ITXGEMM: performance

ITXGEMM: Performance

The latest performance numbers have moved to here

Platform (Robert's laptop):

Intel Pentium (TR) III processor (650 MHz) with 256K L2 cache and 16K L1 (data) cache.
Linux Redhat 6.2
double precision (64-bit) arithmetic
ATLAS R3.1 for PIII with a 256K Cache.
This particular version was specifically pre-compiled for us by the Programmer-Formerly-Known-As-Richard.

Matrix-matrix multiplication

To check the performance of the ITXGEMM dgemm routine in isolation, we timed the ATLAS dgemm against our ITXGEMM dgemm.
Case timed: DGEMM( "N", "N", ... )
Comparing only the peak is for sissies. Let's compare all matrix sizes!

Performance results for m,n,k=32:32:512

LU factorization with pivoting

To check the performance of the ITXGEMM dgemm routine in context, we wrote a blocked LU factorization with partial pivoting. The driver routine times the LU factorization and associated forward and backward substitution.

Versions timed:

ATLAS: ATLAS R3.1 precompiled for Pentium (TM) III processors. Uses the Atlas LU factorization as well as the ATLAS BLAS.
ATL-FLAME: Our Formal Linear Algebra Methods Environment implementation of LU factorization with partial pivoting. Uses ATLAS BLAS including the ATLAS dgemm. The outer block size was chosen to equal 120.
ITX-FLAME: Our Formal Linear Algebra Methods Environment implementation of LU factorization with partial pivoting. Uses ATLAS BLAS except for dgemm, for which we use the ITXGEMM dgemm implementation. The outer block size was chosen to equal 128.

Performance:

Performance is in MFLOPS (Millions of floating point operations per second) calculated using an operation count of 2/3 n^3.

Postscript graph

ITX-FLAME

ATLAS

ATL-FLAME

100

200

300

400

500

600

700

800

900

1000

1250

1500

2000

2500

179.4

328.7

359.6

377.7

390.2

402.4

412.8

411.4

423.5

430.9

445.8

454.6

465.4

474.0

234.9

289.9

314.2

337.3

350.4

365.5

377.2

384.0

389.7

398.2

412.7

421.3

432.2

441.0

How to do your own performance evaluation.

Note: ATLAS has implementations of some LAPACK routines as part of the library (e.g. dgetrf). Thus, to do a fair comparison between ATLAS and ITXGEMM, you will need to order the libaries upon linking as follows:

lapack_LINUX.a libITXGEMMR1.0PIII.a libatlas.a libITXauxR1.0PIII.a This will force a routine like dgetrf to be taken from lapack and then linked with the ITXGEMM matrix-matrix multiply. After timing this, you should then link only with
lapack_LINUX.a libatlas.a in that order and time to see how well the same LAPACK routine does with the ATLAS matrix-matrix multiply. Finally link with
libatlas.a libatlas.a in that order and evaluate the ATLAS dgetrf routine with the ATLAS BLAS.
Notice that we have an optimized version of dgetrf that is faster than either ATLAS or LAPACK, but it is not yet part of the ITXGEMM release.

flame@cs.utexas.edu

Last Updated: Nov. 15, 2000