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- /*
- * Simulation of an ensemble of Roessler attractors using NT2 SIMD library
- * This requires the SIMD library headers.
- *
- * Copyright 2014 Mario Mulansky
- *
- * Distributed under the Boost Software License, Version 1.0.
- * (See accompanying file LICENSE_1_0.txt or
- * copy at http://www.boost.org/LICENSE_1_0.txt)
- *
- */
- #include <iostream>
- #include <vector>
- #include <random>
- #include <boost/timer.hpp>
- #include <boost/array.hpp>
- #include <boost/numeric/odeint.hpp>
- #include <boost/simd/sdk/simd/pack.hpp>
- #include <boost/simd/sdk/simd/io.hpp>
- #include <boost/simd/memory/allocator.hpp>
- #include <boost/simd/include/functions/splat.hpp>
- #include <boost/simd/include/functions/plus.hpp>
- #include <boost/simd/include/functions/multiplies.hpp>
- namespace odeint = boost::numeric::odeint;
- namespace simd = boost::simd;
- typedef boost::timer timer_type;
- static const size_t dim = 3; // roessler is 3D
- typedef double fp_type;
- //typedef float fp_type;
-
- typedef simd::pack<fp_type> simd_pack;
- typedef boost::array<simd_pack, dim> state_type;
- // use the simd allocator to get properly aligned memory
- typedef std::vector< state_type, simd::allocator< state_type > > state_vec;
- static const size_t pack_size = simd_pack::static_size;
- //---------------------------------------------------------------------------
- struct roessler_system {
- const fp_type m_a, m_b, m_c;
- roessler_system(const fp_type a, const fp_type b, const fp_type c)
- : m_a(a), m_b(b), m_c(c)
- {}
- void operator()(const state_type &x, state_type &dxdt, const fp_type t) const
- {
- dxdt[0] = -1.0*x[1] - x[2];
- dxdt[1] = x[0] + m_a * x[1];
- dxdt[2] = m_b + x[2] * (x[0] - m_c);
- }
- };
- //---------------------------------------------------------------------------
- int main(int argc, char *argv[]) {
- if(argc<3)
- {
- std::cerr << "Expected size and steps as parameter" << std::endl;
- exit(1);
- }
- const size_t n = atoi(argv[1]);
- const size_t steps = atoi(argv[2]);
- const fp_type dt = 0.01;
- const fp_type a = 0.2;
- const fp_type b = 1.0;
- const fp_type c = 9.0;
- // random initial conditions on the device
- std::vector<fp_type> x(n), y(n), z(n);
- std::default_random_engine generator;
- std::uniform_real_distribution<fp_type> distribution_xy(-8.0, 8.0);
- std::uniform_real_distribution<fp_type> distribution_z(0.0, 20.0);
- auto rand_xy = std::bind(distribution_xy, std::ref(generator));
- auto rand_z = std::bind(distribution_z, std::ref(generator));
- std::generate(x.begin(), x.end(), rand_xy);
- std::generate(y.begin(), y.end(), rand_xy);
- std::generate(z.begin(), z.end(), rand_z);
- state_vec state(n/pack_size);
- for(size_t i=0; i<n/pack_size; ++i)
- {
- for(size_t p=0; p<pack_size; ++p)
- {
- state[i][0][p] = x[i*pack_size+p];
- state[i][1][p] = y[i*pack_size+p];
- state[i][2][p] = z[i*pack_size+p];
- }
- }
- std::cout << "Systems: " << n << std::endl;
- std::cout << "Steps: " << steps << std::endl;
- std::cout << "SIMD pack size: " << pack_size << std::endl;
- std::cout << state[0][0] << std::endl;
- // Stepper type
- odeint::runge_kutta4_classic<state_type, fp_type, state_type, fp_type,
- odeint::array_algebra, odeint::default_operations,
- odeint::never_resizer> stepper;
- roessler_system sys(a, b, c);
- timer_type timer;
- fp_type t = 0.0;
- for(int step = 0; step < steps; step++)
- {
- for(size_t i = 0; i < n/pack_size; ++i)
- {
- stepper.do_step(sys, state[i], t, dt);
- }
- t += dt;
- }
- std::cout.precision(16);
- std::cout << "Integration finished, runtime for " << steps << " steps: ";
- std::cout << timer.elapsed() << " s" << std::endl;
- // compute some accumulation to make sure all results have been computed
- simd_pack s_pack = 0.0;
- for(size_t i = 0; i < n/pack_size; ++i)
- {
- s_pack += state[i][0];
- }
- fp_type s = 0.0;
- for(size_t p=0; p<pack_size; ++p)
- {
- s += s_pack[p];
- }
- std::cout << state[0][0] << std::endl;
- std::cout << s/n << std::endl;
- }
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