near-field hybrid evaluation + convergence check . (#39)

(Mie coeffs are in DP or MP, summation over multipoles - in DP)

* GetFieldEabs Python binding works

* works fine for bulk sphere

* convergence tests for Mie series and near-field. Initial testing of near-field.

* fix bug with reentrance, more near-field test, test data for psi_mul_zeta

* add test data for complex psi

examples/CMakeLists.txt

@@ -1 +1 @@
-add_executable(example-minimal example-minimal.cc)
+#add_executable(example-minimal example-minimal.cc)

examples/Opt.Commun.-2010-Geints-Nanojets_of_dielectric_microspheres/fig1.py

@@ -45,8 +45,8 @@ index_H2O = 1.33+(1e-6)*1j
 
 WL = 0.532 #mkm
 total_r = 125 #mkm
-isMP = False
-# isMP = True
+# isMP = False
+isMP = True
 
 
 nm = 1.0  # host medium

examples/Opt.Commun.-2010-Geints-Nanojets_of_dielectric_microspheres/fig1_polar.py

@@ -31,8 +31,16 @@ import numpy as np
 import matplotlib.pyplot as plt
 from scattnlay import mie, mie_mp
 
-npts = 11/2
-# npts = 11
+# npts = 151/2
+npts = 51/2
+factor = 3  # plot extent compared to sphere radius
+# total_r = 0.055/2/np.pi  # mkm
+total_r = 1
+isMP = False
+# isMP = True
+
+# terms_in = 210
+terms_in = -1
 
 
 from_theta = 0
@@ -41,23 +49,27 @@ outer_arc_points = int(abs(to_theta-from_theta)*npts)
 # outer_arc_points = 600
 
 
-factor = 2 # plot extent compared to sphere radius
 index_H2O = 1.33+(1e-6)*1j
+# index_H2O = 1.001
 
-WL = 0.532 #mkm
-total_r = 125 #mkm
-isMP = False
-# isMP = True
+# WL = 0.532 #mkm
+WL = 1 #mkm
+
+mp = ''
+if isMP: mp = '_mp'
 
 
 nm = 1.0  # host medium
 # x = 2.0 * np.pi * np.array([total_r/2, total_r], dtype=np.float64) / WL
 # m = np.array((index_H2O, index_H2O), dtype=np.complex128) / nm
-
+#
 x = 2.0 * np.pi * np.array([total_r], dtype=np.float64) / WL
 m = np.array((index_H2O), dtype=np.complex128) / nm
 
-from_r = 0.01*x[-1]
+# x = 2.0 * np.pi * np.array([total_r], dtype=np.float64) / 1
+# m = np.array((1.5+1j), dtype=np.complex128) / nm
+
+from_r = x[-1]*0.001
 to_r = x[-1]*factor
 r_points = int(outer_arc_points/abs(to_theta-from_theta))
 
@@ -79,7 +91,7 @@ Qsca =  mie_mp.GetQsca()
 terms = mie_mp.GetMaxTerms()
 
 print("mp Qsca = " + str(Qsca)+" terms = "+str(terms))
-
+# exit(1)
 
 # mie.SetFieldCoords(xp, yp, zp)
 # mie.RunFieldCalculation()
@@ -96,16 +108,20 @@ for i in range(len(r_all)):
     for j in range(len(theta_all)):
         theta.append(theta_all[j])
         r.append(r_all[i])
-
-mie_mp.RunFieldCalculationPolar(outer_arc_points, r_points, from_r, to_r, from_theta, to_theta, 0, 0, True)
-Ec = mie_mp.GetFieldE()
-# mie.RunFieldCalculationPolar(outer_arc_points, r_points, from_r, to_r, from_theta, to_theta, 0, 0, True)
-# Ec = mie.GetFieldE()
-print("Field evaluation done.")
-Er = np.absolute(Ec)
-Eabs = (Er[:, 0]**2 + Er[:, 1]**2 + Er[:, 2]**2)
-# Eabs = np.resize(Eabs2, (outer_arc_points, r_points))
-print("min(Eabs)=", np.min(Eabs)," max(Eabs)=", np.max(Eabs)," terms = "+str(terms), ' size=', Eabs.size)
+if isMP:
+    mie_mp.RunFieldCalculationPolar(4, 3, x[-1], x[-1]*3, 0, np.pi, 0, 0, False, terms_in)
+    mie_mp.RunFieldCalculationPolar(outer_arc_points, r_points, from_r, to_r, from_theta, to_theta, 0, 0, False, terms_in)
+    Eabs = (mie_mp.GetFieldEabs())**2
+    terms = mie_mp.GetMaxTerms()
+else:
+    # mie.RunFieldCalculationPolar(4, 3, x[-1], x[-1]*3, 0, np.pi, 0, 0, True, -1)
+    # Eabs = (mie.GetFieldEabs())**2
+    # print(Eabs)
+    # exit(1)
+    mie.RunFieldCalculationPolar(outer_arc_points, r_points, from_r, to_r, from_theta, to_theta, 0, 0, False, terms_in)
+    Eabs = (mie.GetFieldEabs())**2
+    terms = mie.GetMaxTerms()
+print(mp, "min(Eabs)=", np.min(Eabs)," max(Eabs)=", np.max(Eabs)," terms = "+str(terms), ' size=', Eabs.size)
 
 
 fig, ax = plt.subplots(subplot_kw=dict(projection='polar'))
@@ -121,8 +137,6 @@ ax.yaxis.grid(False)
 ax.xaxis.grid(False)
 
 # ax.plot(theta,r, 'ro', ms=0.1)
-mp = ''
-if isMP: mp = '_mp'
 plt.savefig("R"+str(total_r)+"mkm"+mp+"_polar.jpg",
             dpi=600
             )

src/nmie-basic.hpp

@@ -581,6 +581,8 @@ namespace nmie {
   void MultiLayerMie<FloatType>::calcScattCoeffs() {
 
     isScaCoeffsCalc_ = false;
+    an_.clear();
+    bn_.clear();
 
     const std::vector<FloatType> &x = size_param_;
     const std::vector<std::complex<FloatType> > &m = refractive_index_;
@@ -717,6 +719,7 @@ namespace nmie {
     // first layer is 0 (zero), in future versions all arrays will follow  //
     // this convention to save memory. (13 Nov, 2014)                      //
     //*********************************************************************//
+    FloatType a0=0, b0=0;
     for (int n = 0; n < nmax_; n++) {
       //********************************************************************//
       //Expressions for calculating an and bn coefficients are not valid if //
@@ -729,10 +732,22 @@ namespace nmie {
         an_[n] = calc_an(n + 1, x[L - 1], std::complex<FloatType>(0.0, 0.0), std::complex<FloatType>(1.0, 0.0), PsiXL[n + 1], ZetaXL[n + 1], PsiXL[n], ZetaXL[n]);
         bn_[n] = PsiXL[n + 1]/ZetaXL[n + 1];
       }
+      if (n == 0) {a0 = cabs(an_[0]); b0 = cabs(bn_[0]);}
+      if (n == nmax_ - 1 && nmax_preset_ <= 0) {
+        std::cout << "Failed to converge in Mie series for nmax="<<nmax_ << std::endl;
+        std::cout << "convergence threshold: "<< convergence_threshold_ << std::endl;
+        std::cout << "Mie series a[nmax]/a[1]:" << cabs(an_[n]) / a0 << " and b[nmax]/b[1]:" << cabs(bn_[n]) / b0 << std::endl;
+
+      }
+      if (cabs(an_[n]) / a0 < convergence_threshold_ &&
+          cabs(bn_[n]) / b0 < convergence_threshold_) {
+        if (nmax_preset_ <= 0) nmax_ = n;
+        break;
+      }
+
       if (nmm::isnan(an_[n].real()) || nmm::isnan(an_[n].imag()) ||
           nmm::isnan(bn_[n].real()) || nmm::isnan(bn_[n].imag())
           ) {
-        // TODO somehow notify Python users about it
         std::cout << "nmax value was changed due to unexpected error!!! New values is "<< n
                   << " (was "<<nmax_<<")"<<std::endl;
         nmax_ = n;

src/nmie-nearfield.hpp

@@ -82,6 +82,7 @@ namespace nmie {
       throw std::invalid_argument("(calcExpanCoeffs) You should calculate external coefficients first!");
 
     isExpCoeffsCalc_ = false;
+    aln_.clear(); bln_.clear(); cln_.clear(); dln_.clear();
 
     std::complex<FloatType> c_one(1.0, 0.0), c_zero(0.0, 0.0);
 
@@ -163,24 +164,27 @@ namespace nmie {
       }  // end PEC condition
     }  // end of all l
 
+    int print_precision = 16;
+#ifdef MULTI_PRECISION
+    print_precision = MULTI_PRECISION;
+#endif
     // Check the result and change  aln_[0][n] and aln_[0][n] for exact zero
+    int print_count = 0;
     for (int n = 0; n < nmax_; ++n) {
-      if (cabs(aln_[0][n]) < 1e-10) aln_[0][n] = 0.0;
-      else {
-        //throw std::invalid_argument("Unstable calculation of aln_[0][n]!");
-        std::cout<< std::setprecision(100)
+      if (cabs(aln_[0][n]) > 1e-10 && print_count < 2)  {
+        print_count++;
+        std::cout<< std::setprecision(print_precision)
                  << "Warning: Potentially unstable calculation of aln[0]["
                  << n << "] = "<< aln_[0][n] <<std::endl;
-        aln_[0][n] = 0.0;
       }
-      if (cabs(bln_[0][n]) < 1e-10) bln_[0][n] = 0.0;
-      else {
-        //throw std::invalid_argument("Unstable calculation of bln_[0][n]!");
-        std::cout<< std::setprecision(100)
+      if (cabs(bln_[0][n]) > 1e-10  && print_count < 2)  {
+        print_count++;
+        std::cout<< std::setprecision(print_precision)
                  << "Warning: Potentially unstable calculation of bln[0]["
                  << n << "] = "<< bln_[0][n] <<std::endl;
-        bln_[0][n] = 0.0;
       }
+      aln_[0][n] = 0.0;
+      bln_[0][n] = 0.0;
     }
 
     isExpCoeffsCalc_ = true;
@@ -214,7 +218,7 @@ namespace nmie {
   // This function calculates the electric (E) and magnetic (H) fields inside and     //
   // around the particle.                                                             //
   //
-  // Main troubles of near-field evaluations originate from special functions
+  // Main trouble of near-field evaluations is supposed to originate from special functions
   // evaluation, so we expect that nmax needed for the convergence is the size
   // of Psi vector.
   //                                                                                  //
@@ -237,17 +241,21 @@ namespace nmie {
   //**********************************************************************************//
   template <typename FloatType>  template <typename evalType>
   void MultiLayerMie<FloatType>::calcFieldByComponents(const evalType Rho,
-                                const evalType Theta, const evalType Phi,
-                                const std::vector<std::complex<evalType> > &Psi,
-                                const std::vector<std::complex<evalType> > &D1n,
-                                const std::vector<std::complex<evalType> > &Zeta,
-                                const std::vector<std::complex<evalType> > &D3n,
-                                const std::vector<evalType> &Pi,
-                                const std::vector<evalType> &Tau,
-                                std::vector<std::complex<evalType> > &E,
-                                std::vector<std::complex<evalType> > &H)  {
+                                  const evalType Theta, const evalType Phi,
+                                  const std::vector<std::complex<evalType> > &Psi,
+                                  const std::vector<std::complex<evalType> > &D1n,
+                                  const std::vector<std::complex<evalType> > &Zeta,
+                                  const std::vector<std::complex<evalType> > &D3n,
+                                  const std::vector<evalType> &Pi,
+                                  const std::vector<evalType> &Tau,
+                                  std::vector<std::complex<evalType> > &E,
+                                  std::vector<std::complex<evalType> > &H,
+                                  std::vector<bool> &isConvergedE,
+                                  std::vector<bool> &isConvergedH,
+                                  bool isMarkUnconverged)  {
     auto nmax = Psi.size() - 1;
     std::complex<evalType> c_zero(0.0, 0.0), c_i(0.0, 1.0), c_one(1.0, 0.0);
+//    auto c_nan = ConvertComplex<FloatType>(std::complex<double>(std::nan(""), std::nan("")));
     // Vector containing precomputed integer powers of i to avoid computation
     std::vector<std::complex<evalType> > ipow = {c_one, c_i, -c_one, -c_i};
     std::vector<std::complex<evalType> > M3o1n(3), M3e1n(3), N3o1n(3), N3e1n(3);
@@ -264,6 +272,8 @@ namespace nmie {
     unsigned int l;
     GetIndexAtRadius(Rho, ml, l);
 
+    isConvergedE = {false, false, false}, isConvergedH = {false, false, false};
+//    evalType E0 = 0, H0=0;
     for (unsigned int n = 0; n < nmax; n++) {
       int n1 = n + 1;
       auto rn = static_cast<evalType>(n1);
@@ -277,11 +287,12 @@ namespace nmie {
       *static_cast<evalType>((rn + rn + 1.0)/(rn*rn + rn));
       std::complex<evalType> Ediff, Hdiff;
       std::complex<FloatType> Ediff_ft, Hdiff_ft;
+      auto aln = ConvertComplex<evalType>(aln_[l][n]);
+      auto bln = ConvertComplex<evalType>(bln_[l][n]);
+      auto cln = ConvertComplex<evalType>(cln_[l][n]);
+      auto dln = ConvertComplex<evalType>(dln_[l][n]);
       for (int i = 0; i < 3; i++) {
-        std::complex<evalType> aln = ConvertComplex<evalType>(aln_[l][n]);
-        std::complex<evalType> bln = ConvertComplex<evalType>(bln_[l][n]);
-        std::complex<evalType> cln = ConvertComplex<evalType>(cln_[l][n]);
-        std::complex<evalType> dln = ConvertComplex<evalType>(dln_[l][n]);
+        if (isConvergedE[i] && isConvergedH[i]) continue;
         Ediff = En*(      cln*M1o1n[i] - c_i*dln*N1e1n[i]
                          + c_i*aln*N3e1n[i] -     bln*M3o1n[i]);
         Hdiff = En*(     -dln*M1e1n[i] - c_i*cln*N1o1n[i]
@@ -289,11 +300,25 @@ namespace nmie {
         Ediff_ft = ConvertComplex<FloatType>(Ediff);
         Hdiff_ft = ConvertComplex<FloatType>(Hdiff);
         if ( nmm::isnan(Ediff_ft.real()) || nmm::isnan(Ediff_ft.imag()) ||
-             nmm::isnan(Hdiff_ft.real()) || nmm::isnan(Hdiff_ft.imag()) ) {
+            nmm::isnan(Hdiff_ft.real()) || nmm::isnan(Hdiff_ft.imag()) ) {
           std::cout << "Unexpected truncation during near-field evaluation at n = "<< n
                     << " (of total nmax = "<<nmax<<")!!!"<<std::endl;
           break;
         }
+        if (n!=0) {
+          if (cabs(Ediff) == 0) isConvergedE[i] = true;
+          if (cabs(Hdiff) == 0) isConvergedH[i] = true;
+          if (cabs(E[i]) != 0.)
+            if (cabs(Ediff)/cabs(E[i]) < nearfield_convergence_threshold_) isConvergedE[i] = true;
+          if (cabs(H[i]) != 0.)
+            if (cabs(Hdiff)/cabs(H[i]) < nearfield_convergence_threshold_) isConvergedH[i] = true;
+        }
+        if (isConvergedE[i]) Ediff = c_zero;
+        if (isConvergedH[i]) Hdiff = c_zero;
+        if ((!isConvergedH[i] || !isConvergedE[i]) && n==nmax-1 && GetFieldConvergence()) {
+          std::cout<<"Econv:"<<cabs(Ediff)/cabs(E[i])<<" Hconv:"<<cabs(Hdiff)/cabs(H[i])<<std::endl;
+
+        }
         if (mode_n_ == Modes::kAll) {
           // electric field E [V m - 1] = EF*E0
           E[i] += Ediff;
@@ -325,6 +350,15 @@ namespace nmie {
           nmm::isnan(Hdiff_ft.real()) || nmm::isnan(Hdiff_ft.imag())
           ) break;
     }  // end of for all n
+    if( (!isConvergedE[0] || !isConvergedE[1] ||!isConvergedE[2] ||
+        !isConvergedH[0] || !isConvergedH[1] ||!isConvergedH[2] ) && GetFieldConvergence()) {
+      std::cout << "Field evaluation failed to converge an nmax = "<< nmax << std::endl;
+      std::cout << "Near-field convergence threshold: "<<nearfield_convergence_threshold_<<std::endl;
+      if (isMarkUnconverged) {  //mark as NaN
+        for(auto &ee :E) ee /= c_zero;
+        for(auto &ee :H) ee /= c_zero;
+      }
+    }
 
     // magnetic field
     std::complex<evalType> hffact = ml/static_cast<evalType>(cc_*mu_);
@@ -365,12 +399,13 @@ namespace nmie {
   //   Number of multipolar expansion terms used for the calculations                 //
   //**********************************************************************************//
   template <typename FloatType>
-  void MultiLayerMie<FloatType>::RunFieldCalculation() {
+  void MultiLayerMie<FloatType>::RunFieldCalculation(bool isMarkUnconverged) {
     // Calculate scattering coefficients an_ and bn_
     calcScattCoeffs();
     // Calculate expansion coefficients aln_,  bln_, cln_, and dln_
     calcExpanCoeffs();
-
+    std::vector<bool> isConvergedE = {false, false, false}, isConvergedH = {false, false, false};
+    isConvergedE_ = {true, true, true}, isConvergedH_ = {true, true, true};
     Es_.clear(); Hs_.clear(); coords_polar_.clear();
     long total_points = coords_[0].size();
     for (int point = 0; point < total_points; point++) {
@@ -410,7 +445,9 @@ namespace nmie {
       // Calculate angular functions Pi and Tau
       calcPiTau(nmm::cos(Theta), Pi, Tau);
 
-      calcFieldByComponents(Rho, Theta, Phi, Psi, D1n, Zeta, D3n, Pi, Tau, Es, Hs);
+      calcFieldByComponents(Rho, Theta, Phi, Psi, D1n, Zeta, D3n, Pi, Tau, Es, Hs,
+                            isConvergedE, isConvergedH, isMarkUnconverged);
+      UpdateConvergenceStatus(isConvergedE, isConvergedH);
       Es_.push_back(Es);
       Hs_.push_back(Hs);
     }  // end of for all field coordinates
@@ -456,9 +493,13 @@ void MultiLayerMie<FloatType>::GetIndexAtRadius(const evalType Rho,
 }
 
 template <typename FloatType>
-void MultiLayerMie<FloatType>::calcMieSeriesNeededToConverge(const FloatType Rho) {
-  auto required_near_field_nmax = calcNmax(Rho);
-  SetMaxTerms(required_near_field_nmax);
+void MultiLayerMie<FloatType>::calcMieSeriesNeededToConverge(const FloatType Rho, int nmax_in) {
+  if (nmax_in < 1) {
+    auto required_near_field_nmax = calcNmax(Rho);
+    SetMaxTerms(required_near_field_nmax);
+  } else {
+    SetMaxTerms(nmax_in);
+  }
   // Calculate scattering coefficients an_ and bn_
   calcScattCoeffs();
   // We might be limited with available machine precision
@@ -470,20 +511,21 @@ void MultiLayerMie<FloatType>::calcMieSeriesNeededToConverge(const FloatType Rho
 
 template <typename FloatType>
 void MultiLayerMie<FloatType>::calcRadialOnlyDependantFunctions(const double from_Rho, const double to_Rho,
-                                                                const bool isIgnoreAvailableNmax,
                                                                 std::vector<std::vector<std::complex<FloatType> > > &Psi,
                                                                 std::vector<std::vector<std::complex<FloatType> > > &D1n,
                                                                 std::vector<std::vector<std::complex<FloatType> > > &Zeta,
-                                                                std::vector<std::vector<std::complex<FloatType> > > &D3n) {
+                                                                std::vector<std::vector<std::complex<FloatType> > > &D3n,
+                                                                int nmax_in) {
   auto radius_points = Psi.size();
   std::vector<std::vector<std::complex<FloatType> > > PsiZeta(radius_points);
   double delta_Rho = eval_delta<double>(radius_points, from_Rho, to_Rho);
   for (unsigned int j=0; j < radius_points; j++) {
     auto Rho = static_cast<FloatType>(from_Rho + j*delta_Rho);
 //    if (Rho < 1e-5) Rho = 1e-5; // TODO do we need this?.
-    int near_field_nmax = calcNmax(Rho);
+    int near_field_nmax = nmax_in;
+    if (nmax_in < 1) near_field_nmax = calcNmax(Rho);
+
     // Skip if not enough terms in Mie series (i.e. required near field nmax > available terms )
-    if (near_field_nmax > available_maximal_nmax_ && !isIgnoreAvailableNmax) continue;
     if (near_field_nmax > available_maximal_nmax_)  near_field_nmax = available_maximal_nmax_;
     Psi[j].resize(near_field_nmax + 1); D1n[j].resize(near_field_nmax + 1);
     Zeta[j].resize(near_field_nmax + 1); D3n[j].resize(near_field_nmax + 1);
@@ -510,12 +552,13 @@ void MultiLayerMie<FloatType>::RunFieldCalculationPolar(const int outer_arc_poin
                                                         const double from_Rho, const double to_Rho,
                                                         const double from_Theta, const double to_Theta,
                                                         const double from_Phi, const double to_Phi,
-                                                        const bool isIgnoreAvailableNmax) {
+                                                        const bool isMarkUnconverged,
+                                                        int nmax_in) {
   if (from_Rho > to_Rho || from_Theta > to_Theta || from_Phi > to_Phi
       || outer_arc_points < 1 || radius_points < 1
       || from_Rho < 0.)
     throw std::invalid_argument("Error! Invalid argument for RunFieldCalculationPolar() !");
-  auto nmax_old = nmax_;
+//  auto nmax_old = nmax_;
   int theta_points = 0, phi_points = 0;
   if (to_Theta-from_Theta > to_Phi-from_Phi) {
     theta_points = outer_arc_points;
@@ -526,20 +569,24 @@ void MultiLayerMie<FloatType>::RunFieldCalculationPolar(const int outer_arc_poin
   }
   if (theta_points == 0) theta_points = 1;
   if (phi_points == 0) phi_points = 1;
-  calcMieSeriesNeededToConverge(to_Rho);
+  calcMieSeriesNeededToConverge(to_Rho, nmax_in);
 
   std::vector<std::vector<FloatType> >  Pi(theta_points), Tau(theta_points);
   calcPiTauAllTheta(from_Theta, to_Theta, Pi, Tau);
 
   std::vector<std::vector<std::complex<FloatType> > > Psi(radius_points), D1n(radius_points),
       Zeta(radius_points), D3n(radius_points), PsiZeta(radius_points);
-  calcRadialOnlyDependantFunctions(from_Rho, to_Rho, isIgnoreAvailableNmax,
-                                   Psi, D1n, Zeta, D3n);
+  calcRadialOnlyDependantFunctions(from_Rho, to_Rho,
+                                   Psi, D1n, Zeta, D3n,
+                                   nmax_in);
 
+//  std::cout<<"Done evaluation of special functions."<<std::endl;
   double delta_Rho = eval_delta<double>(radius_points, from_Rho, to_Rho);
   double delta_Theta = eval_delta<double>(theta_points, from_Theta, to_Theta);
   double delta_Phi = eval_delta<double>(phi_points, from_Phi, to_Phi);
   Es_.clear(); Hs_.clear(); coords_polar_.clear();
+  std::vector<bool> isConvergedE = {false, false, false}, isConvergedH = {false, false, false};
+  isConvergedE_ = {true, true, true}, isConvergedH_ = {true, true, true};
   for (int j=0; j < radius_points; j++) {
     auto Rho = from_Rho + j * delta_Rho;
     std::vector< std::complex<double> > Psi_dp = ConvertComplexVector<double>(Psi[j]);
@@ -551,31 +598,38 @@ void MultiLayerMie<FloatType>::RunFieldCalculationPolar(const int outer_arc_poin
       std::vector<double> Pi_dp = ConvertVector<double>(Pi[i]);
       std::vector<double> Tau_dp = ConvertVector<double>(Tau[i]);
       for (int k = 0; k < phi_points; k++) {
-
         auto Phi = from_Phi + k * delta_Phi;
         coords_polar_.push_back({Rho, Theta, Phi});
-
-        // This array contains the fields in spherical coordinates
-//        std::vector<std::complex<FloatType> > Es(3), Hs(3);
         std::vector<std::complex<double> > Es(3), Hs(3);
-        calcFieldByComponents(
-            Rho, Theta, Phi,
-                              Psi_dp, D1n_dp, Zeta_dp, D3n_dp,
-                              Pi_dp, Tau_dp, Es, Hs
-//        Rho, Theta, Phi,
-//            Psi[j], D1n[j], Zeta[j], D3n[j],
-//            Pi[i], Tau[i], Es, Hs
-        );
+        calcFieldByComponents( Rho, Theta, Phi,
+                               Psi_dp, D1n_dp, Zeta_dp, D3n_dp, Pi_dp, Tau_dp,
+                               Es, Hs, isConvergedE, isConvergedH,
+                               isMarkUnconverged);
+        UpdateConvergenceStatus(isConvergedE, isConvergedH);
         Es_.push_back(ConvertComplexVector<FloatType>(Es));
         Hs_.push_back(ConvertComplexVector<FloatType>(Hs));
       }
     }
   }
   convertFieldsFromSphericalToCartesian();
-  nmax_ = nmax_old;
 }
 
-// Python interface
+
+template <typename FloatType>
+void MultiLayerMie<FloatType>::UpdateConvergenceStatus(std::vector<bool> isConvergedE, std::vector<bool> isConvergedH) {
+  for (int i = 0; i< 3; i++) isConvergedE_[i] = isConvergedE_[i] && isConvergedE[i];
+  for (int i = 0; i< 3; i++) isConvergedH_[i] = isConvergedH_[i] && isConvergedH[i];
+}
+
+
+template <typename FloatType>
+bool MultiLayerMie<FloatType>::GetFieldConvergence () {
+  bool convergence = true;
+  for (auto conv:isConvergedE_) convergence = convergence && conv;
+  for (auto conv:isConvergedH_) convergence = convergence && conv;
+  return convergence;
+}
+
 
 
 }  // end of namespace nmie

src/nmie-precision.hpp

@@ -66,6 +66,11 @@ namespace nmie {
     if (std::is_same<T, double>::value) return static_cast<T>(std::cos(static_cast<double>(v)));
     return static_cast<T>(nmm::cos(static_cast<FloatType >(v)));
   }
+  template<class T> T sqrt_t(T v) {
+    if (std::is_same<T, double>::value) return static_cast<T>(std::sqrt(static_cast<double>(v)));
+    return static_cast<T>(nmm::sqrt(static_cast<FloatType >(v)));
+  }
+
 
 
 template <typename ToFloatType, typename FromFloatType>

src/pb11_wrapper.cc

@@ -80,28 +80,18 @@ namespace nmie {
 template<typename FloatType>
 class PyMultiLayerMie : public MultiLayerMie<FloatType> {
  public:
-  template<typename outputType>
-  py::array_t<std::complex<outputType>> GetS1();
-  template<typename outputType>
-  py::array_t<std::complex<outputType>> GetS2();
-  template<typename outputType>
-  py::array_t<std::complex<outputType>> GetAn();
-  template<typename outputType>
-  py::array_t<std::complex<outputType>> GetBn();
-  template<typename outputType>
-  py::array GetLayerAn();
-  template<typename outputType>
-  py::array GetLayerBn();
-  template<typename outputType>
-  py::array GetLayerCn();
-  template<typename outputType>
-  py::array GetLayerDn();
-  template<typename outputType>
-  py::array GetFieldE();
-  template<typename outputType>
-  py::array GetFieldH();
-//    template <typename outputType> py::array_t<outputType>  GetFieldEabs();
-//    template <typename outputType> py::array_t<outputType>  GetFieldHabs();
+  template<typename outputType> py::array_t<std::complex<outputType>> GetS1();
+  template<typename outputType> py::array_t<std::complex<outputType>> GetS2();
+  template<typename outputType> py::array_t<std::complex<outputType>> GetAn();
+  template<typename outputType> py::array_t<std::complex<outputType>> GetBn();
+  template<typename outputType> py::array GetLayerAn();
+  template<typename outputType> py::array GetLayerBn();
+  template<typename outputType> py::array GetLayerCn();
+  template<typename outputType> py::array GetLayerDn();
+  template<typename outputType> py::array GetFieldE();
+  template<typename outputType> py::array GetFieldH();
+  template<typename outputType> py::array_t<outputType>  GetFieldEabs();
+  template<typename outputType> py::array_t<outputType>  GetFieldHabs();
 
   template<typename inputType>
   void SetLayersSize(const py::array_t<inputType, py::array::c_style | py::array::forcecast> &py_layer_size);
@@ -156,6 +146,22 @@ py::array_t<std::complex<outputType>> PyMultiLayerMie<FloatType>::GetS2() {
       );
 }
 
+
+template <typename FloatType> template <typename outputType>
+py::array_t<outputType>  PyMultiLayerMie<FloatType>::GetFieldEabs() {
+  return Vector2Py(ConvertVector<double>(
+      this->MultiLayerMie<FloatType>::GetFieldEabs()
+  ));
+}
+
+template <typename FloatType> template <typename outputType>
+py::array_t<outputType>  PyMultiLayerMie<FloatType>::GetFieldHabs() {
+  return Vector2Py(ConvertVector<double>(
+      this->MultiLayerMie<FloatType>::GetFieldHabs()
+  ));
+}
+
+
 template<typename FloatType>
 template<typename outputType>
 py::array_t<std::complex<outputType>> PyMultiLayerMie<FloatType>::GetAn() {
@@ -192,19 +198,6 @@ py::array PyMultiLayerMie<FloatType>::GetFieldH() {
   );
 }
 
-//  template <typename FloatType> template <typename outputType>
-//  py::array_t<outputType>  PyMultiLayerMie<FloatType>::GetFieldEabs() {
-//    return Vector2Py(ConvertVector<double>(
-//    this->MultiLayerMie<FloatType>::GetFieldEabs()
-//    ));
-//  }
-//
-//  template <typename FloatType> template <typename outputType>
-//  py::array_t<outputType>  PyMultiLayerMie<FloatType>::GetFieldHabs() {
-//    return Vector2Py(ConvertVector<double>(
-//    this->MultiLayerMie<FloatType>::GetFieldHabs()
-//    ));
-//  }
 
 template<typename FloatType>
 template<typename outputType>
@@ -315,8 +308,9 @@ void declare_nmie(py::module &m, const std::string &typestr) {
       .def("GetBn", &mie_typed::GetBn<double>)
       .def("GetFieldE", &mie_typed::GetFieldE<double>)
       .def("GetFieldH", &mie_typed::GetFieldH<double>)
-//      .def("GetFieldEabs", &mie_typed::GetFieldEabs<double>)
-//      .def("GetFieldHabs", &mie_typed::GetFieldHabs<double>)
+      .def("GetFieldEabs", &mie_typed::GetFieldEabs<double>)
+      .def("GetFieldHabs", &mie_typed::GetFieldHabs<double>)
+      .def("GetFieldConvergence", &mie_typed::GetFieldConvergence)
       .def("GetLayerAn", &mie_typed::GetLayerAn<double>)
       .def("GetLayerBn", &mie_typed::GetLayerBn<double>)
       .def("GetLayerCn", &mie_typed::GetLayerCn<double>)
@@ -337,3 +331,5 @@ PYBIND11_MODULE(scattnlay_dp, m)
   declare_nmie<nmie::FloatType>(m, precision_name);
 }
 
+
+

src/special-functions-impl.hpp

@@ -137,8 +137,7 @@ void evalBackwardR (const std::complex<FloatType> z,
   for (int n = nmax -1; n >= 0; n--) {
     r[n] = -static_cast<FloatType>(1)/r[n+1] + static_cast<FloatType>(2*n+1)/z;
   }
-//  r[0] = nmm::cos(z)/nmm::sin(z);
-//  nmm::cout << "R0 = " << r[0] <<" at arg = "<<z<<'\n';
+  r[0] = complex_cot(z);
 }
 
 template <typename FloatType>
@@ -172,7 +171,7 @@ template <typename FloatType>
 void evalForwardD1 (const std::complex<FloatType> z,
                    std::vector<std::complex<FloatType> > &D) {
   if (D.size()<1) throw std::invalid_argument("Should have a leas one element!\n");
-  D[0] = std::cos(z)/std::sin(z);
+  D[0] = nmm::cos(z)/nmm::sin(z);
   evalForwardD(z,D);
 }
 
@@ -223,8 +222,8 @@ void evalForwardD1 (const std::complex<FloatType> z,
 //    calcD1D3(z, D1, D3);
 //
 //    // Now, use the upward recurrence to calculate Psi and Zeta - equations (20a) - (21b)
-//    Psi[0] = std::sin(z);
-//    Zeta[0] = std::sin(z) - c_i*std::cos(z);
+//    Psi[0] = nmm::sin(z);
+//    Zeta[0] = nmm::sin(z) - c_i*nmm::cos(z);
 //    for (int n = 1; n <= nmax_; n++) {
 //      Psi[n]  =  Psi[n - 1]*(std::complex<FloatType>(n,0.0)/z - D1[n - 1]);
 //      Zeta[n] = Zeta[n - 1]*(std::complex<FloatType>(n,0.0)/z - D3[n - 1]);
@@ -370,6 +369,16 @@ void evalUpwardD3 (const std::complex<FloatType> z,
   }
 }
 
+template <typename FloatType>
+std::complex<FloatType> complex_sin (const std::complex<FloatType> z){
+  auto a = z.real();
+  auto b = z.imag();
+  auto i = std::complex<FloatType>(0,1);
+  using nmm::sin; using nmm::cos; using nmm::exp;
+  return ((cos(a)+i*sin(a))*exp(-b)
+      - (cos(-a)+i*sin(-a))*exp(b)
+      )/(static_cast<FloatType>(2)*i);
+}
 
 template <typename FloatType>
 void evalUpwardPsi (const std::complex<FloatType> z,
@@ -377,7 +386,7 @@ void evalUpwardPsi (const std::complex<FloatType> z,
                    std::vector<std::complex<FloatType> >& Psi) {
   int nmax = Psi.size() - 1;
   // Now, use the upward recurrence to calculate Psi and Zeta - equations (20a) - (21b)
-  Psi[0] = std::sin(z);
+  Psi[0] = complex_sin(z);
   for (int n = 1; n <= nmax; n++) {
     Psi[n]  =  Psi[n - 1]*(std::complex<FloatType>(n,0.0)/z - D1[n - 1]);
   }
@@ -391,7 +400,7 @@ void evalUpwardZeta (const std::complex<FloatType> z,
   int nmax = Zeta.size() - 1;
   std::complex<FloatType> c_i(0.0, 1.0);
   // Now, use the upward recurrence to calculate Zeta and Zeta - equations (20a) - (21b)
-  Zeta[0] = std::sin(z) - c_i*std::cos(z);
+  Zeta[0] = nmm::sin(z) - c_i*nmm::cos(z);
   for (int n = 1; n <= nmax; n++) {
     Zeta[n]  =  Zeta[n - 1]*(std::complex<FloatType>(n, 0.0)/z - D3[n - 1]);
   }

tests/CMakeLists.txt

@@ -15,13 +15,6 @@ target_link_libraries("test_near_field" ${LIBS})
 add_test(NAME "test_near_field"
         COMMAND "test_near_field")
 
-add_executable("test_near_field_multi_precision"
-        test_near_field.cc)
-target_compile_options("test_near_field_multi_precision"
-        PRIVATE -DMULTI_PRECISION=100)
-target_link_libraries("test_near_field_multi_precision" ${LIBS})
-add_test(NAME "test_near_field_multi_precision"
-        COMMAND "test_near_field_multi_precision")
 
 
 # In included file test_spec_functions_data.hpp there are results of multiple
@@ -47,3 +40,11 @@ target_compile_options("test_bulk_sphere_multi_precision"
 target_link_libraries("test_bulk_sphere_multi_precision" ${LIBS})
 add_test(NAME "test_bulk_sphere_multi_precision"
         COMMAND "test_bulk_sphere_multi_precision")
+
+add_executable("test_near_field_multi_precision"
+        test_near_field.cc)
+target_compile_options("test_near_field_multi_precision"
+        PRIVATE -DMULTI_PRECISION=100)
+target_link_libraries("test_near_field_multi_precision" ${LIBS})
+add_test(NAME "test_near_field_multi_precision"
+        COMMAND "test_near_field_multi_precision")

tests/mpmath_input_arguments.py

@@ -2,29 +2,29 @@ import mpmath as mp
 import numpy as np
 complex_arguments = [
     # // x, [Re(m), Im(m)], Qext, Qsca, test_name
-    # [10000, [1.33,1e-5], 2.004089, 1.723857, 'f'],
-    # [10000, [1.5, 1],    2.004368, 1.236574, 'j'],
-    # [10000, [10,  10],   2.005914, 1.795393, 'm'],
-    # [80, [1.05,  1],   0, 0, 'Yang'],
-    # [0.099, [0.75,0], 7.417859e-06, 7.417859e-06, 'a'],
-    # [0.101, [0.75,0], 8.033538e-06, 8.033538e-06, 'b'],
-    # [10,    [0.75,0],     2.232265, 2.232265, 'c'],
-    # [1000,  [0.75,0],     1.997908, 1.997908, 'd'],
-    # [100,   [1.33,1e-5], 2.101321, 2.096594, 'e'],
-    # [0.055, [1.5, 1],    0.101491, 1.131687e-05, 'g'],
-    # [0.056, [1.5, 1],   0.1033467, 1.216311e-05, 'h'],
-    # [100,   [1.5, 1],    2.097502, 1.283697, 'i'],
-    # [1,     [10,  10],   2.532993, 2.049405, 'k'],
-    # [100,   [10,  10,],  2.071124, 1.836785, 'l'],
-    [11.8104986977059896, [1.33,0], 0,0, 'nanojet 1mkm']
-    # [1, [mp.pi,  1],   0, 0, 'pi'],
-    # [1, [mp.pi,  -1],   0, 0, 'pi'],
-    # [1, [mp.pi,  mp.pi],   0, 0, 'pi'],
-    # [1, [2*mp.pi,  -1],   0, 0, 'pi'],
-    # [1, [2*mp.pi,  mp.pi],   0, 0, 'pi'],
-    # [1, [2*mp.pi,  1],   0, 0, 'pi'],
-    # [1, [mp.pi,  0],   0, 0, 'pi'],
-    # [1, [np.pi,  0],   0, 0, 'pi'],
-    # [2.03575204,[1.4558642,0.20503704],1.952484, 0.9391477, 'water r=1mkm scattnlay 2020/04/22']
+    [10000, [1.33,1e-5], 2.004089, 1.723857, 'f'],
+    [10000, [1.5, 1],    2.004368, 1.236574, 'j'],
+    [10000, [10,  10],   2.005914, 1.795393, 'm'],
+    [80, [1.05,  1],   0, 0, 'Yang'],
+    [0.099, [0.75,0], 7.417859e-06, 7.417859e-06, 'a'],
+    [0.101, [0.75,0], 8.033538e-06, 8.033538e-06, 'b'],
+    [10,    [0.75,0],     2.232265, 2.232265, 'c'],
+    [1000,  [0.75,0],     1.997908, 1.997908, 'd'],
+    [100,   [1.33,1e-5], 2.101321, 2.096594, 'e'],
+    [0.055, [1.5, 1],    0.101491, 1.131687e-05, 'g'],
+    [0.056, [1.5, 1],   0.1033467, 1.216311e-05, 'h'],
+    [100,   [1.5, 1],    2.097502, 1.283697, 'i'],
+    [1,     [10,  10],   2.532993, 2.049405, 'k'],
+    [100,   [10,  10,],  2.071124, 1.836785, 'l'],
+    [11.81049869770599, [1.3300000000000001, 0], 0,0, 'nanojet 1mkm'],
+    [1, [mp.pi,  1],   0, 0, 'pi'],
+    [1, [mp.pi,  -1],   0, 0, 'pi'],
+    [1, [mp.pi,  mp.pi],   0, 0, 'pi'],
+    [1, [2*mp.pi,  -1],   0, 0, 'pi'],
+    [1, [2*mp.pi,  mp.pi],   0, 0, 'pi'],
+    [1, [2*mp.pi,  1],   0, 0, 'pi'],
+    [1, [mp.pi,  0],   0, 0, 'pi'],
+    [1, [np.pi,  0],   0, 0, 'pi'],
+    [2.03575204,[1.4558642,0.20503704],1.952484, 0.9391477, 'water r=1mkm scattnlay 2020/04/22']
 
 ]

tests/mpmath_special_functions_test_generator.py

@@ -81,7 +81,7 @@ class UpdateSpecialFunctionsEvaluations:
                 del self.evaluated_data[i]
 
     def get_n_list(self, z, max_number_of_elements=10):
-        nmax = mrb.LeRu_cutoff(z)
+        nmax = mrb.LeRu_cutoff(z)*10
         factor = nmax ** (1 / (max_number_of_elements - 2))
         n_list = [int(factor ** i) for i in range(max_number_of_elements - 1)]
         n_list.append(0)
@@ -215,30 +215,32 @@ def main():
     # sf_evals.run_test(mrb.bn, 'bn', is_xm=True)
 
     # sf_evals.run_test(mrb.psi, 'psi')
+    # sf_evals.run_test(mrb.ksi, 'zeta')
     # sf_evals.run_test(mrb.psi_div_ksi, 'psi_div_ksi')
     # sf_evals.run_test(mrb.psi_mul_ksi, 'psi_mul_zeta', is_only_x=True)
+    # sf_evals.run_test(mrb.psi_mul_ksi, 'psi_mul_zeta')
     # sf_evals.run_test(mrb.psi_div_xi, 'psi_div_xi')
     with open(sf_evals.filename, 'w') as out_file:
         out_file.write(sf_evals.get_file_content())
 
-    for record in mia.complex_arguments:
-        mp.mp.dps = 20
-        output_dps = 16
-        x = mp.mpf(str(record[0]))
-        mr = str(record[1][0])
-        mi = str(record[1][1])
-        m = mp.mpc(mr, mi)
-        Qext_ref = record[2]
-        Qsca_ref = record[3]
-        test_case = record[4]
-        nmax = int(x + 4.05*x**(1./3.) + 2)+2+28
-        print(f"\n ===== test case: {test_case} =====", flush=True)
-        print(f"x={x}, m={m}, N={nmax} \nQsca_ref = {Qsca_ref}    \tQext_ref = {Qext_ref}", flush=True)
-        Qext_mp = mrb.Qext(x,m,nmax, output_dps)
-        Qsca_mp = mrb.Qsca(x,m,nmax, output_dps)
-        print(f"Qsca_mp  = {mp.nstr(Qsca_mp[-1],output_dps)}    \tQext_mp  = {mp.nstr(Qext_mp[-1],output_dps)}", flush=True)
-        print(mp.nstr(Qsca_mp,output_dps))
-        print(mp.nstr(Qext_mp,output_dps))
+    # for record in mia.complex_arguments:
+    #     mp.mp.dps = 20
+    #     output_dps = 16
+    #     x = mp.mpf(str(record[0]))
+    #     mr = str(record[1][0])
+    #     mi = str(record[1][1])
+    #     m = mp.mpc(mr, mi)
+    #     Qext_ref = record[2]
+    #     Qsca_ref = record[3]
+    #     test_case = record[4]
+    #     nmax = int(x + 4.05*x**(1./3.) + 2)+2+28
+    #     print(f"\n ===== test case: {test_case} =====", flush=True)
+    #     print(f"x={x}, m={m}, N={nmax} \nQsca_ref = {Qsca_ref}    \tQext_ref = {Qext_ref}", flush=True)
+    #     Qext_mp = mrb.Qext(x,m,nmax, output_dps)
+    #     Qsca_mp = mrb.Qsca(x,m,nmax, output_dps)
+    #     print(f"Qsca_mp  = {mp.nstr(Qsca_mp[-1],output_dps)}    \tQext_mp  = {mp.nstr(Qext_mp[-1],output_dps)}", flush=True)
+    #     print(mp.nstr(Qsca_mp,output_dps))
+    #     print(mp.nstr(Qext_mp,output_dps))
 
         # n=1
         # print(f'n={n}, x={x}, m={m}\nbn[{n}]={mp.nstr(mrb.bn(n,x,m), output_dps)}')

tests/test_Riccati_Bessel_logarithmic_derivative.cc

@@ -269,27 +269,28 @@ TEST(D3test, mpmath_generated_input) {
   double re_abs_tol,  im_abs_tol;
   for (const auto &data : D1_test_30digits) {
     parse2_mpmath_data(min_abs_tol, data, x, m, n, D1_mp, re_abs_tol, im_abs_tol);
+    if (n == 0 && nmie::cabs(D1_mp) > 1e14) continue;
     z = m*x;
-    auto Nstop = nmie::LeRu_near_field_cutoff(z)+1;
+//    auto Nstop = nmie::LeRu_near_field_cutoff(z)+1;
 //    auto Nstop = n;
-    std::vector<std::complex<nmie::FloatType>> Db(Nstop),Dold(Nstop), r;
-    int valid_digits = 10;
+    int valid_digits = 16;
     int nstar = nmie::getNStar(n, z, valid_digits);
+    std::vector<std::complex<nmie::FloatType>> Db(nstar),Dold(nstar), r;
     r.resize(nstar);
     Db.resize(nstar);
     nmie::evalBackwardR(z,r);
     nmie::convertRtoD1(z, r, Db);
     if (n > Db.size()) continue;
     EXPECT_NEAR(std::real(Db[n]), std::real(D1_mp), re_abs_tol)
-              << "Db at n=" << n << " Nstop="<< Nstop<<" nstar="<<nstar<< " z="<<z;
+              << "Db at n=" << n <<" nstar="<<nstar<< " z="<<z;
     EXPECT_NEAR(std::imag(Db[n]), std::imag(D1_mp), im_abs_tol)
-              << "Db at n=" << n << " Nstop="<< Nstop<<" nstar="<<nstar<< " z="<<z;
+              << "Db at n=" << n <<" nstar="<<nstar<< " z="<<z;
     nmie::evalDownwardD1(z, Dold);
     if (n > Dold.size()) continue;
     EXPECT_NEAR(std::real(Dold[n]), std::real(D1_mp), re_abs_tol)
-              << "Dold at n=" << n << " Nstop="<< Nstop<< " z="<<z;
+              << "Dold at n=" << n << " z="<<z;
     EXPECT_NEAR(std::imag(Dold[n]), std::imag(D1_mp), im_abs_tol)
-              << "Dold at n=" << n << " Nstop="<< Nstop<< " z="<<z;
+              << "Dold at n=" << n << " z="<<z;
 
   }
 }

tests/test_bulk_sphere.cc

@@ -48,9 +48,11 @@ TEST(BulkSphere, HandlesInput) {
           {1,     {10,  10},   2.532993, 2.049405, 'k'},
           {1000,  {0.75,0},     1.997908, 1.997908, 'd'},
           {100,   {10,  10,},  2.071124, 1.836785, 'l'},
+#ifndef MULTI_PRECISION
           {10000, {1.33,1e-5}, 2.004089, 1.723857, 'f'},
           {10000, {1.5, 1},    2.004368, 1.236574, 'j'},
           {10000, {10,  10},   2.005914, 1.795393, 'm'},
+#endif
       };
   for (const auto &data : parameters_and_results) {
     auto x = std::get<0>(data);

tests/test_cases.hpp

@@ -0,0 +1,32 @@
+#ifndef SCATTNLAY_TESTS_TEST_CASES_HPP_
+#define SCATTNLAY_TESTS_TEST_CASES_HPP_
+//
+//
+#include <vector>
+#include <tuple>
+#include <string>
+#include <complex>
+
+
+std::vector< std::tuple< double, std::complex<double>, std::string > >
+parameters_bulk_sphere
+{
+// x, {Re(m), Im(m)}, test_name
+{0.099, {0.75,0}, "Hong Du testcase:a"},
+{0.101, {0.75,0}, "Hong Du testcase:b"},
+{10,    {0.75,0}, "Hong Du testcase:c"},
+{100,   {1.33,1e-5}, "Hong Du testcase:e"},
+{0.055, {1.5, 1},    "Hong Du testcase:g"},
+{0.056, {1.5, 1}, "Hong Du testcase:h"},
+{100,   {1.5, 1}, "Hong Du testcase:i"},
+{1,     {10,  10},   "Hong Du testcase:k"},
+{1000,  {0.75,0}, "Hong Du testcase:d"},
+#ifdef MULTI_PRECISION
+//{10000, {1.33,1e-5}, "Hong Du testcase:f"}, // passes but takes too long
+//{100,   {10,  10,},  "Hong Du testcase:l"}, // fails in any precision
+//{10000, {1.5, 1},    "Hong Du testcase:j"},
+//{10000, {10,  10},   "Hong Du testcase:m"},
+#endif
+};
+
+#endif //SCATTNLAY_TESTS_TEST_CASES_HPP_

tests/test_near_field.cc

@@ -1,63 +1,49 @@
 #include "gtest/gtest.h"
 #include "../src/nmie-basic.hpp"
 #include "../src/nmie-nearfield.hpp"
+#include "test_cases.hpp"
 
 TEST(RunFieldCalculationPolar, HandlesInput) {
   nmie::MultiLayerMie<nmie::FloatType> nmie;
   EXPECT_THROW(nmie.RunFieldCalculationPolar(0), std::invalid_argument);
   EXPECT_THROW(nmie.RunFieldCalculationPolar(1,1,10,5), std::invalid_argument);
-  nmie.SetLayersSize({1.099});
-  nmie.SetLayersIndex({ {1.,0}});
+  double r = 60;
+//  double r = 1500;
+  nmie.SetLayersSize({r/2, r});
+  nmie.SetLayersIndex({ {1.33,0}, {1.33,0}});
   nmie.RunMieCalculation();
-  nmie.RunFieldCalculationPolar(2, 2, 0.1, 1.5);
+  nmie.RunFieldCalculationPolar(1, 1,
+                                0.5145*r,
+                                r*0.5148,
+                                0, 3.14, 0, 0, true, 1);
+  EXPECT_EQ(1, nmie.GetMaxTerms());
+  EXPECT_FALSE(nmie.GetFieldConvergence());
   auto Eabs = nmie.GetFieldEabs();
-  std::cout<<"nmax = " << nmie.GetMaxTerms() << std::endl;
+  EXPECT_TRUE(std::isnan(static_cast<double>(Eabs[0])));
 
 }
-//TEST(BulkSphere, HandlesInput) {
-//  nmie::MultiLayerMie<nmie::FloatType> nmie;
-//  // A list of tests for a bulk sphere from
-//  // Hong Du, "Mie-scattering calculation," Appl. Opt. 43, 1951-1956 (2004)
-//  // table 1: sphere size and refractive index
-//  // followed by resulting extinction and scattering efficiencies
-//  std::vector< std::tuple< double, std::complex<double>, double, double, char > >
-//      parameters_and_results
-//      {
-//          // x, {Re(m), Im(m)}, Qext, Qsca, test_name
-//          {0.099, {0.75,0}, 7.417859e-06, 7.417859e-06, 'a'},
-//          {0.101, {0.75,0}, 8.033538e-06, 8.033538e-06, 'b'},
-//          {10,    {0.75,0},     2.232265, 2.232265, 'c'},
-//          {100,   {1.33,1e-5}, 2.101321, 2.096594, 'e'},
-//          {0.055, {1.5, 1},    0.10149104, 1.131687e-05, 'g'},
-//          {0.056, {1.5, 1},   0.1033467, 1.216311e-05, 'h'},
-//          {100,   {1.5, 1},    2.097502, 1.283697, 'i'},
-//          {1,     {10,  10},   2.532993, 2.049405, 'k'},
-//          {1000,  {0.75,0},     1.997908, 1.997908, 'd'},
-//          {100,   {10,  10,},  2.071124, 1.836785, 'l'},
-//          {10000, {1.33,1e-5}, 2.004089, 1.723857, 'f'},
-//          {10000, {1.5, 1},    2.004368, 1.236574, 'j'},
-//          {10000, {10,  10},   2.005914, 1.795393, 'm'},
-//      };
-//  for (const auto &data : parameters_and_results) {
-//    auto x = std::get<0>(data);
-//    auto m = std::get<1>(data);
-// //    auto Nstop = nmie::LeRu_near_field_cutoff(m*x)+1;
-//
-//    nmie.SetLayersSize({x});
-//    nmie.SetLayersIndex({m});
-////    nmie.SetMaxTerms(Nstop);
+//#ifndef MULTI_PRECISION
+TEST(BulkSphere, HandlesInput) {
+  nmie::MultiLayerMie<nmie::FloatType> nmie;
+  for (const auto &data : parameters_bulk_sphere) {
+    auto x = std::get<0>(data);
+    auto m = std::get<1>(data);
+    nmie.SetLayersSize({x});
+    nmie.SetLayersIndex({m});
+    nmie.SetMaxTerms(-1);
 //    nmie.RunMieCalculation();
-//    double Qext = static_cast<double>(nmie.GetQext());
-//    double Qsca = static_cast<double>(nmie.GetQsca());
-//    double Qext_Du =  std::get<2>(data);
-//    double Qsca_Du =  std::get<3>(data);
-//    EXPECT_FLOAT_EQ(Qext_Du, Qext)
-//              << "Extinction of the bulk sphere, test case:" << std::get<4>(data)
-//              << "\nnmax_ = " << nmie.GetMaxTerms();
-//    EXPECT_FLOAT_EQ(Qsca_Du, Qsca)
-//              << "Scattering of the bulk sphere, test case:" << std::get<4>(data);
-//  }
-//}
+//    std::cout<<" test case: "<<std::get<2>(data)<<" Qsca="<<nmie.GetQsca()<<std::endl;
+    nmie.RunFieldCalculationPolar(4,3,x,x*3, 0, static_cast<double>(nmie.PI_), 0, static_cast<double>(nmie.PI_),true, -1);
+    auto Eabs = nmie.GetFieldEabs();
+    for (auto &E:Eabs) E=nmie::pow2(E);
+//    print(Eabs)
+    EXPECT_TRUE(nmie.GetFieldConvergence())<<"Outside test for x="<<x<<" m="<<m<<" test case: "<<std::get<2>(data)<<std::endl;
+    nmie.RunFieldCalculationPolar(4,10,x*0.01,x, 0, static_cast<double>(nmie.PI_), 0, static_cast<double>(nmie.PI_),true, -1);
+    EXPECT_TRUE(nmie.GetFieldConvergence())<<"Inside test for x="<<x<<" m="<<m<<" test case: "<<std::get<2>(data)<<std::endl;
+  }
+}
+//#endif
+
 int main(int argc, char **argv) {
   testing::InitGoogleTest(&argc, argv);
   return RUN_ALL_TESTS();

tests/test_spec_functions_data.hpp

@@ -1966,6 +1966,925 @@ psi_mul_zeta_test_16digits
 {{10000.0,0.0},141995,{3.391815853006694e-289545,-0.03530003015880046},3.4e-289561,3.5e-18},
 };
 
+// x, complex(m), n, complex(f(n,z)), abs_err_real, abs_err_imag
+std::vector< std::tuple< nmie::FloatType, std::complex<nmie::FloatType>, int, std::complex<nmie::FloatType>, nmie::FloatType, nmie::FloatType > >
+psi_mul_zeta_test_30digits
+= {
+{0.055,{1.5,1.0},0,{0.0581663827988405358763050707623,-0.0735714224516483332788155624407},5.8e-32,7.4e-32},
+{0.055,{1.5,1.0},1,{0.0184532348903964055844057465668,-0.0274679464523288178832503290649},1.8e-32,2.7e-32},
+{0.055,{1.5,1.0},2,{0.011018230444575883336373160073,-0.0164963768938022013858064297881},1.1e-32,1.6e-32},
+{0.055,{1.5,1.0},3,{0.007863217961077190291573299956,-0.0117845204662883440516563938302},7.9e-33,1.2e-32},
+{0.055,{1.5,1.0},4,{0.00611387227861954534995863752659,-0.00916612523690498188487617250001},6.1e-33,9.2e-33},
+{0.055,{1.5,1.0},5,{0.00500148673035687941671966568337,-0.00749970871763356405999369561248},5.0e-33,7.5e-33},
+{0.055,{1.5,1.0},6,{0.00423166125299268361416146754541,-0.0063459791552383577787838876758},4.2e-33,6.3e-33},
+{0.055,{1.5,1.0},7,{0.00366724385144641834492458949883,-0.00549988699447091559974366185034},3.7e-33,5.5e-33},
+{0.055,{1.5,1.0},8,{0.00323568903088714758070281451364,-0.00485286386994308756319729052423},3.2e-33,4.9e-33},
+{0.055,{1.5,1.0},9,{0.00289501892169483058937121741445,-0.00434205005055973234036267167029},2.9e-33,4.3e-33},
+{0.055,{1.5,1.0},10,{0.00261925611197335542697255121809,-0.00392853062260952697464150628881},2.6e-33,3.9e-33},
+{0.055,{1.5,1.0},11,{0.00239146280206506078885862310455,-0.00358692551109136911742038652173},2.4e-33,3.6e-33},
+{0.055,{1.5,1.0},12,{0.00220012324195811966376657100248,-0.00329997588172242540689178226509},2.2e-33,3.3e-33},
+{0.055,{1.5,1.0},13,{0.00203713478051819109956394721361,-0.00305553642795579473189988488361},2.0e-33,3.1e-33},
+{0.055,{1.5,1.0},14,{0.00189663054943568390666906399527,-0.00284481216116515747683784982594},1.9e-33,2.8e-33},
+{0.055,{1.5,1.0},15,{0.00177425804175281941839874703,-0.00266127770238425040615036718963},1.8e-33,2.7e-33},
+{0.055,{1.5,1.0},17,{0.00157147334320864292725710118189,-0.00235713409639994733926212218907},1.6e-33,2.4e-33},
+{0.055,{1.5,1.0},18,{0.00148652437028033067720263955265,-0.00222972231689162022841424111675},1.5e-33,2.2e-33},
+{0.055,{1.5,1.0},20,{0.00134149124190139074276966984805,-0.00201218967701345231897863312462},1.3e-33,2.0e-33},
+{0.055,{1.5,1.0},22,{0.00122224326041266850833599668048,-0.00183332921686962149458151584727},1.2e-33,1.8e-33},
+{0.055,{1.5,1.0},23,{0.00117023122803830163697117734714,-0.00175531553655194275519667251549},1.2e-33,1.8e-33},
+{0.055,{1.5,1.0},26,{0.00103774871904363338507845708668,-0.00155660125541371066466422451678},1.0e-33,1.6e-33},
+{0.055,{1.5,1.0},28,{0.00096492262490774375833685844678,-0.00144736639709579906710402556898},9.6e-34,1.4e-33},
+{0.055,{1.5,1.0},30,{0.000901647782742151516356328847331,-0.00135245736532213276983649414675},9.0e-34,1.4e-33},
+{0.055,{1.5,1.0},33,{0.000820901889599073950635047035822,-0.0012313420377831750259872206311},8.2e-34,1.2e-33},
+{0.055,{1.5,1.0},36,{0.000753429579560529484666085096155,-0.00113013602327004042063640495003},7.5e-34,1.1e-33},
+{0.055,{1.5,1.0},39,{0.00069620641478954580590545281708,-0.00104430303770516080911904033414},7.0e-34,1.0e-33},
+{0.055,{1.5,1.0},42,{0.000647061940767690559546634660831,-0.00097058762538744877884772372873},6.5e-34,9.7e-34},
+{0.055,{1.5,1.0},46,{0.000591400229250338675219796188682,-0.000887096308575065806802982896226},5.9e-34,8.9e-34},
+{0.055,{1.5,1.0},50,{0.000544556313217370607396558294741,-0.000816831319686064411823993126477},5.4e-34,8.2e-34},
+{0.055,{1.5,1.0},55,{0.000495496894948120188053310807648,-0.00074324296943408009249425568172},5.0e-34,7.4e-34},
+{0.055,{1.5,1.0},60,{0.00045454653485607185971152997571,-0.000681817970450973014650042379851},4.5e-34,6.8e-34},
+{0.056,{1.5,1.0},0,{0.0592714241816308587619838966937,-0.0747469467567292811042229496866},5.9e-32,7.5e-32},
+{0.056,{1.5,1.0},1,{0.0187930796694411756403573930595,-0.0279660400360846371525223437034},1.9e-32,2.8e-32},
+{0.056,{1.5,1.0},2,{0.0112192432761575528162909809625,-0.0167961734466179591571620393658},1.1e-32,1.7e-32},
+{0.056,{1.5,1.0},3,{0.00800641257663979212145175576266,-0.011998739661574116207530180155},8.0e-33,1.2e-32},
+{0.056,{1.5,1.0},4,{0.00622513676364985326368853077001,-0.00933276178234739468228270364058},6.2e-33,9.3e-33},
+{0.056,{1.5,1.0},5,{0.00509247840231744944518294556784,-0.0076360561590879176780456831952},5.1e-33,7.6e-33},
+{0.056,{1.5,1.0},6,{0.00430863387704095758381677083166,-0.00646135406107968902932405982552},4.3e-33,6.5e-33},
+{0.056,{1.5,1.0},7,{0.00373394257744575451114112713726,-0.00559988071463207085701522474534},3.7e-33,5.6e-33},
+{0.056,{1.5,1.0},8,{0.00329453449538098453652448313054,-0.00494109486855881566686911499953},3.3e-33,4.9e-33},
+{0.056,{1.5,1.0},9,{0.00294766616843581532929289624096,-0.00442099435136381794236739994616},2.9e-33,4.4e-33},
+{0.056,{1.5,1.0},10,{0.00266688674007105280170887922035,-0.003999956926984852835728264996},2.7e-33,4.0e-33},
+{0.056,{1.5,1.0},11,{0.00243494986406215241261326678934,-0.00365214117961280442822344290902},2.4e-33,3.7e-33},
+{0.056,{1.5,1.0},12,{0.00224013008725806264871303925028,-0.00335997454188529265303577254789},2.2e-33,3.4e-33},
+{0.056,{1.5,1.0},13,{0.00207417724657294557514294474801,-0.00311109092094689067265521511789},2.1e-33,3.1e-33},
+{0.056,{1.5,1.0},14,{0.00193111768628795892128269095882,-0.00289653544223103463063413942635},1.9e-33,2.9e-33},
+{0.056,{1.5,1.0},15,{0.00180651968845279880899274149841,-0.00270966409811450893016728588496},1.8e-33,2.7e-33},
+{0.056,{1.5,1.0},17,{0.00160004725855666181762998846196,-0.00239999075261515491381629755061},1.6e-33,2.4e-33},
+{0.056,{1.5,1.0},18,{0.00151355350150104290374267067022,-0.00227026244566747339194545277598},1.5e-33,2.3e-33},
+{0.056,{1.5,1.0},20,{0.00136588303142321093450862604958,-0.0020487747404187793709430402558},1.4e-33,2.0e-33},
+{0.056,{1.5,1.0},22,{0.00124446665116576319281039289246,-0.00186666232154944214673754380024},1.2e-33,1.9e-33},
+{0.056,{1.5,1.0},23,{0.00119150884922800468998442480204,-0.00178723022951598104445824280589},1.2e-33,1.8e-33},
+{0.056,{1.5,1.0},26,{0.00105661735841328039519614926347,-0.00158490300233362046661766331233},1.1e-33,1.6e-33},
+{0.056,{1.5,1.0},28,{0.000982467059107920508350673076703,-0.0014736820741487939323961369114},9.8e-34,1.5e-33},
+{0.056,{1.5,1.0},30,{0.000918041694065812538283936231881,-0.00137704743754817652350581468213},9.2e-34,1.4e-33},
+{0.056,{1.5,1.0},33,{0.000835827616389012672789426214705,-0.00125373002828738512761042832588},8.4e-34,1.3e-33},
+{0.056,{1.5,1.0},36,{0.000767128483082824876645343147307,-0.00115068391498462102228641432235},7.7e-34,1.2e-33},
+{0.056,{1.5,1.0},39,{0.000708864858320037277749223146462,-0.00106329033727692182003573746687},7.1e-34,1.1e-33},
+{0.056,{1.5,1.0},42,{0.000658826819791535313178076942649,-0.00098823465033431658983166105012},6.6e-34,9.9e-34},
+{0.056,{1.5,1.0},46,{0.000602153049603486705753517427935,-0.000903225314970875161420622356266},6.0e-34,9.0e-34},
+{0.056,{1.5,1.0},50,{0.000554457406503016222892478275077,-0.000831682784645403580133159798254},5.5e-34,8.3e-34},
+{0.056,{1.5,1.0},55,{0.000504505981687233567094576670028,-0.000756756467739226626388784197691},5.0e-34,7.6e-34},
+{0.056,{1.5,1.0},60,{0.00046281105766991575900012827487,-0.000694214652925753526297069776412},4.6e-34,6.9e-34},
+{0.099,{0.75,0.0},0,{0.00550293865828018182825188551979,-0.0739774041475056580702803184362},5.5e-33,7.4e-32},
+{0.099,{0.75,0.0},1,{0.00000337337347922681535740278610985,-0.0248044504496923732917300770433},3.4e-36,2.5e-32},
+{0.099,{0.75,0.0},2,{7.44139182885322038375531110977e-10,-0.0148578113501430668430935730527},7.4e-40,1.5e-32},
+{0.099,{0.75,0.0},3,{8.37388564587986073262381901727e-14,-0.0106097431767543348996792666261},8.4e-44,1.1e-32},
+{0.099,{0.75,0.0},4,{5.70011077436343991002134067804e-18,-0.00825118167125720730583886230624},5.7e-48,8.3e-33},
+{0.099,{0.75,0.0},5,{2.59731324120634696594855545924e-22,-0.00675063622281735647109137665545},2.6e-52,6.8e-33},
+{0.099,{0.75,0.0},6,{8.47334908167335398504483335319e-27,-0.00571192017636048662554321082192},8.5e-57,5.7e-33},
+{0.099,{0.75,0.0},7,{2.07627213669541111951650633626e-31,-0.00495024698478867518608707526642},2.1e-61,5.0e-33},
+{0.099,{0.75,0.0},8,{3.96090270614170264861648732166e-36,-0.00436781604528041722265278340991},4.0e-66,4.4e-33},
+{0.099,{0.75,0.0},9,{6.04911568946225163169344852063e-41,-0.00390801543992793609397898023005},6.0e-71,3.9e-33},
+{0.099,{0.75,0.0},10,{7.56233881959418886763624690917e-46,-0.00353580350023347613956134445817},7.6e-76,3.5e-33},
+{0.099,{0.75,0.0},11,{7.88136976374356144214294572678e-51,-0.00322832867214715529506546875688},7.9e-81,3.2e-33},
+{0.099,{0.75,0.0},12,{6.95219101927669338421719886365e-56,-0.00297005273507348627539707914744},7.0e-86,3.0e-33},
+{0.099,{0.75,0.0},13,{5.2576684964652563834991030067e-61,-0.00275004182420294183524232943229},5.3e-91,2.8e-33},
+{0.099,{0.75,0.0},15,{1.97728674858496327836594878994e-71,-0.00239518888678026318088970967663},2.0e-101,2.4e-33},
+{0.099,{0.75,0.0},16,{1.00101097256876208770106516089e-76,-0.00225002286558862528136989640744},1.0e-106,2.3e-33},
+{0.099,{0.75,0.0},17,{4.50504738221531554251563263252e-82,-0.00212144772905068784412904710993},4.5e-112,2.1e-33},
+{0.099,{0.75,0.0},19,{6.57595520417735134750887371886e-93,-0.00190385999186617222335619952533},6.6e-123,1.9e-33},
+{0.099,{0.75,0.0},20,{2.1566852335824776161129229354e-98,-0.00181098751687702708872778731338},2.2e-128,1.8e-33},
+{0.099,{0.75,0.0},22,{1.7507147748082720998167323426e-109,-0.00165000900210590152960550368422},1.8e-139,1.7e-33},
+{0.099,{0.75,0.0},24,{1.00326889658381749111349383423e-120,-0.0015153130928580678009601577218},1.0e-150,1.5e-33},
+{0.099,{0.75,0.0},26,{4.17363536137429173720225456119e-132,-0.00140094890320269923691111837507},4.2e-162,1.4e-33},
+{0.099,{0.75,0.0},28,{1.29070857782057762320549494979e-143,-0.00130263600515756752918945180996},1.3e-173,1.3e-33},
+{0.099,{0.75,0.0},30,{3.02867666561236205516260565724e-155,-0.00121721672551650552986278792413},3.0e-185,1.2e-33},
+{0.099,{0.75,0.0},33,{6.74182610929666566604115359357e-173,-0.00110821167970451560717064459685},6.7e-203,1.1e-33},
+{0.099,{0.75,0.0},36,{8.83280151634114196291058361969e-191,-0.0010171253937676501695794578849},8.8e-221,1.0e-33},
+{0.099,{0.75,0.0},39,{7.11084847547020094003111946172e-209,-0.000939875079287868500859765677225},7.1e-239,9.4e-34},
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+{10000.0,{1.5,1.0},2135,{0.0,0.0},0.0,0.0},
+{10000.0,{1.5,1.0},2735,{0.0,0.0},0.0,0.0},
+{10000.0,{1.5,1.0},3502,{0.0,0.0},0.0,0.0},
+{10000.0,{1.5,1.0},4485,{0.0,0.0},0.0,0.0},
+{10000.0,{1.5,1.0},5743,{0.0,0.0},0.0,0.0},
+{10000.0,{1.5,1.0},7355,{0.0,0.0},0.0,0.0},
+{10000.0,{1.5,1.0},9418,{0.0,0.0},0.0,0.0},
+{10000.0,{1.5,1.0},12061,{0.0,0.0},0.0,0.0},
+{10000.0,{1.5,1.0},15445,{0.0,0.0},0.0,0.0},
+{10000.0,{1.5,1.0},19779,{0.0,0.0},0.0,0.0},
+{10000.0,{1.5,1.0},25328,{0.277345934887828485556071125317,-0.243106153493052192669182927622},2.8e-31,2.4e-31},
+{10000.0,{1.5,1.0},32435,{0.195665458369767972725970974875,-0.212368086031483371706217406145},2.0e-31,2.1e-31},
+{10000.0,{1.5,1.0},41535,{0.140585040293343329766373111095,-0.173612689153450829830788733899},1.4e-31,1.7e-31},
+{10000.0,{1.5,1.0},53189,{0.103651282046794513933322689184,-0.138274741276041716742578070928},1.0e-31,1.4e-31},
+{10000.0,{1.5,1.0},68113,{0.0779920871093564571648703868784,-0.108974277914943798425668405786},7.8e-32,1.1e-31},
+{10000.0,{1.5,1.0},87224,{0.059501510872494988476224641693,-0.0854905571853734203738529569186},6.0e-32,8.5e-32},
+{10000.0,{1.5,1.0},111697,{0.0457990130543050932882399315697,-0.0669234561808983815741859108289},4.6e-32,6.7e-32},
+{10000.0,{1.5,1.0},143037,{0.0354481956071842617748279540635,-0.0523318121178128274264411005636},3.5e-32,5.2e-32},
+{10000.0,{1.5,1.0},183169,{0.0275313657782697754328341939654,-0.0408982121948080775303861806721},2.8e-32,4.1e-32},
+{10000.0,{10.0,10.0},0,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},1,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},2,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},3,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},4,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},5,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},7,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},10,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},13,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},18,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},24,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},32,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},42,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},57,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},76,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},102,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},136,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},181,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},242,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},324,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},433,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},578,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},772,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},1031,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},1376,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},1838,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},2454,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},3277,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},4376,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},5843,{0.0,0.0},0.0,0.0},
+{10000.0,{10.0,10.0},250572,{0.222382896036709206626693823127,-0.162554943791400307795315318207},2.2e-31,1.6e-31},
+{10000.0,{10.0,10.0},334572,{0.160786724088392140240939433513,-0.134605309522324663364972228784},1.6e-31,1.3e-31},
+{10000.0,{10.0,10.0},446731,{0.117078944798352978034273437456,-0.105932224219006195661765125529},1.2e-31,1.1e-31},
+{10000.0,{10.0,10.0},596490,{0.0860758113210653586757686022167,-0.0813732654502762323578212004733},8.6e-32,8.1e-32},
+{10000.0,{10.0,10.0},796452,{0.0637440528693559213367832630809,-0.0617659418546109998933049171477},6.4e-32,6.2e-32},
+{10000.0,{10.0,10.0},1063448,{0.0474269960234450747354171488127,-0.0465956808007587323764291139162},4.7e-32,4.7e-32},
+{10000.0,{10.0,10.0},1419949,{0.0353858530237609572815286237325,-0.0350365884022086293707572993023},3.5e-32,3.5e-32},
+};
+
 // complex(z), n, complex(f(n,z)), abs_err_real, abs_err_imag
 std::vector< std::tuple< std::complex<double>, int, std::complex<double>, double, double > >
 psi_test_16digits
@@ -2193,6 +3112,927 @@ psi_test_16digits
 {{10000.0,0.0},141995,{5.82392981843591e-144773,0.0},5.8e-144789,0.0},
 };
 
+// x, complex(m), n, complex(f(n,z)), abs_err_real, abs_err_imag
+std::vector< std::tuple< nmie::FloatType, std::complex<nmie::FloatType>, int, std::complex<nmie::FloatType>, nmie::FloatType, nmie::FloatType > >
+psi_test_30digits
+= {
+{0.055,{1.5,1.0},0,{0.0825311170780080312892651809573,0.0548405732968954810870306799325},8.3e-32,5.5e-32},
+{0.055,{1.5,1.0},1,{0.00126268421130933995304596085296,0.00302271191762463847647884534162},1.3e-33,3.0e-33},
+{0.055,{1.5,1.0},2,{-0.0000124334205761699290226082963091,0.0000637679360155862417353143522742},1.2e-35,6.4e-35},
+{0.055,{1.5,1.0},3,{-0.000000647703579791751608145249863954,0.000000653805439677373187723182029488},6.5e-37,6.5e-37},
+{0.055,{1.5,1.0},4,{-0.00000000993332632953711144960223696233,0.0000000020341950693091911760553190919},9.9e-39,2.0e-39},
+{0.055,{1.5,1.0},5,{-8.46709773017288345114068960426e-11,-3.4416452153137803366978290006e-11},8.5e-41,3.4e-41},
+{0.055,{1.5,1.0},6,{-3.91707738645789418602057352504e-13,-5.76664877060132305198412906976e-13},3.9e-43,5.8e-43},
+{0.055,{1.5,1.0},7,{-3.97912759969868839356470494039e-17,-4.60798827376311997167420920934e-15},4.0e-47,4.6e-45},
+{0.055,{1.5,1.0},8,{1.47158968159670570772308169021e-17,-2.24908823314492275171711725752e-17},1.5e-47,2.2e-47},
+{0.055,{1.5,1.0},9,{1.29005633479682131316404515238e-19,-5.50567174130185399938004711516e-20},1.3e-49,5.5e-50},
+{0.055,{1.5,1.0},10,{6.51006822249119330412370004443e-22,1.21590833905084527820310350327e-22},6.5e-52,1.2e-52},
+{0.055,{1.5,1.0},11,{2.04435446631059809155467468941e-24,1.99294185018579900330159629608e-24},2.0e-54,2.0e-54},
+{0.055,{1.5,1.0},12,{2.36176200800516566071776418799e-27,1.10743817200008965990446838351e-26},2.4e-57,1.1e-56},
+{0.055,{1.5,1.0},13,{-1.53429527456313978453024100532e-29,3.86493940862047892095171619461e-29},1.5e-59,3.9e-59},
+{0.055,{1.5,1.0},14,{-1.16949938269459754319346635004e-31,8.08513184975537307574530258098e-32},1.2e-61,8.1e-62},
+{0.055,{1.5,1.0},15,{-4.5468537526576826648994238683e-34,7.6730003585566940774264937443e-36},4.5e-64,7.7e-66},
+{0.055,{1.5,1.0},17,{-1.54879803202650070574510205164e-39,-3.54745300130512588984488141189e-39},1.5e-69,3.5e-69},
+{0.055,{1.5,1.0},18,{1.81990892366820971078864653937e-42,-1.02121440809976691751215267448e-41},1.8e-72,1.0e-71},
+{0.055,{1.5,1.0},20,{6.22623053621098531819906825338e-47,-1.38198989828541211207467377461e-47},6.2e-77,1.4e-77},
+{0.055,{1.5,1.0},22,{1.86481483486308184696542289301e-52,2.65002112423992846072024713427e-52},1.9e-82,2.7e-82},
+{0.055,{1.5,1.0},23,{1.72229992942004525421356860507e-56,6.8338748493664745042578556476e-55},1.7e-86,6.8e-85},
+{0.055,{1.5,1.0},26,{-4.96041593484841360314566375531e-63,-8.41404735686996104262974410211e-64},5.0e-93,8.4e-94},
+{0.055,{1.5,1.0},28,{-3.54723480518696691016420247861e-69,-1.53740066315552363156686038651e-68},3.5e-99,1.5e-98},
+{0.055,{1.5,1.0},30,{3.50394071117644481320819443847e-74,-2.50968842527858021477568111329e-74},3.5e-104,2.5e-104},
+{0.055,{1.5,1.0},33,{6.36032505134981474316700724327e-83,1.39297314586047552593257014925e-82},6.4e-113,1.4e-112},
+{0.055,{1.5,1.0},36,{-4.05911431197094384863265570792e-91,9.72332069473400053682118184457e-92},4.1e-121,9.7e-122},
+{0.055,{1.5,1.0},39,{-3.73538527968843981096290261364e-101,-8.91046884134946672831156162069e-100},3.7e-131,8.9e-130},
+{0.055,{1.5,1.0},42,{1.50391201155616186732214596994e-108,2.29322782120967910726719014186e-109},1.5e-138,2.3e-139},
+{0.055,{1.5,1.0},46,{-1.80213094172261770420391085666e-120,1.33689577220321214590476743624e-120},1.8e-150,1.3e-150},
+{0.055,{1.5,1.0},50,{3.35346875882393130828669222821e-133,-2.32976146369016274720428260132e-132},3.4e-163,2.3e-162},
+{0.055,{1.5,1.0},55,{9.43851734854840339995929825014e-149,1.60835073152661070797134796135e-147},9.4e-179,1.6e-177},
+{0.055,{1.5,1.0},60,{-1.81443081069616772806423693528e-163,-6.81530518706186733517613153632e-163},1.8e-193,6.8e-193},
+{0.056,{1.5,1.0},0,{0.0840328423903315659662440184128,0.0558317188480844497258551047454},8.4e-32,5.6e-32},
+{0.056,{1.5,1.0},1,{0.00130910363469871996421977118469,0.00313354090123170772169713111306},1.3e-33,3.1e-33},
+{0.056,{1.5,1.0},2,{-0.0000131222813240769328354268179024,0.0000673094565667857410557548958753},1.3e-35,6.7e-35},
+{0.056,{1.5,1.0},3,{-0.000000696091273710574038049508269641,0.000000702674984103938167131571427086},7.0e-37,7.0e-37},
+{0.056,{1.5,1.0},4,{-0.0000000108696936893321623689889196812,0.00000000222612038661620373992759663306},1.1e-38,2.2e-39},
+{0.056,{1.5,1.0},5,{-9.43379731532054779754995829294e-11,-3.83444154315088352921321567713e-11},9.4e-41,3.8e-41},
+{0.056,{1.5,1.0},6,{-4.44369868318811281392641981972e-13,-6.54177465849479431361328136137e-13},4.4e-43,6.5e-43},
+{0.056,{1.5,1.0},7,{-4.60130585472709497820059664427e-17,-5.32245816315511139285910252833e-15},4.6e-47,5.3e-45},
+{0.056,{1.5,1.0},8,{1.73064251834392883470799393061e-17,-2.64505943718988177911901859484e-17},1.7e-47,2.6e-47},
+{0.056,{1.5,1.0},9,{1.54475335303644289177896021458e-19,-6.59280640520993151211523640924e-20},1.5e-49,6.6e-50},
+{0.056,{1.5,1.0},10,{7.93713066070192854905165395313e-22,1.48238634686058592016803596229e-22},7.9e-52,1.5e-52},
+{0.056,{1.5,1.0},11,{2.53782612661940378301960288097e-24,2.47397043335740423390244222662e-24},2.5e-54,2.5e-54},
+{0.056,{1.5,1.0},12,{2.98522425619945710092669594202e-27,1.3997394074150072116132099887e-26},3.0e-57,1.4e-56},
+{0.056,{1.5,1.0},13,{-1.97449642859578105171941459281e-29,4.9739036229155283197043786985e-29},2.0e-59,5.0e-59},
+{0.056,{1.5,1.0},14,{-1.53241881317977993622653533183e-31,1.05942342509496200401832474169e-31},1.5e-61,1.1e-61},
+{0.056,{1.5,1.0},15,{-6.06618199623059356881228873374e-34,1.02399900274212895376781282636e-35},6.1e-64,1.0e-65},
+{0.056,{1.5,1.0},17,{-2.14217292203598815879255521622e-39,-4.90649158180664192844730059549e-39},2.1e-69,4.9e-69},
+{0.056,{1.5,1.0},18,{2.56283053923266665755664674374e-42,-1.43812919934192499115947977034e-41},2.6e-72,1.4e-71},
+{0.056,{1.5,1.0},20,{9.08983941615394400913248025749e-47,-2.01764070854641930209573551069e-47},9.1e-77,2.0e-77},
+{0.056,{1.5,1.0},22,{2.82240948831153470509541966483e-52,4.01079416955988466690942923236e-52},2.8e-82,4.0e-82},
+{0.056,{1.5,1.0},23,{2.65445165474795993525910774968e-56,1.05311177667497575537722877865e-54},2.7e-86,1.1e-84},
+{0.056,{1.5,1.0},26,{-8.06866866862567890538150604915e-63,-1.36861333159002574451767434683e-63},8.1e-93,1.4e-93},
+{0.056,{1.5,1.0},28,{-5.98176746175390750164740573489e-69,-2.59251369041811215732004123361e-68},6.0e-99,2.6e-98},
+{0.056,{1.5,1.0},30,{6.12549107700062088044623051015e-74,-4.38739155353626768375930717409e-74},6.1e-104,4.4e-104},
+{0.056,{1.5,1.0},33,{1.17366092357965392088569784806e-82,2.57041533950405041548387274964e-82},1.2e-112,2.6e-112},
+{0.056,{1.5,1.0},36,{-7.90620620693074150017284713609e-91,1.89389423034637031496084504652e-91},7.9e-121,1.9e-121},
+{0.056,{1.5,1.0},39,{-7.68015218929167511044057821643e-101,-1.83195012995029234084367984067e-99},7.7e-131,1.8e-129},
+{0.056,{1.5,1.0},42,{3.26371119703446662199562191907e-108,4.97657917508316356088989405328e-109},3.3e-138,5.0e-139},
+{0.056,{1.5,1.0},46,{-4.20316389233693496072394399396e-120,3.11809341319137224301848770599e-120},4.2e-150,3.1e-150},
+{0.056,{1.5,1.0},50,{8.40584365479923058111213491639e-133,-5.8398740277192284504255625328e-132},8.4e-163,5.8e-162},
+{0.056,{1.5,1.0},55,{2.5890075481703589274395776817e-148,4.41163280428085946545155422579e-147},2.6e-178,4.4e-177},
+{0.056,{1.5,1.0},60,{-5.44612949410553211167801604133e-163,-2.04564606554806672384187149721e-162},5.4e-193,2.0e-192},
+{0.099,{0.75,0.0},0,{0.0741817946552938406884704613341,0.0},7.4e-32,0.0},
+{0.099,{0.75,0.0},1,{0.00183667457085538573571884902642,0.0},1.8e-33,0.0},
+{0.099,{0.75,0.0},2,{0.0000272789146207344920890952887983,0.0},2.7e-35,0.0},
+{0.099,{0.75,0.0},3,{0.000000289376668822485769049209160644,0.0},2.9e-37,0.0},
+{0.099,{0.75,0.0},4,{0.00000000238749047628748456752769331287,0.0},2.4e-39,0.0},
+{0.099,{0.75,0.0},5,{1.61161820578148935415439472793e-11,0.0},1.6e-41,0.0},
+{0.099,{0.75,0.0},6,{9.20507962033645528914692491113e-14,0.0},9.2e-44,0.0},
+{0.099,{0.75,0.0},7,{4.55661292704944504540780566394e-16,0.0},4.6e-46,0.0},
+{0.099,{0.75,0.0},8,{1.99020167474095515308753397792e-18,0.0},2.0e-48,0.0},
+{0.099,{0.75,0.0},9,{7.77760611593454996795380281119e-21,0.0},7.8e-51,0.0},
+{0.099,{0.75,0.0},10,{2.74997069431552104088289847461e-23,0.0},2.7e-53,0.0},
+{0.099,{0.75,0.0},11,{8.87770790448951493443897342699e-26,0.0},8.9e-56,0.0},
+{0.099,{0.75,0.0},12,{2.63670078303866200831930046739e-28,0.0},2.6e-58,0.0},
+{0.099,{0.75,0.0},13,{7.2509782074319161364847057882e-31,0.0},7.3e-61,0.0},
+{0.099,{0.75,0.0},15,{4.44666925752856424243608947831e-36,0.0},4.4e-66,0.0},
+{0.099,{0.75,0.0},16,{1.00050535859072843233694360691e-38,0.0},1.0e-68,0.0},
+{0.099,{0.75,0.0},17,{2.12250968954568392154412956611e-41,0.0},2.1e-71,0.0},
+{0.099,{0.75,0.0},19,{8.10922635285102357310327154539e-47,0.0},8.1e-77,0.0},
+{0.099,{0.75,0.0},20,{1.46856570625303572629146491067e-49,0.0},1.5e-79,0.0},
+{0.099,{0.75,0.0},22,{4.18415436475313623175878953332e-55,0.0},4.2e-85,0.0},
+{0.099,{0.75,0.0},24,{1.0016331147599990821269389609e-60,0.0},1.0e-90,0.0},
+{0.099,{0.75,0.0},26,{2.0429477138131293195610717206e-66,0.0},2.0e-96,0.0},
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+{10000.0,{1.5,1.0},180,{9.22334007551021806661808924158e+4341,-2.50299449138820246650640842402e+4342},9.2e+4311,2.5e+4312},
+{10000.0,{1.5,1.0},230,{2.35073959180906846199236744355e+4341,1.93021018043166466383333916948e+4342},2.4e+4311,1.9e+4312},
+{10000.0,{1.5,1.0},295,{-7.05058411869313088529751400316e+4341,9.07354279540849867309969528447e+4341},7.1e+4311,9.1e+4311},
+{10000.0,{1.5,1.0},378,{3.9250520999793221199717789307e+4341,-2.86423450346929216173390692111e+4341},3.9e+4311,2.9e+4311},
+{10000.0,{1.5,1.0},484,{1.09524213069910333747368035171e+4341,4.6324369702825066804040645777e+4340},1.1e+4311,4.6e+4310},
+{10000.0,{1.5,1.0},620,{-1.17412287189976397564229136265e+4340,-8.6754653533798871776153650401e+4338},1.2e+4310,8.7e+4308},
+{10000.0,{1.5,1.0},794,{2.07729622988199079509074854491e+4338,1.66387482645688444013550820637e+4338},2.1e+4308,1.7e+4308},
+{10000.0,{1.5,1.0},1017,{-3.70385752159700164286823501828e+4335,3.77471588001700364458257093593e+4335},3.7e+4305,3.8e+4305},
+{10000.0,{1.5,1.0},1302,{6.71931700720811773554372673728e+4330,1.87946639915550009349472808406e+4331},6.7e+4300,1.9e+4301},
+{10000.0,{1.5,1.0},1667,{-1.07604327397187472541608700573e+4324,2.41966698513322562617944700711e+4323},1.1e+4294,2.4e+4293},
+{10000.0,{1.5,1.0},2135,{1.17170873863317889006375159871e+4312,-5.45679990742642822317089379607e+4311},1.2e+4282,5.5e+4281},
+{10000.0,{1.5,1.0},2735,{8.5376246674968482980580026575e+4291,2.8803357852509110865835496142e+4292},8.5e+4261,2.9e+4262},
+{10000.0,{1.5,1.0},3502,{-1.37083508784014072284336526457e+4260,9.58474222787520314266034460019e+4259},1.4e+4230,9.6e+4229},
+{10000.0,{1.5,1.0},4485,{-6.81457655415724249244671087136e+4206,6.88635325343707150122342940534e+4206},6.8e+4176,6.9e+4176},
+{10000.0,{1.5,1.0},5743,{2.01427265434223894247908151277e+4118,-8.19729734347461319796920582279e+4118},2.0e+4088,8.2e+4088},
+{10000.0,{1.5,1.0},7355,{1.33440322517496780186707910333e+3971,-1.68421041894792346100124151269e+3972},1.3e+3941,1.7e+3942},
+{10000.0,{1.5,1.0},9418,{7.66221463402341105464782971674e+3725,3.74234723647802651875935590925e+3725},7.7e+3695,3.7e+3695},
+{10000.0,{1.5,1.0},12061,{1.35091163983511561385223695588e+3306,-2.68931777392158932376665246059e+3306},1.4e+3276,2.7e+3276},
+{10000.0,{1.5,1.0},15445,{3.11359958256400926554378066189e+2581,3.04532304876841172538001087552e+2581},3.1e+2551,3.0e+2551},
+{10000.0,{1.5,1.0},19779,{-1.33555818662353611088478660456e+1321,1.51574972470886664617377412166e+1321},1.3e+1291,1.5e+1291},
+{10000.0,{1.5,1.0},25328,{-6.96057863067652413950074100608e-827,-2.49850927819121603448389242713e-827},7.0e-857,2.5e-857},
+{10000.0,{1.5,1.0},32435,{-2.46669895101122253192948014725e-4337,2.2844633577207462749474980418e-4337},2.5e-4367,2.3e-4367},
+{10000.0,{1.5,1.0},41535,{-6.55568918737239678667295419182e-9834,-3.29177720570342005305990111648e-9833},6.6e-9864,3.3e-9863},
+{10000.0,{1.5,1.0},53189,{3.68192276097978882685411828322e-18154,-3.73429009194196714533867248738e-18154},3.7e-18184,3.7e-18184},
+{10000.0,{1.5,1.0},68113,{1.53919938368073282963218732623e-30441,-6.08693007184102846575788324295e-30442},1.5e-30471,6.1e-30472},
+{10000.0,{1.5,1.0},87224,{-6.95934283983957949024675007376e-48254,3.98837520962280477226884035182e-48254},7.0e-48284,4.0e-48284},
+{10000.0,{1.5,1.0},111697,{1.10053067842262000495824674353e-73712,-2.74592721412831150461186289905e-73713},1.1e-73742,2.7e-73743},
+{10000.0,{1.5,1.0},143037,{-1.17854222533732387879114953056e-109697,6.27185349758468938911426406908e-109698},1.2e-109727,6.3e-109728},
+{10000.0,{1.5,1.0},183169,{-5.9484003076508545485616262537e-160101,1.28210604527768848864512627837e-160101},5.9e-160131,1.3e-160131},
+{10000.0,{10.0,10.0},0,{5.01674207236672167311413685597e+43427,-1.40243468104134857858518636024e+43429},5.0e+43397,1.4e+43399},
+{10000.0,{10.0,10.0},1,{1.40242791970504699017837709002e+43429,5.01601577131583916521647869211e+43427},1.4e+43399,5.0e+43397},
+{10000.0,{10.0,10.0},2,{-5.01456319025059436504139104316e+43427,1.40241439702491870025620846706e+43429},5.0e+43397,1.4e+43399},
+{10000.0,{10.0,10.0},3,{-1.40239411298591892985946194515e+43429,-5.01238437124352060360671213617e+43427},1.4e+43399,5.0e+43397},
+{10000.0,{10.0,10.0},4,{5.00947937740215012556575669143e+43427,-1.40236706756549412832587464824e+43429},5.0e+43397,1.4e+43399},
+{10000.0,{10.0,10.0},5,{1.40233326073359831359124378538e+43429,5.0058482928674927832735952412e+43427},1.4e+43399,5.0e+43397},
+{10000.0,{10.0,10.0},7,{-1.40224536267788371493045848727e+43429,-4.99640829343706735620410949954e+43427},1.4e+43399,5.0e+43397},
+{10000.0,{10.0,10.0},10,{-4.97680592677550253925911421938e+43427,1.40206280382917661652948391141e+43429},5.0e+43397,1.4e+43399},
+{10000.0,{10.0,10.0},13,{1.40181938920973733274804940157e+43429,4.95067738752561725466751936316e+43427},1.4e+43399,5.0e+43397},
+{10000.0,{10.0,10.0},18,{-4.89264648708855188156413966096e+43427,1.401278456370076250217694462e+43429},4.9e+43397,1.4e+43399},
+{10000.0,{10.0,10.0},24,{4.79916610296839723491278649246e+43427,-1.4004061692617299942256373598e+43429},4.8e+43397,1.4e+43399},
+{10000.0,{10.0,10.0},32,{4.63422988401822727787438375846e+43427,-1.39886435532010103063293494136e+43429},4.6e+43397,1.4e+43399},
+{10000.0,{10.0,10.0},42,{-4.36374382137911967690591001579e+43427,1.39632821709165007417405023933e+43429},4.4e+43397,1.4e+43399},
+{10000.0,{10.0,10.0},57,{1.39125503888856165390601104716e+43429,3.82571531146901550537297018175e+43427},1.4e+43399,3.8e+43397},
+{10000.0,{10.0,10.0},76,{2.92145122592813007060609343959e+43427,-1.38264178050642562517973943955e+43429},2.9e+43397,1.4e+43399},
+{10000.0,{10.0,10.0},102,{-1.29739478651930248580493024297e+43427,1.36689143608139523288768202576e+43429},1.3e+43397,1.4e+43399},
+{10000.0,{10.0,10.0},136,{-1.44978190342442896295029582825e+43427,-1.339385060841607306428952149e+43429},1.4e+43397,1.3e+43399},
+{10000.0,{10.0,10.0},181,{1.29098829333384416315707214223e+43429,-6.02023245835283830647149705502e+43427},1.3e+43399,6.0e+43397},
+{10000.0,{10.0,10.0},242,{1.34509327059948899822028821666e+43428,1.2039791380600870881842086376e+43429},1.3e+43398,1.2e+43399},
+{10000.0,{10.0,10.0},324,{-2.43249046403215239778864193842e+43428,-1.05074117084120246639946868156e+43429},2.4e+43398,1.1e+43399},
+{10000.0,{10.0,10.0},433,{7.95908008645693780249488237835e+43428,-3.68929394154307260992302020461e+43428},8.0e+43398,3.7e+43398},
+{10000.0,{10.0,10.0},578,{4.3643533909869537202275201755e+43428,4.23108389696421803380923086857e+43428},4.4e+43398,4.2e+43398},
+{10000.0,{10.0,10.0},772,{-3.13601463226006386524932601748e+43428,-3.61156340064891326810095407773e+43427},3.1e+43398,3.6e+43397},
+{10000.0,{10.0,10.0},1031,{8.53144122579199622946399612629e+43427,4.8550014345854194240012207074e+43427},8.5e+43397,4.9e+43397},
+{10000.0,{10.0,10.0},1376,{1.23002975462447124061446184888e+43427,1.38742297030601924751922209897e+43425},1.2e+43397,1.4e+43395},
+{10000.0,{10.0,10.0},1838,{2.54178700161150015055714491289e+43425,-1.59495411233172923932545721488e+43425},2.5e+43395,1.6e+43395},
+{10000.0,{10.0,10.0},2454,{2.54566577340033352082363117978e+43422,-3.13132923790043604295858747379e+43422},2.5e+43392,3.1e+43392},
+{10000.0,{10.0,10.0},3277,{-3.48407534594162166924138612214e+43416,-3.02546969005546476429417980996e+43417},3.5e+43386,3.0e+43387},
+{10000.0,{10.0,10.0},4376,{1.47668207686661867708139746465e+43408,1.67975501457856455565087626779e+43408},1.5e+43378,1.7e+43378},
+{10000.0,{10.0,10.0},5843,{1.02824693185627227337186184006e+43392,-5.56068571005351497238543486328e+43391},1.0e+43362,5.6e+43361},
+{10000.0,{10.0,10.0},140546,{-2.1026190622110974023155781049e+20826,-2.52458426314043600043213403614e+20827},2.1e+20796,2.5e+20797},
+{10000.0,{10.0,10.0},187662,{3.13136092139898156574675100081e+2735,4.92287277092044184240916740022e+2735},3.1e+2705,4.9e+2705},
+{10000.0,{10.0,10.0},250572,{6.83562990873109978081338306593e-28516,-5.32228373981795069063488131892e-28516},6.8e-28546,5.3e-28546},
+{10000.0,{10.0,10.0},334572,{-8.20262999952290482792410419621e-80393,3.42800515477394145557795940956e-80392},8.2e-80423,3.4e-80422},
+{10000.0,{10.0,10.0},446731,{1.38320901487185083766271021448e-163563,-7.51169870117344480616752009843e-163564},1.4e-163593,7.5e-163594},
+{10000.0,{10.0,10.0},596490,{-3.67843655382789320433727785107e-293344,9.89083114225354327072893398005e-293345},3.7e-293374,9.9e-293375},
+{10000.0,{10.0,10.0},796452,{-8.02605403216878189390124251648e-491705,-9.43928194332799230074849574007e-491706},8.0e-491735,9.4e-491736},
+{10000.0,{10.0,10.0},1063448,{1.9204762397085456425327050839e-790072,-3.0675856365573334739379154689e-790072},1.9e-790102,3.1e-790102},
+{10000.0,{10.0,10.0},1419949,{-9.47695849439555580733573269139e-1233217,1.77549788736440499565063728204e-1233216},9.5e-1233247,1.8e-1233246},
+};
+
 // complex(z), n, complex(f(n,z)), abs_err_real, abs_err_imag
 std::vector< std::tuple< std::complex<double>, int, std::complex<double>, double, double > >
 xi_test_16digits
@@ -2646,3 +4486,922 @@ zeta_test_16digits
 {{10000.0,0.0},111461,{2.619912559375462e-101959,-1.71914792791431e+101957},2.6e-101975,1.7e+101941},
 {{10000.0,0.0},141995,{5.82392981843591e-144773,-6.061204591967546e+144770},5.8e-144789,6.1e+144754},
 };
+
+// x, complex(m), n, complex(f(n,z)), abs_err_real, abs_err_imag
+std::vector< std::tuple< nmie::FloatType, std::complex<nmie::FloatType>, int, std::complex<nmie::FloatType>, nmie::FloatType, nmie::FloatType > >
+zeta_test_30digits
+= {
+{0.055,{1.5,1.0},0,{0.077996477145475366750021798225,-0.9432659671849841469091734368},7.8e-32,9.4e-31},
+{0.055,{1.5,1.0},1,{-5.56576247888720007297429645477,-8.429859010980169560393557202},5.6e-30,8.4e-30},
+{0.055,{1.5,1.0},2,{-281.675245080965945350330473001,-117.865562635607535029863514925},2.8e-28,1.2e-28},
+{0.055,{1.5,1.0},3,{-15109.9148041520625357412697434,2942.04947097055059768725231562},1.5e-26,2.9e-27},
+{0.055,{1.5,1.0},4,{-772080.613688081565195754934405,764654.49814588158809953356991},7.7e-25,7.6e-25},
+{0.055,{1.5,1.0},5,{-19795786.8766709071668174866199,96621176.8213661512737687329067},2.0e-23,9.7e-23},
+{0.055,{1.5,1.0},6,{4119387250.23582903686011901505,10136315475.2692469847177826806},4.1e-21,1.0e-20},
+{0.055,{1.5,1.0},7,{1186594075832.18507381683672317,806091448835.3998295008393226},1.2e-18,8.1e-19},
+{0.055,{1.5,1.0},8,{217001410340051.367546579453785,1881592139426.66113912064675403},2.2e-16,1.9e-18},
+{0.055,{1.5,1.0},9,{31134606580981863.5452916492687,-20370279524878169.0459513146693},3.1e-14,2.0e-14},
+{0.055,{1.5,1.0},10,{2798669580885032811.10930391251,-6557263372488269357.6829785846},2.8e-12,6.6e-12},
+{0.055,{1.5,1.0},11,{-277202821456232019409.83607225,-1484320090878327842392.12444073},2.8e-10,1.5e-9},
+{0.055,{1.5,1.0},12,{-244494319958764353814115.761776,-250809544788705688603940.574607},2.4e-7,2.5e-7},
+{0.055,{1.5,1.0},13,{-86370495486248784233031529.6423,-18420892914076139726954125.3768},8.6e-5,1.8e-5},
+{0.055,{1.5,1.0},14,{-22351471174900357510138708041.9,8872738726236444735619844346.62},0.022,0.0089},
+{0.055,{1.5,1.0},15,{-3.99979935284610062874336592663e+30,5.78551100082799499246692002989e+30},4.0,5.8},
+{0.055,{1.5,1.0},17,{3.95638337545198404698046586439e+35,6.15719847729988447628195748994e+35},4.0e+5,6.2e+5},
+{0.055,{1.5,1.0},18,{2.36762036517516464989959877985e+38,1.03370949221185872181688223984e+38},2.4e+8,1.0e+8},
+{0.055,{1.5,1.0},20,{2.73706917510637278556239273379e+43,-2.62426756031628063447321190894e+43},2.7e+13,2.6e+13},
+{0.055,{1.5,1.0},22,{-2.45625509224584125850142340831e+48,-6.34066399873475561981810779871e+48},2.5e+18,6.3e+18},
+{0.055,{1.5,1.0},23,{-2.5237913622407625239569830097e+51,-1.77600338262179008284767002219e+51},2.5e+21,1.8e+21},
+{0.055,{1.5,1.0},26,{-1.51614951869393282323099451172e+59,3.39522091703191233660952675503e+59},1.5e+29,3.4e+29},
+{0.055,{1.5,1.0},28,{7.56358559847497012017862829848e+64,8.02146633165725447918071136421e+64},7.6e+34,8.0e+34},
+{0.055,{1.5,1.0},30,{3.5279494036500055065106102167e+70,-1.33293347544808101258082621391e+70},3.5e+40,1.3e+40},
+{0.055,{1.5,1.0},33,{-5.08806447519754230850248701132e+78,-8.21637755505253861660555298494e+78},5.1e+48,8.2e+48},
+{0.055,{1.5,1.0},36,{-2.38615703602365496318492414869e+87,2.21260662634900911535904458693e+87},2.4e+57,2.2e+57},
+{0.055,{1.5,1.0},39,{1.13724242489928153814280224328e+96,8.29010026381208111440247554692e+95},1.1e+66,8.3e+65},
+{0.055,{1.5,1.0},42,{3.24302514148797500450298156266e+104,-6.94826274510310898028654760666e+104},3.2e+74,6.9e+74},
+{0.055,{1.5,1.0},46,{-4.47219673503553206565332380083e+116,1.60482355153180424406926036323e+116},4.5e+86,1.6e+86},
+{0.055,{1.5,1.0},50,{3.76452126401926156503534158794e+128,1.79552402779734934108076071255e+128},3.8e+98,1.8e+98},
+{0.055,{1.5,1.0},55,{-4.42511666027576136763403566695e+143,-3.34046190786710459226335909149e+143},4.4e+113,3.3e+113},
+{0.055,{1.5,1.0},60,{7.68398173532865886328052602935e+158,8.71519397367156000979614925002e+158},7.7e+128,8.7e+128},
+{0.056,{1.5,1.0},0,{0.0793319162242378177090449021635,-0.94220523484458935050344782937},7.9e-32,9.4e-31},
+{0.056,{1.5,1.0},1,{-5.46532260027443893259070319269,-8.28064932551611607850144405721},5.5e-30,8.3e-30},
+{0.056,{1.5,1.0},2,{-271.705154321627113818601883027,-113.711389072843353262048138321},2.7e-28,1.1e-28},
+{0.056,{1.5,1.0},3,{-14315.1149124350009454067214633,2786.79907548930963051612989311},1.4e-26,2.8e-27},
+{0.056,{1.5,1.0},4,{-718415.729198108826255179563575,711471.92391480228147560498287},7.2e-25,7.1e-25},
+{0.056,{1.5,1.0},5,{-18092086.1430065134669912925227,88297282.0780278636366182934355},1.8e-23,8.8e-23},
+{0.056,{1.5,1.0},6,{3697150731.65611584397705133982,9097739637.19988408860372252379},3.7e-21,9.1e-21},
+{0.056,{1.5,1.0},7,{1045979930277.86142469698838654,710587325871.044135631258556411},1.0e-18,7.1e-19},
+{0.056,{1.5,1.0},8,{187871898010353.750972898424286,1631099391849.45770518882331637},1.9e-16,1.6e-18},
+{0.056,{1.5,1.0},9,{26474020442737092.6374605767241,-17320651420753632.5554375994909},2.6e-14,1.7e-14},
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