@(@\newcommand{\W}[1]{ \; #1 \; }
\newcommand{\R}[1]{ {\rm #1} }
\newcommand{\B}[1]{ {\bf #1} }
\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }
\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }
\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }
\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }@)@This is cppad-20221105 documentation. Here is a link to its
current documentation
.
Timing Test of Multi-Threaded Summation of 1/i
Syntax ok = harmonic_time( time_out, test_time, num_threads, mega_sum
)
Purpose
Runs a correctness and timing test for a multi-threaded
computation of the summation that defines the harmonic series
@[@
1 + 1/2 + 1/3 + ... + 1/n
@]@
Thread
It is assumed that this function is called by thread zero in sequential
mode; i.e., not in_parallel
.
ok
This return value has prototype
bool ok
If it is true,
harmonic_time passed the correctness test.
Otherwise it is false.
time_out
This argument has prototype
double& time_out
The input value of the argument does not matter.
Upon return it is the number of wall clock seconds required for
to compute the summation.
test_time
Is the minimum amount of wall clock time that the test should take.
The number of repeats for the test will be increased until this time
is reached.
The reported
time_out
is the total wall clock time divided by the
number of repeats.
num_threads
This argument has prototype
size_t num_threads
It specifies the number of threads that are available for this test.
If it is zero, the test is run without the multi-threading environment and
1 == thread_alloc::num_threads()
when harmonic_time is called.
If it is non-zero, the test is run with the multi-threading and
num_threads = thread_alloc::num_threads()
when harmonic_time is called.
mega_sum
This argument has prototype
size_t& mega_sum
and is greater than zero.
The value @(@
n
@)@ in the summation
is equal to @(@
10^6
@)@ times
mega_sum
.
# include <cstring>
# include <limits>
# include <iostream>
# include <cstdlib>
# include <algorithm>
// Note there is no mention of parallel mode in the documentation for// speed_test (so it is safe to use without special consideration).# include <cppad/utility/time_test.hpp>
namespace {
// value of sum resulting from most recent call to test_once
double sum_ = 0.;
//
void test_once(void)
{ if( mega_sum_ < 1 )
{ std::cerr << "harmonic_time: mega_sum < 1" << std::endl;
exit(1);
}
size_t num_sum = mega_sum_ * 1000000;
bool ok = harmonic_sum(sum_, num_sum);
if( ! ok )
{ std::cerr << "harmonic: error" << std::endl;
exit(1);
}
return;
}
//
void test_repeat(size_t repeat)
{ size_t i;
for(i = 0; i < repeat; i++)
test_once();
return;
}
}
// This is the only routine that is accessible outside of this file
bool harmonic_time(
double& time_out, double test_time, size_t num_threads, size_t mega_sum)
{ bool ok = true;
ok &= thread_alloc::thread_num() == 0;
// arguments passed to harmonic_sum
num_threads_ = num_threads;
mega_sum_ = mega_sum;
// create team of threads
ok &= thread_alloc::in_parallel() == false;
if( num_threads > 0 )
{ team_create(num_threads);
ok &= num_threads == thread_alloc::num_threads();
}
else
{ ok &= 1 == thread_alloc::num_threads();
}
// run the test case and set the time return value
time_out = CppAD::time_test(test_repeat, test_time);
// destroy team of threadsif( num_threads > 0 )
team_destroy();
ok &= thread_alloc::in_parallel() == false;
// Correctness check
double eps1000 =
double(mega_sum_) * 1e3 * std::numeric_limits<double>::epsilon();
size_t i = mega_sum_ * 1000000;
double check = 0.;
while(i)
check += 1. / double(i--);
ok &= std::fabs(sum_ - check) <= eps1000;
return ok;
}
