"), tr("Enter material name:"));
+
+	//if a real part was given, load both
+	/*if(nFileName != QString::null)
+		LoadMaterial(kFileName.toAscii().data(), nFileName.toAscii().data(), matName.toAscii().data());
+	else
+		LoadMaterial(kFileName.toAscii().data(), matName.toAscii().data());*/
+	LoadMaterial(fileName.toAscii().data(), matName.toAscii().data());
+
+	//add the new material to the combo box
+	refreshUI();
+}
+void on_mnuLoadSource_triggered() {
+	cout<<"Load source."<<endl;
+}
+void on_chkSourceSpectrum_clicked(bool b) {
+
+	useSourceSpectrum = b;
+	SimulateSpectrum();
+	UpdateDisplay();
+
+}
+
+void on_mnuSaveSim_triggered() {
+	//first load the imaginary part
+	QString fileName = QFileDialog::getSaveFileName(this, tr("Save Simulated Spectrum"));
+	SaveSimulation(fileName.toAscii().data());
+}
+
+/*void on_mnuSaveK_triggered() {
+	//first load the imaginary part
+	QString fileName = QFileDialog::getSaveFileName(this, tr("Save Imaginary Index of Refraction (k)"));
+	SaveK(fileName.toAscii().data());
+}*/
+
+void on_mnuSaveMaterial_triggered() {
+	//first load the imaginary part
+	QString fileName = QFileDialog::getSaveFileName(this, tr("Save Real Index of Refraction (n)"));
+	SaveMaterial(fileName.toAscii().data());
+}
+
+
+
+};
+
+#endif // INTERACTIVEMIE_H
@@ -23,13 +23,16 @@
       <x>20</x>
       <y>170</y>
       <width>151</width>
-      <height>161</height>
+      <height>191</height>
      </rect>
     </property>
     <property name="title">
      <string>Material</string>
     </property>
     <widget class="QDoubleSpinBox" name="spinScaleK">
+     <property name="enabled">
+      <bool>false</bool>
+     </property>
      <property name="geometry">
       <rect>
        <x>80</x>
@@ -39,13 +42,16 @@
       </rect>
      </property>
      <property name="singleStep">
-      <double>0.100000000000000</double>
+      <double>0.010000000000000</double>
      </property>
      <property name="value">
       <double>1.000000000000000</double>
      </property>
     </widget>
     <widget class="QDoubleSpinBox" name="spinBaseIR">
+     <property name="enabled">
+      <bool>false</bool>
+     </property>
      <property name="geometry">
       <rect>
        <x>80</x>
@@ -67,14 +73,17 @@
     <widget class="QLabel" name="label_8">
      <property name="geometry">
       <rect>
-       <x>30</x>
+       <x>20</x>
        <y>50</y>
        <width>46</width>
-       <height>13</height>
+       <height>21</height>
       </rect>
      </property>
      <property name="text">
-      <string>base IR</string>
+      <string>mean n</string>
+     </property>
+     <property name="alignment">
+      <set>Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter</set>
      </property>
     </widget>
     <widget class="QDoubleSpinBox" name="spinRadius">
@@ -99,34 +108,40 @@
     <widget class="QLabel" name="label_4">
      <property name="geometry">
       <rect>
-       <x>30</x>
+       <x>20</x>
        <y>20</y>
        <width>46</width>
-       <height>13</height>
+       <height>21</height>
       </rect>
      </property>
      <property name="text">
       <string>radius</string>
      </property>
+     <property name="alignment">
+      <set>Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter</set>
+     </property>
     </widget>
     <widget class="QLabel" name="label_9">
      <property name="geometry">
       <rect>
-       <x>30</x>
+       <x>20</x>
        <y>80</y>
        <width>46</width>
-       <height>13</height>
+       <height>21</height>
       </rect>
      </property>
      <property name="text">
-      <string>scale K</string>
+      <string>scale k</string>
+     </property>
+     <property name="alignment">
+      <set>Qt::AlignRight|Qt::AlignTrailing|Qt::AlignVCenter</set>
      </property>
     </widget>
     <widget class="QCheckBox" name="chkApplyMaterial">
      <property name="geometry">
       <rect>
        <x>20</x>
-       <y>110</y>
+       <y>130</y>
        <width>121</width>
        <height>17</height>
       </rect>
@@ -142,12 +157,28 @@
      <property name="geometry">
       <rect>
        <x>20</x>
-       <y>140</y>
+       <y>160</y>
        <width>111</width>
        <height>22</height>
       </rect>
      </property>
     </widget>
+    <widget class="QCheckBox" name="chkAdjustIR">
+     <property name="geometry">
+      <rect>
+       <x>20</x>
+       <y>110</y>
+       <width>101</width>
+       <height>17</height>
+      </rect>
+     </property>
+     <property name="text">
+      <string>Adjust IR</string>
+     </property>
+     <property name="checked">
+      <bool>false</bool>
+     </property>
+    </widget>
    </widget>
    <widget class="QGroupBox" name="groupBox_2">
     <property name="geometry">
@@ -644,7 +675,7 @@
       </rect>
      </property>
      <property name="singleStep">
-      <double>0.100000000000000</double>
+      <double>0.010000000000000</double>
      </property>
     </widget>
     <widget class="QDoubleSpinBox" name="spinDispScaleN">
@@ -657,7 +688,7 @@
       </rect>
      </property>
      <property name="singleStep">
-      <double>0.100000000000000</double>
+      <double>0.010000000000000</double>
      </property>
     </widget>
     <widget class="QCheckBox" name="chkNormalize">
@@ -791,7 +822,7 @@
     <property name="geometry">
      <rect>
       <x>20</x>
-      <y>340</y>
+      <y>370</y>
       <width>201</width>
       <height>111</height>
      </rect>
@@ -860,7 +891,7 @@
       </rect>
      </property>
      <property name="text">
-      <string>Estimate K</string>
+      <string>Estimate k</string>
      </property>
     </widget>
     <widget class="QPushButton" name="btnResetK">
@@ -873,7 +904,7 @@
       </rect>
      </property>
      <property name="text">
-      <string>Reset K</string>
+      <string>Reset k</string>
      </property>
     </widget>
     <widget class="QLabel" name="label_5">
@@ -913,8 +944,7 @@
      <string>Save</string>
     </property>
     <addaction name="mnuSaveSim"/>
-    <addaction name="mnuSaveK"/>
-    <addaction name="mnuSaveN"/>
+    <addaction name="mnuSaveMaterial"/>
    </widget>
    <widget class="QMenu" name="menuVersion_0_6">
     <property name="title">
@@ -954,9 +984,9 @@
     <string>k</string>
    </property>
   </action>
-  <action name="mnuSaveN">
+  <action name="mnuSaveMaterial">
    <property name="text">
-    <string>n</string>
+    <string>Material</string>
    </property>
   </action>
   <action name="mnuLoadSource">
+nu	k
 600	0.0241342
 602	0.027446631
 604	0.02823961
+nu	k
+898.665771	0.119797
+902.522705	0.113611
+906.379639	0.106711
+910.236572	0.099793
+914.093506	0.099635
+917.950439	0.101204
+921.807373	0.104875
+925.664307	0.107064
+929.52124	0.103106
+933.378174	0.102888
+937.235107	0.105524
+941.092041	0.112168
+944.948975	0.118147
+948.805908	0.123335
+952.662842	0.125731
+956.519775	0.123265
+960.376709	0.123469
+964.233643	0.121685
+968.090576	0.12018
+971.94751	0.118345
+975.804443	0.115624
+979.661377	0.115624
+983.518311	0.115935
+987.375244	0.117921
+991.232178	0.12058
+995.089111	0.126018
+998.946045	0.135758
+1002.802979	0.149488
+1006.659912	0.166032
+1010.516846	0.184224
+1014.373779	0.199554
+1018.230713	0.205409
+1022.087646	0.208976
+1025.94458	0.209979
+1029.801514	0.204706
+1033.658447	0.195665
+1037.515381	0.185283
+1041.372314	0.177356
+1045.229248	0.171783
+1049.086182	0.168174
+1052.943115	0.165209
+1056.800049	0.164215
+1060.656982	0.164634
+1064.513916	0.167807
+1068.37085	0.175054
+1072.227783	0.183043
+1076.084717	0.192604
+1079.94165	0.201534
+1083.798584	0.209008
+1087.655518	0.216408
+1091.512451	0.224841
+1095.369385	0.230546
+1099.226318	0.228466
+1103.083252	0.221409
+1106.940186	0.212899
+1110.797119	0.205085
+1114.654053	0.195571
+1118.510986	0.189145
+1122.36792	0.190001
+1126.224854	0.195114
+1130.081787	0.206932
+1133.938721	0.231471
+1137.795654	0.277626
+1141.652588	0.362189
+1145.509521	0.508769
+1149.366455	0.675979
+1153.223389	0.742934
+1157.080322	0.713568
+1160.937256	0.634251
+1164.794189	0.538205
+1168.651123	0.451822
+1172.508057	0.371445
+1176.36499	0.304973
+1180.221924	0.272547
+1184.078857	0.278284
+1187.935791	0.311813
+1191.792725	0.370434
+1195.649658	0.456571
+1199.506592	0.571005
+1203.363525	0.690027
+1207.220459	0.768029
+1211.077393	0.801994
+1214.934326	0.81201
+1218.79126	0.815038
+1222.648193	0.807314
+1226.505249	0.790257
+1230.362061	0.760849
+1234.219116	0.717067
+1238.07605	0.664946
+1241.932861	0.597291
+1245.789917	0.520156
+1249.646851	0.441294
+1253.503784	0.37302
+1257.360718	0.314789
+1261.217651	0.254094
+1265.074585	0.189348
+1268.931519	0.136625
+1272.788452	0.107828
+1276.645386	0.096242
+1280.502319	0.091956
+1284.359253	0.090309
+1288.216187	0.090969
+1292.07312	0.090918
+1295.930054	0.090126
+1299.786987	0.088419
+1303.643921	0.081592
+1307.500854	0.073385
+1311.357788	0.066815
+1315.214722	0.063703
+1319.071655	0.062516
+1322.928589	0.061202
+1326.785522	0.061311
+1330.642456	0.061893
+1334.49939	0.063851
+1338.356323	0.066716
+1342.213257	0.068291
+1346.07019	0.068949
+1349.927124	0.071117
+1353.784058	0.074663
+1357.640991	0.077776
+1361.497925	0.080936
+1365.354858	0.080985
+1369.211792	0.079623
+1373.068726	0.079098
+1376.925659	0.07642
+1380.782593	0.073569
+1384.639526	0.07403
+1388.49646	0.074968
+1392.353394	0.075173
+1396.210327	0.077807
+1400.067261	0.079196
+1403.924194	0.080566
+1407.781128	0.083056
+1411.638062	0.084542
+1415.494995	0.089578
+1419.351929	0.093261
+1423.208862	0.091348
+1427.065796	0.09023
+1430.922729	0.091503
+1434.779663	0.094947
+1438.636597	0.09386
+1442.49353	0.090456
+1446.350464	0.0896
+1450.207397	0.087377
+1454.064331	0.088299
+1457.921265	0.090942
+1461.778198	0.0866
+1465.635132	0.085919
+1469.492065	0.089903
+1473.348999	0.094438
+1477.205933	0.094567
+1481.062866	0.092036
+1484.9198	0.096689
+1488.776733	0.100191
+1492.633667	0.099245
+1496.490601	0.097936
+1500.347534	0.094544
+1504.204468	0.100589
+1508.061401	0.105907
+1511.918335	0.09782
+1515.775269	0.095739
+1519.632202	0.100649
+1523.489136	0.098981
+1527.346069	0.094213
+1531.203003	0.092945
+1535.059937	0.095972
+1538.91687	0.10604
+1542.773804	0.106572
+1546.630737	0.098688
+1550.487671	0.096871
+1554.344604	0.104288
+1558.201538	0.114593
+1562.058472	0.106013
+1565.915405	0.100332
+1569.772339	0.101925
+1573.629272	0.102216
+1577.486206	0.102323
+1581.34314	0.099031
+1585.200073	0.098575
+1589.057007	0.099345
+1592.91394	0.098173
+1596.770874	0.099296
+1600.627808	0.098506
+1604.484741	0.099291
+1608.341675	0.099866
+1612.198608	0.10207
+1616.055542	0.108292
+1619.912476	0.108942
+1623.769409	0.111048
+1627.626343	0.10924
+1631.483276	0.109778
+1635.34021	0.114933
+1639.197144	0.108015
+1643.054077	0.103923
+1646.911011	0.106034
+1650.767944	0.112606
+1654.624878	0.112221
+1658.481812	0.104846
+1662.338745	0.105472
+1666.195679	0.106895
+1670.052612	0.109738
+1673.909546	0.111448
+1677.766479	0.109629
+1681.623413	0.11616
+1685.480347	0.117894
+1689.33728	0.111271
+1693.194214	0.112307
+1697.051147	0.121065
+1700.908081	0.121781
+1704.765015	0.11577
+1708.621948	0.1102
+1712.478882	0.110347
+1716.335815	0.117381
+1720.192749	0.113735
+1724.049683	0.108096
+1727.906738	0.109655
+1731.76355	0.115723
+1735.620605	0.11899
+1739.477539	0.117061
+1743.334473	0.117513
+1747.191406	0.119943
+1751.04834	0.120675
+1754.905273	0.117093
+1758.762207	0.116268
+1762.619141	0.116788
+1766.476074	0.116819
+1770.333008	0.122916
+1774.189941	0.121082
+1778.046875	0.117999
+1781.903809	0.118654
+1785.760742	0.117828
+1789.617676	0.120904
+1793.474609	0.12157
+1797.331543	0.120378
+1801.188477	0.119121
+1805.04541	0.118429
+1808.902344	0.120929
+1812.759277	0.121934
+1816.616211	0.121768
+1820.473145	0.122502
+1824.330078	0.125022
+1828.187012	0.126044
+1832.043945	0.124735
+1835.900879	0.122494
+1839.757812	0.121608
+1843.614746	0.12354
+1847.47168	0.122387
+1851.328613	0.120089
+1855.185547	0.119761
+1859.04248	0.119944
+1862.899414	0.121586
+1866.756348	0.12588
+1870.613281	0.126864
+1874.470215	0.125077
+1878.327148	0.126259
+1882.184082	0.126898
+1886.041016	0.12878
+1889.897949	0.130889
+1893.754883	0.130154
+1897.611816	0.128743
+1901.46875	0.12709
+1905.325684	0.126148
+1909.182617	0.12448
+1913.039551	0.124467
+1916.896484	0.126429
+1920.753418	0.126745
+1924.610352	0.125931
+1928.467285	0.126244
+1932.324219	0.128196
+1936.181152	0.129263
+1940.038086	0.130692
+1943.89502	0.132099
+1947.751953	0.132385
+1951.608887	0.132089
+1955.46582	0.13207
+1959.322754	0.132502
+1963.179688	0.133091
+1967.036621	0.134334
+1970.893555	0.133633
+1974.750488	0.132941
+1978.607422	0.132207
+1982.464355	0.130382
+1986.321289	0.130208
+1990.178223	0.130239
+1994.035156	0.130694
+1997.89209	0.130857
+2001.749023	0.131523
+2005.605957	0.132631
+2009.462891	0.13381
+2013.319824	0.135877
+2017.176758	0.137253
+2021.033691	0.137779
+2024.890625	0.137152
+2028.747559	0.136642
+2032.604492	0.136288
+2036.461426	0.136501
+2040.318359	0.136449
+2044.175293	0.13475
+2048.032227	0.134343
+2051.88916	0.134235
+2055.746094	0.134563
+2059.603027	0.134534
+2063.459961	0.135336
+2067.316895	0.137324
+2071.173828	0.138357
+2075.030762	0.140503
+2078.887695	0.141893
+2082.744629	0.142863
+2086.601562	0.144135
+2090.458496	0.144251
+2094.31543	0.144278
+2098.172363	0.144239
+2102.029297	0.144004
+2105.88623	0.143478
+2109.743164	0.143511
+2113.600098	0.143151
+2117.457031	0.143559
+2121.313965	0.144096
+2125.170898	0.144133
+2129.027832	0.145068
+2132.884766	0.144984
+2136.741699	0.144745
+2140.598633	0.145628
+2144.455566	0.147823
+2148.3125	0.150011
+2152.169434	0.151872
+2156.026367	0.153301
+2159.883301	0.153103
+2163.740234	0.154012
+2167.597168	0.155013
+2171.454102	0.155685
+2175.311035	0.155886
+2179.167969	0.155053
+2183.024902	0.154117
+2186.881836	0.153234
+2190.73877	0.153008
+2194.595703	0.152778
+2198.452637	0.152969
+2202.30957	0.153286
+2206.166504	0.154937
+2210.023438	0.157569
+2213.880371	0.159214
+2217.737305	0.161321
+2221.594238	0.163009
+2225.451172	0.165156
+2229.308105	0.166447
+2233.165039	0.16597
+2237.021973	0.165728
+2240.878906	0.16592
+2244.73584	0.165315
+2248.592773	0.163689
+2252.449707	0.163399
+2256.306641	0.163338
+2260.163574	0.163126
+2264.020508	0.16376
+2267.877441	0.165369
+2271.734375	0.166799
+2275.591309	0.167143
+2279.448242	0.168417
+2283.305176	0.169971
+2287.162109	0.172706
+2291.019043	0.174338
+2294.875977	0.17392
+2298.73291	0.172741
+2302.589844	0.170809
+2306.446777	0.169791
+2310.303711	0.167444
+2314.160645	0.167382
+2318.017578	0.169346
+2321.874512	0.1687
+2325.731445	0.169079
+2329.588379	0.171429
+2333.445312	0.172005
+2337.302246	0.17173
+2341.15918	0.177313
+2345.016113	0.172166
+2348.873047	0.164887
+2352.72998	0.170921
+2356.586914	0.179951
+2360.443848	0.187692
+2364.300781	0.193336
+2368.157715	0.196336
+2372.014648	0.19635
+2375.871582	0.190763
+2379.728516	0.186245
+2383.585449	0.182521
+2387.442383	0.180239
+2391.299316	0.178919
+2395.15625	0.178212
+2399.013184	0.178546
+2402.870117	0.178607
+2406.727051	0.178765
+2410.583984	0.180182
+2414.440918	0.182686
+2418.297852	0.184782
+2422.154785	0.186519
+2426.011719	0.187862
+2429.868652	0.188519
+2433.725586	0.188641
+2437.58252	0.188783
+2441.439453	0.188943
+2445.296387	0.188549
+2449.15332	0.188368
+2453.010254	0.187423
+2456.867432	0.186584
+2460.724121	0.186132
+2464.581299	0.185374
+2468.437988	0.185088
+2472.294922	0.18578
+2476.1521	0.186438
+2480.008789	0.186875
+2483.865967	0.188714
+2487.7229	0.189906
+2491.579834	0.190912
+2495.436768	0.192349
+2499.293701	0.193208
+2503.150635	0.194736
+2507.007568	0.195032
+2510.864502	0.194682
+2514.721436	0.194575
+2518.578369	0.194022
+2522.435303	0.192652
+2526.292236	0.190689
+2530.14917	0.188958
+2534.006104	0.188007
+2537.863037	0.188064
+2541.719971	0.188482
+2545.576904	0.190521
+2549.433838	0.192907
+2553.290771	0.194646
+2557.147705	0.195373
+2561.004639	0.19598
+2564.861572	0.198918
+2568.718506	0.200591
+2572.575439	0.200731
+2576.432373	0.199931
+2580.289307	0.199108
+2584.14624	0.199044
+2588.003174	0.198248
+2591.860107	0.198056
+2595.717041	0.197357
+2599.573975	0.196511
+2603.430908	0.195941
+2607.287842	0.196022
+2611.144775	0.196668
+2615.001709	0.197505
+2618.858643	0.199575
+2622.715576	0.200912
+2626.57251	0.203322
+2630.429443	0.205753
+2634.286377	0.206707
+2638.143311	0.207317
+2642.000244	0.20686
+2645.857178	0.206699
+2649.714111	0.207118
+2653.571045	0.207081
+2657.427979	0.204599
+2661.284912	0.202973
+2665.141846	0.203807
+2668.998779	0.20409
+2672.855713	0.204505
+2676.712646	0.204402
+2680.56958	0.205393
+2684.426514	0.207695
+2688.283447	0.210657
+2692.140381	0.21329
+2695.997314	0.213214
+2699.854248	0.213629
+2703.711182	0.215489
+2707.568115	0.217552
+2711.425049	0.219984
+2715.281982	0.220446
+2719.138916	0.21845
+2722.99585	0.217402
+2726.852783	0.217728
+2730.709717	0.217692
+2734.56665	0.217954
+2738.423584	0.219007
+2742.280518	0.219831
+2746.137451	0.219937
+2749.994385	0.221145
+2753.851318	0.223599
+2757.708252	0.226448
+2761.565186	0.228654
+2765.422119	0.230751
+2769.279053	0.23316
+2773.135986	0.233946
+2776.99292	0.235595
+2780.849854	0.237077
+2784.706787	0.237037
+2788.563721	0.237783
+2792.420654	0.238303
+2796.277588	0.23844
+2800.134521	0.237748
+2803.991455	0.23761
+2807.848389	0.239399
+2811.705322	0.242356
+2815.562256	0.245029
+2819.419189	0.247127
+2823.276123	0.249953
+2827.133057	0.252941
+2830.98999	0.255616
+2834.846924	0.256416
+2838.703857	0.257745
+2842.560791	0.261174
+2846.417725	0.263504
+2850.274658	0.265136
+2854.131592	0.266484
+2857.988525	0.267884
+2861.845459	0.268755
+2865.702393	0.269319
+2869.559326	0.270306
+2873.41626	0.270931
+2877.273193	0.27218
+2881.130127	0.274424
+2884.987061	0.277215
+2888.843994	0.279752
+2892.700928	0.28225
+2896.557861	0.285606
+2900.414795	0.289405
+2904.271729	0.29194
+2908.128662	0.293517
+2911.985596	0.295321
+2915.842529	0.297343
+2919.699463	0.30078
+2923.556396	0.303916
+2927.41333	0.304841
+2931.270264	0.304886
+2935.127197	0.307534
+2938.984131	0.310065
+2942.841064	0.309946
+2946.697998	0.312969
+2950.554932	0.319969
+2954.411865	0.330884
+2958.268799	0.341583
+2962.125732	0.345956
+2965.982666	0.343104
+2969.8396	0.335753
+2973.696533	0.330953
+2977.553467	0.327567
+2981.4104	0.32633
+2985.267334	0.327893
+2989.124268	0.328081
+2992.981201	0.327513
+2996.838135	0.32761
+3000.695068	0.329393
+3004.552002	0.330277
+3008.408936	0.330659
+3012.265869	0.331638
+3016.122803	0.333973
+3019.979736	0.337387
+3023.83667	0.339392
+3027.693604	0.343113
+3031.550537	0.346716
+3035.407471	0.348999
+3039.264404	0.349565
+3043.121338	0.350472
+3046.978271	0.354745
+3050.835205	0.356839
+3054.692139	0.35844
+3058.549072	0.360373
+3062.406006	0.359955
+3066.262939	0.358908
+3070.119873	0.358617
+3073.976807	0.359479
+3077.83374	0.360783
+3081.690674	0.362895
+3085.547607	0.365378
+3089.404541	0.368972
+3093.261475	0.372506
+3097.118408	0.376024
+3100.975342	0.379468
+3104.832275	0.381968
+3108.689209	0.385588
+3112.546143	0.386591
+3116.403076	0.385214
+3120.26001	0.386689
+3124.116943	0.390244
+3127.973877	0.392708
+3131.830811	0.394077
+3135.687744	0.393566
+3139.544678	0.391412
+3143.401611	0.393047
+3147.258545	0.396304
+3151.115479	0.398407
+3154.972412	0.400344
+3158.829346	0.402014
+3162.686279	0.404263
+3166.543213	0.406683
+3170.400146	0.40869
+3174.25708	0.411274
+3178.114014	0.415657
+3181.970947	0.419736
+3185.827881	0.42175
+3189.684814	0.419426
+3193.541748	0.419143
+3197.398682	0.424583
+3201.255615	0.426743
+3205.112549	0.428647
+3208.969482	0.429678
+3212.826416	0.429757
+3216.68335	0.433223
+3220.540283	0.436215
+3224.397217	0.439306
+3228.25415	0.441374
+3232.111084	0.44311
+3235.968018	0.445396
+3239.824951	0.448125
+3243.681885	0.451367
+3247.538818	0.454258
+3251.395752	0.456481
+3255.252686	0.456045
+3259.109619	0.457979
+3262.966553	0.460119
+3266.823486	0.459373
+3270.68042	0.4599
+3274.537354	0.461298
+3278.394287	0.463606
+3282.251221	0.467458
+3286.108154	0.471413
+3289.965088	0.472572
+3293.822021	0.473989
+3297.678955	0.476511
+3301.535889	0.478557
+3305.392822	0.483234
+3309.249756	0.489315
+3313.106689	0.4922
+3316.963623	0.492279
+3320.820557	0.494391
+3324.67749	0.497505
+3328.534424	0.501519
+3332.391357	0.503834
+3336.248291	0.503075
+3340.105225	0.50296
+3343.962158	0.502158
+3347.819092	0.502881
+3351.676025	0.504862
+3355.532959	0.509708
+3359.389893	0.516957
+3363.246826	0.52107
+3367.10376	0.521195
+3370.960693	0.522663
+3374.817627	0.527924
+3378.674561	0.529786
+3382.531494	0.532712
+3386.388428	0.53422
+3390.245361	0.53586
+3394.102295	0.541357
+3397.959229	0.539042
+3401.816162	0.538392
+3405.673096	0.542694
+3409.530029	0.546009
+3413.386963	0.547949
+3417.243896	0.551694
+3421.10083	0.557508
+3424.957764	0.558706
+3428.814697	0.559973
+3432.671631	0.560578
+3436.528564	0.562476
+3440.385498	0.566948
+3444.242432	0.571401
+3448.099609	0.572987
+3451.956299	0.573218
+3455.813232	0.577121
+3459.67041	0.577896
+3463.5271	0.579122
+3467.384277	0.578371
+3471.241211	0.579208
+3475.098145	0.582138
+3478.955078	0.58127
+3482.812012	0.586469
+3486.668945	0.589135
+3490.525879	0.591052
+3494.382812	0.593125
+3498.239746	0.59621
+3502.09668	0.603276
+3505.953613	0.606524
+3509.810547	0.607297
+3513.66748	0.601191
+3517.524414	0.603099
+3521.381348	0.615545
+3525.238281	0.624269
+3529.095215	0.622593
+3532.952148	0.614592
+3536.809082	0.609326
+3540.666016	0.609761
+3544.522949	0.6258
+3548.379883	0.629168
+3552.236816	0.623019
+3556.09375	0.618341
+3559.950684	0.619473
+3563.807617	0.663041
+3567.664551	0.680265
+3571.521484	0.653292
+3575.378418	0.637676
+3579.235352	0.627736
+3583.092285	0.647582
+3586.949219	0.679846
+3590.806152	0.673906
+3594.663086	0.666062
+3598.52002	0.659118
+3602.376953	0.642123
+3606.233887	0.662345
+3610.09082	0.686657
+3613.947754	0.699009
+3617.804688	0.708261
+3621.661621	0.677506
+3625.518555	0.718444
+3629.375488	0.775054
+3633.232422	0.721214
+3637.089355	0.668287
+3640.946289	0.635247
+3644.803223	0.693072
+3648.660156	0.801296
+3652.51709	0.782912
+3656.374023	0.733296
+3660.230957	0.668873
+3664.087891	0.63726
+3667.944824	0.688064
+3671.801758	0.787399
+3675.658691	0.837877
+3679.515625	0.748979
+3683.372559	0.700056
+3687.229492	0.776031
+3691.086426	0.78917
+3694.943359	0.730333
+3698.800293	0.715288
+3702.657227	0.705007
+3706.51416	0.722261
+3710.371094	0.787614
+3714.228027	0.76146
+3718.084961	0.711827
+3721.941895	0.71987
+3725.798828	0.698932
+3729.655762	0.71304
+3733.512695	0.784518
+3737.369629	0.77511
+3741.226562	0.775089
+3745.083496	0.865942
+3748.94043	0.962277
+3752.797363	0.942017
+3756.654297	0.869403
+3760.51123	0.822932
+3764.368164	0.805583
+3768.225098	0.818461
+3772.082031	0.794773
+3775.938965	0.773548
+3779.795898	0.787632
+3783.652832	0.773566
+3787.509766	0.742363
+3791.366699	0.706796
+3795.223633	0.713586
+3799.080566	0.779534
+3802.9375	0.843259
+3806.794434	0.824484
+3810.651367	0.753229
+3814.508301	0.766034
+3818.365234	0.846253
+3822.222168	0.86147
+3826.079102	0.80157
+3829.936035	0.755
+3833.792969	0.791943
+3837.649902	0.869714
+3841.506836	0.868459
+3845.36377	0.758025
+3849.220703	0.758536
+3853.077637	0.911496
 \ No newline at end of file
+nu	k
+898.665771	0.042801
+902.522705	0.038246
+906.379639	0.040294
+910.236572	0.039488
+914.093506	0.037618
+917.950439	0.03536
+921.807373	0.03278
+925.664307	0.03156
+929.52124	0.028804
+933.378174	0.032099
+937.235107	0.031952
+941.092041	0.033633
+944.948975	0.036991
+948.805908	0.040887
+952.662842	0.044517
+956.519775	0.043966
+960.376709	0.044863
+964.233643	0.044314
+968.090576	0.045241
+971.94751	0.043188
+975.804443	0.039329
+979.661377	0.034324
+983.518311	0.027772
+987.375244	0.024005
+991.232178	0.018819
+995.089111	0.017644
+998.946045	0.01743
+1002.802979	0.01892
+1006.659912	0.022698
+1010.516846	0.025522
+1014.373779	0.027914
+1018.230713	0.028447
+1022.087646	0.030539
+1025.94458	0.030134
+1029.801514	0.030709
+1033.658447	0.030649
+1037.515381	0.027764
+1041.372314	0.024089
+1045.229248	0.017639
+1049.086182	0.013155
+1052.943115	0.007972
+1056.800049	0.004678
+1060.656982	0.002414
+1064.513916	0.000656
+1068.37085	0.000452
+1072.227783	0.000186
+1076.084717	0.00315
+1079.94165	0.005205
+1083.798584	0.009191
+1087.655518	0.012551
+1091.512451	0.013487
+1095.369385	0.01366
+1099.226318	0.012324
+1103.083252	0.011624
+1106.940186	0.009228
+1110.797119	0.007841
+1114.654053	0.005534
+1118.510986	0.003409
+1122.36792	0.001855
+1126.224854	0
+1130.081787	0.000719
+1133.938721	0.001989
+1137.795654	0.005403
+1141.652588	0.008195
+1145.509521	0.012699
+1149.366455	0.01768
+1153.223389	0.021147
+1157.080322	0.025829
+1160.937256	0.029061
+1164.794189	0.032397
+1168.651123	0.034385
+1172.508057	0.036836
+1176.36499	0.03735
+1180.221924	0.035023
+1184.078857	0.033782
+1187.935791	0.032161
+1191.792725	0.032158
+1195.649658	0.031863
+1199.506592	0.033038
+1203.363525	0.035069
+1207.220459	0.037485
+1211.077393	0.041366
+1214.934326	0.045119
+1218.79126	0.04902
+1222.648193	0.050622
+1226.505249	0.053244
+1230.362061	0.054526
+1234.219116	0.054043
+1238.07605	0.053686
+1241.932861	0.051393
+1245.789917	0.049385
+1249.646851	0.045921
+1253.503784	0.043153
+1257.360718	0.041048
+1261.217651	0.039754
+1265.074585	0.038579
+1268.931519	0.037209
+1272.788452	0.037321
+1276.645386	0.036889
+1280.502319	0.038267
+1284.359253	0.039353
+1288.216187	0.040998
+1292.07312	0.042425
+1295.930054	0.04231
+1299.786987	0.042156
+1303.643921	0.04027
+1307.500854	0.038994
+1311.357788	0.035638
+1315.214722	0.031839
+1319.071655	0.027074
+1322.928589	0.022097
+1326.785522	0.019314
+1330.642456	0.016466
+1334.49939	0.01724
+1338.356323	0.019304
+1342.213257	0.020191
+1346.07019	0.020463
+1349.927124	0.022886
+1353.784058	0.024824
+1357.640991	0.026467
+1361.497925	0.032192
+1365.354858	0.03319
+1369.211792	0.032069
+1373.068726	0.029896
+1376.925659	0.025182
+1380.782593	0.020386
+1384.639526	0.01788
+1388.49646	0.017692
+1392.353394	0.01595
+1396.210327	0.018172
+1400.067261	0.017101
+1403.924194	0.01655
+1407.781128	0.018251
+1411.638062	0.019087
+1415.494995	0.025939
+1419.351929	0.030871
+1423.208862	0.033849
+1427.065796	0.035628
+1430.922729	0.0422
+1434.779663	0.051804
+1438.636597	0.054932
+1442.49353	0.058626
+1446.350464	0.063101
+1450.207397	0.074238
+1454.064331	0.099416
+1457.921265	0.209105
+1461.778198	0.321291
+1465.635132	0.28369
+1469.492065	0.267381
+1473.348999	0.253731
+1477.205933	0.128331
+1481.062866	0.06213
+1484.9198	0.05394
+1488.776733	0.057298
+1492.633667	0.056345
+1496.490601	0.05445
+1500.347534	0.054085
+1504.204468	0.058144
+1508.061401	0.064828
+1511.918335	0.055856
+1515.775269	0.052929
+1519.632202	0.059563
+1523.489136	0.05584
+1527.346069	0.048296
+1531.203003	0.043625
+1535.059937	0.046385
+1538.91687	0.056596
+1542.773804	0.054466
+1546.630737	0.043963
+1550.487671	0.041193
+1554.344604	0.048176
+1558.201538	0.058085
+1562.058472	0.049177
+1565.915405	0.041398
+1569.772339	0.042723
+1573.629272	0.042759
+1577.486206	0.040069
+1581.34314	0.034118
+1585.200073	0.031186
+1589.057007	0.031601
+1592.91394	0.030593
+1596.770874	0.030831
+1600.627808	0.028967
+1604.484741	0.02833
+1608.341675	0.028289
+1612.198608	0.028776
+1616.055542	0.033643
+1619.912476	0.034205
+1623.769409	0.035702
+1627.626343	0.033927
+1631.483276	0.034108
+1635.34021	0.042011
+1639.197144	0.038127
+1643.054077	0.036647
+1646.911011	0.04247
+1650.767944	0.048308
+1654.624878	0.045178
+1658.481812	0.034997
+1662.338745	0.034021
+1666.195679	0.036197
+1670.052612	0.038175
+1673.909546	0.039106
+1677.766479	0.037529
+1681.623413	0.045005
+1685.480347	0.05006
+1689.33728	0.044082
+1693.194214	0.045592
+1697.051147	0.057514
+1700.908081	0.061893
+1704.765015	0.056482
+1708.621948	0.051541
+1712.478882	0.053415
+1716.335815	0.061049
+1720.192749	0.056453
+1724.049683	0.049607
+1727.906738	0.05118
+1731.76355	0.05872
+1735.620605	0.061749
+1739.477539	0.058433
+1743.334473	0.058925
+1747.191406	0.06168
+1751.04834	0.061892
+1754.905273	0.058246
+1758.762207	0.058189
+1762.619141	0.059579
+1766.476074	0.060041
+1770.333008	0.066851
+1774.189941	0.066629
+1778.046875	0.063365
+1781.903809	0.063274
+1785.760742	0.061577
+1789.617676	0.063319
+1793.474609	0.063621
+1797.331543	0.061639
+1801.188477	0.060149
+1805.04541	0.057813
+1808.902344	0.056311
+1812.759277	0.054928
+1816.616211	0.053613
+1820.473145	0.053938
+1824.330078	0.057278
+1828.187012	0.060054
+1832.043945	0.058871
+1835.900879	0.056005
+1839.757812	0.056531
+1843.614746	0.059206
+1847.47168	0.057401
+1851.328613	0.054448
+1855.185547	0.053538
+1859.04248	0.051986
+1862.899414	0.050818
+1866.756348	0.053157
+1870.613281	0.051802
+1874.470215	0.04774
+1878.327148	0.047584
+1882.184082	0.047928
+1886.041016	0.05107
+1889.897949	0.055251
+1893.754883	0.056678
+1897.611816	0.056701
+1901.46875	0.056308
+1905.325684	0.057764
+1909.182617	0.058333
+1913.039551	0.058837
+1916.896484	0.061175
+1920.753418	0.061958
+1924.610352	0.06037
+1928.467285	0.058767
+1932.324219	0.058077
+1936.181152	0.05759
+1940.038086	0.058999
+1943.89502	0.060248
+1947.751953	0.060227
+1951.608887	0.06155
+1955.46582	0.064083
+1959.322754	0.066146
+1963.179688	0.068457
+1967.036621	0.070872
+1970.893555	0.07175
+1974.750488	0.073
+1978.607422	0.074496
+1982.464355	0.076088
+1986.321289	0.077477
+1990.178223	0.077673
+1994.035156	0.078181
+1997.89209	0.077858
+2001.749023	0.077439
+2005.605957	0.077198
+2009.462891	0.078891
+2013.319824	0.082924
+2017.176758	0.085872
+2021.033691	0.087082
+2024.890625	0.087384
+2028.747559	0.08829
+2032.604492	0.08848
+2036.461426	0.088407
+2040.318359	0.089069
+2044.175293	0.089026
+2048.032227	0.088623
+2051.88916	0.087477
+2055.746094	0.08616
+2059.603027	0.083997
+2063.459961	0.081664
+2067.316895	0.079261
+2071.173828	0.077244
+2075.030762	0.076483
+2078.887695	0.075797
+2082.744629	0.075846
+2086.601562	0.075997
+2090.458496	0.076488
+2094.31543	0.076722
+2098.172363	0.077003
+2102.029297	0.077852
+2105.88623	0.077923
+2109.743164	0.078499
+2113.600098	0.0785
+2117.457031	0.078399
+2121.313965	0.077331
+2125.170898	0.075105
+2129.027832	0.073147
+2132.884766	0.070562
+2136.741699	0.068282
+2140.598633	0.067026
+2144.455566	0.066793
+2148.3125	0.06594
+2152.169434	0.065716
+2156.026367	0.067029
+2159.883301	0.069187
+2163.740234	0.072229
+2167.597168	0.073334
+2171.454102	0.07447
+2175.311035	0.076316
+2179.167969	0.077651
+2183.024902	0.077775
+2186.881836	0.076711
+2190.73877	0.07568
+2194.595703	0.074338
+2198.452637	0.073547
+2202.30957	0.072207
+2206.166504	0.070938
+2210.023438	0.071166
+2213.880371	0.072989
+2217.737305	0.075587
+2221.594238	0.077353
+2225.451172	0.079876
+2229.308105	0.082352
+2233.165039	0.086501
+2237.021973	0.091213
+2240.878906	0.093793
+2244.73584	0.096032
+2248.592773	0.096721
+2252.449707	0.096175
+2256.306641	0.096046
+2260.163574	0.095994
+2264.020508	0.095129
+2267.877441	0.094074
+2271.734375	0.093223
+2275.591309	0.092793
+2279.448242	0.09338
+2283.305176	0.094035
+2287.162109	0.096031
+2291.019043	0.098612
+2294.875977	0.101782
+2298.73291	0.104571
+2302.589844	0.106189
+2306.446777	0.108411
+2310.303711	0.111481
+2314.160645	0.115452
+2318.017578	0.1163
+2321.874512	0.116496
+2325.731445	0.117256
+2329.588379	0.117223
+2333.445312	0.118796
+2337.302246	0.118167
+2341.15918	0.120538
+2345.016113	0.115249
+2348.873047	0.105582
+2352.72998	0.106231
+2356.586914	0.117235
+2360.443848	0.125922
+2364.300781	0.125306
+2368.157715	0.127072
+2372.014648	0.127012
+2375.871582	0.116702
+2379.728516	0.10674
+2383.585449	0.101542
+2387.442383	0.098892
+2391.299316	0.096576
+2395.15625	0.094014
+2399.013184	0.091325
+2402.870117	0.088611
+2406.727051	0.085887
+2410.583984	0.084275
+2414.440918	0.083137
+2418.297852	0.082863
+2422.154785	0.083674
+2426.011719	0.083869
+2429.868652	0.084283
+2433.725586	0.085037
+2437.58252	0.086494
+2441.439453	0.087925
+2445.296387	0.08872
+2449.15332	0.088704
+2453.010254	0.088184
+2456.867432	0.088997
+2460.724121	0.088295
+2464.581299	0.086279
+2468.437988	0.084932
+2472.294922	0.083665
+2476.1521	0.0818
+2480.008789	0.080394
+2483.865967	0.080496
+2487.7229	0.080721
+2491.579834	0.082332
+2495.436768	0.084785
+2499.293701	0.087751
+2503.150635	0.090758
+2507.007568	0.092693
+2510.864502	0.095352
+2514.721436	0.098152
+2518.578369	0.100501
+2522.435303	0.101241
+2526.292236	0.100269
+2530.14917	0.097869
+2534.006104	0.095432
+2537.863037	0.093501
+2541.719971	0.092148
+2545.576904	0.093745
+2549.433838	0.095068
+2553.290771	0.095236
+2557.147705	0.095116
+2561.004639	0.095723
+2564.861572	0.098358
+2568.718506	0.100349
+2572.575439	0.102338
+2576.432373	0.104696
+2580.289307	0.107025
+2584.14624	0.108889
+2588.003174	0.110354
+2591.860107	0.110847
+2595.717041	0.110923
+2599.573975	0.110253
+2603.430908	0.10792
+2607.287842	0.108422
+2611.144775	0.110512
+2615.001709	0.112134
+2618.858643	0.111506
+2622.715576	0.111099
+2626.57251	0.11527
+2630.429443	0.118538
+2634.286377	0.121323
+2638.143311	0.122503
+2642.000244	0.121947
+2645.857178	0.122436
+2649.714111	0.122898
+2653.571045	0.123706
+2657.427979	0.12365
+2661.284912	0.123909
+2665.141846	0.12298
+2668.998779	0.121291
+2672.855713	0.118508
+2676.712646	0.113969
+2680.56958	0.112845
+2684.426514	0.11388
+2688.283447	0.115424
+2692.140381	0.115946
+2695.997314	0.116087
+2699.854248	0.11892
+2703.711182	0.123892
+2707.568115	0.127081
+2711.425049	0.127712
+2715.281982	0.129201
+2719.138916	0.130355
+2722.99585	0.132832
+2726.852783	0.136051
+2730.709717	0.137992
+2734.56665	0.139079
+2738.423584	0.139874
+2742.280518	0.142823
+2746.137451	0.14439
+2749.994385	0.144809
+2753.851318	0.146405
+2757.708252	0.149177
+2761.565186	0.152907
+2765.422119	0.156536
+2769.279053	0.160128
+2773.135986	0.163716
+2776.99292	0.170169
+2780.849854	0.176736
+2784.706787	0.182123
+2788.563721	0.18825
+2792.420654	0.195435
+2796.277588	0.203335
+2800.134521	0.209338
+2803.991455	0.216905
+2807.848389	0.224688
+2811.705322	0.231271
+2815.562256	0.240789
+2819.419189	0.252931
+2823.276123	0.268691
+2827.133057	0.288805
+2830.98999	0.319675
+2834.846924	0.37317
+2838.703857	0.490491
+2842.560791	0.752726
+2846.417725	1.278588
+2850.274658	3.547169
+2854.131592	1.864663
+2857.988525	1.020072
+2861.845459	0.678025
+2865.702393	0.520933
+2869.559326	0.455058
+2873.41626	0.442317
+2877.273193	0.468809
+2881.130127	0.52601
+2884.987061	0.601824
+2888.843994	0.6806
+2892.700928	0.756426
+2896.557861	0.831596
+2900.414795	0.907269
+2904.271729	1.0234
+2908.128662	1.20281
+2911.985596	1.481329
+2915.842529	2.010163
+2919.699463	8.159303
+2923.556396	8.159303
+2927.41333	8.159303
+2931.270264	8.159303
+2935.127197	1.344721
+2938.984131	0.846779
+2942.841064	0.599405
+2946.697998	0.462005
+2950.554932	0.384985
+2954.411865	0.339581
+2958.268799	0.311217
+2962.125732	0.293415
+2965.982666	0.280584
+2969.8396	0.266669
+2973.696533	0.25436
+2977.553467	0.24508
+2981.4104	0.238963
+2985.267334	0.23609
+2989.124268	0.234872
+2992.981201	0.233873
+2996.838135	0.232613
+3000.695068	0.233535
+3004.552002	0.233868
+3008.408936	0.232737
+3012.265869	0.233329
+3016.122803	0.234665
+3019.979736	0.235345
+3023.83667	0.236011
+3027.693604	0.236947
+3031.550537	0.238511
+3035.407471	0.241039
+3039.264404	0.240936
+3043.121338	0.239143
+3046.978271	0.238718
+3050.835205	0.24097
+3054.692139	0.245612
+3058.549072	0.247351
+3062.406006	0.247046
+3066.262939	0.248492
+3070.119873	0.251256
+3073.976807	0.25365
+3077.83374	0.253988
+3081.690674	0.252814
+3085.547607	0.253247
+3089.404541	0.256518
+3093.261475	0.257485
+3097.118408	0.256107
+3100.975342	0.258556
+3104.832275	0.261868
+3108.689209	0.262195
+3112.546143	0.26374
+3116.403076	0.264531
+3120.26001	0.266315
+3124.116943	0.271453
+3127.973877	0.272884
+3131.830811	0.273801
+3135.687744	0.274658
+3139.544678	0.27568
+3143.401611	0.278555
+3147.258545	0.278531
+3151.115479	0.280644
+3154.972412	0.282855
+3158.829346	0.282387
+3162.686279	0.283106
+3166.543213	0.285258
+3170.400146	0.287859
+3174.25708	0.2904
+3178.114014	0.294073
+3181.970947	0.292664
+3185.827881	0.291102
+3189.684814	0.295654
+3193.541748	0.300153
+3197.398682	0.304076
+3201.255615	0.304851
+3205.112549	0.304563
+3208.969482	0.305357
+3212.826416	0.306796
+3216.68335	0.310194
+3220.540283	0.31221
+3224.397217	0.313876
+3228.25415	0.314126
+3232.111084	0.313369
+3235.968018	0.315882
+3239.824951	0.317707
+3243.681885	0.31754
+3247.538818	0.319288
+3251.395752	0.321948
+3255.252686	0.324138
+3259.109619	0.326708
+3262.966553	0.32804
+3266.823486	0.3278
+3270.68042	0.329835
+3274.537354	0.33465
+3278.394287	0.337762
+3282.251221	0.340154
+3286.108154	0.342881
+3289.965088	0.345075
+3293.822021	0.347906
+3297.678955	0.350114
+3301.535889	0.351199
+3305.392822	0.351983
+3309.249756	0.3562
+3313.106689	0.36275
+3316.963623	0.366295
+3320.820557	0.36812
+3324.67749	0.370943
+3328.534424	0.373606
+3332.391357	0.374156
+3336.248291	0.377316
+3340.105225	0.381299
+3343.962158	0.382803
+3347.819092	0.384863
+3351.676025	0.387344
+3355.532959	0.391755
+3359.389893	0.396881
+3363.246826	0.401809
+3367.10376	0.40365
+3370.960693	0.405394
+3374.817627	0.408003
+3378.674561	0.406788
+3382.531494	0.410868
+3386.388428	0.416363
+3390.245361	0.418181
+3394.102295	0.418514
+3397.959229	0.420373
+3401.816162	0.425953
+3405.673096	0.427757
+3409.530029	0.430295
+3413.386963	0.432285
+3417.243896	0.4355
+3421.10083	0.440059
+3424.957764	0.438144
+3428.814697	0.438745
+3432.671631	0.440176
+3436.528564	0.441479
+3440.385498	0.446113
+3444.242432	0.454693
+3448.099609	0.458408
+3451.956299	0.453192
+3455.813232	0.453524
+3459.67041	0.454045
+3463.5271	0.453562
+3467.384277	0.454329
+3471.241211	0.453832
+3475.098145	0.455571
+3478.955078	0.458273
+3482.812012	0.463572
+3486.668945	0.467153
+3490.525879	0.468294
+3494.382812	0.467316
+3498.239746	0.46946
+3502.09668	0.476743
+3505.953613	0.480509
+3509.810547	0.481056
+3513.66748	0.477007
+3517.524414	0.476513
+3521.381348	0.48312
+3525.238281	0.494273
+3529.095215	0.498595
+3532.952148	0.489976
+3536.809082	0.483772
+3540.666016	0.483548
+3544.522949	0.497348
+3548.379883	0.507212
+3552.236816	0.503781
+3556.09375	0.497842
+3559.950684	0.492978
+3563.807617	0.529133
+3567.664551	0.56289
+3571.521484	0.538575
+3575.378418	0.509557
+3579.235352	0.488392
+3583.092285	0.49707
+3586.949219	0.539608
+3590.806152	0.551493
+3594.663086	0.545023
+3598.52002	0.545352
+3602.376953	0.531468
+3606.233887	0.545
+3610.09082	0.574529
+3613.947754	0.583345
+3617.804688	0.601032
+3621.661621	0.576763
+3625.518555	0.59285
+3629.375488	0.666404
+3633.232422	0.629983
+3637.089355	0.574148
+3640.946289	0.534971
+3644.803223	0.56094
+3648.660156	0.676182
+3652.51709	0.677093
+3656.374023	0.626823
+3660.230957	0.571434
+3664.087891	0.525168
+3667.944824	0.557497
+3671.801758	0.650441
+3675.658691	0.720812
+3679.515625	0.656422
+3683.372559	0.584071
+3687.229492	0.639159
+3691.086426	0.689051
+3694.943359	0.635556
+3698.800293	0.611035
+3702.657227	0.600736
+3706.51416	0.59881
+3710.371094	0.659889
+3714.228027	0.659443
+3718.084961	0.602004
+3721.941895	0.604124
+3725.798828	0.590578
+3729.655762	0.583357
+3733.512695	0.655091
+3737.369629	0.667907
+3741.226562	0.649775
+3745.083496	0.722164
+3748.94043	0.828452
+3752.797363	0.834798
+3756.654297	0.7622
+3760.51123	0.704227
+3764.368164	0.680495
+3768.225098	0.692232
+3772.082031	0.675462
+3775.938965	0.640782
+3779.795898	0.651172
+3783.652832	0.648195
+3787.509766	0.620286
+3791.366699	0.587595
+3795.223633	0.584694
+3799.080566	0.646239
+3802.9375	0.710322
+3806.794434	0.709429
+3810.651367	0.642264
+3814.508301	0.626551
+3818.365234	0.709295
+3822.222168	0.752153
+3826.079102	0.703719
+3829.936035	0.641066
+3833.792969	0.653867
+3837.649902	0.732171
+3841.506836	0.760431
+3845.36377	0.661533
+3849.220703	0.611614
+3853.077637	0.757909
 \ No newline at end of file
@@ -8,15 +8,19 @@ using namespace std;
 #include <QGraphicsPixmapItem>
 #include <QLayout>
 #include "qtSpectrumDisplay.h"
+//#include "qwtSpectrumDisplay.h"
 #include "globals.h"
 #include "rtsGUIConsole.h"
 #include "PerformanceData.h"
 #include <complex>
+#include <sstream>
 //#include <direct.h>
  
+
 PerformanceData PD;
  
 qtSpectrumDisplay* gpSpectrumDisplay;
+//qwtSpectrumDisplay* SpectrumDisplay;
  
 QGraphicsScene* distortionScene = NULL;
 QGraphicsView* distortionWindow = NULL;
@@ -43,6 +47,9 @@ double dNu = 2;
 double aMin = 0;
 double aMax = 1;
  
+double nMag = 1.0;
+double kMax = 1.0;
+
 double scaleI0 = 1.0;
 double refSlope = 0.0;
  
@@ -67,7 +74,7 @@ double cA = 1.0;
 //vector<SpecPair> NMaterial;
 bool applyMaterial = true;
 vector<Material> MaterialList;
-int currentMaterial = 0;
+int currentMaterial = -1;
  
 //optical parameters
 double cNAi = 0.0;
@@ -91,93 +98,106 @@ void TempSimSpectrum()
 		temp.A = sin((double)i/200);
 		SimSpectrum.push_back(temp);
 	}
-}
+	}
  
-void UpdateDisplay(){
+	void UpdateDisplay() {
 	gpSpectrumDisplay->updateGL();
+	//SpectrumDisplay->replot();
 }
  
-void LoadMaterial(string fileNameK, string fileNameN, string materialName)
+void LoadMaterial(string fileName, string materialName)
 {
-	Material newMaterial;
-	newMaterial.name = materialName;
-
-	vector<SpecPair> KMaterial = LoadSpectrum(fileNameK.c_str());
-	vector<SpecPair> NMaterial = LoadSpectrum(fileNameN.c_str());
-
-	//make sure that the sizes are the same
-	if(KMaterial.size() != NMaterial.size()){
-		cout<<"Error, material properties don't match."<<endl;
-		exit(1);
+	//open the file
+	ifstream inFile(fileName.c_str());
+	if(!inFile)
+	{
+		cout<<"Error loading material: "<<fileName<<endl;
+		return;
 	}
  
-	complex<double> eta;
-	//int j;
-	for(unsigned int i=0; i<KMaterial.size(); i++){
-		newMaterial.nu.push_back(KMaterial[i].nu);
-		eta = complex<double>(NMaterial[i].A, KMaterial[i].A);
-		newMaterial.eta.push_back(eta);
+	Material newMaterial;
+	newMaterial.validN = false;
+	newMaterial.validK = false;
+	//read the header
+	string units;
+	getline(inFile, units, '\t');
+	char c = 0;
+	while(c != '\n')
+	{
+		inFile.get(c);
+		if(c == 'n') newMaterial.validN = true;
+		if(c == 'k') newMaterial.validK = true;
 	}
-	MaterialList.push_back(newMaterial);
-}
-
-void LoadMaterial(string fileNameK, string materialName){
  
-	//load the material absorbance
-	vector<SpecPair> KMaterial = LoadSpectrum(fileNameK.c_str());
-	vector<SpecPair> NMaterial;
-	//KMaterial = LoadSpectrum("eta_TolueneK.txt");
+	//read the entire refractive index (both real and imaginary)
+	float nu;
+	float n;
+	float k;
  
-	//compute the real IR using Kramers Kronig
-	//copy the absorbance values into a linear array
-	double* k = (double*)malloc(sizeof(double) * KMaterial.size());
-	double* n = (double*)malloc(sizeof(double) * KMaterial.size());
-	for(unsigned int i=0; i<KMaterial.size(); i++)
-		k[i] = KMaterial[i].A;
+	while(inFile>>nu)
+	{
+		n = 1.0;
+		k = 0.0;
+		if(newMaterial.validN)
+			inFile>>n;
+		if(newMaterial.validK)
+			inFile>>k;
+		//ignore the rest of the line
+		inFile.ignore();
+
+		newMaterial.nu.push_back(nu);
+		newMaterial.eta.push_back(complex<double>(n, k));
+	}
  
-	//use Kramers Kronig to determine the real part of the index of refraction
-	cudaKramersKronig(n, k, KMaterial.size(), KMaterial[0].nu, KMaterial.back().nu, baseIR);
-	SpecPair temp;
-	for(unsigned int i=0; i<KMaterial.size(); i++)
+	//iterate through the material to compute the necessary bounds for display
+	float minN = 9999;
+	float maxN = -9999;
+	float sumN = 0;
+	float maxK = 0;
+	for(int i = 0; i<newMaterial.nu.size(); i++)
 	{
-		temp.nu =  KMaterial[i].nu;
-		temp.A = n[i];
-		NMaterial.push_back(temp);
+		n = newMaterial.eta[i].real();
+		k = newMaterial.eta[i].imag();
+
+		if(n < minN) minN = n;
+		if(n > maxN) maxN = n;
+		if(k > maxK) maxK = k;
+		sumN += n;
 	}
+	float meanN = sumN / newMaterial.nu.size();
  
-	//create the material
-	Material newMaterial;
+	nMag = max(maxN - meanN, meanN - minN);
+	kMax = maxK;
+	baseIR = meanN;
+
+	//set the name of the material object
 	newMaterial.name = materialName;
-	complex<double> eta;
-	for(unsigned int i=0; i<KMaterial.size(); i++){
-		newMaterial.nu.push_back(KMaterial[i].nu);
-		eta = complex<double>(NMaterial[i].A, KMaterial[i].A);
-		newMaterial.eta.push_back(eta);
-	}
  
+	//add it to the material list
 	MaterialList.push_back(newMaterial);
+	currentMaterial = MaterialList.size() - 1;
 }
  
 void LoadSource(string fileNameSource)
 {
-	SourceSpectrum = LoadSpectrum(fileNameSource);  
+	SourceSpectrum = LoadSpectrum(fileNameSource);
 }
  
 void ResampleSource()
 {
 	//clear the current resampled spectrum
 	SourceResampled.clear();
-	
+
 	//get the number of source and material samples
 	int nMatSamples = EtaK.size();
 	int nSourceSamples = SourceSpectrum.size();
-	
+
 	float nu, I;
 	for(int i=0; i<nMatSamples; i++)
 	{
 		SpecPair newSample;
 		newSample.nu = EtaK[i].nu;
-		
+
 		//iterate through the SourceSpectrum to find the bounding wavelengths
 		if(newSample.nu < SourceSpectrum[0].nu)
 			newSample.A = 0.0;
@@ -188,20 +208,20 @@ void ResampleSource()
 			int k=1;
 			while(SourceSpectrum[k].nu < newSample.nu)
 				k++;
-			
+
 			//interpolate
 			float a = (newSample.nu - SourceSpectrum[k-1].nu)/(SourceSpectrum[k].nu - SourceSpectrum[k-1].nu);
 			newSample.A = a * SourceSpectrum[k].A + (1.0 - a) * SourceSpectrum[k-1].A;
 		}
-		
+
 		//insert the new spectral point into the resampled spectrum
 		SourceResampled.push_back(newSample);
 		//cout<<newSample.nu<<"   "<<newSample.A<<endl;
 	}
-  
+
 }
  
-void FitDisplay(){
+void FitDisplay() {
 	double minA = 99999.0;
 	double maxA = -99999.0;
 	double k, n;
@@ -265,7 +285,7 @@ void FitDisplay(){
 	UpdateDisplay();
 }
  
-void ChangeAbsorbance(){
+void ChangeAbsorbance() {
  
 	//compute the real part of the index of refraction
  
@@ -289,9 +309,9 @@ void ChangeAbsorbance(){
  
 	//load the imaginary IR from the absorbance data
 	double nu;
-	for(int i=0; i<nSamples; i++){
+	for(int i=0; i<nSamples; i++) {
 		nu = MaterialList[currentMaterial].nu[i];
-		if(nu >= nuMin && nu <= nuMax){
+		if(nu >= nuMin && nu <= nuMax) {
 			temp.nu = nu;
 			temp.A = k[i];
 			EtaK.push_back(temp);
@@ -309,6 +329,7 @@ void SetMaterial()
 {
 	EtaK.clear();
 	EtaN.clear();
+	if(currentMaterial == -1) return;
  
 	int nSamples = MaterialList[currentMaterial].eta.size();
 	double nu;
@@ -317,7 +338,7 @@ void SetMaterial()
 	//initialize the current nuMin and nuMax values
 	nuMin = MaterialList[currentMaterial].nu[0];
 	nuMax = nuMin;
-	for(int i=0; i<nSamples; i++){
+	for(int i=0; i<nSamples; i++) {
 		nu = MaterialList[currentMaterial].nu[i];
 		//if(nu >= nuMin && nu <= nuMax){
  
@@ -325,14 +346,14 @@ void SetMaterial()
 		if(nu < nuMin) nuMin = nu;
 		if(nu > nuMax) nuMax = nu;
  
-			temp.nu = nu;
-			temp.A = MaterialList[currentMaterial].eta[i].imag();
-			EtaK.push_back(temp);
-			temp.A = MaterialList[currentMaterial].eta[i].real();
-			EtaN.push_back(temp);
+		temp.nu = nu;
+		temp.A = MaterialList[currentMaterial].eta[i].imag();
+		EtaK.push_back(temp);
+		temp.A = MaterialList[currentMaterial].eta[i].real();
+		EtaN.push_back(temp);
 	}
 	cA = 1.0;
-	
+
 	//resample the source spectrum
 	if(SourceSpectrum.size() != 0)
 		ResampleSource();
@@ -348,22 +369,33 @@ int main(int argc, char *argv[])
 	//load the default project file (any previous optical settings)
 	LoadState();
  
+
 	//load the default materials
-	LoadMaterial("eta_TolueneK.txt", "eta_TolueneN.txt", "Toluene");
+	LoadMaterial("etaToluene.txt", "Toluene");
 	LoadMaterial("kPMMA.txt", "PMMA");
-	LoadMaterial("eta_polystyreneK.txt", "Polystyrene");
+	LoadMaterial("kPolyethylene.txt", "Polyethylene");
+	LoadMaterial("kPTFE.txt", "Teflon");
+
+
+	//LoadMaterial("eta_TolueneK.txt", "eta_TolueneN.txt", "Toluene");
+	//LoadMaterial("kPMMA.txt", "PMMA");
+	//LoadMaterial("eta_polystyreneK.txt", "Polystyrene");
 	//LoadMaterial("../../../../data/materials/rtsSU8_k.txt", "../../../../data/materials/rtsSU8_n.txt", "SU8");
 	SetMaterial();
-	
+
+
 	//load a mid-infrared source
 	LoadSource("source_midIR.txt");
+
 	ResampleSource();
  
 	//compute the analytical solution for the Mie scattered spectrum
 	SimulateSpectrum();
  
 	QApplication a(argc, argv);
-	
+
+	//SpectrumDisplay = new qwtSpectrumDisplay();
+
 	InteractiveMie w;
 	w.show() ;
 	w.move(0, 0);
@@ -385,6 +417,8 @@ int main(int argc, char *argv[])
 	gpSpectrumDisplay->move(uiFrame.width(), 0);
 	gpSpectrumDisplay->show();
  
+
+
 	//distortion dialog box
 	distortionDialog = new qtDistortionDialog();
 	distortionDialog->move(0, 0);
-#include "qtDistortionDialog.h"
-
-qtDistortionDialog::qtDistortionDialog(QWidget *parent, Qt::WFlags flags)
-	: QDialog(parent, flags)
-{
-	ui.setupUi(this);
-}
-
-qtDistortionDialog::~qtDistortionDialog()
-{
-	updating = false;
+#include "qtDistortionDialog.h"
+
+qtDistortionDialog::qtDistortionDialog(QWidget *parent, Qt::WFlags flags)
+    : QDialog(parent, flags)
+{
+    ui.setupUi(this);
+}
+
+qtDistortionDialog::~qtDistortionDialog()
+{
+    updating = false;
 }
@@ -17,18 +17,18 @@ extern QGraphicsPixmapItem* pixmapItem;
  
 class qtDistortionDialog : public QDialog
 {
-	Q_OBJECT
+    Q_OBJECT
  
 public:
-	qtDistortionDialog(QWidget *parent = 0, Qt::WFlags flags = 0);
-	~qtDistortionDialog();
-	bool updating;
+    qtDistortionDialog(QWidget *parent = 0, Qt::WFlags flags = 0);
+    ~qtDistortionDialog();
+    bool updating;
  
 private:
-	Ui::DistortionDialogClass ui;
+    Ui::DistortionDialogClass ui;
  
 public slots:
-    void on_btnComputeDistortionMap_clicked(){
+    void on_btnComputeDistortionMap_clicked() {
  
         int steps = 100;
  
@@ -49,7 +49,7 @@ public slots:
         //compute the extrema
         float minDistortion = 99999;
         float maxDistortion = distortionMap[0];
-        for(int i=1; i<steps*steps; i++){
+        for(int i=1; i<steps*steps; i++) {
             if(distortionMap[i] < minDistortion && distortionMap[i] > 0)
                 minDistortion = distortionMap[i];
             if(distortionMap[i] > maxDistortion)
@@ -62,11 +62,14 @@ public slots:
         float intensity;
         float v;
         for(i=0; i<steps; i++)
-            for(o=0; o<steps; o++){
+            for(o=0; o<steps; o++) {
                 v = distortionMap[o * steps + i];
                 intensity = (v - minDistortion) / (maxDistortion - minDistortion) * 255;
  
-                if(intensity < 0) {cout<<"low intensity"<<endl; intensity = 0;}
+                if(intensity < 0) {
+                    cout<<"low intensity"<<endl;
+                    intensity = 0;
+                }
  
                 //QColor color(intensity, (float)o / (float)steps * 255, (float)i / (float)steps * 255);
                 QColor color(intensity, intensity, intensity);
-#include <QtGui>
-#include <QtOpenGL/QtOpenGL>
-#include <GL/glu.h>
-
-#include <math.h>
-
-#include "qtSpectrumDisplay.h"
-
-qtSpectrumDisplay::qtSpectrumDisplay(QWidget *parent)
- : QGLWidget(parent)
-{
- object = 0;
- xRot = 0;
- yRot = 0;
- zRot = 0;
-
- qtGreen = QColor::fromCmykF(0.40, 0.0, 1.0, 0.0);
- qtPurple = QColor::fromCmykF(0.39, 0.39, 0.0, 0.0);
-}
-
-qtSpectrumDisplay::~qtSpectrumDisplay()
-{
- makeCurrent();
- glDeleteLists(object, 1);
-}
-
-QSize qtSpectrumDisplay::minimumSizeHint() const
-{
- return QSize(50, 50);
-}
-
-QSize qtSpectrumDisplay::sizeHint() const
-{
- return QSize(400, 400);
-}
-
-void qtSpectrumDisplay::initializeGL()
-{
- qglClearColor(qtPurple.dark());
- //object = makeObject();
- glShadeModel(GL_FLAT);
- glEnable(GL_DEPTH_TEST);
- glEnable(GL_CULL_FACE);
-}
-
-void qtSpectrumDisplay::printWavenumber(int xPos)
-{
- int viewParams[4];
- glGetIntegerv(GL_VIEWPORT, viewParams);
-
- float a = (float)xPos/(float)viewParams[2];
-
- int wn = a * (nuMax - nuMin) + nuMin;
- cout<<wn<<endl;
-
-
-
-}
-
-void qtSpectrumDisplay::paintGL()
+#include <QtGui>
+#include <QtOpenGL/QtOpenGL>
+#include <GL/glu.h>
+
+#include <math.h>
+
+#include "qtSpectrumDisplay.h"
+
+int axisMargins = 50;
+
+qtSpectrumDisplay::qtSpectrumDisplay(QWidget *parent)
+    : QGLWidget(parent)
+{
+    object = 0;
+    xRot = 0;
+    yRot = 0;
+    zRot = 0;
+
+    qtGreen = QColor::fromCmykF(0.40, 0.0, 1.0, 0.0);
+    qtPurple = QColor::fromCmykF(0.39, 0.39, 0.0, 0.0);
+}
+
+qtSpectrumDisplay::~qtSpectrumDisplay()
+{
+    makeCurrent();
+    glDeleteLists(object, 1);
+}
+
+QSize qtSpectrumDisplay::minimumSizeHint() const
 {
-    //prepare the projection (orthographic, bounded by spectral values)
-    glMatrixMode(GL_PROJECTION);
-    glLoadIdentity();
-    gluOrtho2D(nuMin, nuMax, aMin, aMax);
-    glMatrixMode(GL_MODELVIEW);
+    return QSize(50, 50);
+}
+
+QSize qtSpectrumDisplay::sizeHint() const
+{
+    return QSize(400, 400);
+}
+
+void qtSpectrumDisplay::initializeGL()
+{
+    //qglClearColor(qtPurple.dark());
+    glClearColor(0.0, 0.0, 0.0, 0.0);
+    //object = makeObject();
+    glShadeModel(GL_FLAT);
+    glEnable(GL_DEPTH_TEST);
+    glEnable(GL_CULL_FACE);
+}
+
+void qtSpectrumDisplay::printWavenumber(int xPos)
+{
+    int viewParams[4];
+    glGetIntegerv(GL_VIEWPORT, viewParams);
+
+    float a = (float)xPos/(float)viewParams[2];
+
+    int wn = a * (nuMax - nuMin) + nuMin;
+    cout<<wn<<endl;
+
+
+
+}
+
+void qtSpectrumDisplay::paintGL()
+{
+
+    //*************  Draw Absorbance/Intensity  **************************
+    //get the window size
+    int w = width();
+    int h = height();
+    glViewport(50, 30, w, h);
+
+    //prepare the projection for spectra (orthographic, bounded by spectral values)
+    glMatrixMode(GL_PROJECTION);
+    glLoadIdentity();
+    gluOrtho2D(nuMin, nuMax, aMin, aMax);
+    glMatrixMode(GL_MODELVIEW);
     glLoadIdentity();
  
     //clear the screen
-    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
-
-    //set the line width
-    glLineWidth(2);
-
-    //draw the simulated spectrum (in white)
-    if(dispSimSpec)
-    {
-     glColor3f(1.0, 1.0, 1.0);
-     glBegin(GL_LINE_STRIP);
-     for(unsigned int i=0; i<SimSpectrum.size(); i++)
-         glVertex2f(SimSpectrum[i].nu, SimSpectrum[i].A);
-     glEnd();
+    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
+
+    //set the line width
+    glLineWidth(1);
+
+    //draw the simulated spectrum (in white)
+    if(dispSimSpec)
+    {
+        glColor3f(1.0, 1.0, 1.0);
+        glBegin(GL_LINE_STRIP);
+        for(unsigned int i=0; i<SimSpectrum.size(); i++)
+            glVertex2f(SimSpectrum[i].nu, SimSpectrum[i].A);
+        glEnd();
+    }
+    //draw the reference spectrum in gray
+    if(dispRefSpec && RefSpectrum.size() > 0)
+    {
+        glColor3f(0.5, 0.5, 0.5);
+        glBegin(GL_LINE_STRIP);
+        float nu;
+        for(unsigned int i=0; i<RefSpectrum[currentSpec].size(); i++)
+        {
+            nu = RefSpectrum[currentSpec][i].nu;
+            glVertex2f(nu, RefSpectrum[currentSpec][i].A + nu * refSlope);
+        }
+        glEnd();
     }
-    //draw the reference spectrum in gray
-    if(dispRefSpec && RefSpectrum.size() > 0)
-    {
-     glColor3f(0.5, 0.5, 0.5);
-     glBegin(GL_LINE_STRIP);
-     float nu;
-     for(unsigned int i=0; i<RefSpectrum[currentSpec].size(); i++)
-     {
-         nu = RefSpectrum[currentSpec][i].nu;
-         glVertex2f(nu, RefSpectrum[currentSpec][i].A + nu * refSlope);
-     }
-     glEnd();
-    }
-
-    //draw the material properties
-
-    //change the viewport properties (materials are plotted on a different scale)
  
     //compute the maximum k and n
     int nSamples = MaterialList[currentMaterial].eta.size();
     float maxK = 0.0;
     float maxN = 0.0;
     float thisN, thisK;
-    for(int i=0; i<nSamples; i++)
+
+
+
+    //*************  Draw k  **************************
+    //change the viewport properties and draw n
+    glMatrixMode(GL_PROJECTION);
+    glLoadIdentity();
+    gluOrtho2D(nuMin, nuMax, 0.0, kMax);
+    //glMatrixMode(GL_MODELVIEW);
+    //glLoadIdentity();
+
+    float nu;
+    if(dispMatK)
+    {
+
+        glColor3f(1.0, 0.0, 0.0);
+        glBegin(GL_LINE_STRIP);
+        for(int i=0; i<nSamples; i++)
+        {
+            nu = MaterialList[currentMaterial].nu[i];
+            glVertex2f(nu, MaterialList[currentMaterial].eta[i].imag());
+        }
+        glEnd();
+    }
+    if(dispSimK)
     {
-        thisN = fabs(MaterialList[currentMaterial].eta[i].real() - 1.49);
-        if(thisN > maxN)
-            maxN = thisN;
-        thisK = fabs(MaterialList[currentMaterial].eta[i].imag());
-        if(thisK > maxK)
-            thisK = maxK;
+        glColor3f(1.0, 1.0, 0.0);
+        glBegin(GL_LINE_STRIP);
+        for(unsigned int i=0; i<EtaK.size(); i++)
+        {
+            nu = EtaK[i].nu;
+            glVertex2f(nu, EtaK[i].A);
+        }
+        glEnd();
     }
-    cout<<maxN<<"---------"<<maxK<<endl;
  
+    //*************  Draw n  **************************
+    //change the viewport properties and draw n
+    glMatrixMode(GL_PROJECTION);
+    glLoadIdentity();
+    if(nMag < 0.1) nMag = 0.1;
+    gluOrtho2D(nuMin, nuMax, baseIR - nMag, baseIR + nMag);
+    if(dispMatN)
+    {
+        glColor3f(0.0, 1.0, 0.0);
+        glBegin(GL_LINE_STRIP);
+        for(int i=0; i<nSamples; i++)
+        {
+            nu = MaterialList[currentMaterial].nu[i];
+            glVertex2f(nu, MaterialList[currentMaterial].eta[i].real());
+        }
+        glEnd();
+    }
+    if(dispSimN)
+    {
+        glColor3f(0.0, 1.0, 1.0);
+        glBegin(GL_LINE_STRIP);
+        for(unsigned int i=0; i<EtaN.size(); i++)
+        {
+            nu = EtaN[i].nu;
+            glVertex2f(nu, EtaN[i].A);
+        }
+        glEnd();
+    }
  
-    glMatrixMode(GL_PROJECTION);
-    glLoadIdentity();
-    gluOrtho2D(nuMin, nuMax, aMin, aMax);
-
-
-    float nu;
-    //display absorbance
-    if(dispMatK)
-    {
-
-     glColor3f(1.0, 0.0, 0.0);
-     glBegin(GL_LINE_STRIP);
-     for(int i=0; i<nSamples; i++){
-         nu = MaterialList[currentMaterial].nu[i];
-         glVertex2f(nu, MaterialList[currentMaterial].eta[i].imag() * dispScaleK);
-     }
-     glEnd();
-    }
-    if(dispSimK)
-    {
-     glColor3f(1.0, 1.0, 0.0);
-     glBegin(GL_LINE_STRIP);
-     for(unsigned int i=0; i<EtaK.size(); i++){
-         glVertex2f(EtaK[i].nu, EtaK[i].A * dispScaleK);
-     }
-     glEnd();
-}
-
-//display refractive index (real)
-if(dispMatN)
-{
- glColor3f(0.0, 1.0, 0.0);
- glBegin(GL_LINE_STRIP);
- for(int i=0; i<nSamples; i++){
-     nu = MaterialList[currentMaterial].nu[i];
-     glVertex2f(nu, (MaterialList[currentMaterial].eta[i].real() - baseIR) * dispScaleN);
- }
- glEnd();
-}
-if(dispSimN)
-{
- glColor3f(0.0, 1.0, 1.0);
- glBegin(GL_LINE_STRIP);
- for(unsigned int i=0; i<EtaN.size(); i++)
-     glVertex2f(EtaN[i].nu, (EtaN[i].A - baseIR) * dispScaleN);
- glEnd();
-}
-
-
-glCallList(object);
-
-glFlush();
-
-//display the values at the mouse location
-renderText(50, 50, "test");
-}
-
-void qtSpectrumDisplay::resizeGL(int width, int height)
-{
- int side = qMin(width, height);
- glViewport(0, 0, width, height);
-
-}
-
-void qtSpectrumDisplay::mousePressEvent(QMouseEvent *event)
-{
- lastPos = event->pos();
-
- if(event->buttons() & Qt::LeftButton)
- {
-     int wn = 0;
-     printWavenumber(event->x());
- }
-}
-
-void qtSpectrumDisplay::mouseMoveEvent(QMouseEvent *event)
-{
- int dx = event->x() - lastPos.x();
- int dy = event->y() - lastPos.y();
-
- lastPos = event->pos();
-}
-
-void qtSpectrumDisplay::quad(GLdouble x1, GLdouble y1, GLdouble x2, GLdouble y2,
-                 GLdouble x3, GLdouble y3, GLdouble x4, GLdouble y4)
-{
- qglColor(qtGreen);
-
- glVertex3d(x1, y1, -0.05);
- glVertex3d(x2, y2, -0.05);
- glVertex3d(x3, y3, -0.05);
- glVertex3d(x4, y4, -0.05);
-
- glVertex3d(x4, y4, +0.05);
- glVertex3d(x3, y3, +0.05);
- glVertex3d(x2, y2, +0.05);
- glVertex3d(x1, y1, +0.05);
-}
-
-void qtSpectrumDisplay::normalizeAngle(int *angle)
-{
- while (*angle < 0)
-     *angle += 360 * 16;
- while (*angle > 360 * 16)
-     *angle -= 360 * 16;
+
+    glCallList(object);
+
+    glFlush();
+
+    //***********************  Display axes values  ****************************
+
+
+    ostringstream buff;
+    glViewport(0, 0, w, h);
+    int nDivs = 11;
+    glColor3f(1.0, 1.0, 1.0);
+    for(int i = 0; i < nDivs; i++)
+    {
+        float divStep = (aMax - aMin)/(nDivs - 1);
+        float pixStep = (float)(h - 10)/(nDivs - 1);
+
+        buff<<aMin + i * divStep;
+        renderText(0, h - i * pixStep, buff.str().c_str());
+        buff.clear(); buff.str("");
+    }
+}
+
+void qtSpectrumDisplay::resizeGL(int width, int height)
+{
+    int side = qMin(width, height);
+
+
+}
+
+void qtSpectrumDisplay::mousePressEvent(QMouseEvent *event)
+{
+    lastPos = event->pos();
+
+    if(event->buttons() & Qt::LeftButton)
+    {
+        int wn = 0;
+        printWavenumber(event->x());
+    }
+}
+
+void qtSpectrumDisplay::mouseMoveEvent(QMouseEvent *event)
+{
+    int dx = event->x() - lastPos.x();
+    int dy = event->y() - lastPos.y();
+
+    lastPos = event->pos();
+}
+
+void qtSpectrumDisplay::quad(GLdouble x1, GLdouble y1, GLdouble x2, GLdouble y2,
+                             GLdouble x3, GLdouble y3, GLdouble x4, GLdouble y4)
+{
+    qglColor(qtGreen);
+
+    glVertex3d(x1, y1, -0.05);
+    glVertex3d(x2, y2, -0.05);
+    glVertex3d(x3, y3, -0.05);
+    glVertex3d(x4, y4, -0.05);
+
+    glVertex3d(x4, y4, +0.05);
+    glVertex3d(x3, y3, +0.05);
+    glVertex3d(x2, y2, +0.05);
+    glVertex3d(x1, y1, +0.05);
+}
+
+void qtSpectrumDisplay::normalizeAngle(int *angle)
+{
+    while (*angle < 0)
+        *angle += 360 * 16;
+    while (*angle > 360 * 16)
+        *angle -= 360 * 16;
 }
- #ifndef GLWIDGET_H
- #define GLWIDGET_H
-
-#include <QtOpenGL/QGLWidget>
-#include "globals.h"
-
- class qtSpectrumDisplay : public QGLWidget
- {
-     Q_OBJECT
-
- public:
-     qtSpectrumDisplay(QWidget *parent = 0);
-     ~qtSpectrumDisplay();
-
-     QSize minimumSizeHint() const;
-     QSize sizeHint() const;
-
- public slots:
-     /*void setXRotation(int angle);
-     void setYRotation(int angle);
-     void setZRotation(int angle);*/
-
- signals:
-     void xRotationChanged(int angle);
-     void yRotationChanged(int angle);
-     void zRotationChanged(int angle);
-
- protected:
-     void initializeGL();
-     void paintGL();
-     void resizeGL(int width, int height);
-     void mousePressEvent(QMouseEvent *event);
-     void mouseMoveEvent(QMouseEvent *event);
-
- private:
-     //GLuint makeObject();
-     void quad(GLdouble x1, GLdouble y1, GLdouble x2, GLdouble y2,
-               GLdouble x3, GLdouble y3, GLdouble x4, GLdouble y4);
-     //void extrude(GLdouble x1, GLdouble y1, GLdouble x2, GLdouble y2);
-     void normalizeAngle(int *angle);
-	 void printWavenumber(int wn);
-
-     GLuint object;
-     int xRot;
-     int yRot;
-     int zRot;
-     QPoint lastPos;
-     QColor qtGreen;
-     QColor qtPurple;
- };
-
- #endif
 \ No newline at end of file
+#ifndef GLWIDGET_H
+#define GLWIDGET_H
+
+#include <QtOpenGL/QGLWidget>
+#include "globals.h"
+
+class qtSpectrumDisplay : public QGLWidget
+{
+    Q_OBJECT
+
+public:
+    qtSpectrumDisplay(QWidget *parent = 0);
+    ~qtSpectrumDisplay();
+
+    QSize minimumSizeHint() const;
+    QSize sizeHint() const;
+
+public slots:
+    /*void setXRotation(int angle);
+    void setYRotation(int angle);
+    void setZRotation(int angle);*/
+
+signals:
+    void xRotationChanged(int angle);
+    void yRotationChanged(int angle);
+    void zRotationChanged(int angle);
+
+protected:
+    void initializeGL();
+    void paintGL();
+    void resizeGL(int width, int height);
+    void mousePressEvent(QMouseEvent *event);
+    void mouseMoveEvent(QMouseEvent *event);
+
+private:
+    //GLuint makeObject();
+    void quad(GLdouble x1, GLdouble y1, GLdouble x2, GLdouble y2,
+              GLdouble x3, GLdouble y3, GLdouble x4, GLdouble y4);
+    //void extrude(GLdouble x1, GLdouble y1, GLdouble x2, GLdouble y2);
+    void normalizeAngle(int *angle);
+    void printWavenumber(int wn);
+
+    GLuint object;
+    int xRot;
+    int yRot;
+    int zRot;
+    QPoint lastPos;
+    QColor qtGreen;
+    QColor qtPurple;
+};
+
+#endif