A COMPONENT-BASED DEFINITION OF SPATIAL

LOCALITY

Xiaoming Gu Chengliang Zhang

Chen DingUniversity of

RochesterMicrosoft Corporation

TRADITIONAL DEFINITION OF SPATIAL LOCALITY

When a data element is accessed, the nearby data elements will also be accessed

Overall miss rate The fewer the misses, the better the layout

QUESTIONS

Can the overall spatial locality be decomposed into finer components?

How much can the locality of a given data layout be improved?

Can a data layout be improved if the miss rate cannot be lowered?

A COMPONENT-BASED DEFINITION OF SPATIAL LOCALITY

Based on the reuse distance Based on components

REUSE DISTANCE

The reuse distance of a memory access is the number of distinct data elements accessed between this and the previous access to the same data.

∞ ∞ ∞ 2 0 2 0 1a b c a a b b a

REUSE SIGNATURE

The distribution of all reuse distances In our experiment, we use log sized bins

0 1 2 ∞0

1

2

3

0 1 2-3 ∞2 1 2 3

A COMPONENT-BASED DEFINITION OFSPATIAL LOCALITY

Spatial locality measures the change in reuse distance when the data block size changes from b1 to twice the size b2 = 2*b1.

∞ ∞ ∞ 2 0 2 0 1∞ 0 ∞ 1 0 0 0 0a b c a a b b a

b1

b2

CASES OF CHANGEx yData layout

xTrace ...........................................

Case 1: ...........................................

Case 2: ...........................................

c d

x

x x

x xy

b2

b1

x y

s

Data layout

CHANGES OF REUSE SIGNATURE

2 1 2 3

5 1 0 2

0-0 1-1 2-3 ∞

b2

b1

DATA LAYOUT QUALITY

Effective spatial reuse: the bin they are located has been moved to left by at least C bins, when the block size is doubled

Ineffective spatial reuse: the other reuses In our experiment, we pick C to be 3 The data layout quality of a bin:

2 * effective spatial reuse / total spatial reuse

COMPONENT

Data reuses of nearby bins that have a similar portion of effective spatial reuse

The spatial locality of a component is the weighted average of the spatial locality of each bin

We manually examine the bins and groups them into components

EXPERIMENTAL SETTING

7 SPEC2000 (equake, art, swim, gzip, mcf, crafty, twolf) and 1 SPEC2006 (milc) Data size varies from 1.2MB to 72MB Trace length varies from 7.7 billion to 400 billion

Valgrind [NethercoteSeward’07] to collect traces

Augmented reuse distance analyzer [DingZhong’03] Several hundred times slower

SWIM

WHY OPTIMIZED SWIM BETTER

L1 miss rate L2 miss rate

Original version 10.4% 5.33%

Optimized version 9.7% 5.33%

L1 miss rate reduced by 6.7%

Performance increased by 8.1%

4% reference: 0.16 -> 0.99

Good temporal locality

Good spatial locality

Poor Spatial locality

DIFFERENT INPUTS

Component Spatial locality

Size (%)

ref input

swim-c1 0.25 5.1swim-c2 1 5.2

train input

swim-c1 0.25 5.1swim-c2 0.98 5.2

POSSIBLE USES

User tuning [Levinthal] Superpage management Data-based cache hints [ Fang’05,

BeylsD’Hollander’05]

RELATED WORK

Spatial locality [BuntMurphy’84,Weinberg+’05]

Component-based analysis [DingZhong’03,Shen+’03]

Spatial uses within a loop [WolfLam’91,McKiney+’96]

SUMMARY

A quantitative model of spatial locality We have tested our new model on 8 SPEC

benchmark programs Among 18 components, 2 have good temporal

locality, 6 have good spatial locality, 4 have poor spatial locality/poor temporal locality/large

Possible uses