Accession Number:

ADA561679

Title:

Communication Avoiding and Overlapping for Numerical Linear Algebra

Descriptive Note:

Technical rept.

Corporate Author:

CALIFORNIA UNIV BERKELEY DEPT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

Personal Author(s):

• Georganas, Evangelos
• Gonzalez-Dominguez, Jorge
• Solomonik, Edgar
• Zheng, Yili
• Tourino, Juan
• Yelick, Katherine A.

Report Date:

2012-05-08

Pagination or Media Count:

20.0

Abstract:

To efficiently scale dense linear algebra problems to future exascale systems, communication cost must be avoided or overlapped. Communication-avoiding 2.5D algorithms improve scalability by reducing inter-processor data transfer volume at the cost of extra memory usage. Communication overlap attempts to hide messaging latency by pipelining messages and overlapping with computational work. We study the interaction and compatibility of these two techniques for two matrix multiplication algorithms Cannon and SUMMA, triangular solve, and Cholesky factorization. For each algorithm, we construct a detailed performance model which considers both critical path dependencies and idle time. We give novel implementations of 2.5D algorithms with overlap for each of these problems. Our software employs UPC, a partitioned global address space PGAS language that provides fast one-sided communication. We show communication avoidance and overlap provide a cumulative benefit as core counts scale, including results using over 24K cores of a Cray XE6 system.

Descriptors:

• *LINEAR ALGEBRA
• ALGORITHMS
• COMMUNICATION AND RADIO SYSTEMS
• COMPUTER PROGRAMS
• CRITICAL PATH METHODS
• NUMERICAL ANALYSIS
• OVERLAP

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE