fma.cpp

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/******************************************************************************
** Copyright © 2002 by J.M.McGuiness, coder@hussar.me.uk
**
** This library is free software; you can redistribute it and/or
** modify it under the terms of the GNU Lesser General Public
** License as published by the Free Software Foundation; either
** version 2.1 of the License, or (at your option) any later version.
**
** This library is distributed in the hope that it will be useful,
** but WITHOUT ANY WARRANTY; without even the implied warranty of
** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
** Lesser General Public License for more details.
**
** You should have received a copy of the GNU Lesser General Public
** License along with this library; if not, write to the Free Software
** Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
 
#include "stdafx.h"
 
#define BOOST_TEST_MODULE libjmmcg_tests
#include <boost/test/included/unit_test.hpp>
 
#include <boost/mpl/list.hpp>
 
#include "core/ave_deviation_meter.hpp"
#include "core/fma.hpp"
 
#include <chrono>
 
using namespace libjmmcg;
 
BOOST_AUTO_TEST_SUITE(fma_tests)
 
BOOST_AUTO_TEST_CASE(all_zero)
{
   using namespace fma;
 
   const double m=0;
   const double x=0;
   const double c=0;
   const double y=dbl(x)*m+c;
   BOOST_CHECK_EQUAL(y, 0.0);
}
 
BOOST_AUTO_TEST_CASE(all_zero_commute_multiply)
{
   using namespace fma;
 
   const double m=3;
   const double x=4;
   const double c=5;
   const double y=m*dbl(x)+c;
   BOOST_CHECK_EQUAL(y, 17.0);
}
 
BOOST_AUTO_TEST_CASE(all_zero_commute_add)
{
   using namespace fma;
 
   const double m=3;
   const double x=4;
   const double c=5;
   const double y=c+dbl(x)*m;
   BOOST_CHECK_EQUAL(y, 17.0);
}
 
BOOST_AUTO_TEST_CASE(all_zero_commute_multipy_and_add)
{
   using namespace fma;
 
   const double m=3;
   const double x=4;
   const double c=5;
   const double y=c+m*dbl(x);
   BOOST_CHECK_EQUAL(y, 17.0);
}
 
BOOST_AUTO_TEST_CASE(all_zero_nest)
{
   using namespace fma;
 
   const double m=3;
   const double x=4;
   const double c=5;
   const double y=dbl(dbl(x)*m+c)*m+c;
   BOOST_CHECK_EQUAL(y, 56.0);
}
 
BOOST_AUTO_TEST_CASE(m_one_others_zero)
{
   using namespace fma;
 
   const double m=1;
   const double x=0;
   const double c=0;
   const double y=dbl(x)*m+c;
   BOOST_CHECK_EQUAL(y, 0.0);
}
 
BOOST_AUTO_TEST_CASE(all_ones)
{
   using namespace fma;
 
   const double m=1;
   const double x=1;
   const double c=1;
   const double y=dbl(x)*m+c;
   BOOST_CHECK_EQUAL(y, 2.0);
}
 
BOOST_AUTO_TEST_CASE(one_two)
{
   using namespace fma;
 
   const double m=1;
   const double x=2;
   const double c=1;
   const double y=dbl(x)*m+c;
   BOOST_CHECK_EQUAL(y, 3.0);
}
 
BOOST_AUTO_TEST_CASE(all_twos)
{
   using namespace fma;
 
   const double m=2;
   const double x=2;
   const double c=2;
   const double y=dbl(x)*m+c;
   BOOST_CHECK_EQUAL(y, 6.0);
}
 
BOOST_AUTO_TEST_CASE(subtract_twos)
{
   using namespace fma;
 
   const double m=2;
   const double x=2;
   const double c=2;
   const double y=dbl(x)*m-c;
   BOOST_CHECK_EQUAL(y, 2.0);
}
 
BOOST_AUTO_TEST_CASE(associative_subtract_twos)
{
   using namespace fma;
 
   const double m=2;
   const double x=2;
   const double c=2;
   const double y=c-dbl(x)*m;
   BOOST_CHECK_EQUAL(y, -2.0);
}
 
BOOST_AUTO_TEST_CASE(all_zero_two_surrounding_multiplies)
{
   using namespace fma;
 
   const double m=3;
   const double x=4;
   const double c=5;
   const double y=m*dbl(x)*m+c;
   BOOST_CHECK_EQUAL(y, 41.0);
}
 
BOOST_AUTO_TEST_CASE(all_zero_two_post_multiplies)
{
   using namespace fma;
 
   const double m=3;
   const double x=4;
   const double c=5;
   const double y=dbl(x)*m*m+c;
   BOOST_CHECK_EQUAL(y, 41.0);
}
 
BOOST_AUTO_TEST_CASE(all_zero_two_preceeding_multiplies)
{
   using namespace fma;
 
   const double m=3;
   const double x=4;
   const double c=5;
   const double y=m*m*dbl(x)+c;
   BOOST_CHECK_EQUAL(y, 41.0);
}
 
BOOST_AUTO_TEST_CASE(all_zero_two_dbls_add)
{
   using namespace fma;
 
   const dbl m=3;
   const double x=4;
   const dbl c=5;
   const dbl y=m*m*dbl(x)+c;
   BOOST_CHECK_EQUAL(y, 41.0);
}
 
BOOST_AUTO_TEST_CASE(all_zero_two_dbls_subtract)
{
   using namespace fma;
 
   const dbl m=3;
   const double x=4;
   const dbl c=5;
   const dbl y=m*m*dbl(x)-c;
   BOOST_CHECK_EQUAL(y, 31.0);
}
 
BOOST_AUTO_TEST_CASE(all_zero_two_dbls_associative_add)
{
   using namespace fma;
 
   const dbl m=2;
   const double x=3;
   const dbl c=4;
   const dbl y=c+m*m*dbl(x);
   BOOST_CHECK_EQUAL(y, 16.0);
}
 
BOOST_AUTO_TEST_CASE(all_zero_two_dbls_associative_subtract)
{
   using namespace fma;
 
   const dbl m=3;
   const double x=4;
   const dbl c=5;
   const dbl y=c-m*m*dbl(x);
   BOOST_CHECK_EQUAL(y, -31.0);
}
 
BOOST_AUTO_TEST_CASE(multiply_equals_add)
{
   using namespace fma;
 
   const double m=3;
   const double c=5;
   double y=4;
   y*=dbl(m)+c;
   BOOST_CHECK_EQUAL(y, 17.0);
}
 
BOOST_AUTO_TEST_CASE(multiply_equals_subtract)
{
   using namespace fma;
 
   const double m=3;
   const double c=5;
   double y=4;
   y*=dbl(m)-c;
   BOOST_CHECK_EQUAL(y, 7.0);
}
 
BOOST_AUTO_TEST_CASE(add_equals)
{
   using namespace fma;
 
   const double m=3;
   const double x=4;
   double y=5;
   y+=x*dbl(m);
   BOOST_CHECK_EQUAL(y, 17.0);
}
 
BOOST_AUTO_TEST_CASE(subtract_equals)
{
   using namespace fma;
 
   const double m=3;
   const double x=4;
   double y=5;
   y-=x*dbl(m);
   BOOST_CHECK_EQUAL(y, 7.0);
}
 
typedef boost::mpl::list<
   double,
   fma::dbl
> check_fma_tests;
 
BOOST_AUTO_TEST_CASE_TEMPLATE(performance_all_zero_commute_multiply, T, check_fma_tests)
{
   using timed_results_t=ave_deviation_meter<double>;
 
#ifdef JMMCG_PERFORMANCE_TESTS
   const unsigned long test_size=2<<19;
   const unsigned long num_reps=10000;
#else
   const unsigned long test_size=2<<2;
   const unsigned long num_reps=2;
#endif
 
   const std::pair<timed_results_t, bool> timed_results(compute_average_deviation<timed_results_t::value_type>(
      0.1,
      num_reps,
      []() {
         const double m=3;
         const double x=4;
         const double c=5;
         double y=0;
         const auto t1=std::chrono::high_resolution_clock::now();
         for (unsigned long num_loops=0;num_loops<test_size;++num_loops) {
            y+=m*T(x)+c;
         }
         const auto t2=std::chrono::high_resolution_clock::now();
         BOOST_CHECK_EQUAL(y, test_size*17.0);
         return timed_results_t::value_type(std::chrono::duration_cast<std::chrono::nanoseconds>(t2 - t1).count())/test_size;
      }
   ));
   std::cout<<"Time per "<<typeid(T).name()<<" operation: "<<timed_results.first<<" nanosec."<<std::endl;
#ifdef JMMCG_PERFORMANCE_TESTS
   BOOST_CHECK(!timed_results.second);
#endif
}
 
BOOST_AUTO_TEST_SUITE_END()