1 /* Boost libs/numeric/odeint/examples/multiprecision/cmp_precision.cpp
2
3 Copyright 2013 Karsten Ahnert
4 Copyright 2013 Mario Mulansky
5
6 example comparing double to multiprecision using Boost.Multiprecision
7
8 Distributed under the Boost Software License, Version 1.0.
9 (See accompanying file LICENSE_1_0.txt or
10 copy at http://www.boost.org/LICENSE_1_0.txt)
11 */
12
13
14 #include <iostream>
15 #include <boost/numeric/odeint.hpp>
16 #include <boost/multiprecision/cpp_dec_float.hpp>
17
18 using namespace std;
19 using namespace boost::numeric::odeint;
20
21 typedef boost::multiprecision::cpp_dec_float_50 mp_50;
22
23 /* we solve the simple ODE x' = 3/(2t^2) + x/(2t)
24 * with initial condition x(1) = 0.
25 * Analytic solution is x(t) = sqrt(t) - 1/t
26 */
27
rhs_m(const mp_50 x,mp_50 & dxdt,const mp_50 t)28 void rhs_m( const mp_50 x , mp_50 &dxdt , const mp_50 t )
29 { // version for multiprecision
30 dxdt = mp_50(3)/(mp_50(2)*t*t) + x/(mp_50(2)*t);
31 }
32
rhs_d(const double x,double & dxdt,const double t)33 void rhs_d( const double x , double &dxdt , const double t )
34 { // version for double precision
35 dxdt = 3.0/(2.0*t*t) + x/(2.0*t);
36 }
37
38 // state_type = mp_50 = deriv_type = time_type = mp_50
39 typedef runge_kutta4< mp_50 , mp_50 , mp_50 , mp_50 , vector_space_algebra , default_operations , never_resizer > stepper_type_m;
40
41 typedef runge_kutta4< double , double , double , double , vector_space_algebra , default_operations , never_resizer > stepper_type_d;
42
main()43 int main()
44 {
45
46 stepper_type_m stepper_m;
47 stepper_type_d stepper_d;
48
49 mp_50 dt_m( 0.5 );
50 double dt_d( 0.5 );
51
52 cout << "dt" << '\t' << "mp" << '\t' << "double" << endl;
53
54 while( dt_m > 1E-20 )
55 {
56
57 mp_50 x_m = 0; //initial value x(1) = 0
58 stepper_m.do_step( rhs_m , x_m , mp_50( 1 ) , dt_m );
59 double x_d = 0;
60 stepper_d.do_step( rhs_d , x_d , 1.0 , dt_d );
61
62 cout << dt_m << '\t';
63 cout << abs((x_m - (sqrt(1+dt_m)-mp_50(1)/(1+dt_m)))/x_m) << '\t' ;
64 cout << abs((x_d - (sqrt(1+dt_d)-mp_50(1)/(1+dt_d)))/x_d) << endl ;
65 dt_m /= 2;
66 dt_d /= 2;
67 }
68 }
69