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69 lines
1.9 KiB
C++
69 lines
1.9 KiB
C++
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/* Boost libs/numeric/odeint/examples/multiprecision/cmp_precision.cpp
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Copyright 2013 Karsten Ahnert
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Copyright 2013 Mario Mulansky
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example comparing double to multiprecision using Boost.Multiprecision
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or
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copy at http://www.boost.org/LICENSE_1_0.txt)
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*/
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#include <iostream>
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#include <boost/numeric/odeint.hpp>
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#include <boost/multiprecision/cpp_dec_float.hpp>
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using namespace std;
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using namespace boost::numeric::odeint;
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typedef boost::multiprecision::cpp_dec_float_50 mp_50;
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/* we solve the simple ODE x' = 3/(2t^2) + x/(2t)
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* with initial condition x(1) = 0.
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* Analytic solution is x(t) = sqrt(t) - 1/t
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*/
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void rhs_m( const mp_50 x , mp_50 &dxdt , const mp_50 t )
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{ // version for multiprecision
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dxdt = mp_50(3)/(mp_50(2)*t*t) + x/(mp_50(2)*t);
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}
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void rhs_d( const double x , double &dxdt , const double t )
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{ // version for double precision
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dxdt = 3.0/(2.0*t*t) + x/(2.0*t);
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}
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// state_type = mp_50 = deriv_type = time_type = mp_50
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typedef runge_kutta4< mp_50 , mp_50 , mp_50 , mp_50 , vector_space_algebra , default_operations , never_resizer > stepper_type_m;
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typedef runge_kutta4< double , double , double , double , vector_space_algebra , default_operations , never_resizer > stepper_type_d;
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int main()
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{
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stepper_type_m stepper_m;
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stepper_type_d stepper_d;
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mp_50 dt_m( 0.5 );
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double dt_d( 0.5 );
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cout << "dt" << '\t' << "mp" << '\t' << "double" << endl;
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while( dt_m > 1E-20 )
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{
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mp_50 x_m = 0; //initial value x(1) = 0
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stepper_m.do_step( rhs_m , x_m , mp_50( 1 ) , dt_m );
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double x_d = 0;
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stepper_d.do_step( rhs_d , x_d , 1.0 , dt_d );
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cout << dt_m << '\t';
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cout << abs((x_m - (sqrt(1+dt_m)-mp_50(1)/(1+dt_m)))/x_m) << '\t' ;
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cout << abs((x_d - (sqrt(1+dt_d)-mp_50(1)/(1+dt_d)))/x_d) << endl ;
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dt_m /= 2;
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dt_d /= 2;
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}
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}
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