PARA'04 State-of-the-Art
in Scientific Computing
June 20-23, 2004 (Home page)
Updated: 3 May 2004

A General Purpose Compiler that obtains High Performance for some common Dense Linear Algebra Codes

John A. Gunnels and Fred G. Gustavson
IBM T.J. Watson Research Center
Yorktown Heights NY 10598, USA
and
Keshav Pingali and Kamen Yotov
Cornell University
Ithaca, NY 14853, USA

Abstract:

In this talk we present beginning research on how a general purpose compiler such as Fortran and C can produce High Performance Linear Algebra Codes. For a program P that access and modify standard two dimensional arrays we try to produce an equivalent program Q that performs the same operations but by doing them using the Elementary Operations of Linear Algebra. If possible we then substitute Q for P. In the second phase we use the theory of Linear Algebra to produce a High Performance version of Q, called R. A second key idea is to replace each scalar operation ( on 1 by 1 submatrices ) of Q by submatrix operations on order NB submatrices in Program R. We discuss as examples of programs P the level 3 BLAS, Cholesky Factorization, $LU = PA$ and $QR = A$.

Home page