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On Channel Restructuring for Complete FIFO Recovery

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HAL Id: hal-02433318

https://hal.inria.fr/hal-02433318

Submitted on 9 Jan 2020

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On Channel Restructuring for Complete FIFO Recovery

Christophe Alias

To cite this version:

Christophe Alias. On Channel Restructuring for Complete FIFO Recovery. ICCD 2019 - 37th IEEE International Conference on Computer Design, Nov 2019, Abu Dhabi, United Arab Emirates. �hal- 02433318�

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www.cnrs.fr/ www.ens-lyon.fr/ www.inria.fr/ www.ens-lyon.fr/LIP/ www.univ-lyon1.fr/ www.universite-lyon.fr/

On Channel Restructuring for Complete FIFO Recovery

Focus: Dataflow models as an intermediate representation for High-Level Synthesis Challenge: Recover FIFO channels after code restructuring

Contributions: HLS algorithm for channel restructuring + Dataflow model to ensure completeness

1) Polyhedral Process Networks

for i := 0 to N + 1

• load( a [0 , i ]);

for t := 1 to T for i := 1 to N

• a [ t, i ] :=

a [ t − 1 , i − 1] + a [ t − 1 , i ] + a [ t − 1 , i + 1];

for i := 1 to N

◦ store( a [ T, i ]);

i

i

t

i

0 1 2 3 4 5 6 N = 7

1 2 3 4 5 = T

1 3 2 1 3

6 5 4

7 7 7 7 7 7

Load 2

1

3

C 4

5

6

7 Store

Challenge addressed:

Channel synthesis

3) Our FIFO Recovery Algorithm

i

t

3 4 5 6 7 8

4 5 6 7 8 9 10 11

12 i

t

3 4 5 6 7 8

4 5 6 7 8 9 10 11 12

1

2 3

4

1 SPLIT (→ c , θ P , θ C )

2 for k := 1 to n

3 ADD (→ c ∩{( x, y ) , θ P ( x ) k θ C ( y )});

4 ADD (→ c ∩{( x, y ) , θ P ( x ) ≈ n θ C ( y )});

5 FIFOIZE ((P , C ))

6 for each channel c

7 {→ 1 c , . . . , → n c +1 } := SPLIT (→ c , θ P c , θ C c );

8 if fifo(→ k c , ≺ θ Pc , ≺ θ Cc ) ∀ k

9 REMOVE (→ c );

10 INSERT (→ k c ) ∀ k ;

i

t

3 4 5 6 7 8

4 5 6 7 8 9 10 11 12

Theorem: FIFO recovery is complete on our DPN model

2) Data-aware Process Networks

i

t

3 4 5 6 7 8

4 5 6 7 8 9 10 11 12

~ τ

1

~ τ

2

3

2 1

6 5 4

9 8 7

12 11 10

15 14 13

1 3 5

2 4 6

Load

2

1 3

C 1

4 5 6

8

7 9

C 2

10 11 12

14

13 15

Store

Features:

• PPN partitioning based on loop tiling

• Incoming dependences (1,2,3) are loaded

• Outgoing dependences (13,14,15) are stored

• Internal dependences (4 to 12) are solved through local channels

4) Experimental Results

Kernel PPN PPN with tiling DPN

#fifo #rem #rec % #rem #rec %

trmm 2 1 1 100 1 1 100

gemm 2 1 1 100 1 1 100

syrk 2 1 1 100 1 1 100

symm 6 3 3 100 5 1 100

gemver 4 2 2 100 3 1 100

gesummv 6 6 0 100 6 0 100

syr2k 2 1 1 100 1 1 100

lu 3 0 3 100 0 3 100

trisolv 4 3 1 100 3 1 100 cholesky 6 3 3 100 4 2 100 doitgen 3 2 1 100 2 1 100

bicg 4 2 2 100 2 2 100

mvt 2 0 2 100 0 2 100

3mm 6 2 2 50 3 3 100

2mm 4 2 1 50 2 2 100

covariance 7 4 2 66 4 3 100 correlation 13 9 3 75 9 4 100 fdtd-2d 12 0 6 50 5 7 100 jacobi-2d 10 0 2 20 2 8 100 seidel-2d 9 0 3 33 2 7 100 jacobi-1d 6 1 5 100 2 4 100 heat-3d 20 0 0 0 2 18 100

Experimental setup:

• We have run our algorithm on the kernels of PolyBench/C v3.2

• We have checked the completeness of our algorithm on PPN with DPN partitioning (DPN)

• We have studied the behavior of our algorithm on general PPN, without DPN partitioning (PPN with tiling).

Christophe Alias, Faculty Research Scientist http://perso.ens-lyon.fr/christophe.alias

INRIA, ENS de Lyon, France

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