Added a new parallelFor api to the thread pool device.

unsupported/Eigen/CXX11/src/Tensor/TensorDeviceThreadPool.h

@@ -172,7 +172,105 @@ struct ThreadPoolDevice {
     pool_->Schedule(func);
   }
 
+  // parallelFor executes f with [0, size) arguments in parallel and waits for
+  // completion. Block size is choosen between min_block_size and
+  // 2 * min_block_size to achieve the best parallel efficiency.
+  // If min_block_size == -1, parallelFor uses block size of 1.
+  // If hard_align > 0, block size is aligned to hard_align.
+  // If soft_align > hard_align, block size is aligned to soft_align provided
+  // that it does not increase block size too much.
+  void parallelFor(Index size, Index min_block_size, Index hard_align,
+                   Index soft_align,
+                   std::function<void(Index, Index)> f) const {
+    if (size <= 1 || (min_block_size != -1 && size < min_block_size) ||
+        numThreads() == 1) {
+      f(0, size);
+      return;
+    }
+
+    Index block_size = 1;
+    Index block_count = size;
+    if (min_block_size != -1) {
+      // Calculate block size based on (1) estimated cost and (2) parallel
+      // efficiency. We want blocks to be not too small to mitigate
+      // parallelization overheads; not too large to mitigate tail effect and
+      // potential load imbalance and we also want number of blocks to be evenly
+      // dividable across threads.
+      min_block_size = numext::maxi<Index>(min_block_size, 1);
+      block_size = numext::mini(min_block_size, size);
+      // Upper bound on block size:
+      const Index max_block_size = numext::mini(min_block_size * 2, size);
+      block_size = numext::mini(
+          alignBlockSize(block_size, hard_align, soft_align), size);
+      block_count = divup(size, block_size);
+      // Calculate parallel efficiency as fraction of total CPU time used for
+      // computations:
+      double max_efficiency =
+          static_cast<double>(block_count) /
+          (divup<int>(block_count, numThreads()) * numThreads());
+      // Now try to increase block size up to max_block_size as long as it
+      // doesn't decrease parallel efficiency.
+      for (Index prev_block_count = block_count; prev_block_count > 1;) {
+        // This is the next block size that divides size into a smaller number
+        // of blocks than the current block_size.
+        Index coarser_block_size = divup(size, prev_block_count - 1);
+        coarser_block_size =
+            alignBlockSize(coarser_block_size, hard_align, soft_align);
+        if (coarser_block_size > max_block_size) {
+          break;  // Reached max block size. Stop.
+        }
+        // Recalculate parallel efficiency.
+        const Index coarser_block_count = divup(size, coarser_block_size);
+        eigen_assert(coarser_block_count < prev_block_count);
+        prev_block_count = coarser_block_count;
+        const double coarser_efficiency =
+            static_cast<double>(coarser_block_count) /
+            (divup<int>(coarser_block_count, numThreads()) * numThreads());
+        if (coarser_efficiency + 0.01 >= max_efficiency) {
+          // Taking it.
+          block_size = coarser_block_size;
+          block_count = coarser_block_count;
+          if (max_efficiency < coarser_efficiency) {
+            max_efficiency = coarser_efficiency;
+          }
+        }
+      }
+    }
+
+    // Recursively divide size into halves until we reach block_size.
+    // Division code rounds mid to block_size, so we are guaranteed to get
+    // block_count leaves that do actual computations.
+    Barrier barrier(block_count);
+    std::function<void(Index, Index)> handleRange;
+    handleRange = [=, &handleRange, &barrier, &f](Index first, Index last) {
+      if (last - first <= block_size) {
+        // Single block or less, execute directly.
+        f(first, last);
+        barrier.Notify();
+        return;
+      }
+      // Split into halves and submit to the pool.
+      Index mid = first + divup((last - first) / 2, block_size) * block_size;
+      pool_->Schedule([=, &handleRange]() { handleRange(mid, last); });
+      pool_->Schedule([=, &handleRange]() { handleRange(first, mid); });
+    };
+    handleRange(0, size);
+    barrier.Wait();
+  }
+
  private:
+  static Index alignBlockSize(Index size, Index hard_align, Index soft_align) {
+    if (soft_align > hard_align && size >= 4 * soft_align) {
+      // Align to soft_align, if it won't increase size by more than 25%.
+      return (size + soft_align - 1) & ~(soft_align - 1);
+    }
+    if (hard_align > 0) {
+      return (size + hard_align - 1) & ~(hard_align - 1);
+    }
+    return size;
+  }
+
+
   ThreadPoolInterface* pool_;
   size_t num_threads_;
 };