data reuse analysis for automated synthesis of...
TRANSCRIPT
DATA REUSE ANALYSIS FOR AUTOMATED SYNTHESIS OF CUSTOM INSTRUCTIONS IN SLIDING WINDOW APPLICATIONS
Georgios Zacharopoulos Laura Pozzi
Università della Svizzera italiana (USI Lugano), Faculty of Informatics
Giovanni Ansaloni
IMPACT 2017
Jan 23, 2017 Stockholm, Sweden
INTRODUCTION
MOORE’S LAW - DENNARD SCALING
Expectation
▸ Performance should keep increasing
Reality
▸ Performance is NOT increasing anymore
2
INTRODUCTION
BREAKDOWN OF DENNARD SCALING
▸ Single core —> Multiple cores
▸ Dark Silicon
3
INTRODUCTION
HETEROGENEOUS ERA
▸ Need for Specialised HW
▸ Multiple cores —> Heterogeneous Computing
http://developer.amd.com/resources/heterogeneous-computing/what-is-heterogeneous-system-architecture-hsa/[1]
[1]
4
BACKGROUND
SPECIALISATION AND PERFORMANCE
5
GENERAL PURPOSE
CPU
DOMAIN SPECIFIC PROCESSORS
(ADSPS)
APPLICATION SPECIFIC INSTRUCTION-SET
PROCESSORS (ASIPS)
ASICS
CPU + HW ACCELERATORS
PERFORMANCE
SPEC
IALIS
ATIO
N
RELATED WORK
DATA TRANSFER IS THE BOTTLENECK
▸ Accelerate data transfer between accelerators and memory
▸ Custom storage as an optimisation
➡ Identify Data reuse for building custom storage
[4] G. Gutin, A. Johnstone, J. Reddington, E. Scott, and A. Yeo. An algorithm for finding input-output constrained convex sets in an acyclic digraph. J. Discrete Algorithms, 13:47–58, 2012. [5] E. Giaquinta, A. Mishra, and L. Pozzi. Maximum convex subgraphs under I/O constraint for automatic identification of custom instructions. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 34(3):483–494, 2015. [6] P. Biswas, N. Dutt, P. Ienne, and L. Pozzi. Automatic identification of application-specific functional units with architecturally visible storage. In Proceedings of the Design, Automation and Test in Europe Conference and Exhibition, pages 212–217, Mar. 2006. [7] M.Haaß,L.Bauer,andJ.Henkel.Automatic Custom Instruction Identification in Memory Streaming Algorithms. In Proceedings of the International Conference on Compilers, Architectures, and Synthesis for Embedded Systems, pages 1–9, Oct. 2014.
[4] [5]
[6] [7]
6
RELATED WORK
DATA TRANSFER IS THE BOTTLENECK
▸ Rely on source-to-source transformations
▸ Limited Parallelism
▸ Large Internal Buffers
[8] W. Meeus and D. Stroobandt. Automating data reuse in high-level synthesis. In Proceedings of the Design, Automation and Test in Europe Conference and Exhibition, pages 1–4, Mar. 2014. [9] L.-N. Pouchet, P. Zhang, P. Sadayappan, and J. Cong. Polyhedral-based data reuse optimization for configurable computing. In Proceedings of the 2013 ACM/SIGDA 21st International Symposium on Field Programmable Gate Arrays, pages 29–38, Feb. 2013. [10] M. Schmid, O. Reiche, F. Hannig, and J. Teich. Loop coarsening in C-based high-level synthesis. In Proceedings of the 26th International Conference on Application-specific Systems, Architectures and Processors, pages 166–173, July 2015.
[8] [9] [10]
7
[8] [9]
[10]
RELATED WORK
DATA TRANSFER IS THE BOTTLENECK
▸ Rely on source-to-source transformations
▸ Limited Parallelism
▸ Large Internal Buffers
[8] W. Meeus and D. Stroobandt. Automating data reuse in high-level synthesis. In Proceedings of the Design, Automation and Test in Europe Conference and Exhibition, pages 1–4, Mar. 2014. [9] L.-N. Pouchet, P. Zhang, P. Sadayappan, and J. Cong. Polyhedral-based data reuse optimization for configurable computing. In Proceedings of the 2013 ACM/SIGDA 21st International Symposium on Field Programmable Gate Arrays, pages 29–38, Feb. 2013. [10] M. Schmid, O. Reiche, F. Hannig, and J. Teich. Loop coarsening in C-based high-level synthesis. In Proceedings of the 26th International Conference on Application-specific Systems, Architectures and Processors, pages 166–173, July 2015.
[8] [9] [10]
8
[8] [9]
[10]
➡Multiple Datapaths ➡Area efficient Accelerators
METHODOLOGY
SW ANALYSIS FOR DATA REUSE
9
void Sobelsystem() {
outer_loop:for(i = 1; i < 100; i++) {
inner_loop:for(j = 1; j < 100; j++) {
Sobelmodule(image[i-1][j-1], image[i][j-1], image[i+1][j+1], image[i-1][j], image[i+1][j], image[i-1][j+1], image[i][j+1], image[i+1][j-1], image[i][j]);
}
}
}
LOADS
METHODOLOGY
SW ANALYSIS FOR DATA REUSE
10
METHODOLOGY
SW ANALYSIS FOR DATA REUSE
11
METHODOLOGY
SW ANALYSIS FOR DATA REUSE
12
METHODOLOGY 13
WINDOW 1
METHODOLOGY 14
WINDOW 2
METHODOLOGY 15
WINDOW 2
WINDOW 1
1.1 Divisors and the Abel-Jacobi map
d.
Next, we define the Picard group of X as the sheaf cohomology group
PicX
:= H1(X,O⇤X
) ,
which is well known to be isomorphic to the set of line bundles up to isomorphism, withgroup structure induced by the usual tensor product of coherent sheaves.To any divisor D 2 Div
X
one can associate the line bundle OX
(D) defined over anyopen set U ⇢ X by the prescription
H0(U,OX
(D)) =�f 2 k(X)⇤ | (f)|U +D|U � 0
which can be seen as the line bundle whose global sections are locally controlled by D.In other words, the sections of O
X
(D) are allowed to present poles on any point of thesupport of D, with order bounded by the coefficient of the point appearing in the formalsum.It is an easy consequence of the Riemann-Roch Theorem that every line bundle L onX admits a global section s and, thus, it can be written in the form L = O
X
(D) withD = (s) being the divisor corresponding to such a section. Thus we define the degree
of L to be the degree of the divisor D. We will denote by Pic dX
the set of line bundlesof degree d.Based on the above construction, we give a definition of the so called Abel-Jacobi
map by the assignment
u : DivX
! PicX
D 7! OX
(D)
Remark 1.2. Recall that classically, in the theory of smooth curves over C, the Abel-Jacobi map is defined for a one-point divisor P (and then extended linearly) by meansof the Abelian integrals as
u : Xd
! J(X), P 7!✓ Z
P
P0
!1 , . . . ,
ZP
P0
!g
◆mod ⇤,
where P0 is a fixed point of X, the !i
’s form a basis of the space of Abelian differentialsand ⇤ is a nondegenerate lattice arising from the Riemann bilinear relations.Our definition of the Abel-Jacobi map is simpler, more elegant and does not rely onanalytical tools such as path-integration, nevertheless it turns out to be equivalent toits classical counterpart.
3
UNROLLING
METHODOLOGY 16
WINDOW 2
WINDOW 1
UNROLLING
1.1 Divisors and the Abel-Jacobi map
d.
Next, we define the Picard group of X as the sheaf cohomology group
PicX
:= H1(X,O⇤X
) ,
which is well known to be isomorphic to the set of line bundles up to isomorphism, withgroup structure induced by the usual tensor product of coherent sheaves.To any divisor D 2 Div
X
one can associate the line bundle OX
(D) defined over anyopen set U ⇢ X by the prescription
H0(U,OX
(D)) =�f 2 k(X)⇤ | (f)|U +D|U � 0
which can be seen as the line bundle whose global sections are locally controlled by D.In other words, the sections of O
X
(D) are allowed to present poles on any point of thesupport of D, with order bounded by the coefficient of the point appearing in the formalsum.It is an easy consequence of the Riemann-Roch Theorem that every line bundle L onX admits a global section s and, thus, it can be written in the form L = O
X
(D) withD = (s) being the divisor corresponding to such a section. Thus we define the degree
of L to be the degree of the divisor D. We will denote by Pic dX
the set of line bundlesof degree d.Based on the above construction, we give a definition of the so called Abel-Jacobi
map by the assignment
u : DivX
! PicX
D 7! OX
(D)
Remark 1.2. Recall that classically, in the theory of smooth curves over C, the Abel-Jacobi map is defined for a one-point divisor P (and then extended linearly) by meansof the Abelian integrals as
u : Xd
! J(X), P 7!✓ Z
P
P0
!1 , . . . ,
ZP
P0
!g
◆mod ⇤,
where P0 is a fixed point of X, the !i
’s form a basis of the space of Abelian differentialsand ⇤ is a nondegenerate lattice arising from the Riemann bilinear relations.Our definition of the Abel-Jacobi map is simpler, more elegant and does not rely onanalytical tools such as path-integration, nevertheless it turns out to be equivalent toits classical counterpart.
3
PIPELINING
METHODOLOGY 17
WINDOW 2
WINDOW 1
UNROLLING
PIPELINING
METHODOLOGY
COMPILERS
▸ Perform Source Code Analysis
▸ Identify Data Reuse in Sliding Window Applications
18
METHODOLOGY
COMPILERS
▸ Perform Source Code Analysis
▸ Identify Data Reuse in Sliding Window Applications
[2] C. Lattner and V. Adve. LLVM: A Compilation Framework for Lifelong Program Analysis & Transformation. In Proceedings of the 2nd International Symposium on Code generation and optimization, Palo Alto, California, Mar 2004. [3] T. Grosser, H. Zheng, R. Aloor, A. Simbürger, A. Größlinger, and L.-N. Pouchet. Polly-polyhedral optimization in llvm. In Proceedings of the First International Workshop on Polyhedral Compilation Techniques (IMPACT), volume 2011, 2011.
19
[2] [3]
METHODOLOGY
LLVM POLLY SCOP ANALYSIS FOR DATA REUSE
20
1.1 Divisors and the Abel-Jacobi map
d.
Next, we define the Picard group of X as the sheaf cohomology group
PicX
:= H1(X,O⇤X
) ,
which is well known to be isomorphic to the set of line bundles up to isomorphism, withgroup structure induced by the usual tensor product of coherent sheaves.To any divisor D 2 Div
X
one can associate the line bundle OX
(D) defined over anyopen set U ⇢ X by the prescription
H0(U,OX
(D)) =�f 2 k(X)⇤ | (f)|U +D|U � 0
which can be seen as the line bundle whose global sections are locally controlled by D.In other words, the sections of O
X
(D) are allowed to present poles on any point of thesupport of D, with order bounded by the coefficient of the point appearing in the formalsum.It is an easy consequence of the Riemann-Roch Theorem that every line bundle L onX admits a global section s and, thus, it can be written in the form L = O
X
(D) withD = (s) being the divisor corresponding to such a section. Thus we define the degree
of L to be the degree of the divisor D. We will denote by Pic dX
the set of line bundlesof degree d.Based on the above construction, we give a definition of the so called Abel-Jacobi
map by the assignment
u : DivX
! PicX
D 7! OX
(D)
Remark 1.2. Recall that classically, in the theory of smooth curves over C, the Abel-Jacobi map is defined for a one-point divisor P (and then extended linearly) by meansof the Abelian integrals as
u : Xd
! J(X), P 7!✓ Z
P
P0
!1 , . . . ,
ZP
P0
!g
◆mod ⇤,
where P0 is a fixed point of X, the !i
’s form a basis of the space of Abelian differentialsand ⇤ is a nondegenerate lattice arising from the Riemann bilinear relations.Our definition of the Abel-Jacobi map is simpler, more elegant and does not rely onanalytical tools such as path-integration, nevertheless it turns out to be equivalent toits classical counterpart.
3
WINDOW SIZE
METHODOLOGY
LLVM POLLY SCOP ANALYSIS FOR DATA REUSE
21
STRIDE
1.1 Divisors and the Abel-Jacobi map
d.
Next, we define the Picard group of X as the sheaf cohomology group
PicX
:= H1(X,O⇤X
) ,
which is well known to be isomorphic to the set of line bundles up to isomorphism, withgroup structure induced by the usual tensor product of coherent sheaves.To any divisor D 2 Div
X
one can associate the line bundle OX
(D) defined over anyopen set U ⇢ X by the prescription
H0(U,OX
(D)) =�f 2 k(X)⇤ | (f)|U +D|U � 0
which can be seen as the line bundle whose global sections are locally controlled by D.In other words, the sections of O
X
(D) are allowed to present poles on any point of thesupport of D, with order bounded by the coefficient of the point appearing in the formalsum.It is an easy consequence of the Riemann-Roch Theorem that every line bundle L onX admits a global section s and, thus, it can be written in the form L = O
X
(D) withD = (s) being the divisor corresponding to such a section. Thus we define the degree
of L to be the degree of the divisor D. We will denote by Pic dX
the set of line bundlesof degree d.Based on the above construction, we give a definition of the so called Abel-Jacobi
map by the assignment
u : DivX
! PicX
D 7! OX
(D)
Remark 1.2. Recall that classically, in the theory of smooth curves over C, the Abel-Jacobi map is defined for a one-point divisor P (and then extended linearly) by meansof the Abelian integrals as
u : Xd
! J(X), P 7!✓ Z
P
P0
!1 , . . . ,
ZP
P0
!g
◆mod ⇤,
where P0 is a fixed point of X, the !i
’s form a basis of the space of Abelian differentialsand ⇤ is a nondegenerate lattice arising from the Riemann bilinear relations.Our definition of the Abel-Jacobi map is simpler, more elegant and does not rely onanalytical tools such as path-integration, nevertheless it turns out to be equivalent toits classical counterpart.
3
METHODOLOGY
LLVM POLLY SCOP ANALYSIS FOR DATA REUSE
22
FRAME SIZE
METHODOLOGY
HW IMPLEMENTATION
Parameters retrieved with LLVM Polly Analysis Pass:
23
▸ Horizontal and Vertical Window Size
▸ Stride
▸ Iteration Domain (Frame Size)
METHODOLOGY
HW IMPLEMENTATION
24
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HW IMPLEMENTATION
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METHODOLOGY
HW IMPLEMENTATION
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METHODOLOGY
HW IMPLEMENTATION
27
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METHODOLOGY
HW IMPLEMENTATION
28
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Vertical Width = Vertical Win. Size
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METHODOLOGY
HW IMPLEMENTATION
29
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METHODOLOGY 30
WINDOW 2
WINDOW 1
1.1 Divisors and the Abel-Jacobi map
d.
Next, we define the Picard group of X as the sheaf cohomology group
PicX
:= H1(X,O⇤X
) ,
which is well known to be isomorphic to the set of line bundles up to isomorphism, withgroup structure induced by the usual tensor product of coherent sheaves.To any divisor D 2 Div
X
one can associate the line bundle OX
(D) defined over anyopen set U ⇢ X by the prescription
H0(U,OX
(D)) =�f 2 k(X)⇤ | (f)|U +D|U � 0
which can be seen as the line bundle whose global sections are locally controlled by D.In other words, the sections of O
X
(D) are allowed to present poles on any point of thesupport of D, with order bounded by the coefficient of the point appearing in the formalsum.It is an easy consequence of the Riemann-Roch Theorem that every line bundle L onX admits a global section s and, thus, it can be written in the form L = O
X
(D) withD = (s) being the divisor corresponding to such a section. Thus we define the degree
of L to be the degree of the divisor D. We will denote by Pic dX
the set of line bundlesof degree d.Based on the above construction, we give a definition of the so called Abel-Jacobi
map by the assignment
u : DivX
! PicX
D 7! OX
(D)
Remark 1.2. Recall that classically, in the theory of smooth curves over C, the Abel-Jacobi map is defined for a one-point divisor P (and then extended linearly) by meansof the Abelian integrals as
u : Xd
! J(X), P 7!✓ Z
P
P0
!1 , . . . ,
ZP
P0
!g
◆mod ⇤,
where P0 is a fixed point of X, the !i
’s form a basis of the space of Abelian differentialsand ⇤ is a nondegenerate lattice arising from the Riemann bilinear relations.Our definition of the Abel-Jacobi map is simpler, more elegant and does not rely onanalytical tools such as path-integration, nevertheless it turns out to be equivalent toits classical counterpart.
3
BUFFER
METHODOLOGY 31
WINDOW 2
WINDOW 1
STRIDE - STORE NEW ROW
1.1 Divisors and the Abel-Jacobi map
d.
Next, we define the Picard group of X as the sheaf cohomology group
PicX
:= H1(X,O⇤X
) ,
which is well known to be isomorphic to the set of line bundles up to isomorphism, withgroup structure induced by the usual tensor product of coherent sheaves.To any divisor D 2 Div
X
one can associate the line bundle OX
(D) defined over anyopen set U ⇢ X by the prescription
H0(U,OX
(D)) =�f 2 k(X)⇤ | (f)|U +D|U � 0
which can be seen as the line bundle whose global sections are locally controlled by D.In other words, the sections of O
X
(D) are allowed to present poles on any point of thesupport of D, with order bounded by the coefficient of the point appearing in the formalsum.It is an easy consequence of the Riemann-Roch Theorem that every line bundle L onX admits a global section s and, thus, it can be written in the form L = O
X
(D) withD = (s) being the divisor corresponding to such a section. Thus we define the degree
of L to be the degree of the divisor D. We will denote by Pic dX
the set of line bundlesof degree d.Based on the above construction, we give a definition of the so called Abel-Jacobi
map by the assignment
u : DivX
! PicX
D 7! OX
(D)
Remark 1.2. Recall that classically, in the theory of smooth curves over C, the Abel-Jacobi map is defined for a one-point divisor P (and then extended linearly) by meansof the Abelian integrals as
u : Xd
! J(X), P 7!✓ Z
P
P0
!1 , . . . ,
ZP
P0
!g
◆mod ⇤,
where P0 is a fixed point of X, the !i
’s form a basis of the space of Abelian differentialsand ⇤ is a nondegenerate lattice arising from the Riemann bilinear relations.Our definition of the Abel-Jacobi map is simpler, more elegant and does not rely onanalytical tools such as path-integration, nevertheless it turns out to be equivalent toits classical counterpart.
3
STRIDE - DISCARD TOPMOST ROW
1.1 Divisors and the Abel-Jacobi map
d.
Next, we define the Picard group of X as the sheaf cohomology group
PicX
:= H1(X,O⇤X
) ,
which is well known to be isomorphic to the set of line bundles up to isomorphism, withgroup structure induced by the usual tensor product of coherent sheaves.To any divisor D 2 Div
X
one can associate the line bundle OX
(D) defined over anyopen set U ⇢ X by the prescription
H0(U,OX
(D)) =�f 2 k(X)⇤ | (f)|U +D|U � 0
which can be seen as the line bundle whose global sections are locally controlled by D.In other words, the sections of O
X
(D) are allowed to present poles on any point of thesupport of D, with order bounded by the coefficient of the point appearing in the formalsum.It is an easy consequence of the Riemann-Roch Theorem that every line bundle L onX admits a global section s and, thus, it can be written in the form L = O
X
(D) withD = (s) being the divisor corresponding to such a section. Thus we define the degree
of L to be the degree of the divisor D. We will denote by Pic dX
the set of line bundlesof degree d.Based on the above construction, we give a definition of the so called Abel-Jacobi
map by the assignment
u : DivX
! PicX
D 7! OX
(D)
Remark 1.2. Recall that classically, in the theory of smooth curves over C, the Abel-Jacobi map is defined for a one-point divisor P (and then extended linearly) by meansof the Abelian integrals as
u : Xd
! J(X), P 7!✓ Z
P
P0
!1 , . . . ,
ZP
P0
!g
◆mod ⇤,
where P0 is a fixed point of X, the !i
’s form a basis of the space of Abelian differentialsand ⇤ is a nondegenerate lattice arising from the Riemann bilinear relations.Our definition of the Abel-Jacobi map is simpler, more elegant and does not rely onanalytical tools such as path-integration, nevertheless it turns out to be equivalent toits classical counterpart.
3
METHODOLOGY 32
WINDOW 2
WINDOW 1
METHODOLOGY 33
WINDOW 2
WINDOW 1
METHODOLOGY 34
WINDOW 2
WINDOW 1
METHODOLOGY 35
WINDOW 2
WINDOW 1
METHODOLOGY 36
WINDOW 2
WINDOW 1
1.1
Div
isor
san
dth
eA
bel
-Jac
obim
ap
d. Nex
t,w
ede
fine
the
Pic
ard
grou
pof
Xas
the
shea
fcoh
omol
ogy
grou
p
PicX
:=H
1(X
,O⇤ X
),
whi
chis
wel
lkno
wn
tobe
isom
orph
icto
the
set
oflin
ebu
ndle
sup
tois
omor
phis
m,w
ithgr
oup
stru
ctur
ein
duce
dby
the
usua
lten
sor
prod
uct
ofco
here
ntsh
eave
s.To
any
divi
sorD
2Div
X
one
can
asso
ciat
eth
elin
ebu
ndle
OX
(D)
defin
edov
eran
yop
ense
tU
⇢X
byth
epr
escr
iptio
n
H0(U
,OX
(D))
=� f
2k(X
)⇤|(f) |U
+D
|U�
0
whi
chca
nbe
seen
asth
elin
ebu
ndle
who
segl
obal
sect
ions
are
loca
llyco
ntro
lled
byD
.In
othe
rw
ords
,the
sect
ions
ofOX
(D)
are
allo
wed
topr
esen
tpo
les
onan
ypo
int
ofth
esu
ppor
tofD
,with
orde
rbou
nded
byth
eco
effici
ento
fthe
poin
tapp
earin
gin
the
form
alsu
m.
Itis
anea
syco
nseq
uenc
eof
the
Rie
man
n-R
och
The
orem
that
ever
ylin
ebu
ndle
Lon
Xad
mits
agl
obal
sect
ions
and,
thus
,it
can
bew
ritte
nin
the
form
L=
OX
(D)
with
D=
(s)
bein
gth
edi
viso
rco
rres
pond
ing
tosu
cha
sect
ion.
Thu
sw
ede
fine
the
degr
ee
ofL
tobe
the
degr
eeof
the
divi
sorD
.W
ew
illde
note
byPic
d
X
the
set
oflin
ebu
ndle
sof
degr
eed.
Bas
edon
the
abov
eco
nstr
uctio
n,w
egi
vea
defin
ition
ofth
eso
calle
dA
bel
-Jac
obi
map
byth
eas
sign
men
t
u:Div
X
!PicX
D7!
OX
(D)
Rem
ark
1.2.
Rec
allt
hat
clas
sica
lly,i
nth
eth
eory
ofsm
ooth
curv
esov
erC
,the
Abe
l-Ja
cobi
map
isde
fined
for
aon
e-po
int
divi
sorP
(and
then
exte
nded
linea
rly)
bym
eans
ofth
eA
belia
nin
tegr
als
as
u:X
d
!J(X
),P
7!✓ Z
P
P
0
!1,...,
Z P P
0
!g
◆mod⇤,
whe
reP0
isa
fixed
poin
tof
X,t
he!i
’sfo
rma
basi
sof
the
spac
eof
Abe
lian
diffe
rent
ials
and⇤
isa
nond
egen
erat
ela
ttic
ear
isin
gfr
omth
eR
iem
ann
bilin
ear
rela
tions
.O
urde
finiti
onof
the
Abe
l-Jac
obi
map
issi
mpl
er,
mor
eel
egan
tan
ddo
esno
tre
lyon
anal
ytic
alto
ols
such
aspa
th-in
tegr
atio
n,ne
vert
hele
ssit
turn
sou
tto
beeq
uiva
lent
toits
clas
sica
lcou
nter
part
.
3
DISPLACEMENT
METHODOLOGY 37
WINDOW 2
WINDOW 1
1.1
Div
isor
san
dth
eA
bel
-Jac
obim
ap
d. Nex
t,w
ede
fine
the
Pic
ard
grou
pof
Xas
the
shea
fcoh
omol
ogy
grou
p
PicX
:=H
1(X
,O⇤ X
),
whi
chis
wel
lkno
wn
tobe
isom
orph
icto
the
set
oflin
ebu
ndle
sup
tois
omor
phis
m,w
ithgr
oup
stru
ctur
ein
duce
dby
the
usua
lten
sor
prod
uct
ofco
here
ntsh
eave
s.To
any
divi
sorD
2Div
X
one
can
asso
ciat
eth
elin
ebu
ndle
OX
(D)
defin
edov
eran
yop
ense
tU
⇢X
byth
epr
escr
iptio
n
H0(U
,OX
(D))
=� f
2k(X
)⇤|(f) |U
+D
|U�
0
whi
chca
nbe
seen
asth
elin
ebu
ndle
who
segl
obal
sect
ions
are
loca
llyco
ntro
lled
byD
.In
othe
rw
ords
,the
sect
ions
ofOX
(D)
are
allo
wed
topr
esen
tpo
les
onan
ypo
int
ofth
esu
ppor
tofD
,with
orde
rbou
nded
byth
eco
effici
ento
fthe
poin
tapp
earin
gin
the
form
alsu
m.
Itis
anea
syco
nseq
uenc
eof
the
Rie
man
n-R
och
The
orem
that
ever
ylin
ebu
ndle
Lon
Xad
mits
agl
obal
sect
ions
and,
thus
,it
can
bew
ritte
nin
the
form
L=
OX
(D)
with
D=
(s)
bein
gth
edi
viso
rco
rres
pond
ing
tosu
cha
sect
ion.
Thu
sw
ede
fine
the
degr
ee
ofL
tobe
the
degr
eeof
the
divi
sorD
.W
ew
illde
note
byPic
d
X
the
set
oflin
ebu
ndle
sof
degr
eed.
Bas
edon
the
abov
eco
nstr
uctio
n,w
egi
vea
defin
ition
ofth
eso
calle
dA
bel
-Jac
obi
map
byth
eas
sign
men
t
u:Div
X
!PicX
D7!
OX
(D)
Rem
ark
1.2.
Rec
allt
hat
clas
sica
lly,i
nth
eth
eory
ofsm
ooth
curv
esov
erC
,the
Abe
l-Ja
cobi
map
isde
fined
for
aon
e-po
int
divi
sorP
(and
then
exte
nded
linea
rly)
bym
eans
ofth
eA
belia
nin
tegr
als
as
u:X
d
!J(X
),P
7!✓ Z
P
P
0
!1,...,
Z P P
0
!g
◆mod⇤,
whe
reP0
isa
fixed
poin
tof
X,t
he!i
’sfo
rma
basi
sof
the
spac
eof
Abe
lian
diffe
rent
ials
and⇤
isa
nond
egen
erat
ela
ttic
ear
isin
gfr
omth
eR
iem
ann
bilin
ear
rela
tions
.O
urde
finiti
onof
the
Abe
l-Jac
obi
map
issi
mpl
er,
mor
eel
egan
tan
ddo
esno
tre
lyon
anal
ytic
alto
ols
such
aspa
th-in
tegr
atio
n,ne
vert
hele
ssit
turn
sou
tto
beeq
uiva
lent
toits
clas
sica
lcou
nter
part
.
3
DISPLACEMENT
Horiz. Displacement = INw - Horiz. Win. Size + 1
METHODOLOGY 38
WINDOW 2
WINDOW 1
1.1
Div
isor
san
dth
eA
bel
-Jac
obim
ap
d. Nex
t,w
ede
fine
the
Pic
ard
grou
pof
Xas
the
shea
fcoh
omol
ogy
grou
p
PicX
:=H
1(X
,O⇤ X
),
whi
chis
wel
lkno
wn
tobe
isom
orph
icto
the
set
oflin
ebu
ndle
sup
tois
omor
phis
m,w
ithgr
oup
stru
ctur
ein
duce
dby
the
usua
lten
sor
prod
uct
ofco
here
ntsh
eave
s.To
any
divi
sorD
2Div
X
one
can
asso
ciat
eth
elin
ebu
ndle
OX
(D)
defin
edov
eran
yop
ense
tU
⇢X
byth
epr
escr
iptio
n
H0(U
,OX
(D))
=� f
2k(X
)⇤|(f) |U
+D
|U�
0
whi
chca
nbe
seen
asth
elin
ebu
ndle
who
segl
obal
sect
ions
are
loca
llyco
ntro
lled
byD
.In
othe
rw
ords
,the
sect
ions
ofOX
(D)
are
allo
wed
topr
esen
tpo
les
onan
ypo
int
ofth
esu
ppor
tofD
,with
orde
rbou
nded
byth
eco
effici
ento
fthe
poin
tapp
earin
gin
the
form
alsu
m.
Itis
anea
syco
nseq
uenc
eof
the
Rie
man
n-R
och
The
orem
that
ever
ylin
ebu
ndle
Lon
Xad
mits
agl
obal
sect
ions
and,
thus
,it
can
bew
ritte
nin
the
form
L=
OX
(D)
with
D=
(s)
bein
gth
edi
viso
rco
rres
pond
ing
tosu
cha
sect
ion.
Thu
sw
ede
fine
the
degr
ee
ofL
tobe
the
degr
eeof
the
divi
sorD
.W
ew
illde
note
byPic
d
X
the
set
oflin
ebu
ndle
sof
degr
eed.
Bas
edon
the
abov
eco
nstr
uctio
n,w
egi
vea
defin
ition
ofth
eso
calle
dA
bel
-Jac
obi
map
byth
eas
sign
men
t
u:Div
X
!PicX
D7!
OX
(D)
Rem
ark
1.2.
Rec
allt
hat
clas
sica
lly,i
nth
eth
eory
ofsm
ooth
curv
esov
erC
,the
Abe
l-Ja
cobi
map
isde
fined
for
aon
e-po
int
divi
sorP
(and
then
exte
nded
linea
rly)
bym
eans
ofth
eA
belia
nin
tegr
als
as
u:X
d
!J(X
),P
7!✓ Z
P
P
0
!1,...,
Z P P
0
!g
◆mod⇤,
whe
reP0
isa
fixed
poin
tof
X,t
he!i
’sfo
rma
basi
sof
the
spac
eof
Abe
lian
diffe
rent
ials
and⇤
isa
nond
egen
erat
ela
ttic
ear
isin
gfr
omth
eR
iem
ann
bilin
ear
rela
tions
.O
urde
finiti
onof
the
Abe
l-Jac
obi
map
issi
mpl
er,
mor
eel
egan
tan
ddo
esno
tre
lyon
anal
ytic
alto
ols
such
aspa
th-in
tegr
atio
n,ne
vert
hele
ssit
turn
sou
tto
beeq
uiva
lent
toits
clas
sica
lcou
nter
part
.
3
DISPLACEMENT
Horiz. Displacement = INw - Horiz. Win. Size + 1
Example:
Horiz. Displacement = 2
INw = Horizontal Win. Size + 1
▸ ROCCC
▸ Vivado HLS
▸ Our Approach
EXPERIMENTAL SETUP
APPROACHES COMPARED
39
▸ ROCCC
▸ Vivado HLS
▸ Our Approach
EXPERIMENTAL SETUP
APPROACHES COMPARED
40
PIPELINING DATA REUSE
▸ ROCCC
▸ Vivado HLS
▸ Our Approach
EXPERIMENTAL SETUP
APPROACHES COMPARED
41
PIPELINING DATA REUSE
WINDOW 2
WINDOW 1
PIPELINING
▸ ROCCC
▸ Vivado HLS
▸ Our Approach
EXPERIMENTAL SETUP
APPROACHES COMPARED
42
PIPELINING DATA REUSE
ROCCC
WINDOW 2
WINDOW 1
PIPELINING
▸ ROCCC
▸ Vivado HLS
▸ Our Approach
EXPERIMENTAL SETUP
APPROACHES COMPARED
43
PIPELINING DATA REUSE
ROCCC
WINDOW 2
WINDOW 1
VIVADO Manual Rewrite
PIPELINING
▸ ROCCC
▸ Vivado HLS
▸ Our Approach
EXPERIMENTAL SETUP
APPROACHES COMPARED
44
PIPELINING DATA REUSE
ROCCC
WINDOW 2
WINDOW 1
OUR
VIVADO
PIPELINING
Manual Rewrite
▸ ROCCC
▸ Vivado HLS
▸ Our Approach
EXPERIMENTAL SETUP
APPROACHES COMPARED
45
PIPELINING DATA REUSE
ROCCC
OUR
VIVADO
UNROLLING DATA REUSE
Manual Rewrite
▸ ROCCC
▸ Vivado HLS
▸ Our Approach
EXPERIMENTAL SETUP
APPROACHES COMPARED
46
PIPELINING DATA REUSE
ROCCC
OUR
VIVADO
UNROLLING DATA REUSE
UNROLLING
WINDOW 2WINDOW 1
Manual Rewrite
▸ ROCCC
▸ Vivado HLS
▸ Our Approach
EXPERIMENTAL SETUP
APPROACHES COMPARED
47
PIPELINING DATA REUSE
ROCCC
OUR
VIVADO
UNROLLING DATA REUSE
UNROLLING
WINDOW 2WINDOW 1
Manual Rewrite
▸ ROCCC
▸ Vivado HLS
▸ Our Approach
EXPERIMENTAL SETUP
APPROACHES COMPARED
48
PIPELINING DATA REUSE
ROCCC
OUR
VIVADO
UNROLLING DATA REUSE
UNROLLING
WINDOW 2WINDOW 1
Manual Rewrite
▸ ROCCC
▸ Vivado HLS
▸ Our Approach
EXPERIMENTAL SETUP
APPROACHES COMPARED
49
PIPELINING DATA REUSE
ROCCC
OUR
VIVADO
UNROLLING DATA REUSE
UNROLLING
WINDOW 2WINDOW 1
Manual Rewrite
▸ ROCCC
▸ Vivado HLS
▸ Our Approach
EXPERIMENTAL SETUP
APPROACHES COMPARED
50
PIPELINING DATA REUSE
ROCCC
OUR
VIVADO
UNROLLING DATA REUSE
PARAMETRIC I/O WIDTH
Manual Rewrite
▸ ROCCC
▸ Vivado HLS
▸ Our Approach
EXPERIMENTAL SETUP
APPROACHES COMPARED
51
PIPELINING DATA REUSE
ROCCC
OUR
VIVADO
UNROLLING DATA REUSE
PARAMETRIC I/O WIDTH
BUFFER
INPUT WIDTH
Manual Rewrite
▸ ROCCC
▸ Vivado HLS
▸ Our Approach
EXPERIMENTAL SETUP
APPROACHES COMPARED
52
PIPELINING DATA REUSE
ROCCC
OUR
VIVADO
UNROLLING DATA REUSE
PARAMETRIC I/O WIDTH
BUFFER
INPUT WIDTH
Manual Rewrite
▸ ROCCC
▸ Vivado HLS
▸ Our Approach
EXPERIMENTAL SETUP
APPROACHES COMPARED
53
PIPELINING DATA REUSE
ROCCC
OUR
VIVADO
UNROLLING DATA REUSE
PARAMETRIC I/O WIDTH
BUFFER
INPUT WIDTH
Manual Rewrite
▸ ROCCC
▸ Vivado HLS
▸ Our Approach
EXPERIMENTAL SETUP
APPROACHES COMPARED
54
PIPELINING DATA REUSE
ROCCC
OUR
VIVADO
UNROLLING DATA REUSE
PARAMETRIC I/O WIDTH
BUFFER
INPUT WIDTH
Manual Rewrite
▸ Xilinx Virtex7 FPGA (HDL Simulation)
EXPERIMENTAL SETUP
OUR APPROACH
55
▸ Xilinx Virtex7 FPGA (HDL Simulation)
EXPERIMENTAL SETUP
OUR APPROACH
56
3 CONFIGURATIONS
▸ Xilinx Virtex7 FPGA (HDL Simulation)
EXPERIMENTAL SETUP
OUR APPROACH
57
INPUT WIDTH # DATAPATHS
3 CONFIGURATIONS
▸ Xilinx Virtex7 FPGA (HDL Simulation)
EXPERIMENTAL SETUP
OUR APPROACH
58
INPUT WIDTH # DATAPATHS
3 CONFIGURATIONS
SAD
SOBEL
MAX FILTER
WINDOW SIZE
4X4
3X3
8X8
▸ Xilinx Virtex7 FPGA (HDL Simulation)
EXPERIMENTAL SETUP
OUR APPROACH
59
SINGLE DATAPATH SDP
SAD
SOBEL
MAX FILTER
WINDOW SIZE
4X4
3X3
8X8
INPUT WIDTH # DATAPATHS
▸ Xilinx Virtex7 FPGA (HDL Simulation)
EXPERIMENTAL SETUP
OUR APPROACH
60
SINGLE DATAPATH SDP
SAD
SOBEL
MAX FILTER
WINDOW SIZE
4X4
3X3
8X8
INPUT WIDTH # DATAPATHS
4, 1
3, 1
8, 1
▸ Xilinx Virtex7 FPGA (HDL Simulation)
EXPERIMENTAL SETUP
OUR APPROACH
61
SINGLE DATAPATH SDP
SAD
SOBEL
MAX FILTER
MULTIPLE DATAPATHS MDPWINDOW SIZE
4, 1
3, 1
8, 1
4X4
3X3
8X8
INPUT WIDTH # DATAPATHS
▸ Xilinx Virtex7 FPGA (HDL Simulation)
EXPERIMENTAL SETUP
OUR APPROACH
62
SINGLE DATAPATH SDP
SAD
SOBEL
MAX FILTER
MULTIPLE DATAPATHS MDPWINDOW SIZE
4, 1
3, 1
8, 1
4X4
3X3
8X8
8, 5
8, 6
16, 9
INPUT WIDTH # DATAPATHS
▸ Xilinx Virtex7 FPGA (HDL Simulation)
EXPERIMENTAL SETUP
OUR APPROACH
63
SINGLE DATAPATH SDP
SAD
SOBEL
MAX FILTER
MULTIPLE DATAPATHS MDP
EXTRA MULT. DATAPATHS XMDPWINDOW SIZE
4, 1
3, 1
8, 1
4X4
3X3
8X8
8, 5
8, 6
16, 9
INPUT WIDTH # DATAPATHS
▸ Xilinx Virtex7 FPGA (HDL Simulation)
EXPERIMENTAL SETUP
OUR APPROACH
64
SINGLE DATAPATH SDP
SAD
SOBEL
MAX FILTER
MULTIPLE DATAPATHS MDP
EXTRA MULT. DATAPATHS XMDPWINDOW SIZE
4, 1
3, 1
8, 1
4X4
3X3
8X8
8, 5
8, 6
16, 9
INPUT WIDTH # DATAPATHS
16, 13
16, 14
24, 17
EXPERIMENTS
EXECUTION TIME COMPARISON
65
500
5000
50000
500000
Sobel MaxFilter BlockSAD
ROCCCVivado_norevVivado_revCISC=Conf.1CISC=Conf.2CISC=Conf.3
Vivado_norewVivado_rew
Conf.1=========
Conf.3Conf.2
nS
SDP
MDP
XMDP
EXPERIMENTS
EXECUTION TIME COMPARISON
66
500
5000
50000
500000
Sobel MaxFilter BlockSAD
ROCCCVivado_norevVivado_revCISC=Conf.1CISC=Conf.2CISC=Conf.3
Vivado_norewVivado_rew
Conf.1=========
Conf.3Conf.2
nS
SDP
MDP
XMDP
VIVADO_NOREW
PIPELINING DATA REUSE
UNROLLING DATA REUSE
PARAMETRIC I/O WIDTH
EXPERIMENTS
EXECUTION TIME COMPARISON
67
500
5000
50000
500000
Sobel MaxFilter BlockSAD
ROCCCVivado_norevVivado_revCISC=Conf.1CISC=Conf.2CISC=Conf.3
Vivado_norewVivado_rew
Conf.1=========
Conf.3Conf.2
nS
SDP
MDP
XMDP
VIVADO_REW
PIPELINING DATA REUSE
UNROLLING DATA REUSE
PARAMETRIC I/O WIDTH
Manual Rewrite
EXPERIMENTS
EXECUTION TIME COMPARISON
68
▸ Exec. Time to process a 100x100 frame
500
5000
50000
500000
Sobel MaxFilter BlockSAD
ROCCCVivado_norevVivado_revCISC=Conf.1CISC=Conf.2CISC=Conf.3
Vivado_norewVivado_rew
Conf.1=========
Conf.3Conf.2
nS
SDP
MDP
XMDP
EXPERIMENTS
EXECUTION TIME COMPARISON
69
▸ Exec. Time to process a 100x100 frame
500
5000
50000
500000
Sobel MaxFilter BlockSAD
ROCCCVivado_norevVivado_revCISC=Conf.1CISC=Conf.2CISC=Conf.3
Vivado_norewVivado_rew
Conf.1=========
Conf.3Conf.2
nS
SDP
MDP
XMDP
EXPERIMENTS
EXECUTION TIME COMPARISON
70
▸ Exec. Time to process a 100x100 frame
500
5000
50000
500000
Sobel MaxFilter BlockSAD
ROCCCVivado_norevVivado_revCISC=Conf.1CISC=Conf.2CISC=Conf.3
Vivado_norewVivado_rew
Conf.1=========
Conf.3Conf.2
nS
SDP
MDP
XMDP
EXPERIMENTS
EXECUTION TIME COMPARISON
71
▸ Exec. Time to process a 100x100 frame
500
5000
50000
500000
Sobel MaxFilter BlockSAD
ROCCCVivado_norevVivado_revCISC=Conf.1CISC=Conf.2CISC=Conf.3
Vivado_norewVivado_rew
Conf.1=========
Conf.3Conf.2
nS
SDP
MDP
XMDP
EXPERIMENTS
AREA COMPARISON
72
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#$%&' ()*+,'-&. /'$01#23
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6$;>?@
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SDP
MDP
XMDP
FLIP FLOPS LUTS
EXPERIMENTS
AREA COMPARISON
75
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SDP
MDP
XMDP
FLIP FLOPS LUTS
EXPERIMENTS
AREA COMPARISON
76
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7,8)9$:;$.&C7,8)9$:.&C
SDP
MDP
XMDP
FLIP FLOPS LUTS
EXPERIMENTS
AREA COMPARISON
77
!""
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7,8)9$:;$.&C7,8)9$:.&C
SDP
MDP
XMDP
FLIP FLOPS LUTS
EXPERIMENTS
AREA COMPARISON
78
!""
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45666
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#$%&' ()*+,'-&. /'$01#23
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6$;>?@
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45666
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#$%&' ()*+,'-&. /'$01#23
6$;>?!=========
6$;>?A
6$;>?@
7,8)9$:;$.&C7,8)9$:.&C
SDP
MDP
XMDP
FLIP FLOPS LUTS
EXPERIMENTS
SPEEDUP AND AREA
79
!"#$%&''()%''*+(,-"./01 !"#$%2''()%''*+(,-"./01
3&456
737&74
8900-:9
;/0,'"(0/<0,-' =>?@)A
;/0,'"(0/<0,-' =BB)A
SADSOBEL MAX FILTER
SADSOBEL MAX FILTER
MDP vs Vivado_Rew XMDP vs Vivado_Rew
CONCLUSIONS
DATA REUSE ANALYSIS BASED ON POLLY
Optimize HLS of Accelerators for Sliding Window Applications
Use Polly for Better HW Designs
80
CONCLUSIONS
DATA REUSE ANALYSIS BASED ON POLLY
Optimize HLS of Accelerators for Sliding Window Applications
Use Polly for Better HW Designs
81
▸ Exploit Data Locality
CONCLUSIONS
DATA REUSE ANALYSIS BASED ON POLLY
Optimize HLS of Accelerators for Sliding Window Applications
Use Polly for Better HW Designs
82
▸ Exploit Data Locality
▸ Design Efficient Buffers
CONCLUSIONS
DATA REUSE ANALYSIS BASED ON POLLY
Optimize HLS of Accelerators for Sliding Window Applications
Use Polly for Better HW Designs
83
▸ Exploit Data Locality
▸ Design Efficient Buffers
▸ Better Use of Resources
CONCLUSIONS
DATA REUSE ANALYSIS BASED ON POLLY
Optimize HLS of Accelerators for Sliding Window Applications
Use Polly for Better HW Designs
84
▸ Exploit Data Locality
▸ Design Efficient Buffers
▸ Better Use of Resources
▸ Better Performance