Evaluation of Large Matrix Operations on a Reconfigurable

Evaluation of Large Matrix Operations on a Reconfigurable Computing Platform for High Performance Scientific Computations C. Chang, G. Wang, and D. Culler UCBerkeley Reviewed and presented by: Luis E. Cordova USCarolina Cordova 1 CSCE-713 2005/2

GE algorithm: • • • Cordova Pivot row selection Pivot row swapping Pivot column division Sub-matrix elimination Back-solve 2 CSCE-713 2005/2

GE algorithm: • N Pivot row selection A Ax = b N log 2 K > > Cordova Spawns over K/F chips > > > 2 cycles depth comparator log 2 K x ceil((N-i)/K) tree log. C(K/F) x link_delay merge log. C(K/F) x link_delay broadcast 3 CSCE-713 2005/2

GE algorithm: • • Pivot row selection Pivot row swapping N - i + 2 inter-FPGA avg_hops x link_delay network hops log. C(K/F) x link_delay broadcast Cordova 4 CSCE-713 2005/2

GE algorithm: • • • Cordova Pivot row selection Pivot row swapping Pivot column division 5 CSCE-713 2005/2

GE algorithm: • • Cordova Pivot row selection Pivot row swapping Pivot column division Sub-matrix elimination 6 CSCE-713 2005/2

GE algorithm: • • • Cordova Pivot row selection Pivot row swapping Pivot column division Sub-matrix elimination Back-solve 7 CSCE-713 2005/2

BEE 2: 38, 400 LUTs 64 Kbytes 12 PUs 480 x 480 Cordova 8 CSCE-713 2005/2

BEE 2: Cordova 9 CSCE-713 2005/2

BEE 2: Cordova 10 CSCE-713 2005/2

BEE 2: Cordova 11 CSCE-713 2005/2

BEE 2: Cordova 12 CSCE-713 2005/2

BEE 2: Cordova 13 CSCE-713 2005/2

BEE 2: Cordova 14 CSCE-713 2005/2

BEE 2: Cordova 15 CSCE-713 2005/2

Tera. BEE: Cordova 16 CSCE-713 2005/2