1. LOOP FUSION FOR MEMORY SPACE
OPTIMIZATION
Antoine Fraboulet, Karen Kodary, Anne Mignotte
Presenter: Tanzir Musabbir

2.  Group of people from National Institute for Applied
Science, Lyon, France
 Published in IEEE International Symposium on
System Synthesis
 Year 2001.

3. OUTLINE
 Introduction
 Problems
 Some solutions
 Their Proposed Solution
 Experiments and Results
 Conclusion

4. INTRODUCTION
 Multimedia applications are memory intensive
application
 Memory is known to be extremely power
consuming
 Propose a new technique to optimize a behavioral
description of multimedia application
 An optimal algorithm to reduce the use of
temporary arrays by loop fusion
 Polynomial but efficient

5. OUTLINE
 Introduction
 Problems
 Some solutions
 Their Proposed Solution
 Experiments and Results
 Conclusion

6. PROBLEMS
 This paper mainly focused on data flow dominated
embedded systems
 It consume memory for multidimensional data
storage.
 More than half of the surface of this type of
integrated system is filled by memory.
 That’s why control over power consumption is
necessary.

7. OUTLINE
 Introduction
 Problems
 Some Solutions
 Their Proposed Solution
 Experiments and Results
 Conclusion

8. SOME SOLUTIONS
 Memory optimization can be done in several ways:
the reduction of the size of the memory and
improvement data movement strategies over the
memory hierarchy
 It is useful to make optimization before partitioning
 As after hardware-software partitioning is
done, memory has already been divided
 It also allows to optimize both types of
memories, the one that is included in hardware and
the one controlled by software.

9. SOME SOLUTIONS
 In-place-mapping can allow to share memory by
overlapping arrays when possible
 Memory allocation can select memory modules
upon several criteria such as size, number of ports.
 On the opposite, during silicon compilation the
physical memory is optimized all along the design
chain

10. OUTLINE
 Introduction
 Problems
 Some Solutions
 Their Proposed Solution
 Experiments and Results
 Conclusion

11. THEIR PROPOSED SOLUTION
 Proposed a “for” loop transformation to optimize
memory size
 Loop fusion is a program transformation that
collapses several loops into one
 In their proposed solution, memory optimization by
loop fusion is obtained by reducing the size of
temporary arrays that are typically used to store
intermediate results during multimedia processing.

12. THEIR PROPOSED SOLUTION
 Scalar replacement technique can remove an entire
array from the applications memory

13. THEIR PROPOSED SOLUTION
 Sometimes dependencies may not allow to remove
completely an array by scalar replacement
 We can apply intra-array storage order optimization
in such cases

14. THEIR PROPOSED SOLUTION
 Loop fusion increases the number of statements
and accessed arrays within a loop nest.
 Sometimes loops access more data than can be
handled by a cache.
 That’s why further code transformation are needed
to complete the optimization process.

15. THEIR PROPOSED SOLUTION
 They consider a wider class of problems where the
loops being considered for fusion need not have
conformable headers.
 Loops with non conformable headers can be fused
by using conditional statements to control the
execution of operations within the loop nest
 As both scalar replacement and intra-array storage
optimization techniques can handle conditional
control flow.

16. THEIR PROPOSED SOLUTION
 They approximate memory size requirement by the
maximum size of time overlapping arrays
 Memory cost function

17. THEIR PROPOSED SOLUTION

18. THEIR PROPOSED SOLUTION - DFG

19. THEIR PROPOSED SOLUTION – REMOVABLE
ARRAY DETECTION

20. CONFLICTS DETECTIONS AND RESOLUTION
 Some problems can arise when we consider the
removable arrays altogether.

21. CONFLICTS DETECTIONS AND RESOLUTION
 We need to solve all possible conflicts by reducing
the set of starred arrays without compromising the
global optimality.
 Identifies all possible conflicts in the graph
 Solves all these conflicts in a global optimal way

22. CYCLE DETECTION ALGORITHM

23. INTEGER LINEAR PROGRAMMING CONFLICT
RESOLUTION
 ILP formulation for solving dependency cycles
conflicts detected in the previous steps
 We have to decide which array will be taken out of
the set of removable arrays
 It associates a binary variable Xa_i to each starred
array a(i) that could be removed
 If Xa_i = 0 then the array will a_i will be considered
for fusion otherwise (Xa_i = 1) the array will cease
to be starred.

24. INTEGER LINEAR PROGRAMMING CONFLICT
RESOLUTION
 For multi-graphs between two nodes u and v, a new
variable X_uv is introduced to resume the arrays on
this multi-edges.
 If X_uv is set to 1 then all associated variables will
also be set to 1 and all arrays will be unstarred.
Otherwise a variable X_ai can be set to 1 without
interfering with other arrays on the multi-edge.
 The objective of their ILP is to minimize the sum of
the size of arrays that have to be removed from the
set of all possible starred arrays detected in
previous section

25. OUTLINE
 Introduction
 Problems
 Some solutions
 Their Proposed Solution
 Experiments and Results
 Conclusion

26. EXPERIMENTS AND RESULTS
 Tested their algorithms using randomly generated
graphs.
 They have chosen to generate graphs that are a lot
more complex
 Generated graphs were ranging from 10 to 30
nodes.
 Each edge has the probability of 1/3 to be fusion
preventing and all weights were randomly chosen

27. EXPERIMENTS AND RESULTS

28. OUTLINE
 Introduction
 Problems
 Some solutions
 Their Proposed Solution
 Experiments and Results
 Conclusion