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ckormanyos
2025-07-13 13:43:10 +02:00
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example/cpp_complex_examples.cpp
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@@ -6,66 +6,90 @@
// Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at https://www.boost.org/LICENSE_1_0.txt
/*`This example demonstrates the usage of the MPC backend for multiprecision complex numbers.
In the following, we will show how using MPC backend allows for the same operations as the C++ standard library complex numbers.
/*`This example demonstrates the usage of the complex_adaptor backend for multiprecision complex numbers.
In the following, we will show how using the complex_adaptor backend together with number allows for the same operations as the C++ standard library complex numbers.
*/
//[cpp_complex_eg
#include <boost/multiprecision/cpp_complex.hpp>
#include <cmath>
#include <complex>
#include <iostream>
template<class Complex>
template<class NumericType>
void elementary_functions(const NumericType z1)
{
std::cout << "\nElementary special functions:\n";
std::cout << "Absolute value : " << abs(z1) << std::endl;
using std::arg;
std::cout << "Argument : " << arg(z1) << std::endl;
using std::norm;
std::cout << "Norm : " << norm(z1) << std::endl;
using std::conj;
std::cout << "Complex conjugate : " << conj(z1) << std::endl;
using std::proj;
std::cout << "Proj on Riemann sphere : " << proj(z1) << std::endl;
std::cout << "exp(z1) : " << exp(z1) << std::endl;
std::cout << "log(z1) : " << log(z1) << std::endl;
std::cout << "log10(z1) : " << log10(z1) << std::endl;
std::cout << "pow(z1, z1) : " << pow(z1, z1) << std::endl;
std::cout << "Take its square root : " << sqrt(z1) << std::endl;
std::cout << "sin(z1) : " << sin(z1) << std::endl;
std::cout << "cos(z1) : " << cos(z1) << std::endl;
std::cout << "tan(z1) : " << tan(z1) << std::endl;
std::cout << "asin(z1) : " << asin(z1) << std::endl;
std::cout << "acos(z1) : " << acos(z1) << std::endl;
std::cout << "atan(z1) : " << atan(z1) << std::endl;
std::cout << "sinh(z1) : " << sinh(z1) << std::endl;
std::cout << "cosh(z1) : " << cosh(z1) << std::endl;
std::cout << "tanh(z1) : " << tanh(z1) << std::endl;
std::cout << "asinh(z1) : " << asinh(z1) << std::endl;
std::cout << "acosh(z1) : " << acosh(z1) << std::endl;
std::cout << "atanh(z1) : " << atanh(z1) << std::endl;
}
template<class ComplexType>
void complex_number_examples()
{
Complex z1{0, 1};
std::cout << std::setprecision(std::numeric_limits<typename Complex::value_type>::digits10);
std::cout << std::scientific << std::fixed;
std::cout << "Print a complex number: " << z1 << std::endl;
std::cout << "Square it : " << z1*z1 << std::endl;
std::cout << "Real part : " << z1.real() << " = " << real(z1) << std::endl;
std::cout << "Imaginary part : " << z1.imag() << " = " << imag(z1) << std::endl;
using std::abs;
std::cout << "Absolute value : " << abs(z1) << std::endl;
std::cout << "Argument : " << arg(z1) << std::endl;
std::cout << "Norm : " << norm(z1) << std::endl;
std::cout << "Complex conjugate : " << conj(z1) << std::endl;
std::cout << "Projection onto Riemann sphere: " << proj(z1) << std::endl;
typename Complex::value_type r = 1;
typename Complex::value_type theta = 0.8;
using std::polar;
std::cout << "Polar coordinates (phase = 0) : " << polar(r) << std::endl;
std::cout << "Polar coordinates (phase !=0) : " << polar(r, theta) << std::endl;
using complex_type = ComplexType;
using real_type = typename complex_type::value_type;
std::cout << "\nElementary special functions:\n";
std::cout << "exp(z1) = " << exp(z1) << std::endl;
std::cout << "log(z1) = " << log(z1) << std::endl;
std::cout << "log10(z1) = " << log10(z1) << std::endl;
std::cout << "pow(z1, z1) = " << pow(z1, z1) << std::endl;
std::cout << "Take its square root : " << sqrt(z1) << std::endl;
std::cout << "sin(z1) = " << sin(z1) << std::endl;
std::cout << "cos(z1) = " << cos(z1) << std::endl;
std::cout << "tan(z1) = " << tan(z1) << std::endl;
std::cout << "asin(z1) = " << asin(z1) << std::endl;
std::cout << "acos(z1) = " << acos(z1) << std::endl;
std::cout << "atan(z1) = " << atan(z1) << std::endl;
std::cout << "sinh(z1) = " << sinh(z1) << std::endl;
std::cout << "cosh(z1) = " << cosh(z1) << std::endl;
std::cout << "tanh(z1) = " << tanh(z1) << std::endl;
std::cout << "asinh(z1) = " << asinh(z1) << std::endl;
std::cout << "acosh(z1) = " << acosh(z1) << std::endl;
std::cout << "atanh(z1) = " << atanh(z1) << std::endl;
complex_type z1 { real_type(0), real_type(1) };
std::cout << "Print a complex number : " << z1 << std::endl;
std::cout << "Square it : " << z1*z1 << std::endl;
std::cout << "Real part : " << z1.real() << " = " << real(z1) << std::endl;
std::cout << "Imaginary part : " << z1.imag() << " = " << imag(z1) << std::endl;
real_type r { 1 };
real_type theta { 0.75 };
using std::polar;
std::cout << "Polar coord phase = 0 : " << polar(r) << std::endl;
std::cout << "Polar coord phase != 0 : " << polar(r, theta) << std::endl;
elementary_functions(z1);
}
int main()
{
const auto flags_orig = std::cout.flags();
std::cout << std::scientific << std::fixed;
std::cout << "First, some operations we usually perform with std::complex:\n";
std::cout << std::setprecision(std::numeric_limits<typename std::complex<double>::value_type>::digits10);
complex_number_examples<std::complex<double>>();
std::cout << "\nNow the same operations performed using quad precision complex numbers:\n";
std::cout << std::setprecision(std::numeric_limits<typename boost::multiprecision::cpp_complex_quad::value_type>::digits10);
complex_number_examples<boost::multiprecision::cpp_complex_quad>();
return 0;
std::cout << "\nNow the same elementary functions performed using built-in real-valued numbers:\n";
std::cout << std::setprecision(std::numeric_limits<float>::digits10);
elementary_functions(0.125F);
std::cout.flags(flags_orig);
}
//]
@@ -73,35 +97,35 @@ int main()
//[cpp_complex_out
Print a complex number: (0.000000000000000000000000000000000,1.000000000000000000000000000000000)
Square it : -1.000000000000000000000000000000000
Real part : 0.000000000000000000000000000000000 = 0.000000000000000000000000000000000
Imaginary part : 1.000000000000000000000000000000000 = 1.000000000000000000000000000000000
Absolute value : 1.000000000000000000000000000000000
Argument : 1.570796326794896619231321691639751
Norm : 1.000000000000000000000000000000000
Complex conjugate : (0.000000000000000000000000000000000,-1.000000000000000000000000000000000)
Projection onto Riemann sphere: (0.000000000000000000000000000000000,1.000000000000000000000000000000000)
Polar coordinates (phase = 0) : 1.000000000000000000000000000000000
Polar coordinates (phase !=0) : (0.696706709347165389063740022772448,0.717356090899522792567167815703377)
Print a complex number : (0.000000000000000000000000000000000,1.000000000000000000000000000000000)
Square it : -1.000000000000000000000000000000000
Real part : 0.000000000000000000000000000000000 = 0.000000000000000000000000000000000
Imaginary part : 1.000000000000000000000000000000000 = 1.000000000000000000000000000000000
Polar coord phase = 0 : 1.000000000000000000000000000000000
Polar coord phase != 0 : (0.731688868873820886311838753000085,0.681638760023334166733241952779894)
Elementary special functions:
exp(z1) = (0.540302305868139717400936607442977,0.841470984807896506652502321630299)
log(z1) = (0.000000000000000000000000000000000,1.570796326794896619231321691639751)
log10(z1) = (0.000000000000000000000000000000000,0.682188176920920673742891812715678)
pow(z1, z1) = 0.207879576350761908546955619834979
Take its square root : (0.707106781186547524400844362104849,0.707106781186547524400844362104849)
sin(z1) = (0.000000000000000000000000000000000,1.175201193643801456882381850595601)
cos(z1) = 1.543080634815243778477905620757062
tan(z1) = (0.000000000000000000000000000000000,0.761594155955764888119458282604794)
asin(z1) = (0.000000000000000000000000000000000,0.881373587019543025232609324979793)
acos(z1) = (1.570796326794896619231321691639751,-0.881373587019543025232609324979793)
atan(z1) = (0.000000000000000000000000000000000,inf)
sinh(z1) = (0.000000000000000000000000000000000,0.841470984807896506652502321630299)
cosh(z1) = 0.540302305868139717400936607442977
tanh(z1) = (0.000000000000000000000000000000000,1.557407724654902230506974807458360)
asinh(z1) = (0.000000000000000000000000000000000,1.570796326794896619231321691639751)
acosh(z1) = (0.881373587019543025232609324979792,1.570796326794896619231321691639751)
atanh(z1) = (0.000000000000000000000000000000000,0.785398163397448309615660845819876)
Absolute value : 1.000000000000000000000000000000000
Argument : 1.570796326794896619231321691639751
Norm : 1.000000000000000000000000000000000
Complex conjugate : (0.000000000000000000000000000000000,-1.000000000000000000000000000000000)
Proj on Riemann sphere : (0.000000000000000000000000000000000,1.000000000000000000000000000000000)
exp(z1) : (0.540302305868139717400936607442977,0.841470984807896506652502321630299)
log(z1) : (0.000000000000000000000000000000000,1.570796326794896619231321691639751)
log10(z1) : (0.000000000000000000000000000000000,0.682188176920920673742891812715678)
pow(z1, z1) : 0.207879576350761908546955619834979
Take its square root : (0.707106781186547524400844362104849,0.707106781186547524400844362104849)
sin(z1) : (0.000000000000000000000000000000000,1.175201193643801456882381850595601)
cos(z1) : 1.543080634815243778477905620757062
tan(z1) : (0.000000000000000000000000000000000,0.761594155955764888119458282604794)
asin(z1) : (0.000000000000000000000000000000000,0.881373587019543025232609324979792)
acos(z1) : (1.570796326794896619231321691639751,-0.881373587019543025232609324979792)
atan(z1) : (0.000000000000000000000000000000000,inf)
sinh(z1) : (0.000000000000000000000000000000000,0.841470984807896506652502321630299)
cosh(z1) : 0.540302305868139717400936607442977
tanh(z1) : (0.000000000000000000000000000000000,1.557407724654902230506974807458360)
asinh(z1) : (0.000000000000000000000000000000000,1.570796326794896619231321691639751)
acosh(z1) : (0.881373587019543025232609324979792,1.570796326794896619231321691639751)
atanh(z1) : (0.000000000000000000000000000000000,0.785398163397448309615660845819876)
//]
*/