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// Boost.Units - A C++ library for zero-overhead dimensional analysis and
// unit/quantity manipulation and conversion
//
// Copyright (C) 2003-2008 Matthias Christian Schabel
// Copyright (C) 2008 Steven Watanabe
//
// 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)
/**
\file
\brief performance.cpp
\details
Test runtime performance.
Output:
@verbatim
multiplying ublas::matrix<double>(1000, 1000) : 25.03 seconds
multiplying ublas::matrix<quantity>(1000, 1000) : 24.49 seconds
tiled_matrix_multiply<double>(1000, 1000) : 1.12 seconds
tiled_matrix_multiply<quantity>(1000, 1000) : 1.16 seconds
solving y' = 1 - x + 4 * y with double: 1.97 seconds
solving y' = 1 - x + 4 * y with quantity: 1.84 seconds
@endverbatim
**/
#define _SCL_SECURE_NO_WARNINGS
#include <cstdlib>
#include <ctime>
#include <algorithm>
#include <iostream>
#include <iomanip>
#include <boost/config.hpp>
#include <boost/timer.hpp>
#include <boost/utility/result_of.hpp>
#ifdef BOOST_MSVC
#pragma warning(push)
#pragma warning(disable:4267; disable:4127; disable:4244; disable:4100)
#endif
#include <boost/numeric/ublas/matrix.hpp>
#ifdef BOOST_MSVC
#pragma warning(pop)
#endif
#include <boost/units/quantity.hpp>
#include <boost/units/systems/si.hpp>
#include <boost/units/cmath.hpp>
#include <boost/units/io.hpp>
enum {
tile_block_size = 24
};
template<class T0, class T1, class Out>
void tiled_multiply_carray_inner(T0* first,
T1* second,
Out* out,
int totalwidth,
int width2,
int height1,
int common) {
for(int j = 0; j < height1; ++j) {
for(int i = 0; i < width2; ++i) {
Out value = out[j * totalwidth + i];
for(int k = 0; k < common; ++k) {
value += first[k + totalwidth * j] * second[k * totalwidth + i];
}
out[j * totalwidth + i] = value;
}
}
}
template<class T0, class T1, class Out>
void tiled_multiply_carray_outer(T0* first,
T1* second,
Out* out,
int width2,
int height1,
int common) {
std::fill_n(out, width2 * height1, Out());
int j = 0;
for(; j < height1 - tile_block_size; j += tile_block_size) {
int i = 0;
for(; i < width2 - tile_block_size; i += tile_block_size) {
int k = 0;
for(; k < common - tile_block_size; k += tile_block_size) {
tiled_multiply_carray_inner(
&first[k + width2 * j],
&second[k * width2 + i],
&out[j * width2 + i],
width2,
tile_block_size,
tile_block_size,
tile_block_size);
}
tiled_multiply_carray_inner(
&first[k + width2 * j],
&second[k * width2 + i],
&out[j * width2 + i],
width2,
tile_block_size,
tile_block_size,
common - k);
}
int k = 0;
for(; k < common - tile_block_size; k += tile_block_size) {
tiled_multiply_carray_inner(
&first[k + width2 * j],
&second[k * width2 + i],
&out[j * width2 + i],
width2, width2 - i,
tile_block_size,
tile_block_size);
}
tiled_multiply_carray_inner(
&first[k + width2 * j],
&second[k * width2 + i],
&out[j * width2 + i],
width2, width2 - i,
tile_block_size,
common - k);
}
int i = 0;
for(; i < width2 - tile_block_size; i += tile_block_size) {
int k = 0;
for(; k < common - tile_block_size; k += tile_block_size) {
tiled_multiply_carray_inner(
&first[k + width2 * j],
&second[k * width2 + i],
&out[j * width2 + i],
width2,
tile_block_size,
height1 - j,
tile_block_size);
}
tiled_multiply_carray_inner(
&first[k + width2 * j],
&second[k * width2 + i],
&out[j * width2 + i],
width2,
tile_block_size,
height1 - j,
common - k);
}
int k = 0;
for(; k < common - tile_block_size; k += tile_block_size) {
tiled_multiply_carray_inner(
&first[k + width2 * j],
&second[k * width2 + i],
&out[j * width2 + i],
width2,
width2 - i,
height1 - j,
tile_block_size);
}
tiled_multiply_carray_inner(
&first[k + width2 * j],
&second[k * width2 + i],
&out[j * width2 + i],
width2,
width2 - i,
height1 - j,
common - k);
}
enum { max_value = 1000};
template<class F, class T, class N, class R>
R solve_differential_equation(F f, T lower, T upper, N steps, R start) {
typedef typename F::template result<T, R>::type f_result;
T h = (upper - lower) / (1.0*steps);
for(N i = N(); i < steps; ++i) {
R y = start;
T x = lower + h * (1.0*i);
f_result k1 = f(x, y);
f_result k2 = f(x + h / 2.0, y + h * k1 / 2.0);
f_result k3 = f(x + h / 2.0, y + h * k2 / 2.0);
f_result k4 = f(x + h, y + h * k3);
start = y + h * (k1 + 2.0 * k2 + 2.0 * k3 + k4) / 6.0;
}
return(start);
}
using namespace boost::units;
//y' = 1 - x + 4 * y
struct f {
template<class Arg1, class Arg2> struct result;
double operator()(const double& x, const double& y) const {
return(1.0 - x + 4.0 * y);
}
boost::units::quantity<boost::units::si::velocity>
operator()(const quantity<si::time>& x,
const quantity<si::length>& y) const {
using namespace boost::units;
using namespace si;
return(1.0 * meters / second -
x * meters / pow<2>(seconds) +
4.0 * y / seconds );
}
};
template<>
struct f::result<double,double> {
typedef double type;
};
template<>
struct f::result<quantity<si::time>, quantity<si::length> > {
typedef quantity<si::velocity> type;
};
//y' = 1 - x + 4 * y
//y' - 4 * y = 1 - x
//e^(-4 * x) * (dy - 4 * y * dx) = e^(-4 * x) * (1 - x) * dx
//d/dx(y * e ^ (-4 * x)) = e ^ (-4 * x) (1 - x) * dx
//d/dx(y * e ^ (-4 * x)) = e ^ (-4 * x) * dx - x * e ^ (-4 * x) * dx
//d/dx(y * e ^ (-4 * x)) = d/dx((-3/16 + 1/4 * x) * e ^ (-4 * x))
//y * e ^ (-4 * x) = (-3/16 + 1/4 * x) * e ^ (-4 * x) + C
//y = (-3/16 + 1/4 * x) + C/e ^ (-4 * x)
//y = 1/4 * x - 3/16 + C * e ^ (4 * x)
//y(0) = 1
//1 = - 3/16 + C
//C = 19/16
//y(x) = 1/4 * x - 3/16 + 19/16 * e ^ (4 * x)
int main() {
boost::numeric::ublas::matrix<double> ublas_result;
{
boost::numeric::ublas::matrix<double> m1(max_value, max_value);
boost::numeric::ublas::matrix<double> m2(max_value, max_value);
std::srand(1492);
for(int i = 0; i < max_value; ++i) {
for(int j = 0; j < max_value; ++j) {
m1(i,j) = std::rand();
m2(i,j) = std::rand();
}
}
std::cout << "multiplying ublas::matrix<double>("
<< max_value << ", " << max_value << ") : ";
boost::timer timer;
ublas_result = (prod(m1, m2));
std::cout << timer.elapsed() << " seconds" << std::endl;
}
typedef boost::numeric::ublas::matrix<
boost::units::quantity<boost::units::si::dimensionless>
> matrix_type;
matrix_type ublas_resultq;
{
matrix_type m1(max_value, max_value);
matrix_type m2(max_value, max_value);
std::srand(1492);
for(int i = 0; i < max_value; ++i) {
for(int j = 0; j < max_value; ++j) {
m1(i,j) = std::rand();
m2(i,j) = std::rand();
}
}
std::cout << "multiplying ublas::matrix<quantity>("
<< max_value << ", " << max_value << ") : ";
boost::timer timer;
ublas_resultq = (prod(m1, m2));
std::cout << timer.elapsed() << " seconds" << std::endl;
}
std::vector<double> cresult(max_value * max_value);
{
std::vector<double> m1(max_value * max_value);
std::vector<double> m2(max_value * max_value);
std::srand(1492);
for(int i = 0; i < max_value * max_value; ++i) {
m1[i] = std::rand();
m2[i] = std::rand();
}
std::cout << "tiled_matrix_multiply<double>("
<< max_value << ", " << max_value << ") : ";
boost::timer timer;
tiled_multiply_carray_outer(
&m1[0],
&m2[0],
&cresult[0],
max_value,
max_value,
max_value);
std::cout << timer.elapsed() << " seconds" << std::endl;
}
std::vector<
boost::units::quantity<boost::units::si::energy>
> cresultq(max_value * max_value);
{
std::vector<
boost::units::quantity<boost::units::si::force>
> m1(max_value * max_value);
std::vector<
boost::units::quantity<boost::units::si::length>
> m2(max_value * max_value);
std::srand(1492);
for(int i = 0; i < max_value * max_value; ++i) {
m1[i] = std::rand() * boost::units::si::newtons;
m2[i] = std::rand() * boost::units::si::meters;
}
std::cout << "tiled_matrix_multiply<quantity>("
<< max_value << ", " << max_value << ") : ";
boost::timer timer;
tiled_multiply_carray_outer(
&m1[0],
&m2[0],
&cresultq[0],
max_value,
max_value,
max_value);
std::cout << timer.elapsed() << " seconds" << std::endl;
}
for(int i = 0; i < max_value; ++i) {
for(int j = 0; j < max_value; ++j) {
double diff =
std::abs(ublas_result(i,j) - cresult[i * max_value + j]);
if(diff > ublas_result(i,j) /1e14) {
std::cout << std::setprecision(15) << "Uh Oh. ublas_result("
<< i << "," << j << ") = " << ublas_result(i,j)
<< std::endl
<< "cresult[" << i << " * " << max_value << " + "
<< j << "] = " << cresult[i * max_value + j]
<< std::endl;
return(EXIT_FAILURE);
}
}
}
{
std::vector<double> values(1000);
std::cout << "solving y' = 1 - x + 4 * y with double: ";
boost::timer timer;
for(int i = 0; i < 1000; ++i) {
double x = .1 * i;
values[i] = solve_differential_equation(f(), 0.0, x, i * 100, 1.0);
}
std::cout << timer.elapsed() << " seconds" << std::endl;
for(int i = 0; i < 1000; ++i) {
double x = .1 * i;
double value = 1.0/4.0 * x - 3.0/16.0 + 19.0/16.0 * std::exp(4 * x);
if(std::abs(values[i] - value) > value / 1e9) {
std::cout << std::setprecision(15) << "i = : " << i
<< ", value = " << value << " approx = " << values[i]
<< std::endl;
return(EXIT_FAILURE);
}
}
}
{
using namespace boost::units;
using namespace si;
std::vector<quantity<length> > values(1000);
std::cout << "solving y' = 1 - x + 4 * y with quantity: ";
boost::timer timer;
for(int i = 0; i < 1000; ++i) {
quantity<si::time> x = .1 * i * seconds;
values[i] = solve_differential_equation(
f(),
0.0 * seconds,
x,
i * 100,
1.0 * meters);
}
std::cout << timer.elapsed() << " seconds" << std::endl;
for(int i = 0; i < 1000; ++i) {
double x = .1 * i;
quantity<si::length> value =
(1.0/4.0 * x - 3.0/16.0 + 19.0/16.0 * std::exp(4 * x)) * meters;
if(abs(values[i] - value) > value / 1e9) {
std::cout << std::setprecision(15) << "i = : " << i
<< ", value = " << value << " approx = "
<< values[i] << std::endl;
return(EXIT_FAILURE);
}
}
}
}
|
