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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` .
Source

    # 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 threads
         if( 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;
    }

Input File: example/multi_thread/harmonic.cpp