#include <iostream>
#include <cmath>
using namespace std;

#define TRANSCENDENTAL

#include "Complex.h"
#include "Quaternion.h"
#include "Octonion.h"
#include "Sedenion.h"
#include "Trigintaduonion.h"

// The Taylor series coefficients for those functions where it is not too complex too
// trivial (sin, cos, sinh, cosh) or too complex (asec, acsc, acosh, acsch)
// I might try the others at some point in the future, but:
//    asec(x)/sqrt(x - 1) has a Taylor series around x = 1
//    acsc(x)/sqrt(x - 1) has a Taylor series around x = 1
//   acosh(x)/sqrt(x - 1) has a Taylor series around x = 1
//   acosh(x)/sqrt(x - 1) has a Taylor series around x = 1
// Don't know why I didn't do acsch - it's quite straight-forward except for
// the logarithmic term, which I already do for asech.

// Errors tend to occur close to branch cuts, usually when |Re(z)| << |Im(z)|

/**********************************************
 * ****************************************** *
 * *                                        * *
 * *  Tables of Taylor Series Coefficients  * *
 * *                                        * *
 * ****************************************** * 
 **********************************************/

static const double tanc[100] = {
	0, 1.0,                     0, 0.33333333333333333,     0, 0.13333333333333333,
	0, 0.53968253968253968e-1,  0, 0.21869488536155203e-1,  0, 0.88632355299021966e-2,
	0, 0.35921280365724810e-2,  0, 0.14558343870513183e-2,  0, 0.59002744094558598e-3,
	0, 0.23912911424355248e-3,  0, 0.96915379569294503e-4,  0, 0.39278323883316834e-4,
	0, 0.15918905069328965e-4,  0, 0.64516892156554308e-5,  0, 0.26147711512907546e-5,
	0, 0.10597268320104654e-5,  0, 0.42949110782738059e-6,  0, 0.17406618963571648e-6,
	0, 0.70546369464009683e-7,  0, 0.28591366623052539e-7,  0, 0.11587644432798852e-7,
	0, 0.46962953982309016e-8,  0, 0.19033368339312759e-8,  0, 0.77139336353590623e-9,
	0, 0.31263395458920870e-9,  0, 0.12670576930305401e-9,  0, 0.51351914080393677e-10,
	0, 0.20812146867700474e-10, 0, 0.84348454190943383e-11, 0, 0.34185140868111558e-11,
	0, 0.13854715742948469e-11, 0, 0.56151047924146801e-12, 0, 0.22757162553728748e-12,
	0, 0.92231305851395317e-13, 0, 0.37379940310967389e-13, 0, 0.15149519187148605e-13,
	0, 0.61398688626168138e-14, 0, 0.24883951222762789e-14, 0, 0.10085085566354096e-14,
	0, 0.40873312268690138e-15, 0, 0.16565329513786284e-15, 0, 0.67136751750487117e-16,
	0, 0.27209500613044588e-16, 0, 0.11027595233722371e-16, 0, 0.44693160072374125e-17,
	0, 0.18113455516997667e-17, 0, 0.73411070113401475e-18, 0, 0.29752386065361939e-18,
	0, 0.12058187889305073e-18, 0, 0.48869994781043705e-19
};

static const double secc[100] = {
	1.0,                     0, 0.5,                     0, 0.20833333333333333,     0,
	0.84722222222222222e-1,  0, 0.34350198412698413e-1,  0, 0.13922233245149912e-1,  0,
	0.56424968100315323e-2,  0, 0.22868190951648293e-2,  0, 0.92681292737742184e-3,  0,
	0.37562313385259450e-3,  0, 0.15223432221797662e-3,  0, 0.61698246877700525e-4,  0,
	0.25005357609459247e-4,  0, 0.10134289721572026e-4,  0, 0.41072729198567004e-5,  0,
	0.16646150151280280e-5,  0, 0.67464305456632013e-6,  0, 0.27342253129896734e-6,  0,
	0.11081397802278207e-6,  0, 0.44911213669537136e-7,  0, 0.18201829311245770e-7,  0,
	0.73769235610848765e-8,  0, 0.29897545073926764e-8,  0, 0.12117018619561619e-8,  0,
	0.49108426750009155e-9,  0, 0.19902895700495881e-9,  0, 0.80663398011369520e-10, 0,
	0.32691643852499818e-10, 0, 0.13249424201396147e-10, 0, 0.53697893706595739e-11, 0,
	0.21762936597810882e-11, 0, 0.88201859824934000e-12, 0, 0.35746867347671487e-12, 0,
	0.14487659644686842e-12, 0, 0.58716272936280060e-13, 0, 0.23796809091881837e-13, 0,
	0.96444834564008509e-14, 0, 0.39087619176859166e-14, 0, 0.15841615363041244e-14, 0,
	0.64203648775599251e-15, 0, 0.26020758752402585e-15, 0, 0.10545816304260601e-15, 0,
	0.42740583616893926e-16, 0, 0.17322106086512011e-16, 0, 0.70203851674541611e-17, 0,
	0.28452549391662691e-17, 0, 0.11531383928021365e-17, 0, 0.46734938744854201e-18, 0,
	0.18940957244323117e-18, 0, 0.76764808292549220e-19, 0
};

static const double cscc[100] = {
	0, 0.16666666666666667,     0, 0.19444444444444444e-1,  0, 0.20502645502645503e-2,
	0, 0.20998677248677249e-3,  0, 0.21336045641601197e-4,  0, 0.21633474427786597e-5,
	0, 0.21923271344567641e-6,  0, 0.22213930853920415e-7,  0, 0.22507674795567867e-8,
	0, 0.22805107707218212e-9,  0, 0.23106421580996967e-10, 0, 0.23411704028931947e-11,
	0, 0.23721016693292246e-12, 0, 0.24034415154237358e-13, 0, 0.24351953983824320e-14,
	0, 0.24673688033682493e-15, 0, 0.24999672768310464e-16, 0, 0.25329964356669149e-17,
	0, 0.25664619702639552e-18, 0, 0.26003696460089973e-19, 0, 0.26347253044141820e-20,
	0, 0.26695348641570915e-21, 0, 0.27048043221089541e-22, 0, 0.27405397543699319e-23,
	0, 0.27767473173164386e-24, 0, 0.28134332486618781e-25, 0, 0.28506038685312915e-26,
	0, 0.28882655805501747e-27, 0, 0.29264248729476757e-28, 0, 0.29650883196743643e-29,
	0, 0.30042625815347699e-30, 0, 0.30439544073348818e-31, 0, 0.30841706350448099e-32,
	0, 0.31249181929768069e-33, 0, 0.31662041009788535e-34, 0, 0.32080354716440138e-35,
	0, 0.32504195115357679e-36, 0, 0.32933635224295338e-37, 0, 0.33368749025705918e-38,
	0, 0.33809611479486289e-39, 0, 0.34256298535891216e-40, 0, 0.34708887148617804e-41,
	0, 0.35167455288062819e-42, 0, 0.35632081954755155e-43, 0, 0.36102847192965769e-44,
	0, 0.36579832104497434e-45, 0, 0.37063118862656674e-46, 0, 0.37552790726410299e-47,
	0, 0.38048932054728968e-48, 0, 0
};

static const double cotc[100] = {
	0, -0.33333333333333333,     0, -0.22222222222222222e-1,  0, -0.21164021164021164e-2,
	0, -0.21164021164021164e-3,  0, -0.21377799155576933e-4,  0, -0.21644042808063972e-5,
	0, -0.21925947851873778e-6,  0, -0.22214608789979679e-7,  0, -0.22507846516808993e-8,
	0, -0.22805151204592183e-9,  0, -0.23106432599002624e-10, 0, -0.23411706819824884e-11,
	0, -0.23721017400233654e-12, 0, -0.24034415333307706e-13, 0, -0.24351954029183369e-14,
	0, -0.24673688045172075e-15, 0, -0.24999672771220809e-16, 0, -0.25329964357406348e-17,
	0, -0.25664619702826287e-18, 0, -0.26003696460137274e-19, 0, -0.26347253044153801e-20,
	0, -0.26695348641573950e-21, 0, -0.27048043221090310e-22, 0, -0.27405397543699513e-23,
	0, -0.27767473173164435e-24, 0, -0.28134332486618794e-25, 0, -0.28506038685312918e-26,
	0, -0.28882655805501748e-27, 0, -0.29264248729476758e-28, 0, -0.29650883196743643e-29,
	0, -0.30042625815347699e-30, 0, -0.30439544073348818e-31, 0, -0.30841706350448099e-32,
	0, -0.31249181929768069e-33, 0, -0.31662041009788535e-34, 0, -0.32080354716440138e-35,
	0, -0.32504195115357679e-36, 0, -0.32933635224295338e-37, 0, -0.33368749025705918e-38,
	0, -0.33809611479486289e-39, 0, -0.34256298535891216e-40, 0, -0.34708887148617804e-41,
	0, -0.35167455288062819e-42, 0, -0.35632081954755155e-43, 0, -0.36102847192965769e-44,
	0, -0.36579832104497434e-45, 0, -0.37063118862656674e-46, 0, -0.37552790726410299e-47,
	0, -0.38048932054728968e-48, 0, -0.38551628321120260e-49
};

static const double tanhc[100] = {
	0,  1.0,                     0, -0.33333333333333333,     0,  0.13333333333333333,
	0, -0.53968253968253968e-1,  0,  0.21869488536155203e-1,  0, -0.88632355299021966e-2,
	0,  0.35921280365724810e-2,  0, -0.14558343870513183e-2,  0,  0.59002744094558598e-3,
	0, -0.23912911424355248e-3,  0,  0.96915379569294503e-4,  0, -0.39278323883316834e-4,
	0,  0.15918905069328965e-4,  0, -0.64516892156554308e-5,  0,  0.26147711512907546e-5,
	0, -0.10597268320104654e-5,  0,  0.42949110782738059e-6,  0, -0.17406618963571648e-6,
	0,  0.70546369464009683e-7,  0, -0.28591366623052539e-7,  0,  0.11587644432798852e-7,
	0, -0.46962953982309016e-8,  0,  0.19033368339312759e-8,  0, -0.77139336353590623e-9,
	0,  0.31263395458920870e-9,  0, -0.12670576930305401e-9,  0,  0.51351914080393677e-10,
	0, -0.20812146867700474e-10, 0,  0.84348454190943383e-11, 0, -0.34185140868111558e-11,
	0,  0.13854715742948469e-11, 0, -0.56151047924146801e-12, 0,  0.22757162553728748e-12,
	0, -0.92231305851395317e-13, 0,  0.37379940310967389e-13, 0, -0.15149519187148605e-13,
	0,  0.61398688626168138e-14, 0, -0.24883951222762789e-14, 0,  0.10085085566354096e-14,
	0, -0.40873312268690138e-15, 0,  0.16565329513786284e-15, 0, -0.67136751750487117e-16,
	0,  0.27209500613044588e-16, 0, -0.11027595233722371e-16, 0,  0.44693160072374125e-17,
	0, -0.18113455516997667e-17, 0,  0.73411070113401475e-18, 0, -0.29752386065361939e-18,
	0,  0.12058187889305073e-18, 0, -0.48869994781043705e-19
};

static const double sechc[100] = {
	 1.0,                     0, -0.5,                     0,  0.20833333333333333,     0,
	-0.84722222222222222e-1,  0,  0.34350198412698413e-1,  0, -0.13922233245149912e-1,  0,
	 0.56424968100315323e-2,  0, -0.22868190951648293e-2,  0,  0.92681292737742184e-3,  0,
	-0.37562313385259450e-3,  0,  0.15223432221797662e-3,  0, -0.61698246877700525e-4,  0,
	 0.25005357609459247e-4,  0, -0.10134289721572026e-4,  0,  0.41072729198567004e-5,  0,
	-0.16646150151280280e-5,  0,  0.67464305456632013e-6,  0, -0.27342253129896734e-6,  0,
	 0.11081397802278207e-6,  0, -0.44911213669537136e-7,  0,  0.18201829311245770e-7,  0,
	-0.73769235610848765e-8,  0,  0.29897545073926764e-8,  0, -0.12117018619561619e-8,  0,
	 0.49108426750009155e-9,  0, -0.19902895700495881e-9,  0,  0.80663398011369520e-10, 0,
	-0.32691643852499818e-10, 0,  0.13249424201396147e-10, 0, -0.53697893706595739e-11, 0,
	 0.21762936597810882e-11, 0, -0.88201859824934000e-12, 0,  0.35746867347671487e-12, 0,
	-0.14487659644686842e-12, 0,  0.58716272936280060e-13, 0, -0.23796809091881837e-13, 0,
	 0.96444834564008509e-14, 0, -0.39087619176859166e-14, 0,  0.15841615363041244e-14, 0,
	-0.64203648775599251e-15, 0,  0.26020758752402585e-15, 0, -0.10545816304260601e-15, 0,
	 0.42740583616893926e-16, 0, -0.17322106086512011e-16, 0,  0.70203851674541611e-17, 0,
	-0.28452549391662691e-17, 0,  0.11531383928021365e-17, 0, -0.46734938744854201e-18, 0,
	 0.18940957244323117e-18, 0, -0.76764808292549220e-19, 0
};

static const double cschc[100] = {
	0, -0.16666666666666667,     0,  0.19444444444444444e-1,  0, -0.20502645502645503e-2,
	0,  0.20998677248677249e-3,  0, -0.21336045641601197e-4,  0,  0.21633474427786597e-5,
	0, -0.21923271344567641e-6,  0,  0.22213930853920415e-7,  0, -0.22507674795567867e-8,
	0,  0.22805107707218212e-9,  0, -0.23106421580996967e-10, 0,  0.23411704028931947e-11,
	0, -0.23721016693292246e-12, 0,  0.24034415154237358e-13, 0, -0.24351953983824320e-14,
	0,  0.24673688033682493e-15, 0, -0.24999672768310464e-16, 0,  0.25329964356669149e-17,
	0, -0.25664619702639552e-18, 0,  0.26003696460089973e-19, 0, -0.26347253044141820e-20,
	0,  0.26695348641570915e-21, 0, -0.27048043221089541e-22, 0,  0.27405397543699319e-23,
	0, -0.27767473173164386e-24, 0,  0.28134332486618781e-25, 0, -0.28506038685312915e-26,
	0,  0.28882655805501747e-27, 0, -0.29264248729476757e-28, 0,  0.29650883196743643e-29,
	0, -0.30042625815347699e-30, 0,  0.30439544073348818e-31, 0, -0.30841706350448099e-32,
	0,  0.31249181929768069e-33, 0, -0.31662041009788535e-34, 0,  0.32080354716440138e-35,
	0, -0.32504195115357679e-36, 0,  0.32933635224295338e-37, 0, -0.33368749025705918e-38,
	0,  0.33809611479486289e-39, 0, -0.34256298535891216e-40, 0,  0.34708887148617804e-41,
	0, -0.35167455288062819e-42, 0,  0.35632081954755155e-43, 0, -0.36102847192965769e-44,
	0,  0.36579832104497434e-45, 0, -0.37063118862656674e-46, 0,  0.37552790726410299e-47,
	0, -0.38048932054728968e-48, 0
};

static const double cothc[100] = {
	0,  0.33333333333333333,     0, -0.22222222222222222e-1,  0,  0.21164021164021164e-2,
	0, -0.21164021164021164e-3,  0,  0.21377799155576933e-4,  0, -0.21644042808063972e-5,
	0,  0.21925947851873778e-6,  0, -0.22214608789979679e-7,  0,  0.22507846516808993e-8,
	0, -0.22805151204592183e-9,  0,  0.23106432599002624e-10, 0, -0.23411706819824884e-11,
	0,  0.23721017400233654e-12, 0, -0.24034415333307706e-13, 0,  0.24351954029183369e-14,
	0, -0.24673688045172075e-15, 0,  0.24999672771220809e-16, 0, -0.25329964357406348e-17,
	0,  0.25664619702826287e-18, 0, -0.26003696460137274e-19, 0,  0.26347253044153801e-20,
	0, -0.26695348641573950e-21, 0,  0.27048043221090310e-22, 0, -0.27405397543699513e-23,
	0,  0.27767473173164435e-24, 0, -0.28134332486618794e-25, 0,  0.28506038685312918e-26,
	0, -0.28882655805501748e-27, 0,  0.29264248729476758e-28, 0, -0.29650883196743643e-29,
	0,  0.30042625815347699e-30, 0, -0.30439544073348818e-31, 0,  0.30841706350448099e-32,
	0, -0.31249181929768069e-33, 0,  0.31662041009788535e-34, 0, -0.32080354716440138e-35,
	0,  0.32504195115357679e-36, 0, -0.32933635224295338e-37, 0,  0.33368749025705918e-38,
	0, -0.33809611479486289e-39, 0,  0.34256298535891216e-40, 0, -0.34708887148617804e-41,
	0,  0.35167455288062819e-42, 0, -0.35632081954755155e-43, 0,  0.36102847192965769e-44,
	0, -0.36579832104497434e-45, 0,  0.37063118862656674e-46, 0, -0.37552790726410299e-47,
	0,  0.38048932054728968e-48, 0, -0.38551628321120260e-49
};

static const double logc[100] = {
	 0,                      1,                      -0.5,                     0.33333333333333333,
	-0.25,                   0.2,                    -0.16666666666666667,     0.14285714285714286,
	-0.125,                  0.11111111111111111,    -0.1,                     0.90909090909090909e-1,
	-0.83333333333333333e-1, 0.76923076923076923e-1, -0.71428571428571429e-1,  0.66666666666666667e-1,
	-0.625e-1,               0.58823529411764706e-1, -0.55555555555555556e-1,  0.52631578947368421e-1,
	-0.5e-1,                 0.47619047619047619e-1, -0.45454545454545455e-1,  0.43478260869565217e-1,
	-0.41666666666666667e-1, 0.4e-1,                 -0.38461538461538462e-1,  0.37037037037037037e-1,
	-0.35714285714285714e-1, 0.34482758620689655e-1, -0.33333333333333333e-1,  0.32258064516129032e-1,
	-0.3125e-1,              0.30303030303030303e-1, -0.29411764705882353e-1,  0.28571428571428571e-1,
	-0.27777777777777778e-1, 0.27027027027027027e-1, -0.26315789473684211e-1,  0.25641025641025641e-1,
	-0.25e-1,                0.24390243902439024e-1, -0.23809523809523810e-1,  0.23255813953488372e-1,
	-0.22727272727272727e-1, 0.22222222222222222e-1, -0.21739130434782609e-1,  0.21276595744680851e-1,
	-0.20833333333333333e-1, 0.20408163265306122e-1, -0.2e-1,                  0.19607843137254902e-1,
	-0.19230769230769231e-1, 0.18867924528301887e-1, -0.18518518518518519e-1,  0.18181818181818182e-1,
	-0.17857142857142857e-1, 0.17543859649122807e-1, -0.17241379310344828e-1,  0.16949152542372881e-1,
	-0.16666666666666667e-1, 0.16393442622950820e-1, -0.16129032258064516e-1,  0.15873015873015873e-1,
	-0.15625e-1,             0.15384615384615385e-1, -0.15151515151515152e-1,  0.14925373134328358e-1,
	-0.14705882352941176e-1, 0.14492753623188406e-1, -0.14285714285714286e-1,  0.14084507042253521e-1,
	-0.13888888888888889e-1, 0.13698630136986301e-1, -0.13513513513513514e-1,  0.13333333333333333e-1,
	-0.13157894736842105e-1, 0.12987012987012987e-1, -0.12820512820512821e-1,  0.12658227848101266e-1,
	-0.125e-1,               0.12345679012345679e-1, -0.12195121951219512e-1,  0.12048192771084337e-1,
	-0.11904761904761905e-1, 0.11764705882352941e-1, -0.11627906976744186e-1,  0.11494252873563218e-1,
	-0.11363636363636364e-1, 0.11235955056179775e-1, -0.11111111111111111e-1,  0.10989010989010989e-1,
	-0.10869565217391304e-1, 0.10752688172043011e-1, -0.10638297872340426e-1,  0.10526315789473684e-1,
	-0.10416666666666667e-1, 0.10309278350515464e-1, -0.10204081632653061e-1,  0.10101010101010101e-1
};

static const double asinc[100] = {
	0,  1,                       0,  0.16666666666666667,     0,  0.75e-1,
     	0,  0.44642857142857143e-1,  0,  0.30381944444444444e-1,  0,  0.22372159090909091e-1, 
	0,  0.17352764423076923e-1,  0,  0.1396484375e-1,         0,  0.11551800896139706e-1, 
  		0,  0.97616095291940789e-2,  0,  0.83903358096168155e-2,  0,  0.73125258735988451e-2, 
  		0,  0.64472103118896484e-2,  0,  0.57400376708419235e-2,  0,  0.51533096823199042e-2, 
  		0,  0.46601434869150962e-2,  0,  0.42409070936793631e-2,  0,  0.38809645588376692e-2, 
  		0,  0.35692053938259345e-2,  0,  0.32970595034734847e-2,  0,  0.30578216492580307e-2, 
  		0,  0.28461784011089422e-2,  0,  0.26578706382072899e-2,  0,  0.24894486782468835e-2, 
  		0,  0.23380918921119752e-2,  0,  0.22014739737101382e-2,  0,  0.20776610325181674e-2, 
  		0,  0.19650336162772836e-2,  0,  0.18622264064031275e-2,  0,  0.17680811205154182e-2, 
  		0,  0.16816093935831068e-2,  0,  0.16019632753514440e-2,  0,  0.15284115961225676e-2, 
  		0,  0.14603208940791154e-2,  0,  0.13971399176302534e-2,  0,  0.13383869512751784e-2, 
  		0,  0.12836393876290286e-2,  0,  0.12325250985000168e-2,  0,  0.11847152561624393e-2, 
  		0,  0.11399183307022237e-2,  0,  0.10978750465914472e-2,  0,  0.10583541258722429e-2, 
  		0,  0.10211486797106276e-2,  0,  0.98607313698333129e-3,  0,  0.95296061974295640e-3, 
  		0,  0.92166069218363342e-3,  0,  0.89203742309170971e-3,  0,  0.86396771246586756e-3, 
  		0,  0.83733984160271206e-3,  0,  0.81205221290867015e-3
};

static const double acosc[100] = {
	1.5707963267948966,
	   -1,                       0, -0.16666666666666667,     0, -0.75e-1,
	0, -0.44642857142857143e-1,  0, -0.30381944444444444e-1,  0, -0.22372159090909091e-1,
	0, -0.17352764423076923e-1,  0, -0.1396484375e-1,         0, -0.11551800896139706e-1,
	0, -0.97616095291940789e-2,  0, -0.83903358096168155e-2,  0, -0.73125258735988451e-2,
	0, -0.64472103118896484e-2,  0, -0.57400376708419235e-2,  0, -0.51533096823199042e-2,
	0, -0.46601434869150962e-2,  0, -0.42409070936793631e-2,  0, -0.38809645588376692e-2,
	0, -0.35692053938259345e-2,  0, -0.32970595034734847e-2,  0, -0.30578216492580307e-2,
	0, -0.28461784011089422e-2,  0, -0.26578706382072899e-2,  0, -0.24894486782468835e-2,
	0, -0.23380918921119752e-2,  0, -0.22014739737101382e-2,  0, -0.20776610325181674e-2,
	0, -0.19650336162772836e-2,  0, -0.18622264064031275e-2,  0, -0.17680811205154182e-2,
	0, -0.16816093935831068e-2,  0, -0.16019632753514440e-2,  0, -0.15284115961225676e-2,
	0, -0.14603208940791154e-2,  0, -0.13971399176302534e-2,  0, -0.13383869512751784e-2,
	0, -0.12836393876290286e-2,  0, -0.12325250985000168e-2,  0, -0.11847152561624393e-2,
	0, -0.11399183307022237e-2,  0, -0.10978750465914472e-2,  0, -0.10583541258722429e-2,
	0, -0.10211486797106276e-2,  0, -0.98607313698333129e-3,  0, -0.95296061974295640e-3,
	0, -0.92166069218363342e-3,  0, -0.89203742309170971e-3,  0, -0.86396771246586756e-3,
	0, -0.83733984160271206e-3,  0, -0.81205221290867015e-3
};

static const double atanc[100] = {
	0,  1,                       0, -0.33333333333333333,     0,  0.2,
	0, -0.14285714285714286,     0,  0.11111111111111111,     0, -0.90909090909090909e-1,
	0,  0.76923076923076923e-1,  0, -0.66666666666666667e-1,  0,  0.58823529411764706e-1,
	0, -0.52631578947368421e-1,  0,  0.47619047619047619e-1,  0, -0.43478260869565217e-1,
	0,  0.4e-1,                  0, -0.37037037037037037e-1,  0,  0.34482758620689655e-1,
	0, -0.32258064516129032e-1,  0,  0.30303030303030303e-1,  0, -0.28571428571428571e-1,
	0,  0.27027027027027027e-1,  0, -0.25641025641025641e-1,  0,  0.24390243902439024e-1,
	0, -0.23255813953488372e-1,  0,  0.22222222222222222e-1,  0, -0.21276595744680851e-1,
	0,  0.20408163265306122e-1,  0, -0.19607843137254902e-1,  0,  0.18867924528301887e-1,
	0, -0.18181818181818182e-1,  0,  0.17543859649122807e-1,  0, -0.16949152542372881e-1,
	0,  0.16393442622950820e-1,  0, -0.15873015873015873e-1,  0,  0.15384615384615385e-1,
	0, -0.14925373134328358e-1,  0,  0.14492753623188406e-1,  0, -0.14084507042253521e-1,
	0,  0.13698630136986301e-1,  0, -0.13333333333333333e-1,  0,  0.12987012987012987e-1,
	0, -0.12658227848101266e-1,  0,  0.12345679012345679e-1,  0, -0.12048192771084337e-1,
	0,  0.11764705882352941e-1,  0, -0.11494252873563218e-1,  0,  0.11235955056179775e-1,
	0, -0.10989010989010989e-1,  0,  0.10752688172043011e-1,  0, -0.10526315789473684e-1,
	0,  0.10309278350515464e-1,  0, -0.10101010101010101e-1
};

static const double acotc[100] = {
	1.5707963267948966,
   	-1,                      0,  0.33333333333333333,    0, -0.2,
	0,  0.14285714285714286,    0, -0.11111111111111111,    0,  0.90909090909090909e-1,
	0, -0.76923076923076923e-1, 0,  0.66666666666666667e-1, 0, -0.58823529411764706e-1,
	0,  0.52631578947368421e-1, 0, -0.47619047619047619e-1, 0,  0.43478260869565217e-1,
	0, -0.4e-1,                 0,  0.37037037037037037e-1, 0, -0.34482758620689655e-1,
	0,  0.32258064516129032e-1, 0, -0.30303030303030303e-1, 0,  0.28571428571428571e-1,
	0, -0.27027027027027027e-1, 0,  0.25641025641025641e-1, 0, -0.24390243902439024e-1,
	0,  0.23255813953488372e-1, 0, -0.22222222222222222e-1, 0,  0.21276595744680851e-1,
	0, -0.20408163265306122e-1, 0,  0.19607843137254902e-1, 0, -0.18867924528301887e-1,
	0,  0.18181818181818182e-1, 0, -0.17543859649122807e-1, 0,  0.16949152542372881e-1,
	0, -0.16393442622950820e-1, 0,  0.15873015873015873e-1, 0, -0.15384615384615385e-1,
	0,  0.14925373134328358e-1, 0, -0.14492753623188406e-1, 0,  0.14084507042253521e-1,
	0, -0.13698630136986301e-1, 0,  0.13333333333333333e-1, 0, -0.12987012987012987e-1,
	0,  0.12658227848101266e-1, 0, -0.12345679012345679e-1, 0,  0.12048192771084337e-1,
	0, -0.11764705882352941e-1, 0,  0.11494252873563218e-1, 0, -0.11235955056179775e-1,
	0,  0.10989010989010989e-1, 0, -0.10752688172043011e-1, 0,  0.10526315789473684e-1,
	0, -0.10309278350515464e-1, 0,  0.10101010101010101e-1
};

static const double asinhc[100] = {
	0,  1,                       0, -0.16666666666666667,     0,  0.75e-1,
	0, -0.44642857142857143e-1,  0,  0.30381944444444444e-1,  0, -0.22372159090909091e-1,
	0,  0.17352764423076923e-1,  0, -0.1396484375e-1,         0,  0.11551800896139706e-1,
	0, -0.97616095291940789e-2,  0,  0.83903358096168155e-2,  0, -0.73125258735988451e-2,
	0,  0.64472103118896484e-2,  0, -0.57400376708419235e-2,  0,  0.51533096823199042e-2,
	0, -0.46601434869150962e-2,  0,  0.42409070936793631e-2,  0, -0.38809645588376692e-2,
	0,  0.35692053938259345e-2,  0, -0.32970595034734847e-2,  0,  0.30578216492580307e-2,
	0, -0.28461784011089422e-2,  0,  0.26578706382072899e-2,  0, -0.24894486782468835e-2,
	0,  0.23380918921119752e-2,  0, -0.22014739737101382e-2,  0,  0.20776610325181674e-2,
	0, -0.19650336162772836e-2,  0,  0.18622264064031275e-2,  0, -0.17680811205154182e-2,
	0,  0.16816093935831068e-2,  0, -0.16019632753514440e-2,  0,  0.15284115961225676e-2,
	0, -0.14603208940791154e-2,  0,  0.13971399176302534e-2,  0, -0.13383869512751784e-2,
	0,  0.12836393876290286e-2,  0, -0.12325250985000168e-2,  0,  0.11847152561624393e-2,
	0, -0.11399183307022237e-2,  0,  0.10978750465914472e-2,  0, -0.10583541258722429e-2,
	0,  0.10211486797106276e-2,  0, -0.98607313698333129e-3,  0,  0.95296061974295640e-3,
	0, -0.92166069218363342e-3,  0,  0.89203742309170971e-3,  0, -0.86396771246586756e-3,
	0,  0.83733984160271206e-3,  0, -0.81205221290867015e-3
};

static const double atanhc[100] = {
	0,  1,                       0,  0.33333333333333333,     0,  0.2,
	0,  0.14285714285714286,     0,  0.11111111111111111,     0,  0.90909090909090909e-1,
	0,  0.76923076923076923e-1,  0,  0.66666666666666667e-1,  0,  0.58823529411764706e-1,
	0,  0.52631578947368421e-1,  0,  0.47619047619047619e-1,  0,  0.43478260869565217e-1,
	0,  0.4e-1,                  0,  0.37037037037037037e-1,  0,  0.34482758620689655e-1,
	0,  0.32258064516129032e-1,  0,  0.30303030303030303e-1,  0,  0.28571428571428571e-1,
	0,  0.27027027027027027e-1,  0,  0.25641025641025641e-1,  0,  0.24390243902439024e-1,
	0,  0.23255813953488372e-1,  0,  0.22222222222222222e-1,  0,  0.21276595744680851e-1,
	0,  0.20408163265306122e-1,  0,  0.19607843137254902e-1,  0,  0.18867924528301887e-1,
	0,  0.18181818181818182e-1,  0,  0.17543859649122807e-1,  0,  0.16949152542372881e-1,
	0,  0.16393442622950820e-1,  0,  0.15873015873015873e-1,  0,  0.15384615384615385e-1,
	0,  0.14925373134328358e-1,  0,  0.14492753623188406e-1,  0,  0.14084507042253521e-1,
	0,  0.13698630136986301e-1,  0,  0.13333333333333333e-1,  0,  0.12987012987012987e-1,
	0,  0.12658227848101266e-1,  0,  0.12345679012345679e-1,  0,  0.12048192771084337e-1,
	0,  0.11764705882352941e-1,  0,  0.11494252873563218e-1,  0,  0.11235955056179775e-1,
	0,  0.10989010989010989e-1,  0,  0.10752688172043011e-1,  0,  0.10526315789473684e-1,
	0,  0.10309278350515464e-1,  0,  0.10101010101010101e-1
};

static const double asechc[100] = {
	 0.69314718055994531,     0, -0.25,                    0, -0.9375e-1,               0,
	-0.52083333333333333e-1,  0, -0.341796875e-1,          0, -0.24609375e-1,           0,
	-0.18798828125e-1,        0, -0.14962332589285714e-1,  0, -0.12273788452148438e-1,  0,
	-0.10303921169704861e-1,  0, -0.88098526000976562e-2,  0, -0.76449134133078835e-2,  0,
	-0.67158440748850505e-2,  0, -0.59608083504896898e-2,  0, -0.53373564566884722e-2,  0,
	-0.48154816031455994e-2,  0, -0.43734354403568432e-2,  0, -0.39951105752740713e-2,  0,
	-0.36683499880988772e-2,  0, -0.33838242272491028e-2,  0, -0.31342671904894814e-2,  0,
	-0.29139445535162979e-2,  0, -0.27182767890756374e-2,  0, -0.25435671277739897e-2,  0,
	-0.23868021398643080e-2,  0, -0.22455034531843410e-2,  0, -0.21176160523742860e-2,  0,
	-0.20014231276898259e-2,  0, -0.18954804493746119e-2,  0, -0.17985652777656841e-2,  0,
	-0.17096362168094919e-2,  0, -0.16278013926958222e-2,  0, -0.15522930273119828e-2,  0,
	-0.14824469682318293e-2,  0, -0.14176860928895218e-2,  0, -0.13575067648648238e-2,  0,
	-0.13014677124572095e-2,  0, -0.12491808430743414e-2,  0, -0.12003036147961556e-2,  0,
	-0.11545326682753291e-2,  0, -0.11115984846738403e-2,  0, -0.10712608835048312e-2,  0,
	-0.10333052116119446e-2,  0, -0.99753910369243980e-3,  0, -0.96378971769458091e-3,  0,
	-0.93190136654122934e-3,  0, -0.90173348203835873e-3,  0, -0.87315885834316402e-3,  0,
	-0.84606213161940698e-3,  0, -0.82033845997916679e-3,  0
};

static const double acothc[100] = {
	0,  1,                       0,  0.33333333333333333,     0,  0.2,
	0,  0.14285714285714286,     0,  0.11111111111111111,     0,  0.90909090909090909e-1,
	0,  0.76923076923076923e-1,  0,  0.66666666666666667e-1,  0,  0.58823529411764706e-1,
	0,  0.52631578947368421e-1,  0,  0.47619047619047619e-1,  0,  0.43478260869565217e-1,
	0,  0.4e-1,                  0,  0.37037037037037037e-1,  0,  0.34482758620689655e-1,
	0,  0.32258064516129032e-1,  0,  0.30303030303030303e-1,  0,  0.28571428571428571e-1,
	0,  0.27027027027027027e-1,  0,  0.25641025641025641e-1,  0,  0.24390243902439024e-1,
	0,  0.23255813953488372e-1,  0,  0.22222222222222222e-1,  0,  0.21276595744680851e-1,
	0,  0.20408163265306122e-1,  0,  0.19607843137254902e-1,  0,  0.18867924528301887e-1,
	0,  0.18181818181818182e-1,  0,  0.17543859649122807e-1,  0,  0.16949152542372881e-1,
	0,  0.16393442622950820e-1,  0,  0.15873015873015873e-1,  0,  0.15384615384615385e-1,
	0,  0.14925373134328358e-1,  0,  0.14492753623188406e-1,  0,  0.14084507042253521e-1,
	0,  0.13698630136986301e-1,  0,  0.13333333333333333e-1,  0,  0.12987012987012987e-1,
	0,  0.12658227848101266e-1,  0,  0.12345679012345679e-1,  0,  0.12048192771084337e-1,
	0,  0.11764705882352941e-1,  0,  0.11494252873563218e-1,  0,  0.11235955056179775e-1,
	0,  0.10989010989010989e-1,  0,  0.10752688172043011e-1,  0,  0.10526315789473684e-1,
	0,  0.10309278350515464e-1,  0,  0.10101010101010101e-1
};

static const double bessel_J2c[100] = {
	0,
   	0,  0.125,                       0, -0.10416666666666666667e-1,   0,  0.32552083333333333333e-3,
	0, -0.54253472222222222222e-5,   0,  0.56514033564814814815e-7,   0, -0.40367166832010582011e-9,
	0,  0.21024566058338844797e-11,  0, -0.83430817691820812687e-14,  0,  0.26072130528694003965e-16,
	0, -0.65838713456297989810e-19,  0,  0.13716398636728747877e-21,  0, -0.23979717896378929855e-24,
	0,  0.35684104012468645618e-27,  0, -0.45748851298036725151e-30,  0,  0.51058985823701702177e-33,
	0, -0.50057829238923237429e-36,  0,  0.43452976769898643601e-39,  0, -0.33632334961221860372e-42,
	0,  0.23355788167515180814e-45,  0, -0.14633952485911767427e-48,  0,  0.83147457306316860383e-52,
	0, -0.43036986183393820074e-55,  0,  0.20377360882288740565e-58,  0, -0.88597221227342350284e-62,
	0,  0.35495681581467287774e-65,  0, -0.13146548733876773250e-68,  0,  0.45146115157543864182e-72,
	0, -0.14414468441105959190e-75,  0,  0.42900203693767735683e-79,  0, -0.11929978780246867543e-82,
	0,  0.31067653073559550892e-86,  0, -0.75922905849363516354e-90,  0,  0.17445520645533896221e-93,
	0, -0.37760867198125316496e-97,  0,  0.77125954244537002647e-101, 0, -0.14889180356088224449e-104,
	0,  0.27209759422675848774e-108, 0, -0.47140955340741248742e-112, 0,  0.77534466020956001221e-116,
	0, -0.12122336776259537402e-119, 0,  0.18039191631338597324e-123, 0, -0.25580249051813098871e-127,
	0,  0.34605315275721183538e-131, 0, -0.44709709658554500695e-135, 0,  0.55224443748214551254e-139,
	0, -0.65277120269757152782e-143, 0,  0.73909782914127211030e-147, 0, -0.80232070032704310715e-151,
	0,  0.83575072950733656994e-155, 0
};

/**********************************************
 * ****************************************** *
 * *                                        * *
 * *  The Tester Class                      * *
 * *                                        * *
 * ****************************************** * 
 **********************************************/

template <class T>
class Tester {
	private:
		double norm;

		int error_count;

	public:
		Tester( double n = 0.5  ):error_count( 0 ), norm( n ) {
			// empty
		}

		void reset() {
			error_count = 0;
		}

		int count() {
			return error_count;
		}

		void exp_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				T approx = 1.0;
				T term = 1.0;
	
				for ( int j = 1; j < 100; ++j ) {
					term *= z/j;
					approx += term;
				}
	
				if ( abs( approx - z.exp() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "      exp(z) = " << z.exp() << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.exp() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void sin_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				T approx = z;
				T term = z;
	
				for ( int j = 1; j < 50; ++j ) {
					term *= -z.sqr()/((2*j)*(2*j + 1));
					approx += term;
				}
	
				if ( abs( approx - z.sin() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "      sin(z) = " << z.sin() << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.sin() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void cos_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				T approx = 1.0;
				T term = 1.0;
	
				for ( int j = 1; j < 50; ++j ) {
					term *= -z.sqr()/((2*j - 1)*(2*j));
					approx += term;
				}
	
				if ( abs( approx - z.cos() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "      cos(z) = " << z.cos() << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.cos() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void tan_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				T approx = 0.0;
				T term = 1.0;
	
				for ( int j = 1; j < 100; ++j ) {
					term *= z;
					approx += tanc[j]*term;
				}
	
				if ( abs( approx - z.tan() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "      tan(z) = " << z.tan() << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.tan() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void sec_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				T approx = 1.0;
				T term = 1.0;
	
				for ( int j = 1; j < 100; ++j ) {
					term *= z;
					approx += secc[j]*term;
				}
	
				if ( abs( approx - z.sec() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "      sec(z) = " << z.sec() << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.sec() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void csc_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				T approx = 1.0/z;
				T term = 1.0;
	
				for ( int j = 1; j < 100; ++j ) {
					term *= z;
					approx += cscc[j]*term;
				}
	
				if ( abs( approx - z.csc() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "      csc(z) = " << z.csc() << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.csc() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void cot_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				T approx = 1.0/z;
				T term = 1.0;
	
				for ( int j = 1; j < 100; ++j ) {
					term *= z;
					approx += cotc[j]*term;
				}
	
				if ( abs( approx - z.cot() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "      cot(z) = " << z.cot() << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.cot() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void sinh_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				T approx = z;
				T term = z;
	
				for ( int j = 1; j < 50; ++j ) {
					term *= z.sqr()/((2*j)*(2*j + 1));
					approx += term;
				}
	
				if ( abs( approx - z.sinh() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "     sinh(z) = " << z.sinh() << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.sinh() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void cosh_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				T approx = 1.0;
				T term = 1.0;
	
				for ( int j = 1; j < 50; ++j ) {
					term *= z.sqr()/((2*j - 1)*(2*j));
					approx += term;
				}
	
				if ( abs( approx - z.cosh() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "     cosh(z) = " << z.cosh() << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.cosh() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void tanh_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				T approx = 0.0;
				T term = 1.0;
	
				for ( int j = 1; j < 100; ++j ) {
					term *= z;
					approx += tanhc[j]*term;
				}
	
				if ( abs( approx - z.tanh() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "     tanh(z) = " << z.tanh() << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.tanh() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void sech_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				T approx = 1.0;
				T term = 1.0;
	
				for ( int j = 1; j < 100; ++j ) {
					term *= z;
					approx += sechc[j]*term;
				}
	
				if ( abs( approx - z.sech() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "     sech(z) = " << z.sech() << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.sech() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void csch_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				T approx = 1.0/z;
				T term = 1.0;
	
				for ( int j = 1; j < 100; ++j ) {
					term *= z;
					approx += cschc[j]*term;
				}
	
				if ( abs( approx - z.csch() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "     csch(z) = " << z.csch() << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.csch() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void coth_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				T approx = 1.0/z;
				T term = 1.0;
	
				for ( int j = 1; j < 100; ++j ) {
					term *= z;
					approx += cothc[j]*term;
				}
	
				if ( abs( approx - z.coth() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "     coth(z) = " << z.coth() << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.coth() ) << endl << endl;
					++error_count;
				}
			}
		}

		void log_test( int N, double eps = 1e-13 ) {
			T z;

			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
				z += 1.0;
	
				T approx = 0.0;
				T term = 1.0;
	
				for ( int j = 1; j < 100; ++j ) {
					term *= (z - 1.0);
					approx += logc[j]*term;
				}
	
				if ( abs( approx - z.log() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "      log(z) = " << z.log() << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.log() ) << endl << endl;
					++error_count;
				}

				if ( abs( z - z.log().exp() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "      log(z) = " << z.log() << endl;
					cout << " exp(log(z)) = " << z.log().exp() << endl;
					cout << "        Error: " << abs( z - z.log().exp() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void asin_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				T approx = 0.0;
				T term = 1.0;
	
				for ( int j = 1; j < 100; ++j ) {
					term *= z;
					approx += asinc[j]*term;
				}
	
				if ( abs( approx - z.asin() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "     asin(z) = " << z.asin() << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.asin() ) << endl << endl;
					++error_count;
				}
	
				if ( abs( z - z.asin().sin() ) > eps ) {
					cout << "           z  = " << z << endl;
					cout << "          |z| = " << z.abs() << endl;
					cout << "      asin(z) = " << z.asin() << endl;
					cout << " sin(asin(z)) = " << z.asin().sin() << endl;
					cout << "         Error: " << abs( z - z.asin().sin() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void acos_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				T approx = acosc[0];
				T term = 1.0;
	
				for ( int j = 1; j < 100; ++j ) {
					term *= z;
					approx += acosc[j]*term;
				}
	
				if ( abs( approx - z.acos() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "     acos(z) = " << z.acos() << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.acos() ) << endl << endl;
					++error_count;
				}
	
				if ( abs( z - z.acos().cos() ) > eps ) {
					cout << "           z  = " << z << endl;
					cout << "          |z| = " << z.abs() << endl;
					cout << "      acos(z) = " << z.acos() << endl;
					cout << " cos(acos(z)) = " << z.acos().cos() << endl;
					cout << "         Error: " << abs( z - z.acos().cos() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void atan_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				T approx = atanc[0];
				T term = 1.0;
	
				for ( int j = 1; j < 100; ++j ) {
					term *= z;
					approx += atanc[j]*term;
				}
	
				if ( abs( approx - z.atan() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "     atan(z) = " << z.atan() << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.atan() ) << endl << endl;
					++error_count;
				}
	
				if ( abs( z - z.atan().tan() ) > eps ) {
					cout << "           z  = " << z << endl;
					cout << "          |z| = " << z.abs() << endl;
					cout << "      atan(z) = " << z.atan() << endl;
					cout << " tan(atan(z)) = " << z.atan().tan() << endl;
					cout << "         Error: " << abs( z - z.atan().tan() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void asec_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				if ( abs( z - z.asec().sec() ) > eps ) {
					cout << "           z  = " << z << endl;
					cout << "          |z| = " << z.abs() << endl;
					cout << "      asec(z) = " << z.asec() << endl;
					cout << " sec(asec(z)) = " << z.asec().sec() << endl;
					cout << "         Error: " << abs( z - z.asec().sec() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void acsc_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				if ( abs( z - z.acsc().csc() ) > eps ) {
					cout << "           z  = " << z << endl;
					cout << "          |z| = " << z.abs() << endl;
					cout << "      acsc(z) = " << z.acsc() << endl;
					cout << " csc(acsc(z)) = " << z.acsc().csc() << endl;
					cout << "         Error: " << abs( z - z.acsc().csc() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void acot_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				T approx = acotc[0];
				T term = 1.0;
	
				for ( int j = 1; j < 100; ++j ) {
					term *= z;
					approx += acotc[j]*term;
				}
	
				if ( abs( approx - z.acot() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "     acot(z) = " << z.acot() << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.acot() ) << endl << endl;
					++error_count;
				}
	
				if ( abs( z - z.acot().cot() ) > eps ) {
					cout << "           z  = " << z << endl;
					cout << "          |z| = " << z.abs() << endl;
					cout << "      acot(z) = " << z.acot() << endl;
					cout << " cot(acot(z)) = " << z.acot().cot() << endl;
					cout << "         Error: " << abs( z - z.acot().cot() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void asinh_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				T approx = asinhc[0];
				T term = 1.0;
	
				for ( int j = 1; j < 100; ++j ) {
					term *= z;
					approx += asinhc[j]*term;
				}
	
				if ( abs( approx - z.asinh() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "     asinh(z) = " << z.asinh() << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.asinh() ) << endl << endl;
					++error_count;
				}
	
				if ( abs( z - z.asinh().sinh() ) > eps ) {
					cout << "           z  = " << z << endl;
					cout << "          |z| = " << z.abs() << endl;
					cout << "      asinh(z) = " << z.asinh() << endl;
					cout << " sinh(asinh(z)) = " << z.asinh().sinh() << endl;
					cout << "         Error: " << abs( z - z.asinh().sinh() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void acosh_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				if ( abs( z - z.acosh().cosh() ) > eps ) {
					cout << "           z  = " << z << endl;
					cout << "          |z| = " << z.abs() << endl;
					cout << "      acosh(z) = " << z.acosh() << endl;
					cout << " cosh(acosh(z)) = " << z.acosh().cosh() << endl;
					cout << "         Error: " << abs( z - z.acosh().cosh() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void atanh_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				T approx = atanhc[0];
				T term = 1.0;
	
				for ( int j = 1; j < 100; ++j ) {
					term *= z;
					approx += atanhc[j]*term;
				}
	
				if ( abs( approx - z.atanh() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "     atanh(z) = " << z.atanh() << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.atanh() ) << endl << endl;
					++error_count;
				}
	
				if ( abs( z - z.atanh().tanh() ) > eps ) {
					cout << "           z  = " << z << endl;
					cout << "          |z| = " << z.abs() << endl;
					cout << "      atanh(z) = " << z.atanh() << endl;
					cout << " tanh(atanh(z)) = " << z.atanh().tanh() << endl;
					cout << "         Error: " << abs( z - z.atanh().tanh() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void asech_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				T approx = asechc[0] - z.log();

				T term = 1.0;
	
				for ( int j = 1; j < 100; ++j ) {
					term *= z;
					approx += asechc[j]*term;
				}
	
				if ( abs( approx - z.asech() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "     asech(z) = " << z.asech() << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.asech() ) << endl << endl;
					++error_count;
				}
	
				if ( abs( z - z.asech().sech() ) > eps ) {
					cout << "           z  = " << z << endl;
					cout << "          |z| = " << z.abs() << endl;
					cout << "      asech(z) = " << z.asech() << endl;
					cout << " sech(asech(z)) = " << z.asech().sech() << endl;
					cout << "         Error: " << abs( z - z.asech().sech() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void acsch_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				if ( abs( z - z.acsch().csch() ) > eps ) {
					cout << "           z  = " << z << endl;
					cout << "          |z| = " << z.abs() << endl;
					cout << "      acsch(z) = " << z.acsch() << endl;
					cout << " csch(acsch(z)) = " << z.acsch().csch() << endl;
					cout << "         Error: " << abs( z - z.acsch().csch() ) << endl << endl;
					++error_count;
				}
			}
		}
	
		void acoth_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				T approx = z.imag() * ( -1.5707963267948966 / z.imag().abs() );
				T term = 1.0;
	
				for ( int j = 1; j < 100; ++j ) {
					term *= z;
					approx += acothc[j]*term;
				}
	
				if ( abs( approx - z.acoth() ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "     acoth(z) = " << z.acoth() << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.acoth() ) << endl << endl;
					++error_count;
				}
	
				if ( abs( z - z.acoth().coth() ) > eps ) {
					cout << "           z  = " << z << endl;
					cout << "          |z| = " << z.abs() << endl;
					cout << "      acoth(z) = " << z.acoth() << endl;
					cout << " coth(acoth(z)) = " << z.acoth().coth() << endl;
					cout << "         Error: " << abs( z - z.acoth().coth() ) << endl << endl;
					++error_count;
				}
			}
		}

		void bessel_J2_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();
	
				T approx = T::ZERO;
				T term = 1.0;
	
				for ( int j = 1; j < 100; ++j ) {
					term *= z;
					approx += bessel_J2c[j]*term;
				}
	
				if ( abs( approx - z.bessel_J( 2 ) ) > eps ) {
					cout << "          z  = " << z << endl;
					cout << "         |z| = " << z.abs() << endl;
					cout << "      J_2(z) = " << z.bessel_J( 2 ) << endl;
					cout << "Approximation: " << approx << endl;
					cout << "        Error: " << abs( approx - z.bessel_J( 2 ) ) << endl << endl;
					++error_count;
				}
			}
		}

		void sqr_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();

				T z1 = z.sqr();
				T z2 = z*z;
				T z3 = z;
				z3 *= z;
				T z4 = z.pow( 2.0 );

				if ( abs( z1 - z2 ) > eps ) {
					cout << "           z  = " << z << endl;
					cout << "          |z| = " << z.abs() << endl;
					cout << "       sqr(z) = " << z1 << endl;
					cout << "          z*z = " << z2 << endl;
					cout << "         Error: " << abs(z2 - z1) << endl << endl;
					++error_count;
				}

				if ( abs( z1 - z3 ) > eps ) {
					cout << "           z  = " << z << endl;
					cout << "          |z| = " << z.abs() << endl;
					cout << "       sqr(z) = " << z1 << endl;
					cout << "      z *= z -> " << z3 << endl;
					cout << "         Error: " << abs(z3 - z1) << endl << endl;
					++error_count;
				}

				if ( abs( z1 - z4 ) > eps ) {
					cout << "           z  = " << z << endl;
					cout << "          |z| = " << z.abs() << endl;
					cout << "       sqr(z) = " << z1 << endl;
					cout << "     pow(z,2) = " << z4 << endl;
					cout << "         Error: " << abs(z4 - z1) << endl << endl;
					++error_count;
				}
			}
		}

		void conj_test( int N, double eps = 1e-13 ) {
			T z;
	
			for ( int i = 0; i < N; ++i ) {
				z = T::random();
				z *= norm/z.abs();

				T z1 = z.conj();
				T z2 = z*z1;
				T z3 = z1*z;

				if ( abs( z2 - z3 ) > eps ) {
					cout << "           z  = " << z << endl;
					cout << "          |z| = " << z.abs() << endl;
					cout << "      conj(z) = " << z1 << endl;
					cout << "    z*conj(z) = " << z2 << endl;
					cout << "    conj(z)*z = " << z3 << endl << endl;
					++error_count;
				}

				if ( abs_imag( z + z1 ) != 0 ) {
					cout << "           z  = " << z << endl;
					cout << "          |z| = " << z.abs() << endl;
					cout << "  z + conj(z) = " << ( z + z1 ) << endl << endl;
					++error_count;
				}

				if ( z2.abs_imag() > eps ) {
					cout << "                z  = " << z << endl;
					cout << "               |z| = " << z.abs() << endl;
					cout << "       z * conj(z) = " << ( z + z1 ) << endl;
					cout << " |Im(z * conj(z))| = " << abs_imag( z + z1 ) << endl << endl;
					++error_count;
				}

				if ( std::fabs( z2.real() - z.norm() ) > eps ) {
					cout << "                z  = " << z << endl;
					cout << "               |z| = " << z.abs() << endl;
					cout << "       z * conj(z) = " << ( z + z1 ) << endl;
					cout << " |Im(z * conj(z))| = " << abs_imag( z + z1 ) << endl << endl;
					++error_count;
				}
			}
		}

		void arith_test( int N, double eps = 1e-13 ) {
			T z1, z2;
	
			for ( int i = 0; i < N; ++i ) {
				z1 = T::random();
				z1 *= norm/z1.abs();
				z2 = T::random();
				z2 *= norm/z2.abs();

				T z3 = z1*z1 + z2*z1 + z1*z2 + z2*z2; 
				T z4 = (z1 + z2)*(z1 + z2);
				T z5 = pow( z1, 2.0 ) + z2*z1 + z1*z2 + pow( z2, 2.0 );
				T z6 = T::ZERO;
				z6 += z1;
				z6 *= z1;
				z6 += z1*z2;
				z6 += z2*z1;
				z6 += z2*z2;

				if ( abs( z3 - z4 ) > eps ) {
					cout << "                            z1  = " << z1 << endl;
					cout << "                            z2  = " << z2 << endl;
					cout << "  z1*z1 + z2*z1 + z1*z2 + z2*z2 = " << z3 << endl;
					cout << "            (z1 + z2)*(z1 + z2) = " << z4 << endl << endl;
					cout << "                           Error: " << abs( z3 - z4 ) << endl << endl;
					++error_count;
				}

				if ( abs( z3 - z5 ) > eps ) {
					cout << "                                  z1  = " << z1 << endl;
					cout << "                                  z2  = " << z2 << endl;
					cout << "        z1*z1 + z2*z1 + z1*z2 + z2*z2 = " << z3 << endl;
					cout << "pow(z1,2) + z2*z1 + z1*z2 + pow(z2,2) = " << z5 << endl << endl;
					cout << "                                 Error: " << abs( z3 - z5 ) << endl << endl;
					++error_count;
				}


				if ( abs( z3 - z6 ) > eps ) {
					cout << "                           z1  = " << z1 << endl;
					cout << "                           z2  = " << z2 << endl;
					cout << " z1*z1 + z2*z1 + z1*z2 + z2*z2 = " << z3 << endl;
					cout << "        using +=, *=, +=, etc. = " << z6 << endl << endl;
					cout << "                          Error: " << abs( z3 - z6 ) << endl << endl;
					++error_count;
				}

				z3 = z1*z1 - z2*z1 - z1*z2 + z2*z2; 
				z4 = (z1 - z2)*(z1 - z2);
				z5 = pow( z1, 2.0 ) - z2*z1 - z1*z2 + pow( z2, 2.0 );
				z6 = T::ZERO;
				z6 += z1;
				z6 *= z1;
				z6 -= z1*z2;
				z6 -= z2*z1;
				z6 += z2*z2;

				if ( abs( z3 - z4 ) > eps ) {
					cout << "                            z1  = " << z1 << endl;
					cout << "                            z2  = " << z2 << endl;
					cout << "  z1*z1 - z2*z1 - z1*z2 + z2*z2 = " << z3 << endl;
					cout << "            (z1 - z2)*(z1 - z2) = " << z4 << endl << endl;
					cout << "                           Error: " << abs( z3 - z4 ) << endl << endl;
					++error_count;
				}

				if ( abs( z3 - z5 ) > eps ) {
					cout << "                                  z1  = " << z1 << endl;
					cout << "                                  z2  = " << z2 << endl;
					cout << "        z1*z1 - z2*z1 - z1*z2 + z2*z2 = " << z3 << endl;
					cout << "pow(z1,2) - z2*z1 - z1*z2 + pow(z2,2) = " << z5 << endl << endl;
					cout << "                                 Error: " << abs( z3 - z5 ) << endl << endl;
					++error_count;
				}


				if ( abs( z3 - z6 ) > eps ) {
					cout << "                           z1  = " << z1 << endl;
					cout << "                           z2  = " << z2 << endl;
					cout << " z1*z1 - z2*z1 - z1*z2 + z2*z2 = " << z3 << endl;
					cout << "        using +=, *=, -=, etc. = " << z6 << endl << endl;
					cout << "                          Error: " << abs( z3 - z6 ) << endl << endl;
					++error_count;
				}
			}
		}

		void bool_test( int N ) {
			T z1, z2;

			for ( int i = 0; i < N; ++i ) {
				z1 = T::random();
				z2 = T::random();
				bool b1, b2, b3, b4;

				if ( z1 != z1 ) {
					cout << "       z1  = " << z1 << endl;
					cout << " z1 != z1  = " << (z1 != z1 ? "true" : "false") << endl;
					++error_count;
				}

				if ( !(z1 == z1) ) {
					cout << "       z1  = " << z1 << endl;
					cout << " z1 == z1  = " << (z1 == z1 ? "true" : "false") << endl;
					++error_count;
				}

				if ( !(z1 != z2) ) {
					cout << "       z1  = " << z1 << endl;
					cout << "       z2  = " << z2 << endl;
					cout << " z1 != z2  = " << (z1 != z2 ? "true" : "false") << endl;
					++error_count;
				}

				if ( z1 == z2 ) {
					cout << "       z1  = " << z1 << endl;
					cout << "       z2  = " << z2 << endl;
					cout << " z1 == z2  = " << (z1 == z2 ? "true" : "false") << endl;
					++error_count;
				}
			}
		}

		void assign_test( int N, double eps = 1e-15 ) {
			T z1, z2, z3, z4;

			for ( int i = 0; i < N; ++i ) {
				z1 = T::random();
				z2 = T::random();

				z3 = z1;
				z3 += z2;
				z4 = z1 + z2;

				if ( abs( z3 - z4 ) > eps ) {
					cout << "                z1 = " << z1 << endl;
					cout << "                z2 = " << z2 << endl;
					cout << " z3 = z1; z3 += z2 = " << z3 << endl;
					cout << "           z1 + z2 = " << z4 << endl;
					cout << "                          Error: " << abs( z3 - z4 ) << endl << endl;
					++error_count;
				}

				z3 = z1;
				z3 -= z2;
				z4 = z1 - z2;

				if ( abs( z3 - z4 ) > eps ) {
					cout << "                z1 = " << z1 << endl;
					cout << "                z2 = " << z2 << endl;
					cout << " z3 = z1; z3 -= z2 = " << z3 << endl;
					cout << "           z1 - z2 = " << z4 << endl;
					cout << "                          Error: " << abs( z3 - z4 ) << endl << endl;
					++error_count;
				}

				z3 = z1;
				z3 *= z2;
				z4 = z1 * z2;

				if ( abs( z3 - z4 ) > eps ) {
					cout << "                z1 = " << z1 << endl;
					cout << "                z2 = " << z2 << endl;
					cout << " z3 = z1; z3 *= z2 = " << z3 << endl;
					cout << "           z1 * z2 = " << z4 << endl;
					cout << "                          Error: " << abs( z3 - z4 ) << endl << endl;
					++error_count;
				}

				z3 = z1;
				z3 /= z2;
				z4 = z1 / z2;

				if ( abs( z3 - z4 ) > eps ) {
					cout << "                z1 = " << z1 << endl;
					cout << "                z2 = " << z2 << endl;
					cout << " z3 = z1; z3 /= z2 = " << z3 << endl;
					cout << "           z1 / z2 = " << z4 << endl;
					cout << "                          Error: " << abs( z3 - z4 ) << endl << endl;
					++error_count;
				}
			}
		}

		void inverse_arith_test( int N, double eps = 1e-15 ) {
			T z1, z2, z3;

			for ( int i = 0; i < N; ++i ) {
				z1 = T::random();
				z2 = T::random();

				z3 = z1 + z2;
				z3 = z3 - z2;

				if ( abs( z3 - z1 ) > eps ) {
					cout << "                         z1 = " << z1 << endl;
					cout << "                         z2 = " << z2 << endl;
					cout << " z3 = z1 + z2; z3 = z3 - z2 = " << z3 << endl;
					cout << "                       Error: " << abs( z3 - z1 ) << endl << endl;
					++error_count;
				}

				z3 = z1 + z2;
				z3 = (-z2) + z3;

				if ( abs( z3 - z1 ) > eps ) {
					cout << "                            z1 = " << z1 << endl;
					cout << "                            z2 = " << z2 << endl;
					cout << " z3 = z1 + z2; z3 = (-z2) + z3 = " << z3 << endl;
					cout << "                          Error: " << abs( z3 - z1 ) << endl << endl;
					++error_count;
				}

				z3 = z1;
				z3 += z2;
				z3 -= z2;

				if ( abs( z3 - z1 ) > eps ) {
					cout << "                        z1 = " << z1 << endl;
					cout << "                        z2 = " << z2 << endl;
					cout << " z3 = z1; z3 +=2; z3 -= z2 = " << z3 << endl;
					cout << "                      Error: " << abs( z3 - z1 ) << endl << endl;
					++error_count;
				}

				z3 = z1 * z2;
				z3 = z3 / z2;

				if ( abs( z3 - z1 ) > eps ) {
					cout << "                         z1 = " << z1 << endl;
					cout << "                         z2 = " << z2 << endl;
					cout << " z3 = z1 * z2; z3 = z3 / z2 = " << z3 << endl;
					cout << "                       Error: " << abs( z3 - z1 ) << endl << endl;
					++error_count;
				}

				z3 = z1;
				z3 *= z2;
				z3 /= z2;

				if ( abs( z3 - z1 ) > eps ) {
					cout << "                          z1 = " << z1 << endl;
					cout << "                          z2 = " << z2 << endl;
					cout << " z3 = z1; z3 *= z2; z3 /= z2 = " << z3 << endl;
					cout << "                        Error: " << abs( z3 - z1 ) << endl << endl;
					++error_count;
				}
			}
		}

		void inverse_test( int N, double eps = 1e-15 ) {
			T z1, z2, z3;

			for ( int i = 0; i < N; ++i ) {
				z1 = T::random();
				z2 = z1.conj() / z1.norm();

				z3 = z1.inverse();

				if ( abs( z3 - z2 ) > eps ) {
					cout << "                  z1 = " << z1 << endl;
					cout << "   conj(z1)/norm(z1) = " << z2 << endl;
					cout << "         inverse(z1) = " << z3 << endl;
					cout << "                Error: " << abs( z3 - z2 ) << endl << endl;
					++error_count;
				}

				z3 = 1.0/z1;

				if ( abs( z3 - z2 ) > eps ) {
					cout << "                  z1 = " << z1 << endl;
					cout << "   conj(z1)/norm(z1) = " << z2 << endl;
					cout << "            1.0 / z1 = " << z3 << endl;
					cout << "                Error: " << abs( z3 - z2 ) << endl << endl;
					++error_count;
				}

				z3 = z1.pow( -1.0 );

				if ( abs( z3 - z2 ) > eps ) {
					cout << "                  z1 = " << z1 << endl;
					cout << "   conj(z1)/norm(z1) = " << z2 << endl;
					cout << "          pow(z1 -1) = " << z3 << endl;
					cout << "                Error: " << abs( z3 - z2 ) << endl << endl;
					++error_count;
				}
			}
		}

		void horner_test( int N, double eps = 1e-14 ) {
			T z1, z2, z3;

			double * v = new double[10];
			double * c = new double[10];

			// try it with 10 different polynomials

			for ( int i = 0; i < 10; ++i ) {
				for ( int j = 0; j < 10; ++j ) {
					v[j] = 2.0*static_cast<double>( rand() )/RAND_MAX - 1.0;
					c[j] = 2.0*static_cast<double>( rand() )/RAND_MAX - 1.0;
				}

				for ( int k = 0; k < N; ++k ) {
					z1 = T::random();
					z1 *= 0.5/z1.abs();

					z2 = z1.horner( v, 10 );
					z3 = v[0]*z1.pow( 9 )
				   	+ v[1]*z1.pow( 8 )
				   	+ v[2]*z1.pow( 7 )
				   	+ v[3]*z1.pow( 6 )
				   	+ v[4]*z1.pow( 5 )
				   	+ v[5]*z1.pow( 4 )
				   	+ v[6]*z1.pow( 3 )
				   	+ v[7]*z1.pow( 2 )
				   	+ v[8]*z1
				   	+ v[9];

					if ( abs( z3 - z2 ) > eps ) {
						cout << "                  z1 = " << z1 << endl;

						for ( int j = 0; j < 9; ++j ) {
							cout << v[j] << "*z^" << (9 - j) << " + ";
						}

						cout << " " << v[9] << endl;

						cout << "              Horner:  " << z2 << endl;
						cout << "           Polynomial: " << z3 << endl;
						cout << "                Error: " << abs( z3 - z2 ) << endl << endl;
						++error_count;
					}

					z2 = z1.horner( v, c, 10 );
					z3 = v[0]*(z1-c[1])*(z1-c[2])*(z1-c[3])*(z1-c[4])*(z1-c[5])*(z1-c[6])*(z1-c[7])*(z1-c[8])*(z1-c[9])
				   	+ v[1]*(z1-c[2])*(z1-c[3])*(z1-c[4])*(z1-c[5])*(z1-c[6])*(z1-c[7])*(z1-c[8])*(z1-c[9])
				   	+ v[2]*(z1-c[3])*(z1-c[4])*(z1-c[5])*(z1-c[6])*(z1-c[7])*(z1-c[8])*(z1-c[9])
				   	+ v[3]*(z1-c[4])*(z1-c[5])*(z1-c[6])*(z1-c[7])*(z1-c[8])*(z1-c[9])
				   	+ v[4]*(z1-c[5])*(z1-c[6])*(z1-c[7])*(z1-c[8])*(z1-c[9])
				   	+ v[5]*(z1-c[6])*(z1-c[7])*(z1-c[8])*(z1-c[9])
				   	+ v[6]*(z1-c[7])*(z1-c[8])*(z1-c[9])
				   	+ v[7]*(z1-c[8])*(z1-c[9])
				   	+ v[8]*(z1-c[9])
				   	+ v[9];

					if ( abs( z3 - z2 ) > eps ) {
						cout << "                  z1 = " << z1 << endl;

						cout << "v = [" << endl;

						for ( int j = 0; j < 9; ++j ) {
							cout << v[j] << ", ";
						}

						cout << v[9] << "]" << endl;

						cout << "c = [" << endl;

						for ( int j = 0; j < 9; ++j ) {
							cout << c[j] << ", ";
						}

						cout << c[9] << "]" << endl;

						cout << "              Horner:  " << z2 << endl;
						cout << "           Polynomial: " << z3 << endl;
						cout << "                Error: " << abs( z3 - z2 ) << endl << endl;
						++error_count;
					}
				}
			}

			delete [] v;
			delete [] c;
		}

		void rotation_test( int N, double eps = 1e-14 ) {
			T z1, z2, z3, z4;

			for ( int i = 0; i < N; ++i ) {
				T z1 = T::random();
				T z2 = T::random_imag();

				z3 = z1.rotate( z2 )/z2.norm();
				z4 = (z2*z1*z2.conj())/z2.norm();

				if ( abs( z3 - z4 ) > eps ) {
					cout << "             z1 = " << z1 << endl;
					cout << "             z2 = " << z2 << endl;
					cout << "  z1.rotate(z2) = " << z3 << endl;
					cout << " z2*z1*conj(z2) = " << z4 << endl;
					cout << "           Error: " << abs( z3 - z4 ) << endl << endl;

					++error_count;
				}
			}

			for ( int i = 0; i < N; ++i ) {
				T z1 = T::random();
				T z2 = T::random();

				z3 = z1.rotate( z2 )/z2.norm();
				z4 = (z2*z1*z2.conj())/z2.norm();

				if ( abs( z3 - z4 ) > eps ) {
					cout << "             z1 = " << z1 << endl;
					cout << "             z2 = " << z2 << endl;
					cout << "  z1.rotate(z2) = " << z3 << endl;
					cout << " z2*z1*conj(z2) = " << z4 << endl;
					cout << "           Error: " << abs( z3 - z4 ) << endl << endl;

					++error_count;
				}
			}
		}
};

/**********************************************
 * ****************************************** *
 * *                                        * *
 * *  The Actual Tests                      * *
 * *                                        * *
 * *     - Complex                          * *
 * *     - Quaternion                       * *
 * *     - Octonion                         * *
 * *     - Sedenion                         * *
 * *     - Trigintaduonion                  * *
 * *                                        * *
 * ****************************************** * 
 **********************************************/

int main() {
	int N = 1000;

	cout << "************************************************************" << endl;
	cout << "*                            COMPLEX                       *" << endl;
	cout << "************************************************************" << endl;

	Tester< Complex<double> > ctest;

#ifdef TRANSCENDENTAL
	cout << "******************************* EXP *******************************" << endl;
	ctest.exp_test( N );
	cout << "******************************* SIN *******************************" << endl;
	ctest.sin_test( N );
	cout << "******************************* COS *******************************" << endl;
	ctest.cos_test( N );
	cout << "******************************* TAN *******************************" << endl;
	ctest.tan_test( N );
	cout << "******************************* SEC *******************************" << endl;
	ctest.sec_test( N );
	cout << "******************************* CSC *******************************" << endl;
	ctest.csc_test( N );
	cout << "******************************* COT *******************************" << endl;
	ctest.cot_test( N );
	cout << "******************************* SINH ******************************" << endl;
	ctest.sinh_test( N );
	cout << "******************************* COSH ******************************" << endl;
	ctest.cosh_test( N );
	cout << "******************************* TANH ******************************" << endl;
	ctest.tanh_test( N );
	cout << "******************************* SECH ******************************" << endl;
	ctest.sech_test( N );
	cout << "******************************* CSCH ******************************" << endl;
	ctest.csch_test( N );
	cout << "******************************* COTH ******************************" << endl;
	ctest.coth_test( N );
	cout << "******************************* LOG *******************************" << endl;
	ctest.log_test( N );
	cout << "******************************* ASIN ******************************" << endl;
	ctest.asin_test( N );
	cout << "******************************* ACOS ******************************" << endl;
	ctest.acos_test( N );
	cout << "******************************* ATAN ******************************" << endl;
	ctest.atan_test( N );
	cout << "******************************* ASEC ******************************" << endl;
	ctest.asec_test( N );
	cout << "******************************* ACSC ******************************" << endl;
	ctest.acsc_test( N );
	cout << "******************************* ACOT ******************************" << endl;
	ctest.acot_test( N );
	cout << "****************************** ASINH ******************************" << endl;
	ctest.asinh_test( N );
	cout << "****************************** ACOSH ******************************" << endl;
	ctest.acosh_test( N );
	cout << "****************************** ATANH ******************************" << endl;
	ctest.atanh_test( N );
	cout << "****************************** ASECH ******************************" << endl;
	ctest.asech_test( N );
	cout << "****************************** ACSCH ******************************" << endl;
	ctest.acsch_test( N );
	cout << "****************************** ACOTH ******************************" << endl;
	ctest.acoth_test( N );
	cout << "***************************** BESSEL J ****************************" << endl;
	ctest.bessel_J2_test( N );
#endif

	cout << "******************************* Z*Z *******************************" << endl;
	ctest.sqr_test( N, 2.3e-16 );
	cout << "******************************* CONJ ******************************" << endl;
	ctest.conj_test( N, 2.3e-16 );
	cout << "**************************** ARITHMETIC ***************************" << endl;
	ctest.arith_test( N, 3.7e-16 );
	cout << "*************************** BOOLEAN LOGIC *************************" << endl;
	ctest.bool_test( N );
	cout << "***************************** ASSIGNMENT **************************" << endl;
	ctest.assign_test( N );
	cout << "****************************** INVERSE ****************************" << endl;
	ctest.inverse_arith_test( N );
	ctest.inverse_test( N );

	cout << "****************************** HORNER *****************************" << endl;
	ctest.horner_test( N );

	cout << "Total error count: " << ctest.count() << endl;

	cout << "************************************************************" << endl;
	cout << "*                          QUATERNIONS                     *" << endl;
	cout << "************************************************************" << endl;

	Tester< Quaternion<double> > qtest;

#ifdef TRANSCENDENTAL
	cout << "******************************* EXP *******************************" << endl;
	qtest.exp_test( N );
	cout << "******************************* SIN *******************************" << endl;
	qtest.sin_test( N );
	cout << "******************************* COS *******************************" << endl;
	qtest.cos_test( N );
	cout << "******************************* TAN *******************************" << endl;
	qtest.tan_test( N );
	cout << "******************************* SEC *******************************" << endl;
	qtest.sec_test( N );
	cout << "******************************* CSC *******************************" << endl;
	qtest.csc_test( N );
	cout << "******************************* COT *******************************" << endl;
	qtest.cot_test( N );
	cout << "******************************* SINH ******************************" << endl;
	qtest.sinh_test( N );
	cout << "******************************* COSH ******************************" << endl;
	qtest.cosh_test( N );
	cout << "******************************* TANH ******************************" << endl;
	qtest.tanh_test( N );
	cout << "******************************* SECH ******************************" << endl;
	qtest.sech_test( N );
	cout << "******************************* CSCH ******************************" << endl;
	qtest.csch_test( N );
	cout << "******************************* COTH ******************************" << endl;
	qtest.coth_test( N );
	cout << "******************************* LOG *******************************" << endl;
	qtest.log_test( N );
	cout << "******************************* ASIN ******************************" << endl;
	qtest.asin_test( N );
	cout << "******************************* ACOS ******************************" << endl;
	qtest.acos_test( N );
	cout << "******************************* ATAN ******************************" << endl;
	qtest.atan_test( N );
	cout << "******************************* ASEC ******************************" << endl;
	qtest.asec_test( N );
	cout << "******************************* ACSC ******************************" << endl;
	qtest.acsc_test( N );
	cout << "******************************* ACOT ******************************" << endl;
	qtest.acot_test( N );
	cout << "****************************** ASINH ******************************" << endl;
	qtest.asinh_test( N );
	cout << "****************************** ACOSH ******************************" << endl;
	qtest.acosh_test( N );
	cout << "****************************** ATANH ******************************" << endl;
	qtest.atanh_test( N );
	cout << "****************************** ASECH ******************************" << endl;
	qtest.asech_test( N );
	cout << "****************************** ACSCH ******************************" << endl;
	qtest.acsch_test( N );
	cout << "****************************** ACOTH ******************************" << endl;
	qtest.acoth_test( N );
	cout << "***************************** BESSEL J ****************************" << endl;
	qtest.bessel_J2_test( N );
#endif

	cout << "******************************* Z*Z *******************************" << endl;
	qtest.sqr_test( N, 2.3e-16 );
	cout << "******************************* CONJ ******************************" << endl;
	qtest.conj_test( N, 2.3e-16 );
	cout << "**************************** ARITHMETIC ***************************" << endl;
	qtest.arith_test( N, 3.7e-16 );
	cout << "*************************** BOOLEAN LOGIC *************************" << endl;
	qtest.bool_test( N );
	cout << "***************************** ASSIGNMENT **************************" << endl;
	qtest.assign_test( N );
	cout << "****************************** INVERSE ****************************" << endl;
	qtest.inverse_arith_test( N );
	qtest.inverse_test( N );

	cout << "****************************** HORNER *****************************" << endl;
	qtest.horner_test( N );
	cout << "***************************** ROTATION ****************************" << endl;
	qtest.rotation_test( N );

	cout << "Total error count: " << qtest.count() << endl;

	cout << "************************************************************" << endl;
	cout << "*                           OCTONIONS                      *" << endl;
	cout << "************************************************************" << endl;

	Tester< Octonion<double> > otest;

#ifdef TRANSCENDENTAL
	cout << "******************************* EXP *******************************" << endl;
	otest.exp_test( N );
	cout << "******************************* SIN *******************************" << endl;
	otest.sin_test( N );
	cout << "******************************* COS *******************************" << endl;
	otest.cos_test( N );
	cout << "******************************* TAN *******************************" << endl;
	otest.tan_test( N );
	cout << "******************************* SEC *******************************" << endl;
	otest.sec_test( N );
	cout << "******************************* CSC *******************************" << endl;
	otest.csc_test( N );
	cout << "******************************* COT *******************************" << endl;
	otest.cot_test( N );
	cout << "******************************* SINH ******************************" << endl;
	otest.sinh_test( N );
	cout << "******************************* COSH ******************************" << endl;
	otest.cosh_test( N );
	cout << "******************************* TANH ******************************" << endl;
	otest.tanh_test( N );
	cout << "******************************* SECH ******************************" << endl;
	otest.sech_test( N );
	cout << "******************************* CSCH ******************************" << endl;
	otest.csch_test( N );
	cout << "******************************* COTH ******************************" << endl;
	otest.coth_test( N );
	cout << "******************************* LOG *******************************" << endl;
	otest.log_test( N );
	cout << "******************************* ASIN ******************************" << endl;
	otest.asin_test( N );
	cout << "******************************* ACOS ******************************" << endl;
	otest.acos_test( N );
	cout << "******************************* ATAN ******************************" << endl;
	otest.atan_test( N );
	cout << "******************************* ASEC ******************************" << endl;
	otest.asec_test( N );
	cout << "******************************* ACSC ******************************" << endl;
	otest.acsc_test( N );
	cout << "******************************* ACOT ******************************" << endl;
	otest.acot_test( N );
	cout << "****************************** ASINH ******************************" << endl;
	otest.asinh_test( N );
	cout << "****************************** ACOSH ******************************" << endl;
	otest.acosh_test( N );
	cout << "****************************** ATANH ******************************" << endl;
	otest.atanh_test( N );
	cout << "****************************** ASECH ******************************" << endl;
	otest.asech_test( N );
	cout << "****************************** ACSCH ******************************" << endl;
	otest.acsch_test( N );
	cout << "****************************** ACOTH ******************************" << endl;
	otest.acoth_test( N );
	cout << "***************************** BESSEL J ****************************" << endl;
	otest.bessel_J2_test( N );
#endif

	cout << "******************************* Z*Z *******************************" << endl;
	otest.sqr_test( N, 2.3e-16 );
	cout << "******************************* CONJ ******************************" << endl;
	otest.conj_test( N, 2.3e-16 );
	cout << "**************************** ARITHMETIC ***************************" << endl;
	otest.arith_test( N, 3.7e-16 );
	cout << "*************************** BOOLEAN LOGIC *************************" << endl;
	otest.bool_test( N );
	cout << "***************************** ASSIGNMENT **************************" << endl;
	otest.assign_test( N );
	cout << "****************************** INVERSE ****************************" << endl;
	otest.inverse_arith_test( N );
	otest.inverse_test( N );

	cout << "****************************** HORNER *****************************" << endl;
	otest.horner_test( N );
	cout << "***************************** ROTATION ****************************" << endl;
	otest.rotation_test( N );

	cout << "Total error count: " << otest.count() << endl;

	cout << "************************************************************" << endl;
	cout << "*                           SEDENIONS                      *" << endl;
	cout << "************************************************************" << endl;

	Tester< Sedenion<double> > stest;

#ifdef TRANSCENDENTAL
	cout << "******************************* EXP *******************************" << endl;
	stest.exp_test( N );
	cout << "******************************* SIN *******************************" << endl;
	stest.sin_test( N );
	cout << "******************************* COS *******************************" << endl;
	stest.cos_test( N );
	cout << "******************************* TAN *******************************" << endl;
	stest.tan_test( N );
	cout << "******************************* SEC *******************************" << endl;
	stest.sec_test( N );
	cout << "******************************* CSC *******************************" << endl;
	stest.csc_test( N );
	cout << "******************************* COT *******************************" << endl;
	stest.cot_test( N );
	cout << "******************************* SINH ******************************" << endl;
	stest.sinh_test( N );
	cout << "******************************* COSH ******************************" << endl;
	stest.cosh_test( N );
	cout << "******************************* TANH ******************************" << endl;
	stest.tanh_test( N );
	cout << "******************************* SECH ******************************" << endl;
	stest.sech_test( N );
	cout << "******************************* CSCH ******************************" << endl;
	stest.csch_test( N );
	cout << "******************************* COTH ******************************" << endl;
	stest.coth_test( N );
	cout << "******************************* LOG *******************************" << endl;
	stest.log_test( N );
	cout << "******************************* ASIN ******************************" << endl;
	stest.asin_test( N );
	cout << "******************************* ACOS ******************************" << endl;
	stest.acos_test( N );
	cout << "******************************* ATAN ******************************" << endl;
	stest.atan_test( N );
	cout << "******************************* ASEC ******************************" << endl;
	stest.asec_test( N );
	cout << "******************************* ACSC ******************************" << endl;
	stest.acsc_test( N );
	cout << "******************************* ACOT ******************************" << endl;
	stest.acot_test( N );
	cout << "****************************** ASINH ******************************" << endl;
	stest.asinh_test( N );
	cout << "****************************** ACOSH ******************************" << endl;
	stest.acosh_test( N );
	cout << "****************************** ATANH ******************************" << endl;
	stest.atanh_test( N );
	cout << "****************************** ASECH ******************************" << endl;
	stest.asech_test( N );
	cout << "****************************** ACSCH ******************************" << endl;
	stest.acsch_test( N );
	cout << "****************************** ACOTH ******************************" << endl;
	stest.acoth_test( N );
	cout << "***************************** BESSEL J ****************************" << endl;
	stest.bessel_J2_test( N );
#endif

	cout << "******************************* Z*Z *******************************" << endl;
	stest.sqr_test( N, 2.3e-16 );
	cout << "******************************* CONJ ******************************" << endl;
	stest.conj_test( N, 2.3e-16 );
	cout << "**************************** ARITHMETIC ***************************" << endl;
	stest.arith_test( N, 3.7e-16 );
	cout << "*************************** BOOLEAN LOGIC *************************" << endl;
	stest.bool_test( N );
	cout << "***************************** ASSIGNMENT **************************" << endl;
	stest.assign_test( N );
	cout << "****************************** INVERSE ****************************" << endl;
//	stest.inverse_arith_test( N );
	stest.inverse_test( N );

	cout << "****************************** HORNER *****************************" << endl;
	stest.horner_test( N );
	cout << "***************************** ROTATION ****************************" << endl;
	stest.rotation_test( N );

	cout << "Total error count: " << stest.count() << endl;

	cout << "************************************************************" << endl;
	cout << "*                         TRIGINTADUONION                  *" << endl;
	cout << "************************************************************" << endl;

	Tester< Trigintaduonion<double> > ttest;

#ifdef TRANSCENDENTAL
	cout << "******************************* EXP *******************************" << endl;
	ttest.exp_test( N );
	cout << "******************************* SIN *******************************" << endl;
	ttest.sin_test( N );
	cout << "******************************* COS *******************************" << endl;
	ttest.cos_test( N );
	cout << "******************************* TAN *******************************" << endl;
	ttest.tan_test( N );
	cout << "******************************* SEC *******************************" << endl;
	ttest.sec_test( N );
	cout << "******************************* CSC *******************************" << endl;
	ttest.csc_test( N );
	cout << "******************************* COT *******************************" << endl;
	ttest.cot_test( N );
	cout << "******************************* SINH ******************************" << endl;
	ttest.sinh_test( N );
	cout << "******************************* COSH ******************************" << endl;
	ttest.cosh_test( N );
	cout << "******************************* TANH ******************************" << endl;
	ttest.tanh_test( N );
	cout << "******************************* SECH ******************************" << endl;
	ttest.sech_test( N );
	cout << "******************************* CSCH ******************************" << endl;
	ttest.csch_test( N );
	cout << "******************************* COTH ******************************" << endl;
	ttest.coth_test( N );
	cout << "******************************* LOG *******************************" << endl;
	ttest.log_test( N );
	cout << "******************************* ASIN ******************************" << endl;
	ttest.asin_test( N );
	cout << "******************************* ACOS ******************************" << endl;
	ttest.acos_test( N );
	cout << "******************************* ATAN ******************************" << endl;
	ttest.atan_test( N );
	cout << "******************************* ASEC ******************************" << endl;
	ttest.asec_test( N );
	cout << "******************************* ACSC ******************************" << endl;
	ttest.acsc_test( N );
	cout << "******************************* ACOT ******************************" << endl;
	ttest.acot_test( N );
	cout << "****************************** ASINH ******************************" << endl;
	ttest.asinh_test( N );
	cout << "****************************** ACOSH ******************************" << endl;
	ttest.acosh_test( N );
	cout << "****************************** ATANH ******************************" << endl;
	ttest.atanh_test( N );
	cout << "****************************** ASECH ******************************" << endl;
	ttest.asech_test( N );
	cout << "****************************** ACSCH ******************************" << endl;
	ttest.acsch_test( N );
	cout << "****************************** ACOTH ******************************" << endl;
	ttest.acoth_test( N );
	cout << "***************************** BESSEL J ****************************" << endl;
	ttest.bessel_J2_test( N );
#endif

	cout << "******************************* Z*Z *******************************" << endl;
	ttest.sqr_test( N, 2.3e-16 );
	cout << "******************************* CONJ ******************************" << endl;
	ttest.conj_test( N, 2.3e-16 );
	cout << "**************************** ARITHMETIC ***************************" << endl;
	ttest.arith_test( N, 1e-15 );
	cout << "*************************** BOOLEAN LOGIC *************************" << endl;
	ttest.bool_test( N );
	cout << "***************************** ASSIGNMENT **************************" << endl;
	ttest.assign_test( N );
	cout << "****************************** INVERSE ****************************" << endl;
//	ttest.inverse_arith_test( N );
	ttest.inverse_test( N );

	cout << "****************************** HORNER *****************************" << endl;
	ttest.horner_test( N );
	cout << "***************************** ROTATION ****************************" << endl;
	ttest.rotation_test( N );

	cout << "Total error count: " << ttest.count() << endl;
}