updated test D1 passes in double precision

tests/mpmath_special_functions_test_generator.py

@@ -88,6 +88,18 @@ class UpdateSpecialFunctionsEvaluations:
         n_set = set(n_list)
         return sorted(n_set)
 
+    def compose_result_string(self, mpf_x, mpf_m, n, mpf_value, output_dps):
+        return ('{'+
+                 mp.nstr(mpf_x, output_dps * 2) + ',{' +
+                 mp.nstr(mpf_m.real, output_dps * 2) + ',' +
+                 mp.nstr(mpf_m.imag, output_dps * 2) + '},' +
+                 str(n) + ',{' +
+                 mp.nstr(mpf_value.real, output_dps) + ',' +
+                 mp.nstr(mpf_value.imag, output_dps) + '},' +
+                 mp.nstr(mp.fabs(mpf_value.real * 10 ** -output_dps), 2) + ',' +
+                 mp.nstr(mp.fabs(mpf_value.imag * 10 ** -output_dps), 2) +
+                 '},')
+
     def get_test_data_nlist(self, z_record, output_dps, n, func):
         isNeedMoreDPS = False
         x = str(z_record[0])
@@ -95,28 +107,22 @@ class UpdateSpecialFunctionsEvaluations:
         mi = str(z_record[1][1])
         z_str = ''
         try:
-            z = mp.mpf(x) * mp.mpc(mr, mi)
+            mpf_x = mp.mpf(x)
+            mpf_m = mp.mpc(mr, mi)
+            z = mpf_x*mpf_m
             if self.is_only_x: z = mp.mpf(x)
-            D1nz = func(n, z)
-            z_str = ('{{' +
-                     mp.nstr(z.real, output_dps * 2) + ',' +
-                     mp.nstr(z.imag, output_dps * 2) + '},' +
-                     str(n) + ',{' +
-                     mp.nstr(D1nz.real, output_dps) + ',' +
-                     mp.nstr(D1nz.imag, output_dps) + '},' +
-                     mp.nstr(mp.fabs(D1nz.real * 10 ** -output_dps), 2) + ',' +
-                     mp.nstr(mp.fabs(D1nz.imag * 10 ** -output_dps), 2) +
-                     '},')
-            if mp.nstr(D1nz.real, output_dps) == '0.0' \
-                    or mp.nstr(D1nz.imag, output_dps) == '0.0':
+            mpf_value = func(n, z)
+            z_str = self.compose_result_string(mpf_x, mpf_m, n, mpf_value, output_dps)
+            if mp.nstr(mpf_value.real, output_dps) == '0.0' \
+                    or mp.nstr(mpf_value.imag, output_dps) == '0.0':
                 isNeedMoreDPS = True
         except:
             isNeedMoreDPS = True
         return z_str, isNeedMoreDPS
 
     def get_test_data(self, Du_test, output_dps, max_num_elements_of_n_list, func, funcname):
-        output_list = ['// 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 > >',
+        output_list = ['// 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 > >',
                        str(funcname) + '_test_' + str(output_dps) + 'digits', '= {']
         for z_record in Du_test:
             x = str(z_record[0])
@@ -129,9 +135,9 @@ class UpdateSpecialFunctionsEvaluations:
             print(z, n_list)
             failed_evaluations = 0
             for n in n_list:
-                mp.mp.dps = 20
+                mp.mp.dps = output_dps
                 old_z_string, isNeedMoreDPS = self.get_test_data_nlist(z_record, output_dps, n, func, )
-                mp.mp.dps = 37
+                mp.mp.dps = int(output_dps*1.41)
                 new_z_string, isNeedMoreDPS = self.get_test_data_nlist(z_record, output_dps, n, func)
                 while old_z_string != new_z_string \
                         or isNeedMoreDPS:
@@ -190,9 +196,9 @@ class UpdateSpecialFunctionsEvaluations:
 def main():
     sf_evals = UpdateSpecialFunctionsEvaluations(filename='test_spec_functions_data.hpp',
                                                  complex_arguments=mia.complex_arguments,
-                                                 output_dps=16, max_num_elements_of_nlist=51)
-    # output_dps=5, max_num_elements_of_nlist=3)
-    # sf_evals.run_test(mrb.D1, 'D1')
+                                                 output_dps=30, max_num_elements_of_nlist=51)
+                                                 # output_dps=5, max_num_elements_of_nlist=3)
+    sf_evals.run_test(mrb.D1, 'D1')
     # sf_evals.run_test(mrb.D2, 'D2')
     # sf_evals.run_test(mrb.D3, 'D3')
     # sf_evals.run_test(mrb.psi, 'psi', is_only_x=True)
@@ -207,23 +213,23 @@ def main():
     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 = 7
-        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 = 7
+    #     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))
 
 main()

tests/test_Riccati_Bessel_logarithmic_derivative.cc

@@ -61,11 +61,27 @@ void parse_mpmath_data(const double min_abs_tol, const std::tuple< std::complex<
   re_abs_tol *= std::abs(std::round(std::real(func_mp))) + 1;
   im_abs_tol *= std::abs(std::round(std::imag(func_mp))) + 1;
 }
+void parse2_mpmath_data(const nmie::FloatType min_abs_tol,
+                        const std::tuple< nmie::FloatType, std::complex<nmie::FloatType>, int, std::complex<nmie::FloatType>, nmie::FloatType, nmie::FloatType > data,
+                        nmie::FloatType &x, std::complex<nmie::FloatType> &m, int &n, std::complex<nmie::FloatType> &func_mp,
+                        nmie::FloatType &re_abs_tol, nmie::FloatType &im_abs_tol){
+  x = std::get<0>(data);
+  m = std::get<1>(data);
+  n = std::get<2>(data);
+  func_mp = std::get<3>(data);
+  re_abs_tol = ( std::get<4>(data) > min_abs_tol && std::real(func_mp) < min_abs_tol)
+               ? std::get<4>(data) : min_abs_tol;
+  im_abs_tol = ( std::get<5>(data) > min_abs_tol && std::imag(func_mp) < min_abs_tol)
+               ? std::get<5>(data) : min_abs_tol;
+  // if re(func_mp) < 0.5 then round will give 0. To avoid zero tolerance add one.
+  re_abs_tol *= std::abs(std::round(std::real(func_mp))) + 1;
+  im_abs_tol *= std::abs(std::round(std::imag(func_mp))) + 1;
+}
 
 template<class T> inline T pow2(const T value) {return value*value;}
 
-//TEST(zeta_psizeta_test, DISABLED_mpmath_generated_input) {
-TEST(zeta_psizeta_test, mpmath_generated_input) {
+TEST(zeta_psizeta_test, DISABLED_mpmath_generated_input) {
+//TEST(zeta_psizeta_test, mpmath_generated_input) {
   double min_abs_tol = 2e-10;
   std::complex<double> z, zeta_mp;
   int n;
@@ -126,7 +142,8 @@ TEST(zeta_test, DISABLED_mpmath_generated_input) {
 }
 
 
-TEST(psizeta_test, mpmath_generated_input) {
+TEST(psizeta_test, DISABLED_mpmath_generated_input) {
+//TEST(psizeta_test, mpmath_generated_input) {
   double min_abs_tol = 9e-11;
   std::complex<double> z, PsiZeta_mp;
   int n;
@@ -172,8 +189,8 @@ TEST(psi_test, mpmath_generated_input) {
 }
 
 
-//TEST(D3test, DISABLED_mpmath_generated_input) {
-TEST(D3test, mpmath_generated_input) {
+TEST(D3test, DISABLED_mpmath_generated_input) {
+//TEST(D3test, mpmath_generated_input) {
   double min_abs_tol = 2e-11;
   std::complex<double> z, D3_mp;
   int n;
@@ -196,15 +213,16 @@ TEST(D3test, mpmath_generated_input) {
 
 //TEST(D1test, DISABLED_mpmath_generated_input) {
   TEST(D1test, mpmath_generated_input) {
-  double min_abs_tol = 2e-11;
-  std::complex<double> z, D1_mp;
+  double min_abs_tol = 2e-11, x;
+  std::complex<double> m, z, D1_mp;
   int n;
   double re_abs_tol,  im_abs_tol;
-  for (const auto &data : D1_test_16digits) {
-    parse_mpmath_data(min_abs_tol, data, z, n, D1_mp, 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);
+    z = m*x;
     auto Nstop = LeRu_cutoff(z)+1;
-    std::vector<std::complex<nmie::FloatType>> Db(Nstop),Dold(Nstop+35), r;
-    int valid_digits = 6;
+    std::vector<std::complex<nmie::FloatType>> Db(Nstop),Dold(Nstop+135), r;
+    int valid_digits = 14;
     int nstar = nmie::getNStar(Nstop, z, valid_digits);
     r.resize(nstar);
     nmie::evalBackwardR(z,r);

tests/test_spec_functions_data.hpp

@@ -1,569 +1,574 @@
-// complex(z), n, complex(D1(n,z)), abs_err_real, abs_err_imag
-std::vector< std::tuple< std::complex<double>, int, std::complex<double>, double, double > >
-D1_test_16digits
+// 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 > >
+D1_test_30digits
 = {
-{{0.07425,0.0},0,{13.44325436668153,0.0},1.3e-15,0.0},
-{{0.07425,0.0},1,{26.92117459633998,0.0},2.7e-15,0.0},
-{{0.07425,0.0},2,{40.39343233283062,0.0},4.0e-15,0.0},
-{{0.07425,0.0},3,{53.8638034125887,0.0},5.4e-15,0.0},
-{{0.07425,0.0},4,{67.33331707981798,0.0},6.7e-15,0.0},
-{{0.07575,0.0},0,{13.17606046765979,0.0},1.3e-15,0.0},
-{{0.07575,0.0},1,{26.38748777963147,0.0},2.6e-15,0.0},
-{{0.07575,0.0},2,{39.59313798170167,0.0},4.0e-15,0.0},
-{{0.07575,0.0},3,{52.79686337350637,0.0},5.3e-15,0.0},
-{{0.07575,0.0},4,{65.99971402008605,0.0},6.6e-15,0.0},
-{{7.5,0.0},0,{0.3695472563090164,0.0},3.7e-17,0.0},
-{{7.5,0.0},1,{-4.366784043615744,0.0},4.4e-16,0.0},
-{{7.5,0.0},2,{-0.05084479598595977,0.0},5.1e-18,0.0},
-{{7.5,0.0},3,{1.818058207399475,0.0},1.8e-16,0.0},
-{{7.5,0.0},4,{-1.311710105034662,0.0},1.3e-16,0.0},
-{{7.5,0.0},5,{-0.1612017752951218,0.0},1.6e-17,0.0},
-{{7.5,0.0},6,{0.2403642873973738,0.0},2.4e-17,0.0},
-{{7.5,0.0},7,{0.509732566745001,0.0},5.1e-17,0.0},
-{{7.5,0.0},8,{0.7288779051967778,0.0},7.3e-17,0.0},
-{{7.5,0.0},9,{0.9225920223879098,0.0},9.2e-17,0.0},
-{{7.5,0.0},10,{1.101289075837662,0.0},1.1e-16,0.0},
-{{7.5,0.0},11,{1.270228055670032,0.0},1.3e-16,0.0},
-{{7.5,0.0},12,{1.432398653656861,0.0},1.4e-16,0.0},
-{{7.5,0.0},13,{1.589646926286713,0.0},1.6e-16,0.0},
-{{7.5,0.0},14,{1.743184380873933,0.0},1.7e-16,0.0},
-{{7.5,0.0},16,{2.042220854428171,0.0},2.0e-16,0.0},
-{{7.5,0.0},17,{2.188751725980377,0.0},2.2e-16,0.0},
-{{7.5,0.0},18,{2.33376648704411,0.0},2.3e-16,0.0},
-{{7.5,0.0},19,{2.477519013106746,0.0},2.5e-16,0.0},
-{{7.5,0.0},21,{2.761992897922038,0.0},2.8e-16,0.0},
-{{7.5,0.0},22,{2.90300061550683,0.0},2.9e-16,0.0},
-{{7.5,0.0},24,{3.183085123876985,0.0},3.2e-16,0.0},
-{{7.5,0.0},26,{3.461101068633011,0.0},3.5e-16,0.0},
-{{7.5,0.0},27,{3.599479435575162,0.0},3.6e-16,0.0},
-{{7.5,0.0},30,{4.012605389511785,0.0},4.0e-16,0.0},
-{{750.0,0.0},0,{-0.8951915139149222,0.0},9.0e-17,0.0},
-{{750.0,0.0},1,{1.114084720130935,0.0},1.1e-16,0.0},
-{{750.0,0.0},2,{-0.9024181120233614,0.0},9.0e-17,0.0},
-{{750.0,0.0},3,{1.099243620946342,0.0},1.1e-16,0.0},
-{{750.0,0.0},4,{-0.9194850798920686,0.0},9.2e-17,0.0},
-{{750.0,0.0},5,{1.073070000370522,0.0},1.1e-16,0.0},
-{{750.0,0.0},6,{-0.9469054237300034,0.0},9.5e-17,0.0},
-{{750.0,0.0},7,{1.036430596034115,0.0},1.0e-16,0.0},
-{{750.0,0.0},9,{0.990456172692469,0.0},9.9e-17,0.0},
-{{750.0,0.0},10,{-1.036746111869826,0.0},1.0e-16,0.0},
-{{750.0,0.0},11,{0.9364345757891685,0.0},9.4e-17,0.0},
-{{750.0,0.0},13,{0.875701892481254,0.0},8.8e-17,0.0},
-{{750.0,0.0},15,{0.8095451807506758,0.0},8.1e-17,0.0},
-{{750.0,0.0},18,{-1.422356478541503,0.0},1.4e-16,0.0},
-{{750.0,0.0},20,{-1.592210408225887,0.0},1.6e-16,0.0},
-{{750.0,0.0},23,{0.5110077375181897,0.0},5.1e-17,0.0},
-{{750.0,0.0},27,{0.3496666467211573,0.0},3.5e-17,0.0},
-{{750.0,0.0},31,{0.1809968576664919,0.0},1.8e-17,0.0},
-{{750.0,0.0},35,{0.0004860079342239934,0.0},4.9e-20,0.0},
-{{750.0,0.0},41,{-0.317251336807483,0.0},3.2e-17,0.0},
-{{750.0,0.0},47,{-0.7807372174284117,0.0},7.8e-17,0.0},
-{{750.0,0.0},54,{0.4580930397540441,0.0},4.6e-17,0.0},
-{{750.0,0.0},62,{-0.1958618028998245,0.0},2.0e-17,0.0},
-{{750.0,0.0},71,{0.6403656124320398,0.0},6.4e-17,0.0},
-{{750.0,0.0},81,{-0.4803642218027248,0.0},4.8e-17,0.0},
-{{750.0,0.0},93,{3.417692358670104,0.0},3.4e-16,0.0},
-{{750.0,0.0},107,{-0.6675908137518288,0.0},6.7e-17,0.0},
-{{750.0,0.0},123,{0.07336983052954298,0.0},7.3e-18,0.0},
-{{750.0,0.0},141,{0.01864087618833894,0.0},1.9e-18,0.0},
-{{750.0,0.0},162,{0.4662167115741941,0.0},4.7e-17,0.0},
-{{750.0,0.0},186,{1.869792416792102,0.0},1.9e-16,0.0},
-{{750.0,0.0},214,{-0.1962317049357189,0.0},2.0e-17,0.0},
-{{750.0,0.0},246,{-0.9241109217019534,0.0},9.2e-17,0.0},
-{{750.0,0.0},282,{-2.278752089160206,0.0},2.3e-16,0.0},
-{{750.0,0.0},324,{0.1492340462699953,0.0},1.5e-17,0.0},
-{{750.0,0.0},372,{-1.501050800107926,0.0},1.5e-16,0.0},
-{{750.0,0.0},427,{1.251448627689853,0.0},1.3e-16,0.0},
-{{750.0,0.0},490,{-2.307846776579645,0.0},2.3e-16,0.0},
-{{750.0,0.0},562,{-0.6678454189015009,0.0},6.7e-17,0.0},
-{{750.0,0.0},645,{4.123866493958505,0.0},4.1e-16,0.0},
-{{750.0,0.0},740,{-0.04954886515946186,0.0},5.0e-18,0.0},
-{{750.0,0.0},850,{0.5377162125402363,0.0},5.4e-17,0.0},
-{{133.0,-0.001},0,{0.5694948983815571,0.001324324427352377},5.7e-17,1.3e-19},
-{{133.0,-0.001},1,{-1.786944015800289,0.004193067842684484},1.8e-16,4.2e-19},
-{{133.0,-0.001},2,{0.5399040215866582,0.001291157104802603},5.4e-17,1.3e-19},
-{{133.0,-0.001},3,{-1.955480625798034,0.004823242927232421},2.0e-16,4.8e-19},
-{{133.0,-0.001},4,{0.4735591560334697,0.001223127495142088},4.7e-17,1.2e-19},
-{{133.0,-0.001},5,{-2.331337152694187,0.006433469776449445},2.3e-16,6.4e-19},
-{{133.0,-0.001},6,{0.3756798707528821,0.00113876079036902},3.8e-17,1.1e-19},
-{{133.0,-0.001},7,{-3.148105562806491,0.01090750730183105},3.1e-16,1.1e-18},
-{{133.0,-0.001},8,{0.2515418522954845,0.001059202692643652},2.5e-17,1.1e-19},
-{{133.0,-0.001},9,{-5.506034746297112,0.03131226964093978},5.5e-16,3.1e-18},
-{{133.0,-0.001},10,{0.1039785994199451,0.001004592673307026},1.0e-17,1.0e-19},
-{{133.0,-0.001},11,{-46.98874438931292,2.213832762775254},4.7e-15,2.2e-16},
-{{133.0,-0.001},13,{5.89811290505382,0.03577867985992821},5.9e-16,3.6e-18},
-{{133.0,-0.001},14,{-0.2778831807551624,0.001065347008820747},2.8e-17,1.1e-19},
-{{133.0,-0.001},16,{-0.5501021158428141,0.001287235517159257},5.5e-17,1.3e-19},
-{{133.0,-0.001},18,{-0.9604617468736273,0.001903153851503216},9.6e-17,1.9e-19},
-{{133.0,-0.001},20,{-1.781366135936702,0.004149533558522542},1.8e-16,4.1e-19},
-{{133.0,-0.001},22,{-5.364106315522472,0.02974587750840188},5.4e-16,3.0e-18},
-{{133.0,-0.001},24,{5.606849372659069,0.03240384877063995},5.6e-16,3.2e-18},
-{{133.0,-0.001},27,{-0.9371713952326589,0.001835552825885577},9.4e-17,1.8e-19},
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-{{3.1415926535897932384626433832795,-1.0},20,{5.996215350401408,1.955597365867593},6.0e-16,2.0e-16},
-{{3.1415926535897932384626433832795,3.1415926535897932384626433832795},0,{-2.772406603042443e-285,-1.003741873197321},2.8e-301,1.0e-16},
-{{3.1415926535897932384626433832795,3.1415926535897932384626433832795},1,{0.05631023432676338,-0.9842532929662963},5.6e-18,9.8e-17},
-{{3.1415926535897932384626433832795,3.1415926535897932384626433832795},2,{0.1932838439806838,-0.9820447865781992},1.9e-17,9.8e-17},
-{{3.1415926535897932384626433832795,3.1415926535897932384626433832795},3,{0.3699265824204035,-1.027128174680124},3.7e-17,1.0e-16},
-{{3.1415926535897932384626433832795,3.1415926535897932384626433832795},4,{0.5559869776590445,-1.10966762489327},5.6e-17,1.1e-16},
-{{3.1415926535897932384626433832795,3.1415926535897932384626433832795},5,{0.7410609869524249,-1.216012185642558},7.4e-17,1.2e-16},
-{{3.1415926535897932384626433832795,3.1415926535897932384626433832795},6,{0.9226942125877388,-1.337200280531054},9.2e-17,1.3e-16},
-{{3.1415926535897932384626433832795,3.1415926535897932384626433832795},7,{1.100802842322886,-1.467947433294319},1.1e-16,1.5e-16},
-{{3.1415926535897932384626433832795,3.1415926535897932384626433832795},8,{1.275880545379177,-1.605113981437066},1.3e-16,1.6e-16},
-{{3.1415926535897932384626433832795,3.1415926535897932384626433832795},9,{1.448479195149733,-1.746766652042906},1.4e-16,1.7e-16},
-{{3.1415926535897932384626433832795,3.1415926535897932384626433832795},10,{1.619076470209989,-1.891665842771343},1.6e-16,1.9e-16},
-{{3.1415926535897932384626433832795,3.1415926535897932384626433832795},11,{1.78805677376105,-2.03898576446601},1.8e-16,2.0e-16},
-{{3.1415926535897932384626433832795,3.1415926535897932384626433832795},12,{1.955722406219257,-2.188157203986427},2.0e-16,2.2e-16},
-{{3.1415926535897932384626433832795,3.1415926535897932384626433832795},13,{2.122310073438798,-2.338775902756937},2.1e-16,2.3e-16},
-{{3.1415926535897932384626433832795,3.1415926535897932384626433832795},14,{2.288005790801036,-2.490547179941639},2.3e-16,2.5e-16},
-{{3.1415926535897932384626433832795,3.1415926535897932384626433832795},15,{2.452956780753838,-2.643251296520418},2.5e-16,2.6e-16},
-{{3.1415926535897932384626433832795,3.1415926535897932384626433832795},16,{2.617280562926164,-2.796721106255066},2.6e-16,2.8e-16},
-{{3.1415926535897932384626433832795,3.1415926535897932384626433832795},17,{2.781071793755662,-2.950827224606459},2.8e-16,3.0e-16},
-{{3.1415926535897932384626433832795,3.1415926535897932384626433832795},18,{2.94440739842864,-3.105467935915553},2.9e-16,3.1e-16},
-{{3.1415926535897932384626433832795,3.1415926535897932384626433832795},20,{3.269953015162791,-3.416044503953443},3.3e-16,3.4e-16},
-{{3.1415926535897932384626433832795,3.1415926535897932384626433832795},21,{3.432258548223354,-3.571861569112058},3.4e-16,3.6e-16},
-{{3.1415926535897932384626433832795,3.1415926535897932384626433832795},22,{3.594303449441325,-3.72796937979865},3.6e-16,3.7e-16},
-{{6.2831853071795862319959269370884,-1.0},0,{-1.773439590975416e-16,1.313035285499331},1.8e-32,1.3e-16},
-{{6.2831853071795862319959269370884,-1.0},1,{-0.06304185943615409,0.7403873087787056},6.3e-18,7.4e-17},
-{{6.2831853071795862319959269370884,-1.0},2,{0.2949375696085568,1.070592030672524},2.9e-17,1.1e-16},
-{{6.2831853071795862319959269370884,-1.0},3,{-0.2986322034569661,0.9008011017614757},3.0e-17,9.0e-17},
-{{6.2831853071795862319959269370884,-1.0},4,{-0.003223801583153805,0.4398947553395593},3.2e-19,4.4e-17},
-{{6.2831853071795862319959269370884,-1.0},5,{0.3254847904858648,0.3236711082223025},3.3e-17,3.2e-17},
-{{6.2831853071795862319959269370884,-1.0},6,{0.5915216297442743,0.2927648081692745},5.9e-17,2.9e-17},
-{{6.2831853071795862319959269370884,-1.0},7,{0.8216613358485906,0.2889872711150469},8.2e-17,2.9e-17},
-{{6.2831853071795862319959269370884,-1.0},8,{1.031011238016646,0.2965575908077732},1.0e-16,3.0e-17},
-{{6.2831853071795862319959269370884,-1.0},9,{1.227344826394146,0.3098261586314655},1.2e-16,3.1e-17},
-{{6.2831853071795862319959269370884,-1.0},10,{1.414970410777237,0.3263361380815797},1.4e-16,3.3e-17},
-{{6.2831853071795862319959269370884,-1.0},11,{1.596461936103797,0.3448619156356228},1.6e-16,3.4e-17},
-{{6.2831853071795862319959269370884,-1.0},12,{1.773455192293614,0.36472724630896},1.8e-16,3.6e-17},
-{{6.2831853071795862319959269370884,-1.0},13,{1.947042664720708,0.3855292662286455},1.9e-16,3.9e-17},
-{{6.2831853071795862319959269370884,-1.0},14,{2.117983884070411,0.4070131164963634},2.1e-16,4.1e-17},
-{{6.2831853071795862319959269370884,-1.0},15,{2.28682458641427,0.4290096105470636},2.3e-16,4.3e-17},
-{{6.2831853071795862319959269370884,-1.0},16,{2.453967796322013,0.4514019204534639},2.5e-16,4.5e-17},
-{{6.2831853071795862319959269370884,-1.0},18,{2.784310371123592,0.4970627630731119},2.8e-16,5.0e-17},
-{{6.2831853071795862319959269370884,-1.0},19,{2.947928703075273,0.5202242302820364},2.9e-16,5.2e-17},
-{{6.2831853071795862319959269370884,-1.0},20,{3.110719695447307,0.5435558939596922},3.1e-16,5.4e-17},
-{{6.2831853071795862319959269370884,-1.0},22,{3.434270806979098,0.590625695740279},3.4e-16,5.9e-17},
-{{6.2831853071795862319959269370884,-1.0},23,{3.595206946808026,0.6143246109772049},3.6e-16,6.1e-17},
-{{6.2831853071795862319959269370884,-1.0},25,{3.915734156142959,0.6619787064788887},3.9e-16,6.6e-17},
-{{6.2831853071795862319959269370884,-1.0},26,{4.075427821953628,0.6859125175106776},4.1e-16,6.9e-17},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},0,{-1.836418620170526e-18,-1.003741873197321},1.8e-34,1.0e-16},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},1,{0.01415314238170799,-0.9809158089497843},1.4e-18,9.8e-17},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},2,{0.05114736246509357,-0.9580400080884279},5.1e-18,9.6e-17},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},3,{0.09211316557854763,-0.9082339053736075},9.2e-18,9.1e-17},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},4,{0.1846022792219881,-0.8324588456241011},1.8e-17,8.3e-17},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},5,{0.3278509422643821,-0.7787308740926149},3.3e-17,7.8e-17},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},6,{0.490657891841003,-0.7594698540777983},4.9e-17,7.6e-17},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},7,{0.6556002657420997,-0.7661759616695461},6.6e-17,7.7e-17},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},8,{0.8170144707370777,-0.7897178762870168},8.2e-17,7.9e-17},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},9,{0.9738269711673275,-0.8240443504069009},9.7e-17,8.2e-17},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},10,{1.126363788598225,-0.8654702596325609},1.1e-16,8.7e-17},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},11,{1.275267657078007,-0.9117424236160586},1.3e-16,9.1e-17},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},12,{1.421169391490898,-0.9614426612842512},1.4e-16,9.6e-17},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},13,{1.564605168974907,-1.013646817955554},1.6e-16,1.0e-16},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},14,{1.70600982438213,-1.067731854089558},1.7e-16,1.1e-16},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},15,{1.845730814291544,-1.123264438028688},1.8e-16,1.1e-16},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},16,{1.984045299099804,-1.179934666313605},2.0e-16,1.2e-16},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},17,{2.121175274622946,-1.237515369840869},2.1e-16,1.2e-16},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},19,{2.392564196036499,-1.354767638565249},2.4e-16,1.4e-16},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},20,{2.527087793751678,-1.414208223835596},2.5e-16,1.4e-16},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},22,{2.794289611881632,-1.534314595034528},2.8e-16,1.5e-16},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},23,{2.927118403808978,-1.594865107779637},2.9e-16,1.6e-16},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},25,{3.191523552338415,-1.716747727625207},3.2e-16,1.7e-16},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},27,{3.454552595281413,-1.839467692756036},3.5e-16,1.8e-16},
-{{6.2831853071795862319959269370884,3.1415926535897932384626433832795},29,{3.716477216297216,-1.962842613985385},3.7e-16,2.0e-16},
-{{6.2831853071795862319959269370884,1.0},0,{-1.773439590975416e-16,-1.313035285499331},1.8e-32,1.3e-16},
-{{6.2831853071795862319959269370884,1.0},1,{-0.06304185943615409,-0.7403873087787056},6.3e-18,7.4e-17},
-{{6.2831853071795862319959269370884,1.0},2,{0.2949375696085568,-1.070592030672524},2.9e-17,1.1e-16},
-{{6.2831853071795862319959269370884,1.0},3,{-0.2986322034569661,-0.9008011017614757},3.0e-17,9.0e-17},
-{{6.2831853071795862319959269370884,1.0},4,{-0.003223801583153805,-0.4398947553395593},3.2e-19,4.4e-17},
-{{6.2831853071795862319959269370884,1.0},5,{0.3254847904858648,-0.3236711082223025},3.3e-17,3.2e-17},
-{{6.2831853071795862319959269370884,1.0},6,{0.5915216297442743,-0.2927648081692745},5.9e-17,2.9e-17},
-{{6.2831853071795862319959269370884,1.0},7,{0.8216613358485906,-0.2889872711150469},8.2e-17,2.9e-17},
-{{6.2831853071795862319959269370884,1.0},8,{1.031011238016646,-0.2965575908077732},1.0e-16,3.0e-17},
-{{6.2831853071795862319959269370884,1.0},9,{1.227344826394146,-0.3098261586314655},1.2e-16,3.1e-17},
-{{6.2831853071795862319959269370884,1.0},10,{1.414970410777237,-0.3263361380815797},1.4e-16,3.3e-17},
-{{6.2831853071795862319959269370884,1.0},11,{1.596461936103797,-0.3448619156356228},1.6e-16,3.4e-17},
-{{6.2831853071795862319959269370884,1.0},12,{1.773455192293614,-0.36472724630896},1.8e-16,3.6e-17},
-{{6.2831853071795862319959269370884,1.0},13,{1.947042664720708,-0.3855292662286455},1.9e-16,3.9e-17},
-{{6.2831853071795862319959269370884,1.0},14,{2.117983884070411,-0.4070131164963634},2.1e-16,4.1e-17},
-{{6.2831853071795862319959269370884,1.0},15,{2.28682458641427,-0.4290096105470636},2.3e-16,4.3e-17},
-{{6.2831853071795862319959269370884,1.0},16,{2.453967796322013,-0.4514019204534639},2.5e-16,4.5e-17},
-{{6.2831853071795862319959269370884,1.0},18,{2.784310371123592,-0.4970627630731119},2.8e-16,5.0e-17},
-{{6.2831853071795862319959269370884,1.0},19,{2.947928703075273,-0.5202242302820364},2.9e-16,5.2e-17},
-{{6.2831853071795862319959269370884,1.0},20,{3.110719695447307,-0.5435558939596922},3.1e-16,5.4e-17},
-{{6.2831853071795862319959269370884,1.0},22,{3.434270806979098,-0.590625695740279},3.4e-16,5.9e-17},
-{{6.2831853071795862319959269370884,1.0},23,{3.595206946808026,-0.6143246109772049},3.6e-16,6.1e-17},
-{{6.2831853071795862319959269370884,1.0},25,{3.915734156142959,-0.6619787064788887},3.9e-16,6.6e-17},
-{{6.2831853071795862319959269370884,1.0},26,{4.075427821953628,-0.6859125175106776},4.1e-16,6.9e-17},
-{{3.1415926535897932384626433832795,0.0},0,{-2.704418609247059e+282,0.0},2.7e+266,0.0},
-{{3.1415926535897932384626433832795,0.0},1,{-0.3183098861837907,0.0},3.2e-17,0.0},
-{{3.1415926535897932384626433832795,0.0},2,{0.4105777788290164,0.0},4.1e-17,0.0},
-{{3.1415926535897932384626433832795,0.0},3,{0.8821173642494784,0.0},8.8e-17,0.0},
-{{3.1415926535897932384626433832795,0.0},4,{1.283506275095942,0.0},1.3e-16,0.0},
-{{3.1415926535897932384626433832795,0.0},5,{1.654748956488027,0.0},1.7e-16,0.0},
-{{3.1415926535897932384626433832795,0.0},6,{2.010012841716631,0.0},2.0e-16,0.0},
-{{3.1415926535897932384626433832795,0.0},7,{2.355698958080709,0.0},2.4e-16,0.0},
-{{3.1415926535897932384626433832795,0.0},8,{2.695156885492767,0.0},2.7e-16,0.0},
-{{3.1415926535897932384626433832795,0.0},9,{3.030322020436486,0.0},3.0e-16,0.0},
-{{3.1415926535897932384626433832795,0.0},10,{3.362395801011574,0.0},3.4e-16,0.0},
-{{3.1415926535897932384626433832795,0.0},11,{3.692165818289568,0.0},3.7e-16,0.0},
-{{3.1415926535897932384626433832795,0.0},12,{4.02017100538644,0.0},4.0e-16,0.0},
-{{3.1415926535897932384626433832795,0.0},13,{4.346793172787544,0.0},4.3e-16,0.0},
-{{3.1415926535897932384626433832795,0.0},14,{4.672310695202237,0.0},4.7e-16,0.0},
-{{3.1415926535897932384626433832795,0.0},15,{4.996931497029032,0.0},5.0e-16,0.0},
-{{3.1415926535897932384626433832795,0.0},16,{5.320814119475183,0.0},5.3e-16,0.0},
-{{3.1415926535897932384626433832795,0.0},17,{5.644081624955091,0.0},5.6e-16,0.0},
-{{3.1415926535897932384626433832795,0.0},18,{5.966831036716778,0.0},6.0e-16,0.0},
-{{3.1415926535897932384626433832795,0.0},20,{6.611070983143532,0.0},6.6e-16,0.0},
-//{{3.141592653589793,0.0},0,{-4193528956200935.0,0.0},0.42,0.0}, // TODO fails for pi truncated to double precision
-{{3.141592653589793,0.0},1,{-0.3183098861837905,0.0},3.2e-17,0.0},
-{{3.141592653589793,0.0},2,{0.4105777788290165,0.0},4.1e-17,0.0},
-{{3.141592653589793,0.0},3,{0.8821173642494785,0.0},8.8e-17,0.0},
-{{3.141592653589793,0.0},4,{1.283506275095942,0.0},1.3e-16,0.0},
-{{3.141592653589793,0.0},5,{1.654748956488027,0.0},1.7e-16,0.0},
-{{3.141592653589793,0.0},6,{2.010012841716632,0.0},2.0e-16,0.0},
-{{3.141592653589793,0.0},7,{2.355698958080709,0.0},2.4e-16,0.0},
-{{3.141592653589793,0.0},8,{2.695156885492767,0.0},2.7e-16,0.0},
-{{3.141592653589793,0.0},9,{3.030322020436486,0.0},3.0e-16,0.0},
-{{3.141592653589793,0.0},10,{3.362395801011574,0.0},3.4e-16,0.0},
-{{3.141592653589793,0.0},11,{3.692165818289568,0.0},3.7e-16,0.0},
-{{3.141592653589793,0.0},12,{4.02017100538644,0.0},4.0e-16,0.0},
-{{3.141592653589793,0.0},13,{4.346793172787545,0.0},4.3e-16,0.0},
-{{3.141592653589793,0.0},14,{4.672310695202237,0.0},4.7e-16,0.0},
-{{3.141592653589793,0.0},15,{4.996931497029033,0.0},5.0e-16,0.0},
-{{3.141592653589793,0.0},16,{5.320814119475183,0.0},5.3e-16,0.0},
-{{3.141592653589793,0.0},17,{5.644081624955091,0.0},5.6e-16,0.0},
-{{3.141592653589793,0.0},18,{5.966831036716779,0.0},6.0e-16,0.0},
-{{3.141592653589793,0.0},20,{6.611070983143533,0.0},6.6e-16,0.0},
+{0.055,{1.5,1.0},0,{8.36411257086632417805161802858,-5.61276019081108331390757079001},8.4e-30,5.6e-30},
+{0.055,{1.5,1.0},1,{16.7667178551556094176027309859,-11.1998166559046869795781820105},1.7e-29,1.1e-29},
+{0.055,{1.5,1.0},2,{25.1630398855185873499464281292,-16.7910760954753548964102344384},2.5e-29,1.7e-29},
+{0.055,{1.5,1.0},3,{33.5572671100165012325784588331,-22.383734562458543657022226896},3.4e-29,2.2e-29},
+{0.055,{1.5,1.0},4,{41.950542077104701040110101859,-27.9770285802158263291599997509},4.2e-29,2.8e-29},
+{0.055,{1.5,1.0},5,{50.3433042696727764406721141662,-33.5706647130503739752197276732},5.0e-29,3.4e-29},
+{0.056,{1.5,1.0},0,{8.21376265391609712733518768023,-5.51319460541938323883420760048},8.2e-30,5.5e-30},
+{0.056,{1.5,1.0},1,{16.4667176150866353509824561506,-11.0002167597831574900159439215},1.6e-29,1.1e-29},
+{0.056,{1.5,1.0},2,{24.7132751738799796648583369427,-16.4915187734177778992311772646},2.5e-29,1.6e-29},
+{0.056,{1.5,1.0},3,{32.9576998556341496388761472745,-21.9842453336088048343502057669},3.3e-29,2.2e-29},
+{0.056,{1.5,1.0},4,{41.2011549708335168057075901037,-27.477619023587507943936207531},4.1e-29,2.7e-29},
+{0.056,{1.5,1.0},5,{49.4440879900606885600071029339,-32.9713410576881911651850209714},4.9e-29,3.3e-29},
+{0.099,{0.75,0.0},0,{13.4432543666815307037297423125,0.0},1.3e-29,0.0},
+{0.099,{0.75,0.0},1,{26.9211745963399821140396209297,0.0},2.7e-29,0.0},
+{0.099,{0.75,0.0},2,{40.3934323328306157741044239646,0.0},4.0e-29,0.0},
+{0.099,{0.75,0.0},3,{53.8638034125886963781700192119,0.0},5.4e-29,0.0},
+{0.099,{0.75,0.0},4,{67.3333170798179775907657077628,0.0},6.7e-29,0.0},
+{0.101,{0.75,0.0},0,{13.1760604676597854251278771639,0.0},1.3e-29,0.0},
+{0.101,{0.75,0.0},1,{26.3874877796314674196927795896,0.0},2.6e-29,0.0},
+{0.101,{0.75,0.0},2,{39.5931379817016747992033032232,0.0},4.0e-29,0.0},
+{0.101,{0.75,0.0},3,{52.7968633735063707213589804011,0.0},5.3e-29,0.0},
+{0.101,{0.75,0.0},4,{65.9997140200860522244781602823,0.0},6.6e-29,0.0},
+//{1.0,{3.141592653589793,0.0},0,{-4193528956200935.44940210704681,0.0},4.2e-15,0.0}, //TODO it fails
+{1.0,{3.141592653589793,0.0},1,{-0.31830988618379045723644142554,0.0},3.2e-31,0.0},
+{1.0,{3.141592653589793,0.0},2,{0.410577778829016536772047563585,0.0},4.1e-31,0.0},
+{1.0,{3.141592653589793,0.0},3,{0.882117364249478549575956540158,0.0},8.8e-31,0.0},
+{1.0,{3.141592653589793,0.0},4,{1.28350627509594182742011853076,0.0},1.3e-30,0.0},
+{1.0,{3.141592653589793,0.0},5,{1.65474895648802722294908309803,0.0},1.7e-30,0.0},
+{1.0,{3.141592653589793,0.0},6,{2.01001284171663163343136710203,0.0},2.0e-30,0.0},
+{1.0,{3.141592653589793,0.0},7,{2.3556989580807089636275015334,0.0},2.4e-30,0.0},
+{1.0,{3.141592653589793,0.0},8,{2.69515688549276743436155915861,0.0},2.7e-30,0.0},
+{1.0,{3.141592653589793,0.0},9,{3.03032202043648638445429887499,0.0},3.0e-30,0.0},
+{1.0,{3.141592653589793,0.0},10,{3.36239580101157416890855524563,0.0},3.4e-30,0.0},
+{1.0,{3.141592653589793,0.0},11,{3.69216581828956804940195304251,0.0},3.7e-30,0.0},
+{1.0,{3.141592653589793,0.0},12,{4.02017100538644019728337831661,0.0},4.0e-30,0.0},
+{1.0,{3.141592653589793,0.0},13,{4.34679317278754460646714985352,0.0},4.3e-30,0.0},
+{1.0,{3.141592653589793,0.0},14,{4.67231069520223706243680197115,0.0},4.7e-30,0.0},
+{1.0,{3.141592653589793,0.0},15,{4.99693149702903278777277435329,0.0},5.0e-30,0.0},
+{1.0,{3.141592653589793,0.0},16,{5.32081411947518340799146068208,0.0},5.3e-30,0.0},
+{1.0,{3.141592653589793,0.0},17,{5.64408162495509135334284431755,0.0},5.6e-30,0.0},
+{1.0,{3.141592653589793,0.0},18,{5.96683103671677868142566809307,0.0},6.0e-30,0.0},
+{1.0,{3.141592653589793,0.0},20,{6.61107098314353294269578290597,0.0},6.6e-30,0.0},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},0,{-2.6716342902051994927252215966e-231,1.31303528549933130363616124693},2.7e-261,1.3e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},1,{-0.105454733144282573874737514743,0.683525109490997258708886093775},1.1e-31,6.8e-31},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},2,{0.375625526268801268114481216368,0.512975081648671832008667823661},3.8e-31,5.1e-31},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},3,{0.783851283060567238445438250606,0.520073115070454006654550784711},7.8e-31,5.2e-31},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},4,{1.14604488551154019334529698611,0.572490471112493028076614293934},1.1e-30,5.7e-31},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},5,{1.48404359072601097206901667891,0.641733304379550739427032499845},1.5e-30,6.4e-31},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},6,{1.80811624351877378090791630677,0.718912588148377402368142277488},1.8e-30,7.2e-31},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},7,{2.12347980630751576532252355551,0.800452445291865201629029299576},2.1e-30,8.0e-31},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},8,{2.43303696494205830783858553538,0.884649106040885755899158077052},2.4e-30,8.8e-31},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},9,{2.73852738222687009330211647101,0.970588580896081781642230963596},2.7e-30,9.7e-31},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},10,{3.0410569509060891604618551053,1.05773599713031942130130797795},3.0e-30,1.1e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},11,{3.34136260812952743711100056731,1.14575692325188463896185378694},3.3e-30,1.1e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},12,{3.63995462790817336653762591698,1.234431120418641661728201002},3.6e-30,1.2e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},13,{3.93719773020948102455547825667,1.32360738235542208862536026901},3.9e-30,1.3e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},14,{4.23335964545017964042849360761,1.41317829414564700232361756505},4.2e-30,1.4e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},15,{4.52864142199512016467859555213,1.50306534896781795302640202012},4.5e-30,1.5e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},16,{4.82319701874385130081753994655,1.59320977218167917426149042564},4.8e-30,1.6e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},17,{5.11714636116284552978521815319,1.68356664681612135141981731014},5.1e-30,1.7e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},18,{5.41058427404166609975539845822,1.77410102931703950879786333048},5.4e-30,1.8e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,-1.0},20,{5.99621535040140812635283510785,1.95559736586759311172186430919},6.0e-30,2.0e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},0,{-2.71018254115422982591015027278e+230,0.0},2.7e+200,0.0},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},1,{-0.318309886183790671537767526745,0.0},3.2e-31,0.0},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},2,{0.410577778829016403078679407603,0.0},4.1e-31,0.0},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},3,{0.882117364249478415493934816912,0.0},8.8e-31,0.0},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},4,{1.28350627509594167934323821122,0.0},1.3e-30,0.0},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},5,{1.65474895648802705636895284875,0.0},1.7e-30,0.0},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},6,{2.0100128417166314463188136696,0.0},2.0e-30,0.0},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},7,{2.35569895808070875489368658328,0.0},2.4e-30,0.0},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},8,{2.69515688549276720335196669156,0.0},2.7e-30,0.0},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},9,{3.03032202043648613074315705525,0.0},3.0e-30,0.0},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},10,{3.36239580101157389220238864404,0.0},3.4e-30,0.0},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},11,{3.69216581828956774948934910125,0.0},3.7e-30,0.0},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},12,{4.02017100538643987400666352476,0.0},4.0e-30,0.0},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},13,{4.34679317278754425970539399711,0.0},4.3e-30,0.0},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},14,{4.67231069520223669209509601635,0.0},4.7e-30,0.0},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},15,{4.99693149702903239377518208757,0.0},5.0e-30,0.0},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},16,{5.32081411947518299027622332802,0.0},5.3e-30,0.0},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},17,{5.64408162495509091185902151892,0.0},5.6e-30,0.0},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},18,{5.96683103671677821613072547396,0.0},6.0e-30,0.0},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,0.0},20,{6.61107098314353242967621469735,0.0},6.6e-30,0.0},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},0,{-2.6716342902051994927252215966e-231,-1.31303528549933130363616124693},2.7e-261,1.3e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},1,{-0.105454733144282573874737514743,-0.683525109490997258708886093775},1.1e-31,6.8e-31},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},2,{0.375625526268801268114481216368,-0.512975081648671832008667823661},3.8e-31,5.1e-31},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},3,{0.783851283060567238445438250606,-0.520073115070454006654550784711},7.8e-31,5.2e-31},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},4,{1.14604488551154019334529698611,-0.572490471112493028076614293934},1.1e-30,5.7e-31},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},5,{1.48404359072601097206901667891,-0.641733304379550739427032499845},1.5e-30,6.4e-31},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},6,{1.80811624351877378090791630677,-0.718912588148377402368142277488},1.8e-30,7.2e-31},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},7,{2.12347980630751576532252355551,-0.800452445291865201629029299576},2.1e-30,8.0e-31},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},8,{2.43303696494205830783858553538,-0.884649106040885755899158077052},2.4e-30,8.8e-31},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},9,{2.73852738222687009330211647101,-0.970588580896081781642230963596},2.7e-30,9.7e-31},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},10,{3.0410569509060891604618551053,-1.05773599713031942130130797795},3.0e-30,1.1e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},11,{3.34136260812952743711100056731,-1.14575692325188463896185378694},3.3e-30,1.1e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},12,{3.63995462790817336653762591698,-1.234431120418641661728201002},3.6e-30,1.2e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},13,{3.93719773020948102455547825667,-1.32360738235542208862536026901},3.9e-30,1.3e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},14,{4.23335964545017964042849360761,-1.41317829414564700232361756505},4.2e-30,1.4e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},15,{4.52864142199512016467859555213,-1.50306534896781795302640202012},4.5e-30,1.5e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},16,{4.82319701874385130081753994655,-1.59320977218167917426149042564},4.8e-30,1.6e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},17,{5.11714636116284552978521815319,-1.68356664681612135141981731014},5.1e-30,1.7e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},18,{5.41058427404166609975539845822,-1.77410102931703950879786333048},5.4e-30,1.8e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,1.0},20,{5.99621535040140812635283510785,-1.95559736586759311172186430919},6.0e-30,2.0e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,3.14159265358979323846264338327950288419716939937510582097494},0,{-2.76651033493641321335573306744e-233,-1.00374187319732128820155269119},2.8e-263,1.0e-30},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,3.14159265358979323846264338327950288419716939937510582097494},1,{0.0563102343267633802588595634886,-0.984253292966296255927862927266},5.6e-32,9.8e-31},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,3.14159265358979323846264338327950288419716939937510582097494},2,{0.19328384398068375259537842403,-0.982044786578199175924654201079},1.9e-31,9.8e-31},
+{1.0,{3.14159265358979323846264338327950288419716939937510582097494,3.14159265358979323846264338327950288419716939937510582097494},3,{0.369926582420403451826298840749,-1.02712817468012352294588465251},3.7e-31,1.0e-30},
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 };
 
 // complex(z), n, complex(f(n,z)), abs_err_real, abs_err_imag