\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)

harmonic_setup

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Set Up Multi-threading Sum of 1/i

Syntax

ok = harmonic_setup ( num_sum )

Purpose

This routine does the setup for splitting the summation that defines the harmonic series

\[1 + 1/2 + 1/3 + ... + 1/n\]

into separate parts for each thread.

Thread

It is assumed that this function is called by thread zero, and all the other threads are blocked (waiting).

num_sum

The argument num_sum has prototype

size_t num_sum

It specifies the value of \(n\) in the summation.

Source

namespace {
bool harmonic_setup(size_t num_sum)
{  // sum = 1/num_sum + 1/(num_sum-1) + ... + 1
   size_t num_threads  = std::max(num_threads_, size_t(1));
   bool ok             = num_threads == thread_alloc::num_threads();
   ok                 &= thread_alloc::thread_num() == 0;
   ok                 &= num_sum >= num_threads;
   //
   for(size_t thread_num = 0; thread_num < num_threads; thread_num++)
   {  // allocate separate memory for this thread to avoid false sharing
      size_t min_bytes(sizeof(work_one_t)), cap_bytes;
      void* v_ptr = thread_alloc::get_memory(min_bytes, cap_bytes);
      work_all_[thread_num] = static_cast<work_one_t*>(v_ptr);
      //
      // in case this thread's worker does not get called
      work_all_[thread_num]->ok = false;
      // parameters that define the work for this and previous thread
      if( thread_num == 0 )
         work_all_[0]->start = 1;
      else
      {  size_t index  = (num_sum * thread_num) / num_threads;
         work_all_[thread_num-1]->stop = index;
         work_all_[thread_num]->start  = index;
      }
   }
   work_all_[num_threads-1]->stop = num_sum + 1;
   return ok;
}
}