Skip to content Skip to navigation Skip to collection information

OpenStax_CNX

You are here: Home » Content » Cómputo de Alto Rendimiento » Loop Interchange

Navigation

Table of Contents

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Endorsed by Endorsed (What does "Endorsed by" mean?)

This content has been endorsed by the organizations listed. Click each link for a list of all content endorsed by the organization.
  • HPC Open Edu Cup

    This module is included inLens: High Performance Computing Open Education Cup 2008-2009
    By: Ken Kennedy Institute for Information TechnologyAs a part of collection: "High Performance Computing"

    Click the "HPC Open Edu Cup" link to see all content they endorse.

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • NSF Partnership display tagshide tags

    This module is included inLens: NSF Partnership in Signal Processing
    By: Sidney BurrusAs a part of collection: "High Performance Computing"

    Click the "NSF Partnership" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

  • Featured Content

    This module is included inLens: Connexions Featured Content
    By: ConnexionsAs a part of collection: "High Performance Computing"

    Comments:

    "The purpose of Chuck Severence's book, High Performance Computing has always been to teach new programmers and scientists about the basics of High Performance Computing. This book is for learners […]"

    Click the "Featured Content" link to see all content affiliated with them.

Also in these lenses

  • UniqU content

    This module is included inLens: UniqU's lens
    By: UniqU, LLCAs a part of collection: "High Performance Computing"

    Click the "UniqU content" link to see all content selected in this lens.

  • Lens for Engineering

    This module is included inLens: Lens for Engineering
    By: Sidney Burrus

    Click the "Lens for Engineering" link to see all content selected in this lens.

  • eScience, eResearch and Computational Problem Solving

    This module is included inLens: eScience, eResearch and Computational Problem Solving
    By: Jan E. OdegardAs a part of collection: "High Performance Computing"

    Click the "eScience, eResearch and Computational Problem Solving" link to see all content selected in this lens.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Loop Interchange

Module by: Charles Severance, Kevin Dowd. E-mail the authors

Loop interchange is a technique for rearranging a loop nest so that the right stuff is at the center. What the right stuff is depends upon what you are trying to accomplish. In many situations, loop interchange also lets you swap high trip count loops for low trip count loops, so that activity gets pulled into the center of the loop nest.1

Loop Interchange to Move Computations to the Center

When someone writes a program that represents some kind of real-world model, they often structure the code in terms of the model. This makes perfect sense. The computer is an analysis tool; you aren’t writing the code on the computer’s behalf. However, a model expressed naturally often works on one point in space at a time, which tends to give you insignificant inner loops — at least in terms of the trip count. For performance, you might want to interchange inner and outer loops to pull the activity into the center, where you can then do some unrolling. Let’s illustrate with an example. Here’s a loop where KDIM time-dependent quantities for points in a two-dimensional mesh are being updated:


PARAMETER (IDIM = 1000, JDIM = 1000, KDIM = 3) ... DO I=1,IDIM DO J=1,JDIM DO K=1,KDIM D(K,J,I) = D(K,J,I) + V(K,J,I) * DT ENDDO ENDDO ENDDO

In practice, KDIM is probably equal to 2 or 3, where J or I, representing the number of points, may be in the thousands. The way it is written, the inner loop has a very low trip count, making it a poor candidate for unrolling.

By interchanging the loops, you update one quantity at a time, across all of the points. For tuning purposes, this moves larger trip counts into the inner loop and allows you to do some strategic unrolling:


DO K=1,KDIM DO J=1,JDIM DO I=1,IDIM D(K,J,I) = D(K,J,I) + V(K,J,I) * DT ENDDO ENDDO ENDDO

This example is straightforward; it’s easy to see that there are no inter-iteration dependencies. But how can you tell, in general, when two loops can be inter- changed? Interchanging loops might violate some dependency, or worse, only violate it occasionally, meaning you might not catch it when optimizing. Can we interchange the loops below?


DO I=1,N-1 DO J=2,N A(I,J) = A(I+1,J-1) * B(I,J) C(I,J) = B(J,I) ENDDO ENDDO

While it is possible to examine the loops by hand and determine the dependencies, it is much better if the compiler can make the determination. Very few single-processor compilers automatically perform loop interchange. However, the compilers for high-end vector and parallel computers generally interchange loops if there is some benefit and if interchanging the loops won’t alter the program results.2

Footnotes

  1. It’s also good for improving memory access patterns.
  2. When the compiler performs automatic parallel optimization, it prefers to run the outermost loop in parallel to minimize overhead and unroll the innermost loop to make best use of a superscalar or vector processor. For this reason, the compiler needs to have some flexibility in ordering the loops in a loop nest.

Collection Navigation

Content actions

Download:

Collection as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add:

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks