On the Transformation Optimization for Stencil Computation

Round 1

Reviewer 1 Report

The results investigated by the authors are new and interesting. Minor spell check required.

Author Response

Thank you for comments. 

We go through the text and correct some spell errors. 

Such as 

Line 211 As ia shown in Algorithm => As is shown in Algorithm.

Reviewer 2 Report

It is an intersting article and useful for those in the field

Author Response

Thank you for your hard work.

We check the manuscript and fixed some spelling errors. 

Reviewer 3 Report

Manuscript is logically written. Here are some recommendations for small improvements.

Some strange expressions have been found as:

Line 17: “two groups: blocking and parallelism”.

Line 32: “simulation methods, such as geophysics, computational fluids, and biomedicine”.

Line 76: “Cartesian system” - Cartesian coordinate system.

Line 76: “radius of stencil” would be better expressed as grid step.

Background chapter. Add Figure with the 3D stencil scheme with nodes indexation.

Add output variables in the algorithms pseudo code examples.

Add some graphical representations for the Table data. It will be easier for the reader to get the trends.

I am not sure why this work is submitted in the Electronics journal.

Author Response

Thank you for your suggestion.

According to the comments, we go through the manuscprit and revised the expressions. 

1. We replaced "two groups: blocking and parallelism" as "two aspects: blocking and parallelism".  Both of them are the major optimization methods of stencil computation.
2. We added a figure(figure 1) as an example of 3D 7points stencil computation. We also replaced the Table 3~Table 6 with equal Figures for helping understanding the result and trend. 
3.  We improved the expression of the paper according to the comments, such as  Line 32: “computational simulation methods, such as geophysics, computational fluids, and biomedicine”. ->“computation fields, such as geophysics, computational fluids, and biomedicine”

   Line 76: “Cartesian system” ->Cartesian coordinate system.

Reviewer 4 Report

This article on stencil computations is very well written. The description of the problem and the explanations of the various solutions are well developed. This is an important question for all the solutions of partial differential equations which involve space-time, regular grid, image processing, cellular automata, and finite element method. The methodology is sound, in particular the independence of the algorithms vis-a-vis the hardware architecture. The results are well described and honestly analyzed. We are however disappointed by the results, since no algorithm described improves performance in a ratio greater than 2 (1.9 is reached for the best configuration).
Should we not announce that we have reached a threshold and that we will not be able to improve much in this area? In a Turing machine, should we not question the notion of loop in a software program, the concept of linear memory in a Von Neumann architecture, in short, essential notions, in order to put into perspective the question of taking account of a 2D, 3D, 4D space in a computer environment. The mathematical lock comes from the fact that there is no total order in a space of dimension > 1. Should we not then consider specific hardware architectures in order to manage the memory with different topologies and the calculations more efficiently than finite differences?
A reflection, taking a step back on these somewhat philosophical questions, would be interesting in the conclusion.

minor correction 
Line 211 As ia shown in Algorithm => As is shown in Algorithm

Author Contributions : to be filled
Funding: to be filled (This research was funded by NAME OF FUNDER grant number XXX)

Author Response

Thank you for your comments. Here are the responses:

1.  Yes, under certain conditions, we can build an accurate model and judge whether it has reached the upper limit of performance. However, in this article, we focus on examing the influence of varied optimization methods on the  stencil computations. When putting different optimization methods togather, they will affect each other. On the other hand, the hardware architecture， the radius and dimensions of stencil computation  have a great impact on performance. Therefore, we did not deliberately establish a unified model, but to evaluate the impact of different methods. 
2. We check the manuscript and corrected the spell errors.
3. We added the authors' contributions and funding information in the new version of the manuscript.