Minimizing Cache Overhead via Loaded Cache Blocks and Preemption Placement John Cavicchio, Corey Tessler, and Nathan Fisher Department of Computer Science

Minimizing Cache Overhead via

Loaded Cache Blocks and Preemption Placement

John Cavicchio, Corey Tessler, and Nathan Fisher

Department of Computer ScienceWayne State University

Detroit, MI, USA

This research has been supported in part by US National Science Foundation (Grant no.: CNS-0953585).

1. Refined CRPD Calculation;2. Preemption Placement

Algorithm; 3. Simulation of Actual Code Cache-

Behavior.

Preemption Placement to Minimize CRPD inSequential Flowgraphs.

Sequential (Non-Branching) Control Flowgraphs.

Cache-Related Preemption Delay (CRPD) & Limited Preemption Scheduling.

1

Outline

Background

Model

Problem Statement

Solution

Write A Read A

Write B

2

Cache-Related Preemption Delay (CRPD)

Background Model Problem

Statement Solutions Conclusions

CRPD

Cache evictions due to preempting higher-priority jobs.

Cache

TAG AB

Cache eviction

Cache reload

Write B

2




CRPD


1. Delay preemption to maintain cache locality (Limited/Deferred Preemptions).

Write A Read A

Techniques to Reduce CRPD

2




CRPD


1. Delay preemption to maintain spatial locality (Limited/Deferred Preemptions).

2. Decrease CRPD analysis pessimism by considering interdependencies between adjacent preemptions.

Techniques to Reduce CRPD

Write A

Write B

Read A

Write B

Independent Preemption (Single-Valued) Analysis: include a reload of A in the CRPD for each preemption of J1 between the write and the read.

Interdependent Preemption Analysis: CRPD of each preemption depends on location of next. Only account for one reload of A for each preemption of J1 between the write and the read.

3

Opportunity: InterdependentPreemption Placement



Interdependent CRPD (Best-Case)

Single Valued CRPD

Preemption Location in the Sequential Flowgraph

CR

PD

Cost

Opportunity for CRPD Reduction

Reduce CRPD via preemption placement by exploiting preemption interdependencies while preserving system schedulability.

Our goal

4

Related Work: CRPD Calculation



Independent Preemption Calculation

Interdependent Preemption Calculation

Cache-Block Categorization

& Counting Techniques

(UCBs, ECBs,

DC-UCBs,…)

Lee et al. ['96, ’97, ‘98]

Tomiyamay and

Dutt. ['00]

Negi, et al. [‘03]

Tan and Mooney [‘04]

Staschulat and Ernst [‘05]

Altmeyer and

Burguiere [‘11]

Luniss et al. [’13]

….

Cache Partitiong

/Coloring

Mueller [’95]

Lietdtke et al. [‘96]

Mancuso et al. [‘13]

…

Memory Access

Patterns

Ramaprasad and

Mueller [‘06]

Probabilistic Davis et al. [‘13]

Our Work

5

Related Work: Limited Preemption Model



Fixed preemption

point models

Floating preemption point

models

EDF scheduled systems

Burns ['94]

Baruah ['05]

Bertogna and Baruah ['10]

Fixed Priority scheduled systems

Burns ['94], Bril et al. ['09],

Bertogna et al. ['11], Davis et al. ['12]

Yao et al. ['09]

Single valued CRPD

Bertogna et al.['10, '11]

Peng, Fisher, Bertogna ['13]

Interdependent CRPD

Our work

6

Model:Sequential Control Flowgraphs



An arbitrary control sequence of instructions with a single entry point and a single exit point.

Basic Block (Region)

..

Basic block numeric identifier.

Block ID

Task numeric identifier.

Task ID

Block non-preemptive worst case execution time.

Block WCET

7

Model:Sequential Control Flowgraphs



Potential Preemption Point (PPP)Each edge is a potential

program location to (statically) insert a preemption point.

CRPD Cost Matrix

0 1 2 4 4 3 2

- 0 3 5 6 4 3

- - 0 8 7 5 4

- - - 0 8 7 6

- - - - 0 6 7

- - - - - 0 8

- - - - - - 0

Interpretation: Entry i(i, i ) represents the CRPD of preemption inserted after i if a preemption is also inserted after i.

j

j

k

k

8

Preemption Point PlacementProblem



Given: A set of tasks {1, 2, …, n}.Each task i is characterized by:

1. Timing parameters (e.g., deadline and period).

2. Maximum non-preemptive region Qi. Note: Determined

from limited-preemption schedulability analysis (e.g., Baruah, RTSS’05)

9






2. Maximum non-preemptive region Qi.3. Sequential Control Flowgraph &

CRPD Matrix:

Goal: Determine the choice of preemption points to minimize the WCET + CRPD of each task such that any non-preemptive region is at most Qi.

i(i, i ) + bi Qi

j j+1 ℓℓ=j+1

k

9






2. Maximum non-preemptive region Qi.

3. Sequential Control Flowgraph:

Goal: Determine the choice of preemption points to minimize the WCET + CRPD of each task such that any non-preemptive region is at most Qi.

Let be selected preemption points.

Minimize i(i, i ) + bi j j+1 ℓ

ℓ=1

# of blocks

i j

I. Calculation of CRPD for Interdependent Preemptions.

II. Preemption Placement Algorithm.

III.Estimation of CRPD via Cache Simulation.

10

Outline of Solutions Background Model Problem


0 1 2 4 4 3 2

- 0 3 5 6 4 3

- - 0 8 7 5 4

- - - 0 8 7 6

- - - - 0 6 7

- - - - - 0 8

- - - - - - 0

11

CRPD Computation: UCBs

Definition: Useful Cache Block (UCB) [Lee et al., ‘96]



Task

1

Write X Read X

X maps to Cache Block 1

{} {1,2} {1,2,4,8} {1,2,8} {1,2,7,8} {1,2,7,8} {1,2}UCBs:

12

CRPD Computation: ECBs Background Model Problem


A memory block m is called an evicting cache block, at basic block i, if it may be accessed during execution of that basic block.

Definition: Evicting Cache Block (ECB) [Lee et al., ‘96]

j

Task

1

{} {1,2} {1,2,4,8} {1,2,8} {1,2,7,8} {1,2,7,8} {1,2}UCBs: {} {1,2} {3,4,8} {4,5,6,8} {1,2,7,8} {1,2,7,8} {1,2}ECBs: Write X Read X Read XRead X

X maps to Cache Block 1

ECB(τ1) = ECB(1) ={1, 2, 3, 4, 5, 6, 7, 8}Task-LevelView

j

j

13

CRPD Computation: AUCBs Background Model Problem


Definition: Accessed Useful Cache Block (AUCB):

A memory block m is called an accessed useful cache block, if it may be accessed during execution of that basic block and is useful.

Task

1

{} {1,2} {1,2,4,8} {1,2,8} {1,2,7,8} {1,2,7,8} {1,2}UCBs: {} {1,2} {3,4,8} {4,5,6,8} {1,2,7,8} {1,2,7,8} {1,2}ECBs: {} {1,2} {4,8} {8} {1,2,7,8} {1,2,7,8} {1,2}AUCBs:

AUCB(i ) = UCB(i ) ECB(i )

j j j

14

CRPD Computation: LCBs

A memory block m of the preempted task is called a loaded cacheblock, if it may be re-loaded during the non-preemptive region defined by two adjacent selected preemption points.

Definition: Loaded Cache Block (LCB):



LCB(i , i ) = [UCB(i ) [ AUCB(i )]] [ ECB(k)]

curr next curr

v=curr+

1

next v

k hp(i)

Useful blocks of task i at time of a preemption.

Blocks accessed by i between two adjacent preemptions. Contention with higher-priority tasks.

Task

1

icurr inext

14

CRPD Computation: LCBs

A memory block m of the preempted task is called a loaded cacheblock, if it may be re-loaded during the non-preemptive region, defined by two adjacent selected preemption points.

Definition: Loaded Cache Block (LCB):



LCB(i , i ) = [UCB(i ) [ AUCB(i )]] [ ECB(k)]

curr next curr

v=curr+

1

next v

k hp(i)

{} {1,2} {1,2,4,8} {1,2,8} {1,2,7,8} {1,2,7,8} {1,2}UCBs: {} {1,2} {4,8} {8} {1,2,7,8} {1,2,7,8} {1,2}AUCBs:

Task

1

icurr inext

Assume [ ECB(k)] = {1, 2, …, 8}:

LCB(1 , 1 ) = {1, 2, 8}

k hp(i)

curr next

15

CRPD Computation: Interdependent Cost Structure

0 1 2 4 4 3 2

- 0 3 5 6 4 3

- - 0 8 7 5 4

- - - 0 8 7 6

- - - - 0 6 7

- - - - - 0 8

- - - - - - 0



Interdependent CRPD cost between each pair of PPPs.

CRPD CostConsider a pair of PPPs.

Interdependence

i(i , i ) = |LCB(i , i )| BlockReloadTimecurr next curr next

16

CRPD Computation: Single Valued Cost Structure

0 1 2 4 4 3 2

- 0 3 5 6 4 3

- - 0 8 7 5 4

- - - 0 8 7 6

- - - - 0 6 7

- - - - - 0 8

- - - - - - 0



Compared to the interdependent CRPD cost, the single valued approach must use the maximum CRPD cost at each PPP.

Single Valued CRPD Cost

4 6 8 8 7 8 0

17






18

Preemption Placement Algorithm:Dynamic Programming



Optimal SubstructureAssume optimal set of preemption points selected.

Subset of select preemption points must also be optimal for subproblem.

18

Preemption Placement Algorithm:Dynamic Programming



Optimal SubstructureSP1

SP2SP3

…

Qi

Result: Optimal preemption placement for sequential flowgraphs can be done in quadratic complexity in the number of basic blocks.

19






Select ten random tasks from the MRTC Benchmarks.

Compute enhanced preemption cost matrix. Each task compiled for GRSIM LEON3 target Absint’s a3 used to get CFG and WCET. Cache snapshots used to obtain LCB

estimates. Plot CRPD cost as function of preemption

location: Illustrate preemption-cost interdependence &

variation. Breakdown Utilization Evaluation.

20

Simulations:Methodology



ADPCM BSORT100 CNT COVER CRC

FFT1 FIBCALL LMS NDES RECURSION

21

Simulations: Recursion Task CRPD



Emphasizes the interdependence of preemption points

Preemption cost trend

22

Simulations: LMS Task CRPD



Large cost variations


23

Simulations: ADPCM Task CRPD



Large cost variations


24

Simulations: Breakdown Utilization



Preemption Placement & Interdependent PreemptionsPreemption Placement & Independent Preemptions (Bertogna et al.)

UCB-Only(Lee et al., Lunnis et al..)

Conlusions: Enhance CRPD calculation to account for

preemption interdependence. Proposed quadratic dynamic programming

algorithm for selection of optimal preemption points.

Simulations over code show potential for significant CRPD reduction.

Future work: Extend the sequential flow graph structure to an

arbitrary flow graph structure. (E.g., conditional blocks, loops, function calls, and gotos.)

Develop automated & integrated compiler/schedulability tools.

Extend the technique to utilize other CRPD set-theoretic concepts. (E.g., UCB-U Multiset, ECB-U Multiset, DC-UCB).

25

Conclusions and Future Work


Statement Solutions Future Work

26

[email protected]

Thank You!

Deadline: July 24th

Lille, November 4-6

23rd International Conference on Real-Time Networks & Systems

Documents

Minimizing Cache Overhead via Loaded Cache Blocks and Preemption Placement John Cavicchio, Corey Tessler, and Nathan Fisher Department of Computer Science