A Dynamic Programming Approach to Optimal

Integrated Code Generation

Christoph KeßlerAndrzej Bednarski

Linköping University (Sweden)

Outline Code generation Our integrated approach Implementation and results Current and future work Conclusion

Code Generation

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IR

Targetcode

IR-levelInstruction scheduling

Target-levelInstruction scheduling

IR-levelInstruction scheduling

Target-levelInstruction scheduling

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Related Work Heuristics Optimal approaches

ILP Dynamic programming Branch-and-bound Enumeration Constraint logic programming

Integrated Code Generation

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IR

Targetcode

IR-levelInstruction scheduling

Target-levelInstruction scheduling

IR-levelInstruction scheduling

Target-levelInstruction scheduling

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Integrated

Code generation

Integrated Approach Christoph Keßler’s previous work

Scheduling by topological sorting Dynamic programming Selection DAG

Time profile Extended selection DAGBasic block scope of code generation

Topological Sorting

u

v

scheduled(z)

z

scheduled(z’)

u

v

z’

Selection Tree

h

f g

d e

a b c

{a,b,c}

{b,c} {a,c} {a,b}

a cb

{c,d} {b} {c,d} {a,e} {b} {a,e}

… … … … … …

b c a c a b

Selection DAG Merge multiple instances of same

zero indegree set z in one selection node

Selection DAG Selection DAG is leveled in n+1 levels Each schedule S corresponds to one

path in the selection DAG

Selection DAG

h

f g

d e

a b c

{a,b,c}

{b,c} {a,c} {a,b}

a cb

{c,d} {b} {a,e}

… … …

b c ca ab

Towards Time Optimization Machine model

Generic superscalar/VLIW architecture Single/Multiple issue

From IR level to target level Instruction selection Register allocation (homogenous) Imitate instruction dispatcher

behaviour

Time Profile Window of the instructions scheduled

last for each unit that may still influence future scheduling decisions

e f -

c

t

d

- -

--a

b

-

time

u3u2u1

Extended Selection Node An extended selection node (z, t,

P), summarizes all schedules of scheduled(z) that end with the time profile (t, P).

Pruning (formal proof in the paper)time e f -

c

t

d

- -

--a

b

-

u3u2u1

e f -

c

t’

d

- -b

a

u3u2u1

a f -

c

t’

d

- -b

e

u3u2u1

Extended Selection DAGLevel 0

Level 1

Level 2

...

Solution Space Group the extended

selection nodes in each level according to execution time

Construct solution space in order of increasing time

Postpones the combinatorial explosion

Implementation C++ LEDA XML based architecture description

language LCC as C–front-end

Results – Random DAGs

Results – Random DAGs

Results – FIR Filter

Basic Block

DAG#node

sTime

archi. 1Time

archi. 2

BB1 16 3.5s 4.0s

BB2 16 8.0s 9.5s

BB3 303:21:50.

2s4:40:44.9

s

Results – Matrix Multiplication

Basic Block

DAG#node

sTime

archi. 1Time

archi. 2

BB2 30 1:05.0s 1:41.8s

BB2 (unrolle

d)40 6:08.5s 9:47.2s

Results – Jacobi Grid Relax.

Basic Block

DAG#node

sTime

archi. 1Time

archi. 2

Loop body (5)

40 1:15.8s 1:31.8s

Loop body (9)

531:36:13.2

s2:00:51.5

s

Current and Future Work Time-space profile for irregular

register sets Speculative instruction selection Extensions of architecture

description language Beyond basic block level

Time-space profiles as connector descriptions

Conclusion Goal: fully integrated code generation Dynamic programming approach Time profiles to compress the solution space Improved order of solution space construction Feasible for medium sized basic blocks Potential for extensions Alternative to ILP Home page: www.ida.liu.se/~chrke/optimist