Data Local Iterative Methods For The Efficient Solution of Partial Differential Equations

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rb3.F Program Description

File Name:

rb3.F

Description:

Like rb2.F, this algorithmn makes use of the fact that the black nodes in row i-1 can be updated once the red nodes in row i are up to date. Consequently, we work in pairs of rows; once all of the red nodes in one row have been updated, all the black nodes in the previous row are updated. Care must be taken in the first row and the last row of the grid.

Comment:

Like rb2.F, the algorithmn is able to reduce one of the grid transfers from main memory to the cache. However, the algorithm is not able to keep the values of a red/black node pair long enougth in registers to reuse it during the update of the black nodes.

Results:

Memory access behaviour
Size	MBytes /sec	% of all access which go into
Size	MBytes /sec	±	1. Level	2. Level	3. Level	Memory
16	1825.0	3.3	96.7	0.0	0.0	0.0
32	2161.0	4.1	75.3	20.5	0.0	0.0
64	2888.9	0.6	86.2	12.8	0.4	0.0
128	1736.2	1.4	83.8	7.9	6.8	0.0
256	1294.8	7.1	48.1	38.3	6.5	0.0
512	565.4	6.8	29.5	57.1	2.9	3.6
1024	517.3	6.6	25.0	59.8	5.1	3.6
2048	444.5	4.5	30.7	47.8	13.3	3.6

Runtime behaviour
Size	MFlops /sec	% of cycles used for
Size	MFlops /sec	±	Base	Exec	Cache	DTB	Branch	R dep	Nops
16	337.0	5.2	118.9	68.5	0.3	3.9	8.7	27.2	5.1
32	402.4	3.3	122.9	76.6	10.5	5.0	6.4	14.0	7.1
64	519.2	-0.3	151.2	127.0	1.3	16.3	0.0	0.0	6.9
128	314.6	-0.7	114.4	67.7	7.3	36.4	0.0	0.0	3.7
256	248.9	0.0	111.0	46.3	51.7	7.8	0.1	0.0	5.1
512	108.3	0.0	103.9	19.9	78.7	3.3	0.1	0.0	1.9
1024	98.9	0.0	103.0	18.2	80.1	2.9	0.0	0.0	1.8
2048	83.2	0.0	102.5	16.0	81.6	2.5	0.0	0.0	2.4

Table explanation

cs10-dime@fau.de

Last Modified: 10 January 2008