Matrix Multiply on GPU

We have implemented single/double precision matrix multiply programs for RV770/Cypress. In our implementation, we use two input streams for computing C=AB. One is transposed input matrix A (i.e. column major) and other is input matrix B in normal format (i.e. row major). Output matrix C is also row major. We adopted 8x8 block for single precision and 4x4 for double precision. Here is benchmark result for each case. Note we only measure kernel execution time.

Update: we put double-double (DD) precision performance. In this case, we used 2x2 block. On Cypress architecture GPU, we take advantage of FMA_64 instruction. For MAD peak in DD, we assume one DD operation takes 20 DP operations(ops) without FMA and 15 ops with FMA. Precisely, DD add and DD mul without FMA takes ~ 20 ops while DD mul with FMA only takes ~ 8 ops. Even without FMA_64 instruction, we can use MULADD instruction to reduce op count in DD mul. On RV770, we have 13% better performance as indicated with the row with MAD.

Performance Summary

board	Pmax	Nmax	prec	reg. usage	MAD peak	note
HD4850	736	3328	SP	25	1040
HD5870	2140	7424	SP	25	2720
HD4850	177	1408	DP	19	208
HD5870	475	2048	DP	19	544
HD4850	7.5	768	DDP	21	~10.4
HD4850	8.6	1024	DDP	17	~10.4	MAD
HD5870	20	1024	DDP	21	~27.2
HD5870	31	1024	DDP	18	~36.2	FMA

Pmax & MAD in GFLOPS

Source code

Whole source code will be posted later.

Here is the kernel file (SP) written in IL : kernel_single.il​ (ISA code for Cypress dis.txt​)

Single precision

Double precision

Double-Double precision

Useful forum discussions

Discussion on a highly optimized MM kernel

​http://forum.beyond3d.com/showthread.php?t=54842

Discussion on MM kernels in OpenCL

​http://forums.amd.com/devforum/messageview.cfm?catid=390&threadid=127963

IL code generator in C++

CAL++ ​http://sourceforge.net/projects/calpp/

Meta-programing works in reality. Impressive work!

memo

​http://icl.cs.utk.edu/magma/ ​http://saahpc.ncsa.illinois.edu/tutorials/MAGMA_Tomov.pdf