ceph/src/boost/libs/multiprecision/example/cpp_complex_examples.cpp

   1 ///////////////////////////////////////////////////////////////
   2 //  Copyright 2018 Nick Thompson. Distributed under the Boost
   3 //  Software License, Version 1.0. (See accompanying file
   4 //  LICENSE_1_0.txt or copy at https://www.boost.org/LICENSE_1_0.txt
   5
   6 /*`This example demonstrates the usage of the MPC backend for multiprecision complex numbers.
   7 In the following, we will show how using MPC backend allows for the same operations as the C++ standard library complex numbers.
   8 */
   9
  10 //[cpp_complex_eg
  11 #include <iostream>
  12 #include <complex>
  13 #include <boost/multiprecision/cpp_complex.hpp>
  14
  15 template<class Complex>
  16 void complex_number_examples()
  17 {
  18     Complex z1{0, 1};
  19     std::cout << std::setprecision(std::numeric_limits<typename Complex::value_type>::digits10);
  20     std::cout << std::scientific << std::fixed;
  21     std::cout << "Print a complex number: " << z1 << std::endl;
  22     std::cout << "Square it             : " << z1*z1 << std::endl;
  23     std::cout << "Real part             : " << z1.real() << " = " << real(z1) << std::endl;
  24     std::cout << "Imaginary part        : " << z1.imag() << " = " << imag(z1) << std::endl;
  25     using std::abs;
  26     std::cout << "Absolute value        : " << abs(z1) << std::endl;
  27     std::cout << "Argument              : " << arg(z1) << std::endl;
  28     std::cout << "Norm                  : " << norm(z1) << std::endl;
  29     std::cout << "Complex conjugate     : " << conj(z1) << std::endl;
  30     std::cout << "Projection onto Riemann sphere: " <<  proj(z1) << std::endl;
  31     typename Complex::value_type r = 1;
  32     typename Complex::value_type theta = 0.8;
  33     using std::polar;
  34     std::cout << "Polar coordinates (phase = 0)    : " << polar(r) << std::endl;
  35     std::cout << "Polar coordinates (phase !=0)    : " << polar(r, theta) << std::endl;
  36
  37     std::cout << "\nElementary special functions:\n";
  38     using std::exp;
  39     std::cout << "exp(z1) = " << exp(z1) << std::endl;
  40     using std::log;
  41     std::cout << "log(z1) = " << log(z1) << std::endl;
  42     using std::log10;
  43     std::cout << "log10(z1) = " << log10(z1) << std::endl;
  44     using std::pow;
  45     std::cout << "pow(z1, z1) = " << pow(z1, z1) << std::endl;
  46     using std::sqrt;
  47     std::cout << "Take its square root  : " << sqrt(z1) << std::endl;
  48     using std::sin;
  49     std::cout << "sin(z1) = " << sin(z1) << std::endl;
  50     using std::cos;
  51     std::cout << "cos(z1) = " << cos(z1) << std::endl;
  52     using std::tan;
  53     std::cout << "tan(z1) = " << tan(z1) << std::endl;
  54     using std::asin;
  55     std::cout << "asin(z1) = " << asin(z1) << std::endl;
  56     using std::acos;
  57     std::cout << "acos(z1) = " << acos(z1) << std::endl;
  58     using std::atan;
  59     std::cout << "atan(z1) = " << atan(z1) << std::endl;
  60     using std::sinh;
  61     std::cout << "sinh(z1) = " << sinh(z1) << std::endl;
  62     using std::cosh;
  63     std::cout << "cosh(z1) = " << cosh(z1) << std::endl;
  64     using std::tanh;
  65     std::cout << "tanh(z1) = " << tanh(z1) << std::endl;
  66     using std::asinh;
  67     std::cout << "asinh(z1) = " << asinh(z1) << std::endl;
  68     using std::acosh;
  69     std::cout << "acosh(z1) = " << acosh(z1) << std::endl;
  70     using std::atanh;
  71     std::cout << "atanh(z1) = " << atanh(z1) << std::endl;
  72 }
  73
  74 int main()
  75 {
  76     std::cout << "First, some operations we usually perform with std::complex:\n";
  77     complex_number_examples<std::complex<double>>();
  78     std::cout << "\nNow the same operations performed using quad precision complex numbers:\n";
  79     complex_number_examples<boost::multiprecision::cpp_complex_quad>();
  80
  81     return 0;
  82 }
  83 //]
  84
  85 /*
  86
  87 //[cpp_complex_out
  88
  89 Print a complex number: (0.000000000000000000000000000000000,1.000000000000000000000000000000000)
  90 Square it             : -1.000000000000000000000000000000000
  91 Real part             : 0.000000000000000000000000000000000 = 0.000000000000000000000000000000000
  92 Imaginary part        : 1.000000000000000000000000000000000 = 1.000000000000000000000000000000000
  93 Absolute value        : 1.000000000000000000000000000000000
  94 Argument              : 1.570796326794896619231321691639751
  95 Norm                  : 1.000000000000000000000000000000000
  96 Complex conjugate     : (0.000000000000000000000000000000000,-1.000000000000000000000000000000000)
  97 Projection onto Riemann sphere: (0.000000000000000000000000000000000,1.000000000000000000000000000000000)
  98 Polar coordinates (phase = 0)    : 1.000000000000000000000000000000000
  99 Polar coordinates (phase !=0)    : (0.696706709347165389063740022772448,0.717356090899522792567167815703377)
 100
 101 Elementary special functions:
 102 exp(z1) = (0.540302305868139717400936607442977,0.841470984807896506652502321630299)
 103 log(z1) = (0.000000000000000000000000000000000,1.570796326794896619231321691639751)
 104 log10(z1) = (0.000000000000000000000000000000000,0.682188176920920673742891812715678)
 105 pow(z1, z1) = 0.207879576350761908546955619834979
 106 Take its square root  : (0.707106781186547524400844362104849,0.707106781186547524400844362104849)
 107 sin(z1) = (0.000000000000000000000000000000000,1.175201193643801456882381850595601)
 108 cos(z1) = 1.543080634815243778477905620757062
 109 tan(z1) = (0.000000000000000000000000000000000,0.761594155955764888119458282604794)
 110 asin(z1) = (0.000000000000000000000000000000000,0.881373587019543025232609324979793)
 111 acos(z1) = (1.570796326794896619231321691639751,-0.881373587019543025232609324979793)
 112 atan(z1) = (0.000000000000000000000000000000000,inf)
 113 sinh(z1) = (0.000000000000000000000000000000000,0.841470984807896506652502321630299)
 114 cosh(z1) = 0.540302305868139717400936607442977
 115 tanh(z1) = (0.000000000000000000000000000000000,1.557407724654902230506974807458360)
 116 asinh(z1) = (0.000000000000000000000000000000000,1.570796326794896619231321691639751)
 117 acosh(z1) = (0.881373587019543025232609324979792,1.570796326794896619231321691639751)
 118 atanh(z1) = (0.000000000000000000000000000000000,0.785398163397448309615660845819876)
 119 //]
 120 */