Transcript Minimizing Code Size and Guaranteeing Real-Time Requirements

Embedded System Design Framework for
Minimizing Code Size and
Guaranteeing Real-Time Requirements
Insik Shin, Insup Lee, & Sang Lyul Min
CIS, Penn, USA
CSE, SNU, KOREA
Agenda

Background

Period Calibration Method (PCM)

Code size reduction technique

Design framework overview

Optimization problem formulation

Heuristic solutions and evaluations

Conclusion
2
Period Calibration Method (PCM)

Design methodology that transforms realtime system requirements into real-time
task scheduling parameters

Example

Drawback : it may not generate
schedulable solutions

R. Gerber et al. “Guaranteeing End-to-End Timing
Constraints by Calibrating Intermediate
Processes”, RTSS ’94.
3
Code Size Reduction Technique

Code size is a critical design factor for
many embedded systems.

Reduced bit-width instructions

ARM microprocessor

normal mode : 32-bit instruction set

Thumb mode : 16-bit instruction set

code size can be reduced by 30%, while # of
instructions can increase by 40%.
4
Code Size vs Execution Time Tradeoff

A program contains both 16/32 bit
instructions in functions or basic blocks.

Compile-time tradeoff between code size
(s) and execution time (e) of a task
s
e
5
Tradeoff Function

Tradeoff function for each task

i
s = fi(e) (linear or discrete)
s
A
B
e
6
Embedded Real-Time System Design

Problem: design a system satisfying realtime system requirements while minimizing
the total code size of the task system
Real-time System
Requirements
X1
X2
1
2
d1
d2
3
4
Tradeoff
…
Y1
F(Y1|X1)=30, F(Y1|X2)=25,
C(Y1|X1,X2) = 4,
u(Y1)=40, l(Y1)=30
Task 1 Task 2
Task n
7
Design Framework

Goal : deriving task code size and scheduling
parameters while minimizing the system code
size and guaranteeing real-time requirements
Real-time System
Requirements
X1
1
d1
X2
2
d2
Design Framework
Task Scheduling Parameters
3
Y1
4
F(Y1|X1)=30, F(Y1|X2)=25,
C(Y1|X1,X2) = 4,
PCM
0
5
10
0
5
10
u(Y1)=40, l(Y1)=30
Tradeoff
…
Task 1 Task 2
Task n
8
Design Framework Overview
Real-Time System Requirements
Min. Task Exec. Time
Design Framework
PCM
Task Scheduling
Parameters
Task Tradeoff
Feasibility
Analysis
Feasibility
Constraints
Task Exec. Time
Task Code Size
Optimization
Framework
Task Code Size & Scheduling Parameters
9
Design Framework Overview
Real-Time System Requirements
Min. Task Exec. Time
Design Framework
PCM
Task Scheduling
Parameters
Task Tradeoff
Feasibility
Analysis
Feasibility
Constraints
Task Exec. Time
Task Code Size
Optimization
Framework
Task Code Size & Scheduling Parameters
10
Optimization Problem Formulation

Given linear or discrete tradeoff functions and
task scheduling parameters, determine task
execution time solving the following
optimization problem:

Optimization problem:
 objective: minimizing
 constraint: feasibility
n
n
s   f
i
i 1
e
i( i)
i 1
11
Feasibility Analysis


Task model : asynchronous periodic tasks with
pre-period deadlines under EDF scheduling
For the task model, an exact feasibility
condition is
n
 (t , t )  e  t
i
1
2
i
2
 t1
i 1
for all 0  t1  t 2  2TLCM  O max , where i (t1, t 2) is
the number of jobs of task i that must be
completely scheduled in [t1, t2).


Feasibility Analysis is NP-hard [Baruah ’90].
12
Feasibility Analysis

Our contribution: another exact feasibility
condition that can be more efficiently
evaluated.
n
 (t , t )  e  t
i
1
2
i
2
 t1
i 1
for all (t1, t2) ODALL , where ODALL is a set of
possible pair of (offset, deadline) between 0
and 2TLCM + Omax.
13
Optimization Framework

Optimization Problem
 Objective : minimizing
n
 Constraint :
n
s
i
i 1
 (t , t )  e  t
for all (t , t ) OD .
i
1
2

i
n

fi ( ei )
i 1
2
 t1
i 1
1

2
ALL
Complexity of optimization problem
 Linear tradeoff : the optimization problem
can be solved through linear programming.
 Discrete tradeoff: we prove the problem is
NP-hard and present three heuristics.
14
Heuristic Algorithms

Consider the following three tasks
Ti
ei
1
2
3
9
2
7
1
5
2
1
2
3
0
5
10
15
20
15
Heuristic Algorithms

Each job can increase its execution time if there
is an empty slot in its execution window
EDF Schedule
0
5
10
15
20
0
5
10
15
20
1
2
3
16
Heuristic Algorithms

Each job can increase its execution time if there
is an empty slot in its execution window
EDF Schedule
0
5
10
15
20
0
5
10
15
20
1
2
3
17
Heuristic Algorithms

Each job can increase its execution time if there
is an empty slot in its execution window

Cumulative amount of execution time each job can
increase
1
2
3
0
5
10
15
20
18
Heuristic Algorithms

Each job can increase its execution time if there
is an empty slot in its execution window

The maximum amount of execution time a task can
increase is the maximum amount of execution time all
of its jobs can increase together.
1
2
3
0
5
10
15
20
19
Heuristic Algorithms

Highest Best Reduction-Ratio First (HBRF)
 reduction ratio
fi (ei )  fi (ei  i )
i

1
choose a task with the highest reduction ratio
i
ei
2
0
5
10
15
20
20
Heuristic Algorithms

Longest Period First (LPF)
 choose a task with the longest period.
 In general, increasing the execution time of
this task has the least impact on the
schedulability of task set
T1
1
2
T2
0
5
10
15
20
21
Heuristic Algorithms

Highest Best Weighted-Reduction-Ratio First (HBWF)
 Weighted reduction ratio
Ti
TLCM

fi (ei )  fi (ei  i )

i
choose a task with the highest weighted
reduction ratio
T1
1
i
ei
2
T2
0
5
10
15
20
22
Evaluation of Heuristic Algorithms

Closeness to OPT
 S(init) – initial system code size
 S(alg) – system code size obtained with
an heuristic algorithm
 S(opt) – optimal system code size
 Closeness to OPT
S (init )  S (alg )
S (init )  S (opt )
23
Performance of algorithms with 8 tasks
BEST
HBRF
HBWF
LPF
1
Density
0.8
0.6
0.4
0.2
0
60
70
80
90
Closeness to OPT (%)
100
24
Performance of BEST with various task numbers
1
Density
0.8
0.6
4 tasks
6 tasks
8 tasks
10 tasks
12 tasks
0.4
0.2
0
60
70
80
90
Closeness to OPT (%)
100
25
Conclusion
Design framework taking advantage of
the code size vs. execution time tradeoff
 Future work



Energy consumption is another critical design
factor of embedded systems.
Extends this framework so as to utilize
tradeoffs among code size, execution time,
and energy consumption.
26
Real-Time System Requirements

Task graph


dataflow & task precedence
End-to-end timing constraints

freshness from input to output

input correlation

output separation
27
Task Graph

Dataflow & task precedence
X1
1
d1
4
X2
2
d2
5
X3
3
Y1
d4
d3
6
Y2
28
End-to-end timing Constraints

Freshness from input to output: F(Y1|X1)

Input correlation : C(Y1|X1,X2)

Output separation : u(Y1), l(Y1)
X1
1
d1
X2
2
d2
4
Y1
29
Example – System Requirements
X1
1
d1
4
X2
2
d2
5
X3
3
Y1
d4
d3
F(Y1|X1)=30, F(Y1|X2)=30,
F(Y2|X2)=20, F(Y2|X3)=15
C(Y1|X1,X2)=3,
C(Y2|X2,X3)=4
l(Y1)=21, u(Y1)=32,
l(Y2)=29, u(Y2)=41
6
Y2
e1=2, e2=2,
e3=1, e4=3,
e5=2, e6=3
30
Example – Solution Process
1. deriving the period of each task
ei
minimizing utilization ( 
)
Ti
2. deriving the offset and deadline of each task
3. deriving the fixed priority of each task
31
Example – Task Scheduling Parameters
1
2
3
4
5
6
period
26
13
39
26
39
39
offset
0
0
0
21
0
13
deadline
21
12
13
26
13
15
priority
1
2
3
4
5
6
32
Real-Time Task Scheduling Parameters

Period (Ti)

Offset (Oi)

Deadline (Di)

Fixed priority

Execution time (ei)
33