    /************************************************************************

    MODULE: BasicThreadPool

    SUMMARY:

    A simple thread pool class BasicThreadPool, as well as some higher-level macros
    which facilitite simple parallel for loops.

    ***************************************************************************/

    // ********************** Simple parallel for loops **************************
    //
    // We begin with a description of the higher-level macros for writing simple
    // parallel for loops.  These facilitaties are activated only when NTL is
    // configured with NTL_THREAD_BOOST=on (which implies NTL_THREADS=on).
    // However, code that uses these facilties should still compile and run
    // correctly even when NTL_THREAD_BOOST=off, or even when NTL_THREADS=off, so
    // this is the simplest way to write parallel for loops across a range of
    // compile-time and run-time environments.  Note that if NTL_THREADS=on, C++11
    // features are reqired, but when NTL_THREADS=off, these features are not
    // required, so the code should compile on older C++ compilers.
    //
    // Here is a simple recipe for writing parallel for loop.
    //
    // At the start of program execution, your program should execute

       SetNumThreads(nt);

    // You can choose nt to be any positive integer, but for best results, it
    // should correspond to the number of available cores on your machine.
    // [NOTE: if NTL_THREAD_BOOST=off, this function is still defined, but does
    // nothing.]
    //
    // Now consider the following routine:

       void mul(ZZ *x, const ZZ *a, const ZZ *b, long n)
       {
          for (long i = 0; i < n; i++)
             mul(x[i], a[i], b[i]);
       }

    // We can parallelize it as follows:

       void mul(ZZ *x, const ZZ *a, const ZZ *b, long n)
       {
          NTL_EXEC_RANGE(n, first, last)

             for (long i = first; i < last; i++)
                mul(x[i], a[i], b[i]);

          NTL_EXEC_RANGE_END
       }

    // NTL_EXEC_RANGE and NTL_EXEC_RANGE_END are macros that just "do the right
    // thing".  If there are nt threads available, the interval [0..n) will be
    // partitioned into (up to)  nt subintervals, and a different thread will be
    // used to process each subinterval. You still have to write the for loop
    // yourself: the macro just declares and initializes variables "first" and
    // "last" (or whatever you want to call them) of type long that represent the
    // subinterval [first..last) to be processed by one thread.
    //
    // Note that the current thread participates as one of the nt available
    // threads, and that the current thread will wait for all other participating threads
    // to finish their task before proceeding. The current thread can be identified
    // as the one with first == 0.
    //
    // Withing the "body" of this construct, you can freely reference any variables
    // that are visible at this point.  This is implemented using the C++ lambda
    // feature (capturing all variables by reference).
    //
    // This construct will still work even if threads are disabled, in which case
    // it runs single-threaded with first=0 and last=n.
    //
    // Note that the code within the EXEC_RANGE body could call other routines that
    // themselves attempt to execute an EXEC_RANGE: if this happens, the latter
    // EXEC_RANGE will detect this and run single-threaded.
    //
    // You may wish to do other things within the EXEC_RANGE body than just execute
    // a loop.  One thing you may want to do is to declare variables.  Another
    // thing you may want to do is setup a local context for a ZZ_p modulus (or
    // other type of modulus).  Here is an example of doing this:

       void mul(ZZ_p *x, const ZZ_p *a, const ZZ_p *b, long n)
       {
          ZZ_pContext context;
          context.save();

          NTL_EXEC_RANGE(n, first, last)

             context.restore();

             for (long i = first; i < last; i++)
                mul(x[i], a[i], b[i]);

          NTL_EXEC_RANGE_END
       }

    // Another useful function is AvailableThreads(), which will return the number
    // of available threads.  If threads or thread boosting is not enabled, this
    // will return 1.  Even if thread boosting is enabled, this may return 1 if for
    // whatever reason, the thread pool is not available for use (for example,
    // SetNumThreads was never called, or the thread pool is already active).
    //
    // A lower-level set of tools is available, which allow you to simply run a
    // specified number of threads.  Assuming nt <= AvailableThreads(), the code

       NTL_EXEC_INDEX(nt, index)

          ... code ...

       NTL_EXEC_INDEX_END

    // will execute the body on nt different threads, each with a unique index in
    // the range [0..nt).  A variable named "index" (or whatever name you specify)
    // of type long will hold the given index.  Just as with EXEC_RANGE, the current
    // thread will participate as one of the nt threads, and will always be
    // assigned an index of 0.
    //
    // This tool is useful if you need to manage memory a bit more carefully.  For
    // example, the following code will compute an inner product using all
    // available threads:

       ZZ InnerProd(const ZZ *a, const ZZ *b, long n)
       {
          PartitionInfo pinfo(n);

          long cnt = pinfo.NumIntervals();

          Vec<ZZ> acc;
          acc.SetLength(cnt);

          NTL_EXEC_INDEX(cnt, index)

             long first, last;
             pinfo.interval(first, last, index);

             ZZ& sum = acc[index];
             sum = 0;
             for (long i = first; i < last; i++)
                MulAddTo(sum, a[i], b[i]);

          NTL_EXEC_INDEX_END

          ZZ sum;
          sum = 0;
          for (long i = 0; i < cnt; i++)
             sum += acc[i];

          return sum;
       }

    // This example also illustrates the class PartitionInfo, which is useful for
    // partitioning a large interval into smaller intervals (it is used internally
    // by EXEC_RANGE).  The constructor takes a single argument (in this example n)
    // and computes a partition of [0..n) into nearly equally sized subintervals.
    // The method NumIntervals() returns the number of subintervals, and the method
    // interval(first, last, index) sets first and last according to the endpoints
    // of the subinterval [first..last) with the given index.
    //
    // So in this example, cnt threads will run, each accumulating a sum into a
    // corresponding element of the vector acc, and afterwords, these elements are
    // summed.
    //
    // Note that if threads are not enabled or otherwise unavailable, the above
    // code will compile and run correctly (just using one thread).
    //
    // Finally, there is a "guarded" version of NTL_EXEC_RANGE called
    // NTL_GEXEC_RANGE.  This allows one to dynamically "guard" against parallel
    // execution. For example, on very small problems the runtime overhead of a
    // parallel for loop may not be worthwhile, or in other situations parallel
    // execution could cause incorrect behavior.  See below for details.

    // ********************** Simple parallel divide and conquer ************
    //
    // Some tools are provided for parallelizing simple divide and conquer
    // algorithms.  The interface for this set of tools is still experimental
    // and subject to change (but hopefully not).
    //
    // Suppose you have a recursive divide and conquer algorithm:

       void rec_alg(...)
       {
          ...
          // two recursive invocations that can run in parallel
          rec_alg(...call 0...);
          rec_alg(...call 1...);
          ...
       }

    // and this algorithm is invoked initially as

       void alg(...)
       {
          rec_alg(...initial call...);
       }

    // Then the following recipe will paralelize it:

       void rec_alg(..., RecursiveThreadPool *pool)
       {
          ...
          NTL_EXEC_DIVIDE(seq, pool, helper, load,
             rec_alg(...call 0..., helper.subpool(0)),
             rec_alg(...call 1..., helper.subpool(1)) )
          ...
       }

       void alg(...)
       {
          rec_alg(...initial call..., NTL_INIT_DIVIDE);
       }

    // Here, seq is a boolean "guard" value: if true, the two recursive calls will
    // run sequentially, as usual.  Also, load is a floating point number, which
    // represents the fraction of threads that should be assigned to call 0.
    // If the load should be equally balanced, then load=0.5 is a good choice.
    // The name helper is the name of an auxilliary object, which will be in the
    // scope of the two recursive calls.  It supplies a method helper.concurrent(),
    // which returns true if the two calls are being run concurrently, and false
    // otherwise.

    // If thread-boosting is not enabled, these macros will revert to the normal
    // sequential execution, with no overhead.  If thread-boosting is enabled, then
    // the two calls may or may not run concurrently, depending on a number of
    // factors.  If they do run concurrently, call 0 will run on the current
    // thread, while call 1 will run on another thread; in addition, when the
    // current thread finishes execution of call 0, it will wait for the execution
    // of call 1 on the other thread to finish before continuing any further.

    // As one can see, the use cases here are fairly limited to those in which you
    // have a recursive algorithm that calls itself exactly twice.  One example of
    // this is QuickSort.  Another example is a recursive FFT.

    // ************************** Thread Pools ******************************
    //
    // The above facilities are built on top of a more general thread pool class,
    // which you may use for your own purposes.
    //
    // You create a thread pool by constructing a BasicThreadPool object.  For
    // example:

       long nthreads = 4;
       BasicThreadPool pool(nthreads);

    // creates a thread pool of 4 threads.  These threads will exist until the
    // destructor for pool is called.
    //
    // The simplest way to use a thread pools is as follows.  Suppose you have a
    // task that consists of sz subtasks, indexed 0..sz-1.  Then you can write:

       pool.exec_range(sz,
          [&](long first, long last) {
             for (long i = first; i < last; i++) {
                ... code to process subtask i ...
             }
          }
       );

    // The second argument to exec_range is a C++11 "lambda".  The "[&]" indicates
    // that all local variables in the calling context are captured by reference,
    // so the lambda body can reference all visible local variables directly.
    // C++11 provides other methods for capturing local variables.  The interval
    // [0..sz) is partitioned into subintervals of the form [first..last), which
    // are processed by the code in the supplied lambda.
    //
    // A lower-level interface is also provided.  One can write:

       pool.exec_index(cnt,
          [&](long index) {
             ... code to process index i ...
          }
       );

    // This will activate exactly cnt threads with indices 0..cnt-1, and execute
    // the given code on each index.  The parameter cnt must not exceed nthreads,
    // otherwise an error is raised.

    // ====================================================================
    //
    // NOTES:
    //
    // When one activates a thread pool with nthreads threads, the *current* thread
    // (the one activating the pool) will also participate in the computation.
    // This means that the thread pool only contains nthreads-1 other threads.
    //
    // If, during an activation, any thread throws an exception, it will be caught
    // and rethrown in the activating thread when all the threads complete.  If
    // more than one thread throws an exception, the first one that is caught is
    // the one that is rethrown.
    //
    // Methods are also provided for adding, deleting, and moving threads in and
    // among thread pools.
    //
    // If NTL_THREADS=off, the corresponding header file may be included, but the
    // BasicThreadPool class is not defined.
    //
    // Unlike most classes in NTL, the BasicThreadPool is not relocatable and hence
    // cannot be used in a Vec.  One should first wrap it in a pointer class, such
    // as UniquePtr.

    // class BasicThreadPool: provided basic functionality for thread pools

    class BasicThreadPool {
    private:

      BasicThreadPool(const BasicThreadPool&); // disabled
      void operator=(const BasicThreadPool&); // disabled

    public:

      explicit
      BasicThreadPool(long nthreads);
      // creates a pool with nthreads threads, including the current thread
      // (so nthreads-1 other threads get created)

      template<class Fct>
      void exec_range(long sz, const Fct& fct);
      // activate by range (see example usage above)

      template<class Fct>
      void exec_index(long cnt, const Fct& fct);
      // activate by index (see example usage above)

      void add(long n = 1);
      // add n threads to the pool

      long NumThreads() const;
      // return number of threads (including current thread)

      void remove(long n = 1);
      // remove n threads from the pool

      void move(BasicThreadPool& other, long n = 1)
      // move n threads from other pool to this pool

      bool active() const;
      // indicates an activation is in process: invoking any of the methods
      // exec_index, exec_range, add, remove, move, or the destructor
      // whie active will raise an error

      template<class Fct>
      static void relaxed_exec_range(BasicThreadPool *pool, long sz, const Fct& fct);
      // similar to pool->exec_range(sz, fct), but will still work even
      // if !pool or pool->active(), using just the current thread

      template<class Fct>
      static void relaxed_exec_index(BasicThreadPool *pool, long cnt, const Fct& fct);
      // similar to pool->exec_index(cnt, fct), but will still work even
      // if !pool or pool->active(), provided cnt <= 1, using just the current thread

    };

    // THREAD BOOSTING FEATURES:

    void SetNumThreads(long nt);
    // convenience routine to set NTL's thread pool.
    // If called more than once, the old thread pool is destroyed and
    // replaced by a new one.
    // If NTL_THREAD_BOOST=off, then this is still defined, but does nothing.

    long AvailableThreads();
    // Number of threads currently availble to use in NTL's thread pool.  This is
    // always at least 1 (for the current thread).
    // If NTL_THREAD_BOOST=off, then this is still defined, and always returns 1.

    BasicThreadPool *GetThreadPool();
    void ResetThreadPool(BasicThreadPool *pool = 0);
    BasicThreadPool *ReleaseThreadPool();
    // Routines to get and set NTL's thread pool.  The interfaces parallel NTL's
    // UniquePtr class, and indeed, behind the scenes, NTL's thread pool is stored
    // as a UniquePtr<BasicThreadPool>.
    // These are only declared when NTL_THREAD_BOOST=on.

    #define NTL_EXEC_RANGE(sz, first, last) ...
    #define NTL_EXEC_RANGE_END ...
    #define NTL_EXEC_INDEX(cnt, index) ...
    #define NTL_EXEC_INDEX_END ...
    // convenience macros to implement "parallel for loops" using NTL's thread
    // pool.  See examples above for usage.  If NTL_THREAD_BOOST=off, then these
    // are still defined, and code will run on a single thread

    #define NTL_GEXEC_RANGE(seq, sz, first, last) ...
    #define NTL_GEXEC_RANGE_END ...
    // "guarded" version of NTL_EXEC_RANGE: if seq evaluates to true, the code runs
    // on a single thread.  This is useful in avoiding situations where the
    // overhead of a parallel loop is too high.  If seq evaluates to the constant
    // true, a good compiler will optimize code to run on a single thread, with no
    // overhead.

    #define NTL_IMPORT(x)
    // To be used in conjunction with NTL_EXEC_RANGE and friends.  When
    // NTL_THREAD_BOOST=on, this will copy the variable named x from the enclosing
    // scope to a local copy.  This should only be used for types with cheap
    // copies, such as scalars and pointers.  In some situations, this allows the
    // compiler to optimize a bit more aggressively.  One or more of these may be
    // placed right after an NTL_EXEC_RANGE.
    // When NTL_THREAD_BOOST=off, this is still defined, and does nothing.

    // class PartitionInfo: A helper class to facilitate partitioning an interval
    // into subintervals.  NOTE: this class is available, even when
    // NTL_THREAD_BOOST=off.

    class PartitionInfo {
    public:

       explicit
       PartitionInfo(long sz, long nt = AvailableThreads());
       // partitions [0..sz) into at most nt subintervals.  sz may be 0 or
       // negative, in which case the number of subintervals is 0.

       long NumIntervals() const;
       // return the number of subintervals

       void interval(long& first, long& last, long i) const;
       // [first..last) is the ith interval, where i in [0..NumInvervals()).  No
       // range checking is performed.

    };