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CC B
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C
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s
p
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uth
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r
:
A
ld
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n
C
.
S
h
aj
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Dep
ar
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m
en
t o
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E
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n
d
C
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m
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I
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h
o
p
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I
n
d
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ail: a
ld
en
c
s
h
aj
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g
m
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co
m
1.
I
NT
RO
D
UCT
I
O
N
Hig
h
p
er
f
o
r
m
a
n
ce
co
m
p
u
ti
n
g
(
HP
C
)
p
la
y
s
a
v
ital
r
o
le
in
t
h
e
f
ield
o
f
ar
ti
f
icia
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i
n
telli
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ce
(
A
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)
b
y
p
r
o
v
id
in
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co
m
p
u
tat
io
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al
p
o
wer
r
eq
u
ir
ed
f
o
r
tr
ain
i
n
g
an
d
r
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n
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i
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co
m
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lex
m
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els.
M
an
y
HP
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te
m
s
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c
h
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ield
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m
ab
le
g
ate
ar
r
a
y
s
(
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P
GA
s
)
o
r
g
r
ap
h
ic
s
p
r
o
ce
s
s
in
g
u
n
its
(
GP
Us),
to
o
f
f
lo
ad
f
lo
ati
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g
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n
t
co
m
p
u
t
atio
n
s
f
r
o
m
tr
ad
itio
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al
C
P
Us.
T
h
ese
ac
ce
ler
ato
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s
ar
e
o
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tim
ized
f
o
r
p
ar
allel
p
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s
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n
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ig
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-
p
o
i
n
t
-
in
te
n
s
iv
e
w
o
r
k
lo
ad
s
[
1
]
.
Flo
atin
g
-
p
o
in
t
ac
ce
ler
ato
r
s
ar
e
en
g
i
n
ee
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t
o
d
eliv
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b
u
s
t
co
m
p
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tatio
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a
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ca
p
ab
ilit
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w
h
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also
tak
in
g
in
to
ac
co
u
n
t
e
n
er
g
y
e
f
f
icie
n
c
y
,
a
cr
itical
co
n
s
id
er
atio
n
in
HP
C
s
y
s
te
m
s
w
h
er
e
p
o
w
er
co
n
s
u
m
p
tio
n
an
d
h
ea
t
m
a
n
ag
e
m
e
n
t
ar
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m
aj
o
r
ch
allen
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s
.
A
l
s
o
,
s
o
m
e
o
f
th
e
k
e
y
c
h
alle
n
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e
s
ass
o
ciate
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w
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s
p
ar
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m
atr
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x
-
v
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to
r
m
u
lt
ip
licatio
n
(
Sp
MV
)
co
m
p
u
tat
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o
n
FP
GAs
ar
e
ir
r
eg
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lar
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m
o
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atter
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,
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ala
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,
li
m
ited
on
-
ch
ip
m
e
m
o
r
y
r
eso
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r
ce
s
an
d
en
er
g
y
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f
f
icie
n
c
y
.
T
h
e
f
lex
ib
ilit
y
o
f
FP
G
A
s
,
b
ein
g
p
r
o
g
r
a
m
m
ab
l
e
h
ar
d
w
ar
e,
allo
w
s
f
o
r
th
e
cu
s
to
m
izat
io
n
o
f
f
lo
atin
g
-
p
o
in
t
ac
ce
ler
ato
r
s
to
s
u
it
s
p
ec
if
i
c
w
o
r
k
lo
ad
s
.
T
h
is
ad
ap
tab
ilit
y
g
i
v
e
ad
v
an
ta
g
e
in
HP
C
ap
p
licatio
n
s
,
b
y
p
r
o
v
id
in
g
s
o
l
u
tio
n
s
th
at
ca
n
d
eliv
er
o
p
ti
m
al
p
er
f
o
r
m
a
n
ce
f
o
r
d
iv
er
s
e
co
m
p
u
ta
tio
n
al
ta
s
k
s
[
2
]
,
[
3
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4864
I
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R
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o
n
f
i
g
u
r
ab
le
&
E
m
b
ed
d
ed
Sy
s
t
,
Vo
l.
14
,
No
.
2
,
J
u
l
y
20
25
:
375
-
3
8
7
376
Sp
MV
is
a
f
o
u
n
d
atio
n
a
l
o
p
er
atio
n
w
ith
in
HP
C
a
n
d
h
o
l
d
s
v
ital
s
i
g
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i
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ican
ce
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s
s
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g
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ata
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ai
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e
o
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o
elem
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d
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e
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.
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MV
u
tili
t
y
ex
te
n
d
s
to
task
s
s
u
c
h
as
s
o
l
v
in
g
lin
ea
r
eq
u
atio
n
s
y
s
te
m
s
,
s
i
m
u
lati
n
g
p
h
y
s
ical
p
h
en
o
m
en
a,
an
d
co
n
d
u
cti
n
g
g
r
ap
h
co
m
p
u
tatio
n
s
,
u
n
d
er
-
s
co
r
i
n
g
i
ts
ess
e
n
tial
r
o
le
in
d
iv
er
s
e
ap
p
licatio
n
s
[
4
]
.
C
u
s
to
m
m
e
m
o
r
y
ac
ce
s
s
p
atter
n
s
ar
e
cr
itical
f
o
r
i
m
p
r
o
v
i
n
g
t
h
e
p
er
f
o
r
m
a
n
ce
o
f
Sp
MV
o
n
e
m
b
ed
d
ed
FP
GA
s
.
B
y
ta
ilo
r
in
g
m
e
m
o
r
y
h
ier
ar
ch
ie
s
an
d
d
ata
s
tr
u
ctu
r
e
s
,
FP
GAs
ca
n
m
in
i
m
ize
m
e
m
o
r
y
late
n
c
y
an
d
m
a
x
i
m
ize
b
an
d
w
id
th
,
le
ad
in
g
to
en
h
a
n
ce
d
ef
f
icien
c
y
i
n
Sp
MV
co
m
p
u
tati
o
n
s
[
5
]
.
Sp
MV
in
v
o
lv
e
s
ac
ce
s
s
in
g
n
o
n
-
co
n
ti
g
u
o
u
s
m
e
m
o
r
y
lo
ca
tio
n
s
o
w
i
n
g
to
th
e
s
p
ar
s
e
n
at
u
r
e
o
f
m
atr
ices
.
T
h
is
ir
r
eg
u
lar
m
e
m
o
r
y
ac
ce
s
s
p
atter
n
ca
n
lead
to
ca
ch
e
m
is
s
es,
ca
u
s
i
n
g
in
cr
ea
s
ed
m
e
m
o
r
y
late
n
c
y
a
n
d
af
f
ec
tin
g
t
h
e
o
v
er
all
p
er
f
o
r
m
a
n
ce
o
f
b
o
th
C
P
Us
a
n
d
GP
Us
[
6
]
,
[
7
]
.
I
n
ad
d
itio
n
,
t
h
e
w
o
r
k
l
o
ad
in
Sp
MV
is
n
o
t
ev
en
l
y
d
is
tr
ib
u
ted
a
m
o
n
g
t
h
e
p
r
o
ce
s
s
in
g
ele
m
e
n
ts
o
w
i
n
g
t
o
th
e
v
ar
y
i
n
g
s
p
ar
s
it
y
o
f
t
h
e
m
atr
ices.
T
h
is
lo
ad
i
m
b
alan
ce
ca
n
lead
to
in
e
f
f
ici
en
t
u
tili
za
t
io
n
o
f
r
eso
u
r
ce
s
,
e
s
p
ec
iall
y
o
n
GP
Us
w
h
er
e
th
r
ea
d
-
lev
el
p
ar
allelis
m
is
cr
u
cial.
C
o
n
s
eq
u
en
tl
y
,
C
P
Us
an
d
GP
Us
m
a
y
n
o
t
b
e
th
e
m
o
s
t
s
u
itab
le
p
lat
f
o
r
m
s
f
o
r
ac
ce
ler
atin
g
Sp
MV
k
er
n
el
s
.
I
n
co
n
tr
ast,
FP
GAs
e
m
er
g
e
as
a
p
r
o
m
i
s
i
n
g
s
o
l
u
ti
o
n
f
o
r
Sp
MV
ac
ce
ler
atio
n
.
FP
GA
s
b
o
ast
lar
g
e
o
f
f
-
c
h
ip
s
to
r
ag
e
b
an
d
w
id
t
h
,
a
llo
w
i
n
g
th
e
m
to
e
f
f
icie
n
tl
y
h
a
n
d
le
m
e
m
o
r
y
b
o
u
n
d
ap
p
licatio
n
s
.
T
h
eir
tailo
r
ed
lo
g
ical
co
m
p
o
n
e
n
ts
a
n
d
ef
f
ici
en
t
f
lo
atin
g
-
p
o
in
t
co
m
p
u
tatio
n
s
en
h
an
ce
it
s
s
ta
n
d
in
g
e
v
en
m
o
r
e
in
FP
GA
s
a
s
a
n
attr
ac
tiv
e
p
lat
f
o
r
m
f
o
r
ac
ce
ler
atin
g
Sp
MV
co
m
p
u
tatio
n
s
[
8
]
.
R
esear
ch
f
i
n
d
in
g
s
i
n
d
icate
th
at
h
i
g
h
le
v
el
s
y
n
t
h
es
i
s
(
HL
S)
h
o
ld
s
p
r
o
m
i
s
e
f
o
r
f
u
r
n
is
h
in
g
h
ig
h
-
p
er
f
o
r
m
a
n
ce
,
en
er
g
y
-
e
f
f
icie
n
t
s
o
l
u
tio
n
s
,
th
er
eb
y
ex
p
ed
itin
g
ti
m
e
-
to
-
m
ar
k
et
an
d
tack
li
n
g
th
e
co
m
p
le
x
itie
s
o
f
m
o
d
er
n
s
y
s
te
m
s
co
n
cu
r
r
en
tl
y
[
9
]
,
[
1
0
]
.
Ou
r
in
v
est
ig
at
io
n
f
o
cu
s
e
s
o
n
ex
p
lo
r
in
g
th
e
ap
p
licatio
n
o
f
H
L
S,
a
tec
h
n
iq
u
e
th
at
is
g
ai
n
i
n
g
p
o
p
u
l
ar
it
y
f
o
r
ac
ce
ler
atin
g
al
g
o
r
it
h
m
s
o
n
e
m
b
ed
d
ed
h
eter
o
g
e
n
eo
u
s
p
lat
f
o
r
m
s
.
Af
t
er
f
in
d
i
n
g
t
h
e
e
f
f
ic
ien
t
o
p
ti
m
i
za
tio
n
tech
n
iq
u
e
w
e
ca
lc
u
late
d
th
e
k
er
n
el
p
o
w
er
co
n
s
u
m
p
tio
n
in
t
h
e
e
m
b
ed
d
ed
FP
GA
,
th
e
n
p
r
o
p
o
s
e
t
w
o
n
o
v
el
ap
p
r
o
x
i
m
ate
co
m
p
r
es
s
ed
s
p
ec
tr
al
r
eg
r
ess
io
n
(
C
SR
)
m
atr
ix
to
m
i
n
i
m
ize
th
e
ex
ec
u
t
io
n
ti
m
e
f
o
r
th
e
k
er
n
e
l i
n
th
e
h
ar
d
w
ar
e.
T
h
e
r
em
ai
n
d
er
o
f
t
h
is
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
w
s
.
Sectio
n
2
p
r
o
v
id
es
b
ac
k
g
r
o
u
n
d
in
f
o
r
m
atio
n
an
d
r
elate
d
w
o
r
k
o
n
th
e
Sp
MV
an
d
HL
S
f
lo
w
s
.
Sec
tio
n
3
p
r
e
s
en
ts
t
h
e
m
et
h
o
d
o
lo
g
y
u
s
ed
in
t
h
is
s
tu
d
y
p
ap
er
to
b
r
in
g
o
u
t
th
e
r
e
s
u
l
ts
,
i
n
clu
d
i
n
g
t
h
e
u
s
ag
e
o
f
p
r
ag
m
as
a
n
d
a
n
o
v
el
ap
p
r
o
x
i
m
atio
n
m
o
d
el
al
g
o
r
ith
m
.
T
h
e
r
esu
l
t
an
d
d
is
cu
s
s
io
n
ar
e
p
r
esen
ted
in
s
ec
tio
n
4
.
T
h
e
p
ap
er
co
n
clu
d
es
w
it
h
t
h
e
co
n
c
lu
s
io
n
a
n
d
f
u
t
u
r
e
s
co
p
e
in
s
ec
tio
n
5
.
2.
T
H
E
CO
M
P
RE
H
E
NS
I
VE
T
H
E
O
RE
T
I
CA
L
B
ASI
S
2
.
1
.
Sp
a
rse
m
a
t
rix
-
v
ec
t
o
r
m
ultiplica
t
io
n
Sp
ar
s
e
m
atr
ice
s
,
in
co
n
tr
ast
to
d
en
s
e
m
atr
ices
th
at
h
o
l
d
a
s
u
b
s
ta
n
tial
a
m
o
u
n
t
o
f
r
ed
u
n
d
an
t
in
f
o
r
m
atio
n
,
p
r
i
m
ar
il
y
co
n
s
i
s
t
o
f
ze
r
o
v
alu
e
s
,
lead
in
g
to
m
o
r
e
ef
f
icie
n
t
m
e
m
o
r
y
u
s
ag
e.
Sp
MV
in
v
o
lv
e
s
th
e
m
u
ltip
licatio
n
o
f
a
s
p
ar
s
e
m
a
t
r
ix
w
it
h
a
d
en
s
e
v
ec
to
r
,
u
lti
m
atel
y
p
r
o
d
u
cin
g
a
n
e
w
v
ec
to
r
th
at
r
ep
r
esen
t
s
t
h
e
lin
ea
r
tr
an
s
f
o
r
m
atio
n
o
f
t
h
e
o
r
ig
i
n
al
d
ata
ex
p
r
ess
ed
as (
1
)
.
=
∑
∑
×
,
=
0
≠
0
=
0
(
1
)
Sp
ar
s
e
m
atr
ices
ar
e
t
y
p
icall
y
en
co
d
ed
in
co
n
d
en
s
ed
f
o
r
m
at
s
th
at
o
n
l
y
co
n
tai
n
t
h
e
n
o
n
-
ze
r
o
m
e
m
b
er
s
in
o
r
d
er
t
o
r
estrict
th
e
d
ata
c
o
llectio
n
n
ee
d
ed
.
T
h
e
r
atio
o
f
to
tal
ze
r
o
elem
en
ts
to
to
tal
e
le
m
e
n
ts
in
a
s
p
ar
s
e
m
atr
i
x
d
eter
m
i
n
es
th
e
m
at
r
i
x
's
s
p
ar
s
it
y
.
Fi
g
u
r
e
1
p
r
o
v
id
es
an
o
v
er
v
ie
w
o
f
th
e
Sp
MV
p
r
o
ce
s
s
alo
n
g
w
it
h
t
h
e
co
m
m
o
n
co
m
p
r
ess
ed
f
o
r
m
at
s
u
s
ed
to
s
to
r
e
s
p
ar
s
e
m
atr
ice
s
.
T
h
e
ex
am
p
le
Sp
MV
k
er
n
e
l
in
Fig
u
r
e
1
(
a)
is
r
ep
r
esen
ted
u
s
i
n
g
t
h
r
ee
co
m
m
o
n
l
y
u
s
ed
co
m
p
r
ess
ed
f
o
r
m
ats
C
OOr
d
in
ate
(
C
OO)
,
c
o
m
p
r
ess
ed
s
p
ar
s
e
co
lu
m
n
(
C
SC
)
,
a
n
d
co
m
p
r
ess
ed
s
p
ar
s
e
r
o
w
(
C
S
R
)
as
s
h
o
w
n
i
n
Fi
g
u
r
e
1
(
b
)
.
Ou
t
o
f
t
h
ese
w
id
el
y
u
s
ed
is
C
S
R
f
o
r
m
at.
T
h
e
v
al
v
ec
to
r
h
o
ld
s
th
e
n
o
n
-
ze
r
o
elem
e
n
ts
m
en
t
io
n
ed
b
y
n
n
z
d
eter
m
i
n
es
t
h
eir
s
ize
an
d
th
eir
co
r
r
esp
o
n
d
in
g
co
lu
m
n
i
n
d
ices
ar
e
s
av
ed
in
c
o
l
v
ec
to
r
.
I
n
p
tr
v
ec
to
r
,
th
e
d
i
f
f
er
en
ce
b
et
w
ee
n
ad
j
ac
en
t
ce
lls
g
i
v
es
t
h
e
n
o
.
o
f
n
o
n
-
ze
r
o
ele
m
e
n
ts
(
nnz
)
p
r
esen
t
i
n
co
r
r
esp
o
n
d
in
g
r
o
w
in
s
p
ar
s
e
m
atr
ix
.
T
h
e
C
S
R
f
o
r
m
a
t
is
ap
p
r
o
p
r
iate
f
o
r
co
m
p
u
ti
n
g
w
it
h
s
tr
ea
m
i
n
g
d
ata
an
d
o
n
l
y
r
eq
u
ir
es
a
b
r
ie
f
p
r
ep
ar
atio
n
s
ta
g
e
[
1
1
]
.
A
l
s
o
,
C
SR
r
ed
u
ce
t
h
e
m
e
m
o
r
y
n
ee
d
ed
f
r
o
m
O(
m
×
n
)
to
O(
2
n
n
z
+m
)
d
u
e
to
th
is
w
e
h
av
e
u
s
ed
it i
n
o
u
r
w
o
r
k
.
Sp
MV
is
a
v
er
s
atile
o
p
er
atio
n
w
it
h
ap
p
licatio
n
s
in
a
w
id
e
r
an
g
e
o
f
f
ie
ld
s
,
o
f
f
er
i
n
g
co
m
p
u
tat
io
n
al
ef
f
icien
c
y
an
d
m
e
m
o
r
y
s
a
v
i
n
g
s
w
h
en
d
ea
lin
g
w
it
h
s
p
ar
s
e
d
ata
s
tr
u
ctu
r
es.
I
ts
b
r
o
ad
ap
p
licab
ilit
y
m
ak
e
s
it
a
f
u
n
d
a
m
en
ta
l
o
p
er
atio
n
in
v
ar
io
u
s
s
cien
tific
,
en
g
i
n
ee
r
i
n
g
,
an
d
d
ata
-
d
r
iv
en
d
is
cip
li
n
es.
Sp
MV
ap
p
licatio
n
in
co
n
v
o
lu
tio
n
al
n
eu
r
al
n
et
w
o
r
k
s
(
C
NN)
tr
ain
in
g
is
s
h
o
w
n
i
n
Fig
u
r
e
2
,
th
is
tr
ai
n
in
g
s
c
h
e
m
e
w
a
s
u
s
ed
in
[
1
2
]
to
g
et
f
a
s
t
e
x
ec
u
t
io
n
o
f
C
NN
o
n
GP
Us.
Du
r
i
n
g
th
e
f
o
r
w
ar
d
p
ass
o
f
C
N
N
tr
ain
i
n
g
,
Sp
MV
is
ap
p
lied
w
h
en
co
m
p
u
ti
n
g
t
h
e
o
u
tp
u
t
o
f
co
n
v
o
lu
tio
n
al
la
y
er
s
.
T
h
e
s
p
ar
s
e
w
ei
g
h
t
m
atr
ice
s
ar
e
m
u
ltip
lie
d
b
y
th
e
in
p
u
t
d
ata
v
ec
to
r
s
,
an
d
th
e
r
es
u
lti
n
g
s
p
a
r
s
e
v
ec
to
r
co
n
tr
ib
u
tes
to
t
h
e
ac
tiv
atio
n
o
f
n
e
u
r
o
n
s
in
s
u
b
s
e
q
u
en
t
la
y
er
s
.
I
n
t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
R
ec
o
n
f
i
g
u
r
ab
le
&
E
m
b
ed
d
ed
Sy
s
t
I
SS
N:
2089
-
4864
A
n
a
p
p
r
o
xima
te
mo
d
el
S
p
MV
o
n
F
P
GA
a
s
s
is
tin
g
HLS
o
p
tim
iz
a
tio
n
s
fo
r
lo
w
p
o
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er
… (
A
ld
en
C
.
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h
a
ji
)
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b
ac
k
w
ar
d
p
as
s
(
b
ac
k
p
r
o
p
ag
atio
n
)
d
u
r
i
n
g
tr
ain
i
n
g
,
g
r
ad
ie
n
ts
w
it
h
r
esp
ec
t
to
t
h
e
w
e
i
g
h
t
s
ar
e
ca
lc
u
lated
ef
f
icien
tl
y
,
tak
in
g
ad
v
a
n
ta
g
e
o
f
t
h
e
s
p
ar
s
it
y
i
n
b
o
th
t
h
e
in
p
u
t
d
ata
an
d
t
h
e
w
ei
g
h
t
m
atr
ice
s
.
T
h
is
en
ab
les
f
a
s
ter
u
p
d
ates to
th
e
w
ei
g
h
ts
d
u
r
i
n
g
o
p
tim
izatio
n
.
(
a)
(
b
)
Fig
u
r
e
1
.
Sp
ar
s
e
m
atr
ix
-
v
ec
to
r
m
u
l
tip
licatio
n
a
n
d
co
n
v
e
n
tio
n
al
co
m
p
r
es
s
f
o
r
m
at
(
a)
an
ex
a
m
p
le
o
f
Sp
MV
an
d
(
b
)
co
n
v
en
tio
n
a
l c
o
m
p
r
es
s
ed
f
o
r
m
at
s
Fig
u
r
e
2
.
Sp
MV
ap
p
licatio
n
in
C
NN
tr
ain
in
g
2
.
2
.
H
i
g
h
lev
el
s
y
nthesis
Vitis
H
L
S
is
a
to
o
l
p
r
o
v
id
ed
b
y
Xili
n
x
th
a
t
tak
e
s
h
i
g
h
-
lev
e
l
C
o
r
C
++
f
u
n
ctio
n
s
an
d
tr
an
s
l
ates
th
e
m
in
to
R
T
L
co
d
e
,
w
h
ic
h
ca
n
th
e
n
b
e
im
p
le
m
en
ted
in
th
e
p
r
o
g
r
a
m
m
ab
le
lo
g
ic
r
eg
io
n
o
f
a
s
y
s
te
m
o
n
ch
ip
(
So
C
)
.
I
t
g
en
er
ates
a
h
ar
d
w
ar
e
s
o
l
u
tio
n
b
y
co
n
s
id
er
in
g
th
e
d
e
f
i
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ed
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g
et
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w
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d
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a
u
lt
to
o
l
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g
s
,
d
esi
g
n
co
n
s
tr
ain
ts
,
an
d
o
p
ti
m
izatio
n
p
r
ag
m
a
s
p
r
o
v
id
ed
.
Op
tim
iz
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n
d
ir
ec
tiv
es
ar
e
u
tili
ze
d
to
cu
s
to
m
ize
an
d
m
an
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g
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t
h
e
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ter
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al
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d
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p
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ts
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m
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le
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en
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,
s
u
p
er
s
ed
in
g
th
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to
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l’
s
d
ef
au
lt
ac
tio
n
s
a
n
d
co
n
f
i
g
u
r
atio
n
s
.
T
o
attain
o
p
ti
m
al
p
er
f
o
r
m
a
n
ce
f
r
o
m
th
e
h
a
r
d
w
ar
e
g
en
er
ated
,
th
e
HL
S
to
o
l
n
ee
d
s
to
id
en
tify
an
d
u
tili
ze
p
ar
alleli
s
m
i
n
h
er
en
t
in
s
eq
u
e
n
tial
co
d
e,
en
h
a
n
cin
g
o
v
er
all
p
er
f
o
r
m
an
ce
.
Sp
MV
p
s
eu
d
o
co
d
e
i
m
p
le
m
en
ted
u
s
i
n
g
HL
S is
s
h
o
w
n
in
F
ig
u
r
e
3
[
8
]
.
Fig
u
r
e
3
.
Sp
MV
ke
r
n
el
p
s
e
u
d
o
co
d
e
in
HL
S e
n
v
ir
o
n
m
e
n
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4864
I
n
t J
R
ec
o
n
f
i
g
u
r
ab
le
&
E
m
b
ed
d
ed
Sy
s
t
,
Vo
l.
14
,
No
.
2
,
J
u
l
y
20
25
:
375
-
3
8
7
378
I
n
h
i
g
h
le
v
el
la
n
g
u
a
g
e
p
r
o
g
r
a
m
s
,
t
h
e
ar
r
a
y
s
ar
e
ess
e
n
tia
l
f
o
r
s
to
r
in
g
a
n
d
m
a
n
ag
in
g
d
ata.
W
h
en
tr
an
s
lati
n
g
t
h
is
to
h
ar
d
w
ar
e,
a
r
r
ay
s
ar
e
r
ea
lized
as
eith
er
m
e
m
o
r
y
o
r
r
eg
is
ter
s
d
u
r
i
n
g
s
y
n
t
h
esi
s
.
Me
m
o
r
y
ca
n
b
e
eith
er
lo
ca
l
o
r
g
lo
b
al,
w
i
th
g
lo
b
al
m
e
m
o
r
y
o
f
te
n
c
o
r
r
esp
o
n
d
in
g
to
d
o
u
b
le
d
ata
r
ate
(
DDR)
o
r
h
ig
h
-
b
an
d
w
id
t
h
m
e
m
o
r
y
(
HB
M)
m
e
m
o
r
y
b
an
k
s
.
Acc
ess
in
g
g
l
o
b
al
m
e
m
o
r
y
in
c
u
r
s
h
i
g
h
er
l
aten
c
y
an
d
m
u
ltip
le
c
y
cles,
w
h
er
ea
s
lo
ca
l
m
e
m
o
r
y
ac
ce
s
s
is
f
as
ter
an
d
t
y
p
icall
y
co
m
p
leted
w
it
h
in
a
f
e
w
c
y
cles
.
E
f
f
icie
n
t
m
e
m
o
r
y
acces
s
is
e
s
s
e
n
tial
to
m
i
n
i
m
i
ze
th
e
o
v
er
h
ea
d
as
s
o
ciate
d
w
it
h
ac
ce
s
s
i
n
g
g
lo
b
al
m
e
m
o
r
y
.
On
e
s
tr
ateg
y
f
o
r
o
p
tim
izatio
n
i
n
v
o
l
v
es
co
n
s
o
li
d
atin
g
ac
ce
s
s
,
m
ax
i
m
is
i
n
g
co
n
s
ec
u
ti
v
e
ac
ce
s
s
e
s
to
en
ab
le
b
u
r
s
tin
g
.
B
u
r
s
t
ac
ce
s
s
ef
f
ec
tiv
e
l
y
m
a
s
k
s
m
e
m
o
r
y
ac
ce
s
s
late
n
c
y
a
n
d
en
h
a
n
ce
s
m
e
m
o
r
y
b
an
d
w
id
t
h
.
W
h
ile
t
h
e
p
r
o
ce
s
s
o
f
b
lo
ck
s
o
f
d
ata,
s
ev
er
al
lo
o
p
s
o
r
n
ested
lo
o
p
s
ar
e
n
ee
d
ed
.
W
ith
th
e
co
m
b
i
n
atio
n
o
f
m
icr
o
-
le
v
el
H
L
S
p
r
ag
m
as,
it
ca
n
p
er
f
o
r
m
u
n
r
o
ll,
p
ip
elin
e
o
p
er
a
tio
n
s
f
o
r
a
lo
o
p
o
r
n
ested
lo
o
p
s
[
1
3
]
.
HL
S
to
o
ls
ap
p
l
y
v
ar
io
u
s
o
p
tim
i
za
tio
n
s
to
i
m
p
r
o
v
e
th
e
p
er
f
o
r
m
a
n
ce
,
ar
ea
,
an
d
p
o
w
er
ch
a
r
ac
ter
is
tics
o
f
th
e
g
e
n
er
ated
h
ar
d
w
ar
e.
HL
S
to
o
ls
o
f
te
n
p
r
o
v
id
e
s
i
m
u
latio
n
an
d
v
er
if
ica
tio
n
ca
p
a
b
ilit
ies,
it
h
elp
s
to
s
i
m
u
late
t
h
e
b
eh
av
io
u
r
o
f
th
e
g
en
er
ated
h
ar
d
w
ar
e
b
ef
o
r
e
th
e
ac
tu
al
s
y
n
t
h
e
s
is
.
T
h
e
o
u
tp
u
t
o
f
HL
S
ca
n
b
e
tar
g
eted
f
o
r
i
m
p
le
m
e
n
tatio
n
o
n
FP
GAs
f
o
r
r
ap
id
p
r
o
t
o
ty
p
i
n
g
p
r
o
v
id
in
g
f
lex
ib
il
it
y
i
n
th
e
ch
o
ice
o
f
h
ar
d
w
ar
e
p
latf
o
r
m
.
2
.
3
.
Rela
t
ed
wo
rk
T
h
e
co
n
ce
p
t
o
f
s
p
ar
s
e
m
atr
ic
es
an
d
r
elate
d
o
p
er
atio
n
s
lik
e
Sp
MV
ca
n
b
e
tr
ac
ed
b
ac
k
t
o
th
e
ea
r
l
y
d
ay
s
o
f
n
u
m
er
ical
co
m
p
u
t
in
g
an
d
f
i
n
ite
ele
m
e
n
t
an
al
y
s
i
s
.
Var
io
u
s
alg
o
r
it
h
m
s
an
d
s
t
o
r
ag
e
f
o
r
m
ats
w
er
e
d
ev
elo
p
ed
to
ac
ce
ler
ate
Sp
M
V,
f
i
n
d
in
g
u
n
iq
u
e
ch
ar
ac
ter
is
tics
o
f
s
p
ar
s
e
m
atr
ice
s
in
[
1
4
]
,
[
1
5
]
.
I
n
v
ar
io
u
s
s
tu
d
ie
s
th
e
y
h
a
v
e
i
n
v
e
s
ti
g
ated
th
e
o
p
ti
m
izat
io
n
o
f
S
p
MV
o
n
FP
GAs [
1
6
]
,
[
1
7
]
.
T
h
e
m
aj
o
r
ity
o
f
t
h
ese
r
esear
c
h
en
d
ea
v
o
r
s
co
n
ce
n
tr
ate
o
n
le
v
er
ag
i
n
g
h
i
g
h
-
e
n
d
FP
G
A
s
an
d
i
m
p
le
m
e
n
ti
n
g
ap
p
r
o
ac
h
es
g
ea
r
ed
to
w
ar
d
s
p
r
o
ce
s
s
in
g
b
i
g
d
ata
ef
f
icie
n
tl
y
in
[
1
8
]
.
Du
et
a
l.
[
1
9
]
in
v
es
ti
g
ate
a
s
p
ar
s
e
m
atr
i
x
f
o
r
m
at
s
p
ec
if
icall
y
d
e
s
i
g
n
ed
f
o
r
HB
M.
A
n
o
t
h
er
co
m
p
ar
ab
le
ef
f
o
r
t,
R
eDE
SK
[
2
0
]
h
as
ex
a
m
in
ed
Sp
MV
o
p
ti
m
iza
tio
n
s
in
t
h
e
co
n
te
x
t
o
f
h
eter
o
g
e
n
eo
u
s
co
m
p
u
ti
n
g
,
it
i
s
d
esig
n
ed
to
en
ab
le
s
tr
ea
m
in
g
p
r
o
ce
s
s
o
n
th
e
FP
GA
s
id
e
an
d
d
ata
p
r
ef
etch
i
n
g
o
n
th
e
C
P
U
s
id
e.
Desig
n
o
f
b
a
n
d
w
id
th
e
f
f
icien
t
Sp
MV
o
n
FP
G
A
is
t
h
e
m
a
i
n
th
e
m
e
i
n
[
5
]
,
[
2
1
]
.
Fo
w
er
s
et
a
l.
[
2
2
]
p
r
o
p
o
s
ed
an
ar
ch
itectu
r
e
f
o
r
Sp
MV
b
ased
o
n
F
P
GA
,
alo
n
g
w
i
th
a
tech
n
iq
u
e
f
o
r
s
p
ar
s
e
m
atr
i
x
d
ec
o
d
in
g
to
lev
er
ag
e
p
ar
alleli
s
m
ac
r
o
s
s
m
atr
ix
r
o
w
s
.
T
h
e
d
esig
n
as
s
u
m
e
s
th
e
p
r
ese
n
ce
o
f
t
w
o
d
i
s
ti
n
ct
DR
A
M
m
o
d
u
les
in
th
e
s
y
s
te
m
,
a
f
ea
tu
r
e
t
h
at
m
a
y
n
o
t b
e
co
m
m
o
n
l
y
f
o
u
n
d
in
m
a
n
y
e
x
is
tin
g
e
m
b
ed
d
ed
s
y
s
te
m
s
.
Ho
s
s
ei
n
ab
ad
y
an
d
Nu
n
ez
-
Ya
n
ez
[
8
]
in
v
es
tig
a
ted
o
n
h
o
w
p
ar
alleliza
tio
n
an
d
p
ip
elin
i
n
g
ca
n
b
e
ef
f
ec
tiv
e
l
y
ap
p
lied
u
s
i
n
g
H
L
S
to
in
cr
ea
s
e
t
h
e
p
er
f
o
r
m
a
n
c
e
o
f
Sp
MV
o
n
FP
G
A
p
lat
f
o
r
m
s
.
T
h
is
in
cl
u
d
es
s
tr
ateg
ie
s
f
o
r
o
p
ti
m
izi
n
g
d
ata
m
o
v
e
m
en
t
an
d
m
e
m
o
r
y
ac
c
ess
es.
Gar
ib
o
tti
et
a
l
.
[
1
0
]
s
u
g
g
e
s
ted
e
m
p
lo
y
in
g
co
m
m
er
cial
H
L
S
to
o
ls
alo
n
g
w
it
h
d
y
n
a
m
ic
an
a
l
y
s
is
to
p
r
o
d
u
ce
h
ig
h
er
q
u
alit
y
d
esi
g
n
s
.
C
r
ea
tin
g
an
ef
f
ec
tiv
e
f
lo
ati
n
g
-
p
o
in
t
ac
c
u
m
u
la
to
r
,
w
h
ic
h
en
co
m
p
a
s
s
e
s
b
o
th
m
u
ltip
lier
an
d
ad
d
er
co
m
p
o
n
e
n
ts
,
to
i
m
p
r
o
v
e
t
h
e
p
er
f
o
r
m
a
n
ce
o
f
Sp
MV
is
th
e
o
b
j
ec
tiv
e
in
[
2
3
]
,
[
2
4
]
.
R
ec
en
tl
y
,
a
w
o
r
k
[
2
5
]
c
o
m
p
ar
es
th
e
Sp
MV
ca
lcu
latio
n
,
s
h
o
w
ca
s
in
g
t
h
e
p
er
f
o
r
m
an
ce
a
n
d
en
er
g
y
co
m
p
u
tatio
n
o
n
GP
U
an
d
FP
G
A
.
Fu
r
t
h
er
m
o
r
e,
c
u
r
r
en
t o
p
ti
m
izatio
n
s
p
r
im
ar
il
y
tar
g
et
h
al
f
p
r
ec
is
io
n
f
lo
ati
n
g
p
o
in
t
d
ata
ty
p
es,
o
v
er
l
o
o
k
in
g
s
u
p
p
o
r
t
f
o
r
r
e
d
u
ce
d
p
r
ec
is
io
n
f
i
x
ed
p
o
in
t
ar
ith
m
etic
[
2
6
]
.
Ho
w
ev
er
,
r
ec
en
t
s
tu
d
ies
h
a
v
e
i
n
v
esti
g
ated
s
tr
ateg
ies
f
o
r
b
len
d
i
n
g
s
i
n
g
le
a
n
d
d
o
u
b
le
p
r
ec
is
io
n
f
lo
ati
n
g
-
p
o
in
t a
r
it
h
m
etic
[
2
7
]
.
Fin
all
y
,
i
n
co
n
tr
ast
to
o
th
er
w
o
r
k
s
,
th
i
s
p
ap
er
p
r
o
p
o
s
ed
a
n
o
v
el
ap
p
r
o
x
i
m
atio
n
m
o
d
el
Sp
MV
to
r
ed
u
ce
th
e
p
o
w
er
an
d
ex
ec
u
t
io
n
ti
m
e,
u
s
i
n
g
w
h
ic
h
ca
n
s
i
g
n
i
f
ica
n
tl
y
tr
an
s
f
o
r
m
th
e
FP
GA
ac
ce
ler
ato
r
.
W
e
h
av
e
co
m
p
ar
ed
th
e
p
o
w
er
co
n
s
u
m
p
tio
n
a
n
d
ex
ec
u
t
io
n
ti
m
e
o
f
s
a
m
e
m
atr
ices
w
it
h
t
h
e
i
m
p
le
m
en
ta
tio
n
i
n
[
8
]
in
t
h
e
r
es
u
lt
s
.
E
x
p
er
i
m
e
n
tal
w
o
r
k
o
n
H
L
S
p
r
ag
m
as
an
d
a
p
p
r
o
x
im
a
te
al
g
o
r
ith
m
s
ar
e
d
is
cu
s
s
ed
i
n
d
etail
i
n
f
u
r
t
h
er
s
ec
tio
n
s
.
3.
M
E
T
H
O
D
AND
E
XP
E
R
I
M
E
NT
AL
S
E
T
UP
I
n
th
is
s
ec
tio
n
,
th
e
d
etails
o
f
th
e
d
esig
n
m
o
d
el
u
s
ed
f
o
r
Sp
MV
im
p
le
m
en
ta
tio
n
o
n
FP
GA
ar
e
p
r
o
v
id
ed
.
I
n
itiall
y
,
w
e
f
in
d
o
u
t
t
h
e
tr
ad
e
-
o
f
f
b
et
w
ee
n
e
x
ec
u
tio
n
ti
m
e
a
n
d
th
e
r
eso
u
r
ce
u
tili
za
tio
n
u
s
in
g
th
e
HL
S
o
p
ti
m
izatio
n
tec
h
n
iq
u
es
.
T
h
en
w
e
s
elec
t
t
h
e
e
f
f
icie
n
t
tec
h
n
iq
u
e
b
ased
o
n
h
ar
d
w
ar
e
e
m
u
latio
n
a
n
d
i
m
p
le
m
en
ta
tio
n
.
Af
ter
th
a
t
we
ap
p
lied
th
e
ap
p
r
o
x
im
atio
n
m
o
d
el
al
g
o
r
ith
m
to
t
h
e
s
p
ar
s
e
m
atr
ix
a
n
d
d
id
th
e
an
al
y
s
is
.
W
e
h
a
v
e
co
m
p
ar
ed
th
e
r
es
u
lt
s
o
b
tain
ed
i
n
o
u
r
tar
g
et
h
ar
d
w
ar
e
Z
y
b
o
Z
7
-
2
0
b
o
a
r
d
w
ith
Xili
n
x
Z
C
U1
0
2
ev
alu
atio
n
b
o
ar
d
u
s
ed
in
[
8
]
.
3
.
1
.
H
i
g
h lev
el
s
y
nthesis
o
pti
m
iza
t
io
n
t
ec
hn
iqu
e
s
Utilizatio
n
o
f
H
L
S
to
o
ls
is
to
h
ar
n
e
s
s
t
h
e
p
r
o
d
u
cti
v
it
y
b
en
e
f
its
o
f
tr
an
s
lati
n
g
C
/C
++
co
d
e
in
to
R
T
L
f
o
r
h
ar
d
w
ar
e,
o
r
o
b
j
ec
tiv
e
is
to
ac
ce
ler
ate
a
s
u
b
s
et
o
f
a
C
/C
++
al
g
o
r
ith
m
b
y
r
u
n
n
i
n
g
it
o
n
a
s
p
ec
ialize
d
h
ar
d
w
ar
e
b
u
ilt
w
it
h
p
r
o
g
r
a
m
m
i
n
g
lo
g
ic.
Fu
n
ctio
n
s
i
m
p
le
m
en
ted
in
C
/
C
++
a
n
d
tr
a
n
s
f
o
r
m
ed
i
n
to
c
u
s
to
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
R
ec
o
n
f
i
g
u
r
ab
le
&
E
m
b
ed
d
ed
Sy
s
t
I
SS
N:
2089
-
4864
A
n
a
p
p
r
o
xima
te
mo
d
el
S
p
MV
o
n
F
P
GA
a
s
s
is
tin
g
HLS
o
p
tim
iz
a
tio
n
s
fo
r
lo
w
p
o
w
er
… (
A
ld
en
C
.
S
h
a
ji
)
379
h
ar
d
w
ar
e
u
s
i
n
g
p
r
o
g
r
a
m
m
ab
l
e
lo
g
ic
ca
n
o
p
er
ate
at
n
o
tab
le
h
ig
h
er
s
p
ee
d
s
co
m
p
ar
ed
to
w
h
at
is
attai
n
ab
le
o
n
t
y
p
ical
GP
U/C
P
U
s
etu
p
s
,
r
esu
lti
n
g
in
h
i
g
h
er
th
r
o
u
g
h
p
u
t
an
d
p
er
f
o
r
m
a
n
ce
.
T
h
e
p
r
o
p
o
s
ed
Sp
MV
i
m
p
le
m
en
ta
tio
n
h
a
v
e
3
p
r
i
m
a
r
y
tas
k
s
in
v
o
lv
ed
:
Ta
s
k
A
:
r
e
ad
in
g
o
f
d
ata
i
n
to
th
e
FP
G
A
m
e
m
o
r
y
,
Ta
s
k
B
:
in
itiat
in
g
t
h
e
s
tr
ea
m
co
m
p
u
ta
tio
n
en
g
i
n
e
,
an
d
Ta
s
k
C
:
tr
a
n
s
f
er
r
i
n
g
o
u
tp
u
t
o
f
FP
G
A
to
m
ai
n
m
e
m
o
r
y
.
T
h
e
f
o
llo
w
in
g
o
p
ti
m
izatio
n
tec
h
n
i
q
u
es a
r
e
u
s
ed
to
i
m
p
le
m
e
n
t t
h
e
Sp
MV
co
m
p
u
tatio
n
.
3
.
1
.
1
.
L
o
o
p
pip
elinin
g
L
o
o
p
s
ar
e
cr
u
cial
co
n
s
tr
u
c
ts
w
i
th
i
n
a
n
Sp
MV
.
Sin
ce
lo
o
p
b
o
d
y
i
s
e
x
ec
u
ted
r
ep
ea
t
ed
ly
,
th
i
s
ch
ar
ac
ter
is
tic
ca
n
b
e
ef
f
ec
ti
v
el
y
lev
er
a
g
ed
to
en
h
an
ce
p
ar
allelis
m
an
d
o
p
ti
m
ize
p
er
f
o
r
m
an
ce
.
T
o
en
h
an
ce
th
r
o
u
g
h
p
u
t
a
n
d
m
a
k
e
m
o
r
e
e
f
f
icien
t
u
s
e
o
f
co
m
p
u
tatio
n
al
r
eso
u
r
ce
s
,
a
v
al
u
ab
le
ap
p
r
o
ac
h
i
s
to
i
n
tr
o
d
u
ce
p
ip
elin
in
g
in
o
p
er
ato
r
s
,
lo
o
p
s
an
d
f
u
n
ctio
n
s
.
Fig
u
r
e
4
s
h
o
w
s
th
e
ex
a
m
p
l
e
f
lo
w
o
f
3
task
s
(
ea
ch
to
o
k
1
0
u
n
it
s
to
co
m
p
lete)
b
ef
o
r
e
an
d
a
f
ter
p
ip
elin
in
g
.
T
o
f
i
n
is
h
t
h
e
f
ir
s
t
w
o
r
k
lo
ad
it
to
o
k
3
0
u
n
it
s
,
i
s
ca
lled
th
e
iter
atio
n
laten
c
y
.
Af
ter
th
e
co
m
p
let
io
n
o
f
f
ir
s
t
w
o
r
k
lo
ad
,
n
ex
t
t
wo
w
o
r
k
lo
ad
s
o
n
l
y
ta
k
e
1
0
u
n
its
ea
c
h
,
ca
lled
th
e
i
n
itiat
io
n
i
n
ter
v
a
l
(
I
I
)
.
T
h
e
o
v
er
all
co
m
p
letio
n
o
f
al
l
t
h
e
w
o
r
k
lo
ad
s
i
s
ca
lled
t
h
e
to
tal
laten
c
y
,
w
h
ich
i
s
5
0
h
er
e.
T
h
e
g
en
er
al
f
o
r
m
u
la
f
o
r
f
i
n
d
in
g
to
tal
laten
c
y
f
o
r
N
n
o
.
o
f
w
o
r
k
lo
ad
s
is
g
iv
e
n
i
n
(
2
)
.
=
+
×
(
−
1
)
(
2
)
I
n
a
p
ip
elin
ed
f
u
n
ctio
n
o
r
lo
o
p
,
n
e
w
i
n
p
u
t
s
ca
n
b
e
p
r
o
ce
s
s
ed
ev
er
y
s
p
ec
if
ied
II
clo
c
k
c
y
cles.
II
=1
i
m
p
lies
p
r
o
ce
s
s
in
g
a
n
e
w
i
n
p
u
t
e
v
er
y
clo
c
k
c
y
cle.
T
h
e
m
a
x
i
m
u
m
t
h
r
o
u
g
h
p
u
t
t
h
at
a
p
ip
e
lin
ed
lo
o
p
ca
n
r
ea
ch
w
it
h
o
u
t
u
n
r
o
lli
n
g
is
attain
ed
at
th
is
p
o
in
t.
So
m
eti
m
es
th
i
s
n
o
t
p
o
s
s
ib
le,
d
u
e
to
r
eso
u
r
ce
c
o
n
s
tr
ain
ts
a
n
d
lo
o
p
ca
r
r
ied
d
ep
en
d
en
cies.
T
h
e
p
ip
elin
ed
lo
o
p
w
i
ll
a
u
to
m
atica
ll
y
u
n
w
in
d
a
n
y
n
e
s
ti
n
g
lo
o
p
s
.
A
co
m
m
o
n
i
s
s
u
e
i
n
p
ip
elin
ed
lo
o
p
is
m
e
m
o
r
y
co
n
f
lict.
T
h
er
e
ar
e
f
o
u
r
lo
o
p
s
in
t
h
e
k
er
n
e
l
co
d
e
in
w
h
ich
w
e
a
p
p
lied
p
ip
elin
e
o
n
ev
er
y
lo
o
p
w
it
h
II
=1
,
co
n
s
id
er
ed
b
o
th
th
e
ca
s
es o
f
w
i
th
a
n
d
w
it
h
o
u
t p
ip
elin
i
n
g
t
h
e
lo
o
p
s
.
Fig
u
r
e
4
.
P
ip
elin
in
g
f
lo
w
f
o
r
th
r
ee
task
s
P
ip
elin
in
g
r
ed
u
ce
s
th
e
late
n
cy
o
f
th
e
co
m
p
u
ta
tio
n
b
y
allo
w
i
n
g
t
h
e
cr
ea
tio
n
o
f
n
e
w
lo
o
p
iter
atio
n
s
b
ef
o
r
e
th
e
co
m
p
letio
n
o
f
p
r
ev
io
u
s
o
n
es.
T
h
is
i
s
cr
u
cial
i
n
Sp
MV
w
h
er
e
th
e
d
ata
d
ep
en
d
en
cie
s
ar
e
o
f
te
n
s
p
ar
s
e,
an
d
o
v
er
lap
p
in
g
co
m
p
u
tatio
n
s
ca
n
s
ig
n
i
f
ica
n
tl
y
i
m
p
r
o
v
e
o
v
er
all
p
er
f
o
r
m
a
n
ce
.
I
t
ca
n
c
o
n
tr
ib
u
te
to
ac
h
iev
in
g
h
ig
h
er
clo
ck
f
r
eq
u
e
n
cies b
y
b
r
ea
k
i
n
g
d
o
w
n
t
h
e
co
m
p
u
tat
io
n
i
n
to
s
m
aller
,
m
o
r
e
m
an
a
g
ea
b
le
s
ta
g
es.
3
.
1
.
2
.
AXI
bu
rst
t
ra
ns
f
er
B
u
r
s
tin
g
i
s
an
o
p
ti
m
izatio
n
s
tr
ateg
y
ai
m
ed
at
s
m
ar
tl
y
co
n
s
o
lid
atin
g
m
e
m
o
r
y
ac
ce
s
s
es
t
o
DDR
i
n
o
r
d
er
to
r
ed
u
ce
laten
c
y
a
n
d
i
n
cr
ea
s
e
t
h
r
o
u
g
h
p
u
t
b
an
d
w
id
t
h
.
T
h
e
A
XI
4
p
r
o
to
co
l'
s
b
u
r
s
t
f
u
n
ctio
n
alit
y
b
o
o
s
ts
th
e
lo
ad
-
s
to
r
e
f
u
n
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o
p
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o
v
er
all
co
m
p
u
tati
o
n
p
er
f
o
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m
a
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ce
.
I
n
t
h
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h
ar
d
w
ar
e
w
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h
a
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f
o
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r
6
4
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it
AXI
h
ig
h
-
p
er
f
o
r
m
a
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ce
m
e
m
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p
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er
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a
m
m
i
n
g
lo
g
ic
to
D
DR
m
e
m
o
r
y
.
3
.
1
.
3
.
L
o
o
p
un
ro
llin
g
A
i
m
s
to
i
m
p
r
o
v
e
p
er
f
o
r
m
a
n
ce
b
y
r
ed
u
ci
n
g
lo
o
p
o
v
er
h
e
ad
an
d
in
cr
ea
s
i
n
g
p
ar
allelis
m
.
I
n
lo
o
p
u
n
r
o
lli
n
g
m
u
ltip
le
it
er
atio
n
s
o
f
th
e
s
a
m
e
lo
o
p
ar
e
p
er
f
o
r
m
e
d
w
i
th
i
n
a
s
in
g
le
iter
atio
n
.
Un
r
o
llin
g
f
ac
to
r
is
th
e
n
o
.
o
f
iter
atio
n
s
to
ex
ec
u
te
in
ea
ch
u
n
r
o
lled
iter
atio
n
.
T
h
e
l
o
o
p
ca
n
b
e
p
ar
tially
o
r
co
m
p
l
etel
y
u
n
r
o
lled
w
it
h
th
e
UNR
OL
L
p
r
ag
m
a.
Fu
ll
y
u
n
r
o
llin
g
m
a
k
e
s
a
d
u
p
licate
o
f
th
e
lo
o
p
b
o
d
y
f
o
r
ea
ch
iter
atio
n
,
en
ab
lin
g
co
n
cu
r
r
en
t
o
p
er
atio
n
o
f
t
h
e
wh
o
le
lo
o
p
.
On
th
e
o
th
er
h
an
d
,
p
ar
tial
u
n
r
o
lli
n
g
e
n
tail
s
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ett
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g
a
f
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to
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to
m
a
k
e
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co
p
ies
o
f
th
e
lo
o
p
b
o
d
y
an
d
d
ec
r
ea
s
e
th
e
lo
o
p
iter
atio
n
s
ap
p
r
o
p
r
iately
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T
h
e
li
m
it
s
o
f
a
lo
o
p
m
u
s
t
b
e
k
n
o
w
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p
ile
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m
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in
o
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ll
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o
o
p
u
n
r
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g
n
ee
d
s
m
o
r
e
co
m
p
u
tatio
n
a
n
d
s
to
r
ag
e
r
eso
u
r
ce
s
h
en
ce
it
i
s
a
tr
ad
e
-
o
f
f
b
et
w
ee
n
p
er
f
o
r
m
a
n
ce
a
n
d
r
eso
u
r
ce
s
.
I
n
o
u
r
e
x
p
er
i
m
e
n
ts
w
e
i
m
p
l
e
m
en
ted
th
e
k
er
n
el
co
d
e
w
i
th
u
n
r
o
ll
f
ac
to
r
o
f
2
an
d
4
.
Th
e
m
o
s
t
e
f
f
ec
tiv
e
u
n
r
o
ll
f
ac
t
o
r
f
o
r
lo
o
p
u
n
r
o
llin
g
i
n
Sp
MV
u
s
i
n
g
Vit
is
H
L
S
d
ep
en
d
s
o
n
t
h
e
u
n
iq
u
e
ch
ar
ac
ter
is
tic
s
o
f
t
h
e
tar
g
eted
FP
GA
ar
c
h
itect
u
r
e
an
d
t
h
e
s
p
ec
if
ic
at
tr
ib
u
tes
o
f
t
h
e
Sp
MV
p
r
o
b
lem
b
ei
n
g
ad
d
r
ess
ed
.
C
o
n
d
u
cti
n
g
e
x
p
er
i
m
en
ts
w
i
th
v
ar
io
u
s
u
n
r
o
ll
f
a
c
t
o
r
s
an
d
lev
er
ag
in
g
p
er
f
o
r
m
a
n
ce
p
r
o
f
ilin
g
th
r
o
u
g
h
Vitis
H
L
S
r
ep
o
r
ts
is
cr
u
cia
l
f
o
r
id
en
tify
i
n
g
th
e
o
p
ti
m
a
l
co
n
f
i
g
u
r
atio
n
t
h
at
m
a
x
i
m
i
ze
s
co
m
p
u
tatio
n
al
ef
f
icien
c
y
.
T
h
is
iter
ativ
e
p
r
o
c
ess
en
ab
les
f
in
e
-
t
u
n
in
g
an
d
cu
s
to
m
izat
io
n
,
en
s
u
r
in
g
th
e
Sp
MV
k
er
n
el
is
tai
lo
r
ed
f
o
r
o
p
tim
a
l p
er
f
o
r
m
a
n
ce
o
n
th
e
s
p
ec
if
ic
FP
G
A
p
latf
o
r
m
an
d
p
r
o
b
lem
d
o
m
ai
n
.
3
.
1
.
4
.
Arr
a
y
pa
r
t
it
io
nin
g
I
t
in
v
o
lv
e
s
b
r
ea
k
i
n
g
d
o
w
n
a
s
in
g
le
ar
r
a
y
i
n
to
s
m
aller
,
i
n
d
ep
en
d
en
t
p
ar
ts
o
r
s
u
b
s
et
s
s
u
c
h
t
h
at
ea
c
h
p
ar
t
ca
n
b
e
im
p
le
m
e
n
ted
as
a
B
R
A
M,
s
o
th
at
ca
n
ac
c
ess
th
e
m
at
th
e
s
a
m
e
ti
m
e.
A
g
g
r
eg
ate
t
y
p
es
ca
n
b
e
d
iv
id
ed
in
to
s
m
aller
m
e
m
o
r
ie
s
o
r
in
to
th
eir
co
m
p
o
n
e
n
t
p
ar
ts
,
w
h
ic
h
in
cr
ea
s
e
s
th
e
m
e
m
o
r
y
b
an
d
w
id
t
h
an
d
in
cr
ea
s
es
t
h
e
n
u
m
b
er
o
f
m
e
m
o
r
y
ac
ce
s
s
e
s
o
n
ea
ch
c
y
cle.
B
lo
ck
,
cy
c
lic,
an
d
co
m
p
lete
ar
r
a
y
p
ar
titi
o
n
in
g
ar
e
th
e
th
r
ee
t
y
p
e
s
av
ailab
le.
T
h
e
o
p
tio
n
s
lik
e
t
y
p
e
a
n
d
d
i
m
f
o
r
th
e
m
e
m
o
r
y
p
ar
titi
o
n
p
r
ag
m
a
s
p
ec
if
y
t
h
e
p
ar
titi
o
n
t
y
p
e
an
d
d
i
m
en
s
io
n
,
r
esp
ec
ti
v
el
y
.
L
ar
g
e
ar
r
a
y
s
ize
w
ill
b
e
s
y
n
th
e
s
ized
in
to
B
R
A
Ms
i
n
FP
GA
.
Her
e
w
e
d
ec
lar
ed
th
e
v
ar
iab
les
w
ith
ar
r
a
y
p
ar
titi
o
n
i
n
c
y
clic
f
ac
to
r
w
i
th
d
i
m
=1
.
Usi
n
g
#
p
r
ag
m
a
H
L
S
A
R
R
A
Y
_
P
A
R
T
I
T
I
ON
v
ar
iab
le=
x
co
m
p
lete
d
i
m
=1
p
ar
titi
o
n
s
th
e
i
n
p
u
t
m
a
tr
ix
x
alo
n
g
it
s
r
o
w
s
(
s
p
ec
if
ied
b
y
d
i
m
=1
)
.
C
o
m
p
lete
p
ar
titi
o
n
in
g
is
e
m
p
lo
y
ed
,
in
d
icat
in
g
t
h
at
ea
ch
p
ar
tit
io
n
co
m
p
r
is
e
s
a
n
e
n
tire
s
et
o
f
r
o
w
s
f
r
o
m
t
h
e
m
atr
i
x
.
T
h
is
o
p
t
i
m
izatio
n
ai
m
s
to
b
o
o
s
t
p
ar
allelis
m
b
y
en
ab
li
n
g
co
n
cu
r
r
en
t
p
r
o
ce
s
s
in
g
o
f
m
u
l
tip
le
r
o
w
s
w
i
th
i
n
th
e
m
a
tr
ix
.
W
ith
in
th
e
co
m
p
u
tatio
n
lo
o
p
,
p
a
r
tial
s
u
m
s
ar
e
ca
lcu
lated
f
o
r
ea
ch
r
o
w
b
y
le
v
er
ag
i
n
g
th
e
p
ar
titi
o
n
ed
m
atr
i
x
an
d
t
h
e
in
p
u
t
v
ec
to
r
.
T
h
is
ap
p
r
o
ac
h
en
h
an
ce
s
p
ar
allel
ex
ec
u
tio
n
,
t
h
er
eb
y
o
p
ti
m
izi
n
g
m
e
m
o
r
y
ac
ce
s
s
p
atter
n
s
a
n
d
i
m
p
r
o
v
in
g
t
h
e
o
v
er
all
p
er
f
o
r
m
a
n
ce
o
f
Sp
MV
k
er
n
el
s
o
n
FP
G
A
p
latf
o
r
m
s
.
3
.
1
.
5
.
B
ind
s
t
o
ra
g
e
I
t
lin
k
s
a
co
d
e
v
ar
iab
le
to
a
ce
r
tain
m
e
m
o
r
y
t
y
p
e
in
th
e
R
T
L
.
T
h
e
m
e
m
o
r
y
t
y
p
e
a
s
s
o
ciate
d
w
it
h
th
e
ar
r
ay
i
n
f
lu
e
n
ce
s
th
e
n
u
m
b
er
an
d
k
i
n
d
o
f
p
o
r
ts
r
eq
u
ir
ed
in
th
e
R
T
L
,
m
a
k
i
n
g
th
i
s
ele
m
e
n
t
i
m
p
o
r
ta
n
t
f
o
r
th
e
ar
r
ay
s
o
n
th
e
to
p
-
lev
el
f
u
n
c
t
io
n
in
ter
f
ac
e.
T
h
ese
v
ar
iab
le
s
m
u
s
t
u
s
e
t
h
e
s
to
r
ag
e_
t
y
p
e
an
d
s
to
r
ag
e_
i
m
p
l
o
p
tio
n
s
o
f
th
e
B
I
ND_
ST
OR
A
GE
p
r
ag
m
a
to
s
p
ec
if
y
th
e
m
e
m
o
r
y
t
y
p
e
an
d
i
m
p
le
m
e
n
t
atio
n
.
T
h
e
laten
c
y
o
p
tio
n
f
o
r
B
R
A
Ms
o
n
th
e
i
n
ter
f
ac
e
en
ab
les
th
e
m
e
m
o
r
y
t
o
b
e
im
p
le
m
e
n
ted
u
s
i
n
g
m
o
r
e
p
ip
elin
ed
s
tag
es.
T
im
i
n
g
i
s
s
u
es t
h
at
ar
is
e
d
u
r
i
n
g
R
T
L
s
y
n
th
e
s
is
ca
n
b
e
ef
f
ec
ti
v
el
y
r
eso
l
v
ed
b
y
ad
d
in
g
e
x
t
r
a
p
ip
elin
e
s
ta
g
es.
3
.
2
.
Sp
a
rse
m
a
t
rix
-
v
ec
t
o
r
m
ultiplica
t
io
n
-
k
er
nel
A
k
er
n
el
t
y
p
ica
ll
y
r
e
f
er
s
to
a
co
m
p
u
tatio
n
al
r
o
u
tin
e
o
r
alg
o
r
ith
m
t
h
at
is
s
p
ec
ialized
f
o
r
a
p
ar
ticu
lar
o
p
er
atio
n
.
Sp
MV
k
er
n
el
is
a
s
p
ec
if
ic
i
m
p
le
m
e
n
tat
io
n
o
r
r
o
u
tin
e
d
esig
n
ed
to
ef
f
ici
en
tl
y
p
er
f
o
r
m
t
h
e
m
u
ltip
licatio
n
o
f
a
s
p
ar
s
e
m
atr
i
x
w
it
h
a
d
en
s
e
v
ec
to
r
.
Min
i
m
ize
d
y
n
a
m
ic
m
e
m
o
r
y
al
lo
ca
tio
n
s
a
n
d
d
ea
llo
ca
tio
n
s
d
u
r
i
n
g
t
h
e
co
m
p
u
tatio
n
to
av
o
id
u
n
n
ec
e
s
s
ar
y
o
v
er
h
ea
d
.
A
cc
ess
p
atter
n
s
s
h
o
u
ld
b
e
d
esi
g
n
ed
to
m
i
n
i
m
ize
ca
ch
e
m
is
s
es d
u
r
in
g
th
e
m
u
ltip
lica
tio
n
a
n
d
ac
cu
m
u
latio
n
s
tep
s
.
T
h
e
s
o
u
r
ce
co
d
e
f
o
r
th
e
Sp
M
V
k
er
n
el
is
g
iv
e
n
in
Fi
g
u
r
e
5
w
h
ic
h
is
r
ef
er
en
ce
d
f
r
o
m
[
8
]
.
T
h
e
p
s
eu
d
o
co
d
e
co
n
tain
s
f
o
u
r
f
o
r
lo
o
p
s
,
in
w
h
ic
h
d
ata
f
etc
h
in
g
f
r
o
m
th
e
s
p
ar
s
e
m
atr
i
x
is
h
ap
p
en
e
d
f
ir
s
t,
th
e
n
it
w
ill
u
n
co
m
p
r
e
s
s
t
h
e
C
S
R
f
o
r
m
at
m
atr
i
x
b
y
f
etc
h
i
n
g
ea
ch
d
ata
v
alu
e
f
r
o
m
ea
c
h
r
o
w
o
f
th
e
m
at
r
ix
.
Af
ter
g
e
tti
n
g
all
th
e
n
n
z’
s
th
e
n
m
u
ltip
licatio
n
w
it
h
th
e
co
r
r
esp
o
n
d
in
g
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m
e
n
t
in
th
e
d
en
s
e
v
ec
to
r
an
d
ac
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m
u
late
t
h
e
r
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l
t
f
r
o
m
th
e
m
u
l
tip
licatio
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s
tep
i
n
to
th
e
co
r
r
esp
o
n
d
in
g
en
tr
y
o
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th
e
o
u
tp
u
t
v
ec
to
r
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R
ep
ea
t
th
e
m
u
ltip
lica
tio
n
an
d
ac
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m
u
lat
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n
s
tep
s
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o
r
all
n
o
n
-
ze
r
o
ele
m
e
n
t
s
in
th
e
s
p
ar
s
e
m
a
tr
ix
.
T
h
e
last
lo
o
p
is
f
o
r
th
e
tr
an
s
f
er
o
f
th
e
o
u
tp
u
t d
ata
co
n
tai
n
i
n
g
t
h
e
r
es
u
lt o
f
t
h
e
Sp
MV
o
p
er
atio
n
to
th
e
o
u
tp
u
t te
r
m
i
n
al.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
R
ec
o
n
f
i
g
u
r
ab
le
&
E
m
b
ed
d
ed
Sy
s
t
I
SS
N:
2089
-
4864
A
n
a
p
p
r
o
xima
te
mo
d
el
S
p
MV
o
n
F
P
GA
a
s
s
is
tin
g
HLS
o
p
tim
iz
a
tio
n
s
fo
r
lo
w
p
o
w
er
… (
A
ld
en
C
.
S
h
a
ji
)
381
Fig
u
r
e
5
.
Sp
MV
ke
r
n
el
p
s
e
u
d
o
co
d
e
w
it
h
p
ip
elin
i
n
g
3
.
3
.
Appro
x
i
m
a
t
e
s
pa
rse
m
a
t
rix
-
v
ec
t
o
r
m
ultip
lica
t
io
n
a
lg
o
rit
h
m
As
f
ar
as
w
e
ar
e
a
w
ar
e,
th
e
r
e
is
cu
r
r
en
tl
y
n
o
ex
i
s
ti
n
g
r
esear
ch
th
a
t
f
o
cu
s
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o
n
o
p
ti
m
izi
n
g
t
h
e
co
m
p
u
tatio
n
o
f
ap
p
r
o
x
i
m
ate
m
o
d
el
Sp
MV
o
n
FP
GA
.
Desp
ite
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r
ev
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s
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t
u
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ies
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ess
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g
o
p
ti
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izi
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n
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es
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G
A
f
o
r
d
en
s
e
m
atr
i
x
m
u
ltip
licatio
n
s
a
n
d
d
ee
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lear
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g
,
t
h
er
e
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ea
r
s
to
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e
a
g
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in
t
h
e
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atu
r
e
r
eg
ar
d
in
g
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e
s
p
ec
if
i
c
o
p
tim
izat
io
n
o
f
ap
p
r
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x
i
m
ate
m
o
d
el
Sp
MV
o
n
th
ese
h
ar
d
w
ar
e
p
latf
o
r
m
s
.
T
h
e
co
m
p
u
tatio
n
al
p
er
f
o
r
m
a
n
ce
o
f
C
P
Us
in
t
h
is
ta
s
k
i
s
in
h
er
en
t
l
y
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m
ited
b
y
t
h
eir
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estricte
d
m
e
m
o
r
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b
an
d
w
id
th
an
d
th
e
d
if
f
icu
l
t
y
o
f
e
f
f
ic
ien
t
l
y
e
x
ec
u
tin
g
f
r
eq
u
en
t
r
an
d
o
m
ac
ce
s
s
es.
T
h
is
li
m
itatio
n
ar
is
e
s
f
r
o
m
th
e
f
ac
t
th
at
th
er
e
ar
e
n
o
ass
u
r
an
ce
s
th
a
t
t
h
e
r
e
q
u
ir
ed
v
al
u
es
h
av
e
n
o
t
b
ee
n
tak
e
n
f
r
o
m
t
h
e
ca
ch
e,
i
m
p
ed
in
g
t
h
e
ab
ilit
y
to
ac
ce
s
s
d
ata
q
u
ick
l
y
a
n
d
r
eliab
ly
.
T
h
e
m
o
tiv
at
io
n
b
eh
in
d
ap
p
r
o
x
i
m
ate
Sp
MV
alg
o
r
it
h
m
s
i
s
t
o
ac
ce
ler
ate
th
e
co
m
p
u
tatio
n
o
f
m
a
tr
ix
-
v
ec
to
r
m
u
ltip
licat
io
n
i
n
s
ce
n
ar
io
s
w
h
er
e
an
e
x
ac
t
s
o
lu
t
io
n
is
n
o
t
s
tr
ictl
y
n
ec
e
s
s
ar
y
.
T
h
is
is
co
m
m
o
n
i
n
m
ac
h
in
e
lear
n
in
g
,
s
i
g
n
al
p
r
o
ce
s
s
i
n
g
,
a
n
d
o
th
er
ap
p
licatio
n
s
w
h
er
e
an
ap
p
r
o
x
i
m
ate
r
es
u
lt
is
ac
ce
p
tab
le.
T
h
e
k
e
y
tr
ad
e
-
o
f
f
in
ap
p
r
o
x
i
m
ate
Sp
MV
alg
o
r
ith
m
s
is
b
et
w
e
en
co
m
p
u
tatio
n
al
s
p
ee
d
an
d
s
o
lu
tio
n
ac
cu
r
ac
y
.
A
p
p
r
o
x
i
m
ate
Sp
MV
m
o
d
el
s
ca
n
b
e
d
esig
n
ed
to
s
ca
le
b
ett
er
w
it
h
i
n
cr
ea
s
i
n
g
m
atr
i
x
s
ize
s
.
T
h
is
is
esp
ec
iall
y
b
en
ef
icia
l
w
h
e
n
d
ea
lin
g
w
it
h
l
ar
g
e
d
atasets
i
n
s
cie
n
ti
f
ic
s
i
m
u
latio
n
s
o
r
m
ac
h
i
n
e
lear
n
i
n
g
ap
p
licatio
n
s
.
I
n
th
i
s
s
ec
tio
n
,
w
e
s
u
g
g
e
s
te
d
a
u
n
iq
u
e
ap
p
r
o
x
i
m
a
te
m
o
d
el
ap
p
r
o
ac
h
f
o
r
Sp
MV
,
to
s
h
o
r
ten
t
h
e
ex
ec
u
t
io
n
ti
m
e.
E
f
f
icien
c
y
in
Sp
MV
is
o
f
ten
ac
h
ie
v
ed
th
r
o
u
g
h
al
g
o
r
ith
m
s
an
d
d
ata
s
tr
u
ct
u
r
es
th
at
les
s
en
t
h
e
n
u
m
b
er
o
f
ar
it
h
m
etic
o
p
er
atio
n
s
a
n
d
m
e
m
o
r
y
ac
ce
s
s
b
y
tak
in
g
ad
v
a
n
ta
g
e
o
f
th
e
m
atr
i
x
'
s
s
p
ar
s
it
y
.
W
e
h
a
v
e
t
ak
en
th
e
s
p
ar
s
e
m
atr
i
x
S
o
as
t
h
e
in
p
u
t
a
n
d
o
b
tain
th
e
ap
p
r
o
x
i
m
ate
C
SR
f
o
r
m
at
m
atr
ice
s
S
t
an
d
S
v
as
o
u
tp
u
ts
.
I
m
p
le
m
e
n
tatio
n
r
esu
lts
ar
e
s
h
o
w
n
in
s
ec
tio
n
5
.
T
h
is
alg
o
r
ith
m
co
n
tai
n
s
t
w
o
t
y
p
es o
f
ap
p
r
o
x
i
m
atio
n
:
AX
-
1
:
h
er
e
t
h
e
ap
p
r
o
x
i
m
at
io
n
o
f
Sp
MV
is
b
ased
o
n
t
h
r
es
h
o
ld
in
g
th
e
r
o
w
co
u
n
t
o
f
th
e
m
a
tr
ix
.
O
n
l
y
tak
i
n
g
t
h
e
d
ata
v
alu
es
w
h
ic
h
ar
e
h
ig
h
er
th
a
n
th
e
th
r
es
h
o
ld
an
d
s
to
r
es
it
in
S
t
.
T
h
r
esh
o
ld
is
ca
lcu
lated
as
th
e
m
ea
n
o
f
m
a
x
an
d
m
i
n
r
o
w
co
u
n
t
v
al
u
es
o
f
th
e
s
p
ar
s
e
m
atr
i
x
.
I
n
A
l
g
o
r
ith
m
1
,
s
tep
4
–
1
1
co
r
r
esp
o
n
d
s
to
th
is
ap
p
r
o
x
im
a
tio
n
.
AX
-
2
:
h
er
e
t
h
e
ap
p
r
o
x
i
m
atio
n
is
b
ased
o
n
t
h
e
ac
c
u
r
ac
y
o
f
t
h
e
d
ata
v
alu
e.
A
f
ter
s
o
r
tin
g
t
h
e
i
n
p
u
t
s
p
ar
s
e
m
atr
ix
b
ased
o
n
d
ata
v
alu
e,
it
is
class
if
ied
i
n
to
p
o
s
itiv
e
m
atr
i
x
(
S
p
)
an
d
n
eg
ati
v
e
m
atr
ices
(
S
n
)
.
T
h
en
tak
en
o
n
l
y
t
h
e
h
ig
h
ac
cu
r
ac
y
v
alu
e
s
o
f
7
0
%
o
f
to
tal
N
N
Z
’
s
.
B
o
th
m
a
tr
ix
e
s
ar
e
j
o
in
ed
to
g
e
th
er
in
S
v
an
d
ag
ai
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4864
I
n
t J
R
ec
o
n
f
i
g
u
r
ab
le
&
E
m
b
ed
d
ed
Sy
s
t
,
Vo
l.
14
,
No
.
2
,
J
u
l
y
20
25
:
375
-
3
8
7
382
d
o
th
e
s
o
r
tin
g
b
ased
o
n
th
e
r
o
w
v
alu
e
s
.
I
t
is
th
e
n
co
n
v
er
ted
in
to
th
e
C
SR
f
o
r
m
at.
I
n
A
l
g
o
r
ith
m
1
,
s
tep
1
2
–
1
9
co
r
r
esp
o
n
d
s
to
th
is
ap
p
r
o
x
i
m
a
tio
n
.
A
l
g
o
r
ith
m
1
.
A
p
p
r
o
x
i
m
ate
Sp
MV
alg
o
r
ith
m
I
n
p
u
t:
T
h
e
o
r
ig
in
al
s
p
ar
s
e
m
a
tr
ix
,
S
o
;
Ou
tp
u
t:
T
h
e
tar
g
et
ap
p
r
o
x
im
ate
C
S
R
f
o
r
m
at,
S
t
an
d
S
v
;
1
: O
b
tain
th
e
m
atr
i
x
p
ar
a
m
ete
r
s
f
r
o
m
S
o
;
2
: Co
u
n
t t
h
e
n
o
.
o
f
N
N
Z’
s
i
n
ea
ch
r
o
w
a
n
d
s
to
r
e
in
r
o
w
_
co
u
n
t
;
3
: I
n
itial
ize
th
e
m
atr
i
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