//***********************************************************
//
//  NXV4 "Math-on-Paper" software
//
//  package : CPX class _____________________________________
//            
//            supports: move semantix
//                      operators + - * / ^   L,R-val context
//                                += -= *= /=
//                      fabs()
//                      phi ()    [ 0  ... 2.pi] o/p
//                      phi2()    [-pi ...  +pi] o/p
//                      ~  -      unary operators L,R-val
//                      cpx<arithmetic> i.e. int
//                                           float 
//                                           double
//                                           long double
//                      type_casts between the types 
//                      cout << overload 
//
//                      TOTAL = 27+1205 instantiated op/f's
//                      _____________________________________
//
//
//  authors : Mihai-Tiberiu Dima (1)
//            Maria Dima         (2)
//
//             Meshcheryakov Laboratory of Information Techn.
//             Joint Institute for Nuclear Research
//             Dubna-Russia
//
//            on leave from:
//
//             Hyperion Univ. Bucharest-Romania
//
//
//  date    : CPX4/v1.0.alfa   / Mon Dec 27 17:13:57 CET 2021
//                 v2.1.beta   / Mon Mar 07 12:45:54 CET 2022
//
//***********************************************************
#include <cmath>
#include <iostream>

#include "cpx.hh"

using namespace std                                         ;
using namespace cpx4                                        ;


int main()
{

// this is an application example in electronics
//
// RC pi bandpass filter
//
//   o----||-----/\/\/\---------o
//      C1    |    R2      |
//            |            |
//            \           ---
//            /           ---
//            \            |
//            / R1         | C2
//            \            |
//            /            |
//            |            |
//            |            |
//           ===          ===
//
//   here we form Z = R1 // (R2+C2) and calculate
//   from there on, the voltage division between
//   C1 and Z (and R2, C2).
//
// to use this example do the following:
//   rm test.cc
//   ln -s e1.cc test.cc
//   make test
//   make run

  using dblx = double                                       ;
  using real = long double                                  ;

  double e   = exp(1)                                       ;
  double pi  = 3.14159265853                                ;

  cpx<dblx>  j(0,1)                                         ;

  dblx  R1  =  0.1e3  ; //  0.1 kOhms
  dblx  C1  =  3.3e-9 ; //  3.3 nF
  dblx  R2  =  1.0e3  ; //  1.0 kOhms
  dblx  C2  =  1.0e-9 ; //  1.0 nF

  dblx min = 10.0e0 ; // Hz
  dblx max = 10.0e6 ; // Hz
  int  N   = 10000  ; // nr. points log scale

  for (int i=0; i<N; i++) {
    real f = min*exp(i*log(max/min)/N)                      ;
    real w = 2*pi*f                                         ;
    auto Z2 = R2 + 1/(j*w*C2)                               ;
    auto Y  = 1/R1 + 1/Z2                                   ;
    auto G  = 1/(1+Y/(j*w*C1))/(1+j*w*R2*C2)                ;
    cout << f << " " << fabs(G) << " " << phi2(G) << endl   ;}

}