Kongurierbare
Hardwareb eshleuniger für
selbst-organisierende Karten
Zur Erlangung des akademishen Grades
DOKTOR-INGENIEUR (Dr.-Ing.)
der Fakultät für Elektrotehnik, Informatik und Mathematik,
Institut für Elektrotehnik und Informationstehnik
der Universität Paderb orn
von
Dipl.-Ing. Christopher Pohl
aus Verl
Referent: Prof. Dr.-Ing. Ulrih Rükert
Koreferentin: Prof. Dr. Erzséb et Merényi
Paderb orn, den 26. April 2010
Tag der mündlihen Prüfung: 6. Dezemb er 2010
Diss. EIM-E/269
Für Anne, Mathis und Line, und alle, die ih jetzt no h niht sehen kann.
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Referenzvektoren
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int 4 int 8 int 12 int 16 int 20 int 24 int 28 float double
−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Klassifikationsfehler EK
Wortbreite [Bit]
¯
EK
¯
EK±σ(EK)
¯
EK,∅Mul.
¯
EK±σ(EK),∅Mul.
¯
EK(˜
Mref )
|¯
EK−¯
EK(Mref )|=0.01
|¯
EK−¯
EK(Mref )|=0.05
2 3
0 5 10 15 20 25 30 35
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Wortbreite [Bit]
Anteil Versuche mit einer Abweichung zur Referenz von mehr als 5%
+ 0 $
|EK−¯
EK,ref |≥0.05
, 52
O /14 # *.
)
FG 31 FG !A 8 '
($
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5%
# @4!.
> ! 1A ' ?A
< 1 #
8A .; /1 ! 94
51. 11 A ; #
/1 F8 J"(KG < ! 1 <;
44 @4! > !8 , ?O !
1, 1/! ! .1
5! !8 !8 = A $#
& = ! 8 #
4A 8 1 1 :
1, $ 1 /1 21
A # /1#4 1
8A /1 &/ 3
.8 31! 21 A
/1 H8 =
! 8 ; 8 8 <
! A 2 !
4;A 11 /! , 8;
)!
0 #8 *. 4 %4
FG 4 & 1 -
1 4 ,' > .!.
/!4A 1 >
# 7 4 @4!8
¯
EQ(˜
Mref )
A
> # " 3 F31G .1 # 4
> ! ? >
< 8 &1 @4!A 8 9
8 4A $# ; @4!.
#& 7 5! ! /14 7.
.! !8
,' < , &
.!
FG & A >
1 I %4 ! 8 A
> # 3 1, 8 # ;
5%
4
8
)
int 4 int 8 int 12 int 16 int 20 int 24 int 28 float double
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Quantisierungsfehler EQ
Wortbreite [Bit]
¯
EQ
¯
EQ±σ(EQ)
¯
EQ,∅Mul.
¯
EQ±σ(EQ),∅Mul.
¯
EQ(˜
Mref )
¯
EQ=(1±0.01) ·¯
EQ(Mref )
¯
EQ=(1±0.05) ·¯
EQ(Mref )
2 3
0 5 10 15 20 25 30 35
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Wortbreite [Bit]
Anteil Versuche mit einer Abweichung zur Referenz von mehr als 5%
|EQ/¯
EQ,ref −1|≥0.05
, 52
O %4 # *.
)
#! 4!
3 . / < FG !
& 8 4; /14 A
4; > ,' " 3 1 /1 &
; @4!. 5! ! 1A
7. .! .11 . /
!A ! 1 ! - > 4; . /
< F
ET≈1
G
FG !A 8 " 2! >
,' ( 3 < #
5%
; @4!.
48
A 3
>A ! 5&!1 4; . /
% >& %4
> !A 1 . / <
?& ! 1 5 4; !
1# L O @4!#1
> A 4 #1 4
! ! 1# L !;1
. <A ,' > #
,' @4!#1 4 1,A 8
;1 .4 ! 1# 4
A .1 #1 @4!#1
7 1 @A # @4!#1
! #1 & 3 A
#1A >A !4
4 ! & L 8 ! A 3
. / < ! ? #
> 14 4; 3 %&
: . &! ! 1A
&! 4; - F
=1
G 8A -
@! 8 4;
51 4; <1*. > ,' 3
F ) FGG ! 1 > # 8
H=0.95
4
7 3 > 4; <1*
. #
H(˜
M)
# .A
Δ(H)≤0.01
<; 7. .! >A
))
int 4 int 8 int 12 int 16 int 20 int 24 int 28 float double
−0.2
0
0.2
0.4
0.6
0.8
1
1.2
Topografischer Fehler ET
Wortbreite [Bit]
¯
ET
¯
ET±σ(ET)
¯
ET,∅Mul.
¯
ET±σ(ET),∅Mul.
¯
ET(˜
Mref )
|¯
ET−¯
ET(Mref )|=0.01
|¯
ET−¯
ET(Mref )|=0.05
2 3
0 5 10 15 20 25 30 35
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Wortbreite [Bit]
Anteil Versuche mit einer Abweichung zur Referenz von mehr als 5%
|ET−¯
ET,ref|≥0.05
, 52
O . / < # *.
)
int 4 int 8 int 12 int 16 int 20 int 24 int 28 float double
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Entropie H
Wortbreite [Bit]
¯
H
¯
H±σ(H)
¯
H,∅Mul.
¯
H±σ(H),∅Mul.
¯
H(˜
Mref )
¯
H=(1±0.01) ·¯
Href
¯
H=(1±0.05) ·¯
Href
2 3
0 5 10 15 20 25 30 35
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Wortbreite [Bit]
Anteil Versuche mit einer Abweichung zur Referenz von mehr als 5%
|H−¯
Href |≥0.05
, 52
)O . # *.
)6
@4! A 8 #
Δ(H)≥0.2
4P !&!
4 .A ' >A '
! 4A !#& ; $ .1 ,
) FG!A 8 # @4
!. > ,' + 3 ! #
5%
/
&
int 4 int 8 int 12 int 16 int 20 int 24 int 28 float double
−0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Größe der Cluster normiert auf |M|
Wortbreite [Bit]
|¯
C1|
|¯
C1|±σ|C1|
|¯
C1|,∅Mul.
|¯
C1|±σ|C1|,∅Mul.
|¯
C2|
|¯
C2|±σ|C2|
|¯
C2|,∅Mul.
|¯
C2|±σ|C2|,∅Mul.
2 3
O =,' # *.
3 ,'-. 1 F JKG
4; 4 / , ,'-.
& A =
!
X
! 8A 1, ! %/! #
&8 5,' 4 #8
8 # ! 5! L 4
|¯
Ci|
5,' =
i
<1. .! A
|¯
Ci|∅Mul.
.
<1. .! :&! 8 H8
8 ; !
)
5&! ! 1A =,' 1
A 8 4 -! 1# L !;1!4; 71#L
LA 1 #1 ! !
P / 8, 5! !8 = <;
7. .! 8 4 A 3! 4
@4!. H8 8 =
,' & ! ;
1 > & ,'-. O 3
! > # 3 1 5,' 1 = 5,
' ,' = A 8 4 #
ρ→1
4; 1
> 8 ? 1 5! # 3 #&
8 5,' & A E1# 8
1 3 ! >& &!
& !A A 8
.& E1 8 8
<; 7. .! 4!A
5,' 1 # @4! 8A
& =,' 1 E 4;
7.
ρ<0
A 8
) * !+
! 8 &! ! ! &
A ! 1&A E1 1
! & ? 1 >A !8 3.
#A 1 ! ?1 5,'#& @
@4!.A 8
!
%&
7 # 8 4 3 # 31
&! 4; ! * ! # A
3 7. 14 4 3 !
%&1 4 4 $ &/ #!/
% . / <
A 7. ! # !
# 3.A 1 <' ?& &!
8.; ! 4!A 8 !3 . /
< %4A 7 Q! 4;
# 7. ' 4 8A 8
#8 ' #P 1 ' 1
.! #4 , ' 8 /
4 &! 8
)(
:&! ! A 1 ; !
4 98.A @4!.
%&1 4 < A 4
4 8 1 :8 4; &! >
# 6 3 1 8 ,'
5%
4! 4 1
8 &! 1 4 ; 8
8 # 9 1 !
A A ..-
p(X)
% #
X
#& @ 1
p(X)
A 1 ; 0 % E 8
1 ? 9*. A &! 3A 8
,# "
A &
p(X)
!A 4; 3
984 -. ?
8 4
" # %&
7 # ! A 1 .& %
&1 4; Q/! !; ?
!8 !8 7. ! 8 1 8
&/ ; ! ' !4
# 8 ' 8 < /
4 > 8
'
Q
4 11 > 8 /
%&1A
Q(EK,E
T,E
Q,H,|C1|, ..., |Cu|))
A8
u=|C|
! =
|Ci|
5,' /O
Q=(1+ ¯
EK,ref −EK)γK(1 + ET,ref −ET)γT(1 + ¯
Href −H)γH
·EQ,ref
EQγQ⎛
⎝
|C|
i=1 1−
|Ci,ref |−|Ci|
|M|⎞
⎠
γC
|C|
FG
Q
1
n+4
@
%&1A ! ; -.
γK
A
γT
A
γQ
A
γH
γC
8 >& ' 4 ,'
-. 1 1 A 1 & ,'
-. 1 ; & =,'
8 & =,' !8
=
u
2! 2 1 A 8 1
41
u−1=|C|−1
4; ; > 8 1A
½
6 $$ '# 7 2* 2* 8( $
)+
8 @ > 4;
ρ
#A 58
<1 411 8 8
1
Q
1 ' !8 !8 7. >
!8 9 8 !8
7. @4! !A 8 @4!
7.
$%&
2&! .& 8 74 1,
> #
Q
3 8O
•Q1
O 7 < 8 ! 8 7.
%& @4! 4
•Q≈1
O %& ! 8 7.
@4! ?1 A
7. A ! <1 ?
& 1, 1 ; 58
<1 8
•Q1
O<; < ; %& ! 8 7.
@4!A 8 58 !
58
γ
1, > 7 < 8
58 #
γK
! 4
3 /14 <
γK=2
7 4
8 / 1 4
# 7.
8
& #! ( !5.6357
7 6 8 4; 1
Q
&! 4 :&! 8 ! @4!8
? #
±5%
!A 3. 4;
%&#&
<; H ! 1 >A
$ 1 # @4!. 8 5
! # 4; &! !8 ( 3
1 > # > 4;
Q
3
# -
ΔQ=0,05
A 1 !
4 & # .; 1 # @4!
98. 1 4; H ! 1
5! 4 8A 1 :8 %& !8
1 8 1
"
0 5 10 15 20 25 30
0
0.2
0.4
0.6
0.8
1
1.2
Wortbreite [Bit]
Q
abalone, w krit=11
breast_cancer, w krit=11
balance_scale, w krit=8
blood_donator, wkrit=12
echocardiogram, w krit=11
glass, w krit=11
hill_valley, w krit=18
parkinson, w krit=10
6O 1
Q
4;
!A 8. !/ .
0 4 $ A
. # ! A 1 > -A
& #
Q
! 3
. 7 1 > 1 1
%& ! P > 4;
Q
# 1
& # >
<; . 98. !8 ; !
! 4; H ! 8A 8
> 4; $# , 8A !8 $# 4
98 # 4; 8 1 :8 4
!A ,' > 4
5! 1 %&8 A ; 0;
8A 8 ,' >
@ 7.
& %
7 $ &/ ! /A %&#A
8. !/ . #4 8A
0 5 10 15 20 25 30
0
0.2
0.4
0.6
0.8
1
1.2
Wortbreite [Bit]
Q
abalone, w krit=12
breast_cancer, w krit=11
balance_scale, w krit=8
blood_donator, wkrit=12
echocardiogram, w krit=11
glass, w krit=10
hill_valley, w krit=18
parkinson, w krit=10
Q
# +2 6 #
0 5 10 15 20 25 30
0
0.2
0.4
0.6
0.8
1
1.2
Wortbreite [Bit]
Q
abalone, w krit=10
breast_cancer, w krit=10
balance_scale, w krit=7
blood_donator, wkrit=11
echocardiogram, w krit=14
glass, w krit=9
hill_valley, w krit=17
parkinson, w krit=10
Q
125%
"9: ; )#
O $. 4;
. $. F $#A 5,' A
4 #
α
G 8 1, 7
81 < 8
FG FG ! 81 FG ..
$ FG ,'
25%
4
A , ! # $ ! Q
# $ 4;A 8 *.
4 # % . / < F G
! 8 O : /A
0 5 10 15 20 25 30
0
0.2
0.4
0.6
0.8
1
1.2
Wortbreite [Bit]
Q
abalone, w krit=11
breast_cancer, w krit=9
balance_scale, w krit=9
blood_donator, wkrit=10
echocardiogram, w krit=8
glass, w krit=9
hill_valley, w krit=11
parkinson, w krit=9
(O 1
Q
4; =
% . / < 8 $
A E1 4; 41 7.
' ! 8 > @4! 7.
$%
2&!
#8A 1 ? ! !8
7. 4 $ 5' ! 8A
& $ 1 E1 4 81
8. !/ . A 4
1# : / ! $ !
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! 8A , $ 8;
5! ! FGA ,'
81 8. !/ . 1A 8
8 A , $ 1 A8 3
#,' !8 #& 8
& #! ( 8#5.6357
<; = 8 -. 8
4; 8 !
< 1
Q
1 7 ( ! 8 ?
! 7.O ! 1
>
wkrit
> 4;
Q
1 1A
> #
wkrit
8
4; A E& A @4
wkrit
4;
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? > 4;
Q
1 >
O 8& > 4; !
-%
'
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= @4! 7 ? !8
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wkrit
& 'A 4;
=
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A 7. #
& %
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β
γ
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α
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@ . 8
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8. !/ . 1, ! A
3 $# 4
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$ / +& ,- &
:&! ! . %
.1 8
98 &/ 8 .
#A < 1 8
)
0 5 10 15 20 25 30
0
0.2
0.4
0.6
0.8
1
1.2
Wortbreite [Bit]
Q
abalone, w krit=11
breast_cancer, w krit=9
balance_scale, w krit=9
blood_donator, wkrit=10
echocardiogram, w krit=7
glass, w krit=9
hill_valley, w krit=13
parkinson, w krit=8
Q
# +2 6 #
0 5 10 15 20 25 30
0
0.2
0.4
0.6
0.8
1
1.2
Wortbreite [Bit]
Q
abalone, w krit=10
breast_cancer, w krit=8
balance_scale, w krit=8
blood_donator, wkrit=9
echocardiogram, w krit=6
glass, w krit=8
hill_valley, w krit=9
parkinson, w krit=8
Q
125%
"9:
+O $. 4; =
•
(
p1
3(1
3 !8
@4! #1 Q1 L
8 -
wsum,p2=2w+log2(dm)
3
> ,A U 4 H < ! # 3
L F
p1
G8
wsum,p1=w+log2(dm)
3 ,
A
w
3 8 # Q &1
# =.<& > F - 14Q!G 8
8 L .
100 ·wsum,p1/wsum,p2
2! <& . L .
•
91
!4&
8 . $ ! 1 #A
F )G ! 8 #
<; .1 7.A .
8A :E ,
8 4 A 8 = 8O
!4& 8 1 1 . !E4 E
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8 1A 1 <
H $ ! =A ;
9.. 8 8 98
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4 8 # $# 4;
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1 . . 3 $#
8 @4 4 4A 8; !
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4; &! ' . # &
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8
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L441 ! #8O 3
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A 4 1
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r
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r+1
<
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r2+1
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wkrit
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p1
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∅
A +A (A A +A A +A( A + A "A
6
¯
Q(w)
w>w
krit
4; - 8 #
5%
A A "A++ "A+ "A+
[ A A "A++ "A+ "++ "A+6
[ "A++ A A A A A" "A+ A A"6 "A+6
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"A+ "A+ "A+ A "A++ A A" "A++ A A A "A+
A A A A" A") A A A") A"
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Komponenten
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1. . 4 1,
*+
> F > 1 A 58 1 G 8
! 3 ! ,
1 H 7.# # 4 <A
4 4 @ 4 81O 4; .
7. 1 8 .& 3
FJ6 KA 8 8 3 &G
< 3 1. . 7. <
3 #A 4 H <
, 8A ! ! . 4
8 H 1 8 A #
8 7 < 8 1! !
4A 8 *1. 7.
2! 4; 5* O
•
3 ( 0 1
3 8
6
8 3 ,A 4; H
! 2! <1 !
8 8 :&!8 @ 1
$1 4; H ! 2! ,
•
3 ( ((1
7 < 4&
$1A 8
)!
n
;
.
)!
−1
. #1;.4 .
1 8A ?.
/! 8 1 :&!1 4 @ ! !A
- 14Q! 3 ! ,
•
( 1
)!
k
2!
4 8 ;A !8 @4!
#1 ! A 1
)!
k−1
! ! ! 4
. P 8 1 4 !&! @ !
!A - 14Q! 3 ! ,
@ 4 >
4; 7.# &/O 8&
. ! 0&. !
,A8 ,' 1 , <;
1. . ! & 1A 8
# 84 4.A < 8
' 4#!9 (
?& # / @B!! ; 5,' <&
F
A
GA $4 F
P
G $! F
T
G &1 7.
#A ! 2! $. F
!A ! >A > L441
G 8 >& $! F < ! ,
1!*1G 4; H 7. 1 8 1A ;
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11 7. 8 ! 8
8;4 F ! 2!A > .
4 1, ;
8G 9$
* *# !48& A 8 4;
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. 4 3 7. .&!
4; @B!!
66
WTA
CTRL
PE
PE
PE
PE
#
CTRL
PE
PE
PE
PE
#$ #
CTRL
PE
PE
PE
PE
WTA
#$ ! # !
MUX
α
-
REG
Cmp
DP-
RAM
/
REG
MUX
Σ
-
REG
MUX
0
1
+ - <#2#$ , 1/ $ # & -
= #$ # * !
O , 1 4; # . 7.
!A . 1 8 . .
# 8 FG ! . 7.
A H 2! 3
L ; FG ! 1. . !A
H 2! 3 .
L ; 7 FG 8
1. . ! !A H8 !8 1. .
2! ! L !4 8
!, +
A
3 3 <& 4 8
1# +" # ?= * 7
8 <& 4
, @.
A ? !8 #!
! A 1.
$
.
7. 4; <&4 : <
a1
)!
nk +a0
!
)!
nk
A
a0
a1
&
# H8 1 <; 1.
$
.
! : <
)!
k(a0+a1
)!
n+a2
)!
2
n)
A
6
10 20 30 40 50 60 70 80 90 100
0
0.5
1
1.5
2
2.5
3
Anzahl PE
Fläche [mm2]
neuronenparallel, bitserielle Suche
neuronenparallel, Baumsuche
komponentenparallel, Baumsuche
"#$ #
# / + !
0
10
20
30
40
50
0
10
20
30
40
50
0
0.5
1
1.5
2
2.5
3
komponentenparallele PE
neuronenparallele PE (-Gruppen)
Fläche [mm 2]
Abweichung Modell/Messung:
Mittlerer Fehler: 2.6995%
Standardabweichung: 1.9998%
)#
#$ # / + !
O <& 4 7.# ! 4
! 2! . *
: & 8
> 4
!&! Q 4; L
)!
n
4; .
)!
k
7 , 1.
. . ! <& 3
. &! ! 8 8 1
.
6(
PEn×PEkA[mm2]PEn×PEkA[mm2]PEn×PEkA[mm2]
2×50
A)
2×25
A"(
2×10
"A)
4×25
A)
5×10
A"
4×5
"A)+
25 ×4
A"
10 ×5
A"(
5×4
"A)+
50 ×2
A)
25 ×2
A
10 ×2
"A)
O 8& > FG
PEn×PEkP[W]PEn×PEkP[W]PEn×PEkP[W]
2×50
"A+"
2×25
"A)
2×10
"A"(
4×25
"A((
5×10
"A))
4×5
"A"(
25 ×4
"A
10 ×5
"A)
5×4
"A"(
50 ×2
"A))
25 ×2
"A6
10 ×2
"A"+
O 8& > ) FG
%+
P
$4 7.# !
! . A &
. <& 4 4 4
*8 A 7. 8A
$& 8A > 4 3
# /- 81 F"YG & 8
8 # 81 & !
A . >
<; !8 # 4 > &!
7. > A !4;
3 # 7. 4 8
..- $4 4;
! <& 4O 1.
$
. &! 8
;
P=p1
)!
nk +p0
&!A . !
P=
)!
k(p0+p1
)!
n+p2
)!
2
n)
<; $4 8 74 4;
@ 7=A &! 8 1A 8 .#
@1 8 3 38
11 7. @B!! !&!
½
3 $ # +2 * <## )# $ > #
/ #$ # ! 6 * 2# 3
/ $: + + #/ # 2*! # ,!
3 , - 52 + >$
/ 9 -5 *!
6+
10 20 30 40 50 60 70 80 90 100
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Anzahl PE
Leistungsaufnahme [W]
neuronenparallel, bitserielle Suche
neuronenparallel, Baumsuche
komponentenparallel, Baumsuche
"#$ #
# / + !
0
10
20
30
40
50
0
20
40
60
0
0.1
0.2
0.3
0.4
komponentenparallele PE
neuronenparallele PE (-Gruppen)
Leistungsaufnahme [W]
Abweichung Modell/Messung
Mittlerer Fehler: 2.8422%
Standardabweichung: 2.2222%
)#
#$ # / + !
)O $4 7.# ! 4
! 2! *
: & 8
> 4
3 F$!G
T
# 7A
T
4 ! 4 34 &! 8
1 > !&! :1 # 8A
34 1. 8 A 1, 8 .
' &! 8 7 4 8 !&
"
PEn×PEkL[s]PEn×PEkL[s]PEn×PEkL[s]
2×50
)A6
2×25
)A6
2×10
"A6
4×25
A6
5×10
)A("
4×5
(A+6
25 ×4
A+
10 ×5
)A6
5×4
+A+
50 ×2
A")
25 ×2
)A6"
10 ×2
+A(
O 8& > FG
$! A ' 8 .4 4 1
.
+
T
3
T
F : $!
L
!G & 4; ! 7. -1 <
! , 1 ! 8 3#
2
A
'
-%
A 8
3 @ ,' : ,
-%$%
A
$ !"
-$
8
) ! ! . 4; H 1#
l
n
dm
k
H8 5
A > ,' A 8 !
.*1 #4; 2! 1 A
FL . G .
)!
N
)!
k
! 2!A 4; 3 L
!8 . . L #8 8 U 4
Ld
$! 2!
La
!8
Lk
$! !8 .
rh
.
! .41A . <
Q 2! 1! 8 ; 3
! .
< .O
ws
A ! 3
$! >. A
ws
wb+3
#A
8 2 L L!81 8
L ;
wb
3 ; 8 ;
! 11 > 4; 3P 14
Q! 8 * #
F= 500
9!
:& 8 A 1. .
! ! / 8 . 1
4 3 ! 2!
! ;A 2! ! H :
3 8 1,A 8 ! !
0 20 40 60 80 100
0
50
100
150
Anzahl Prozessorelemente
Gesamtlatenz [s]
Neuro.−Par., Bitseriell
Neuro.−Par., Baumsuche
Komp.−Par., Baumsuche
Tmin = 2.72s, 80 PEs, Neuro.−Par., Baumsuche
"#$ #
# / + !
0
10
20
30
40
50
0
20
40
60
0
10
20
30
40
50
komponentenparallele PE (-Gruppen)
neuronenparallele PE
Gesamtlatenz [s]
Latenz [s]
Tmin = 1.94 s, 20 N, 5 K;4 N, 25 K;
)#
#$ # / + !
O 5! 7.# ! 4
! 2! ! . 4
6" L
107
$ 8 : &
8 > 4
! .
5,' @ 8 ! 2! !
A 4 ,' 1& A 8
4 . !A
xy
A #&&' 1 O !
L. 3
l
n(dm+2+
)!
n(2 + Ld))
)!
nl
n(dm+2)
L. 3
l
n(dm+2+
)!
n(2 + Ld))
)!
nl
n(dm+2)
.
dm
kl
)!
kdm
kl
L.
dm
k l
n dm
kdml
nl
(
L. 3
|X| l
n(1 + dm+Ld)|X|(l
n(3 + ws+ws
wb))
L. 3
|X| l
n(1 + dm+Ld)|X| l
n(1 + Lk)
.
|X| dm
k(1 +
)!
n+Ld)|X| dm
k(1 + La)
L.
|X| dm
k l
n(1 + Ld)|X| dm
k l
n(1 + Lk+La)
L. 3
|X| l
n(1 + dm+Ld+rh)
L. 3
|X| l
n(1 + dm+Ld+rh)
.
|X| dm
kl
L.
|X| dm
k l
n+Ld
)O 3 5! 98 #
1
>1
L. 3O L.
A L. 3O L. .A .O .
.A L. L 1. .
! 3& . 44;O J"6K 8
A
1/3
L . 8 >
84 1 ;1A 1 . !
2/3
: 4; . . 8A )6
2& #&&'
3 3 ,A 3
4 ! ! 1,
:1 . & 1
. 8
$ &
7 5! ! .! * ! 3
1 ! 98 ' 4; 3
! 8 1 @A 4;
3 , 8A 8 8 #1
- , ; 8A 4; 1 4
! 4; 8 ? < ,
!!A 1 @ 98 ;
0 20 40 60 80 100
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Anzahl Prozessorelemente
Energie [Ws]
Neuro.−Par., Bitseriell
Neuro.−Par., Baumsuche
Komp.−Par., Baumsuche
Emin = 0.44754Ws, 5 PEs, Komp.−Par., Baumsuche
"#$ #
#
0
10
20
30
40
50
0
20
40
60
0.4
0.6
0.8
1
1.2
1.4
komponentenparallele PE
neuronenparallele PE (-Gruppen)
Energie [Ws]
Energie [Ws]
Emin = 0.47428 Ws, 2N, 5K
)#
#$ #
6O 4 ! 4 ! 2!
! . 4 6" L
107
$
8
. 8 @ 4 . 8
& J+(A K .
U
2
tp
&8 ;
tp∝U
(U
−U
)η
FG
!A 8 8.
UTh
8
K
η≈1
&
CL
$1.!& 5
)
0 20 40 60 80 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Anzahl Prozessorelemente
Energie mit skalierter Versorgungsspannung [Ws]
Neuro.−Par., Bitseriell
Neuro.−Par., Baumsuche
Komp.−Par., Baumsuche
Emin = 0.12763Ws, 25 PEs, Komp.−Par., Baumsuche
"#$ #
#
0
10
20
30
40
50
0
20
40
60
0.1
0.15
0.2
0.25
0.3
0.35
komponentenparallele PE
neuronenparallele PE (-Gruppen)
Energie mit skalierter Versorgungsspannung [Ws]
Energie [Ws]
Emin = 0.13173 Ws, 4N, 5K
)#
#$ #
O 4 1 . ! 4
! 2! ! .
4 6" L
107
$ 8
> :1
tmax
A
$# 8 A 1 ; 1
. 4 0 8 7
6 8 4 4; 3 A 1
. 8 ! .
4 6" L
107
$ !A $!
. 7. L
F 1/G :1 !A 4;
1 . 4 1
.! ! ! 1A 4A 8
# 2! ! 3
1, $4
P∅
A ! 3
& !O
P∅∝dm
)!
k
dm
+l
)!
n
l
FG
! A 4 4; 7.
2! , 848
8 3;1 :1 <Q!
F
.
U
1 8A 1 8 !
2! . 8 ! A
. 4; ! 2! -A ;
, 5 8
1 . 8 ,1
4; @1 4 ? 4; 3
. 1 4; ! 1,A . 4
! "Y 8. ! 8 7 3
8A 8 1 8 * . 8
. J+6K ! ! 1 ! , $1,A
8 1 8 :&! 1 8
. < 3 8 @B!! 8
1 . ;1 8
:#;
7 # 8 !& 3,'
A
A
T
P
4;
# 7.# 98 4
3 # * ,' 8
!A 3 #
l≤100
2! 7.
<
≤2,5
Y ,A 4; ! 1
1. 84 4; * ! "" 2! 4
. 8 <; 8 7. 8
,A 21 84 8 9 1
@B!! <A < /
8 ' ! # 21 84 1
9 . A 8 # 3 @B!!
; 3 2
3 3 2 8 H 21
-. A # 8A 4;
6
H 21 2 1 A
:1 F
A
A
P
A
T
G
%
2 # <&
21 &A A 81 4; ! /
1 @B!!
RE
O
RE−1
i=˜
A
AiγA˜
T
TiγL˜
P
PiγP
FG
˜
A, ˜
P, ˜
T
, L41 A 8 H8
84A
γ
58 . 1
>
γ
8 'A 8 8
)&/#&)$
F
γA=0
A
γP=1
A
γL=1
G @B!
! # $!
T
& A 8 # 1
$
#
! &A @B!! 4; H
! ! 8 7 ) 8 @B!!
.4 4; 8 $4 @41
8 8 !&! ! $1
, . !
8 21A ;1 8 1A
3A 98 4; 8
1 4; 8 1 A
! & F <& 7=G 8
# & 8
- 11 * ! EA
1 4 8 8
&! ! =.0&A $! $4 8
34 # 1 P -
3
Bmax
L. ! 8
1
O
•
L.A O
Bmax,
=1
•
L.A .O
Bmax,
=1
•
. .A O
Bmax,
=
)!
k
•
. .O
Bmax,
=
)!
k
! ! , . & # !
1. . 2! A ,
! 2! 1. . !
,' 3A 4 # . .
! . 1 3
& # ! 2!A # <&
; 7. #!!
<; 8 . )
Bmax =0,487
8
. *1A 8 !8 6 3 > *1 # " 9!
3 # )( 3*T . 3 1. .
7. , 3 4 +A 53*T
2)
7 8 .!. @# 4;
# . 3 4;
8 # .*. 7. 2!4
&
5,' <&
A
A $4
P
$!
T
8 81 #
.' F-. 3. .# .
G @B!!
! A # <&
$
1.
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<& 4 $4 48 5!
! 0- A ! ! 2!
! L
1 ? , 3 #
8 1.- ? 21 ! Q/!A 8
& #& .*. 7.
A 8 . 4;
%&
7 # 8 !A 5
.1 1. . ! 8
,' @B!! ! 3 1
! 5,' 1 A 8 <
. ! A '
# 8 2!4 1
1 .4& 9$ ' 94
# <25 7. ' 98
4; 3 8
2*. 4; , 7= 81 ! #
%
> A 1 98. #
4,A . A 2!
F2 G 4 8 8 ! 2!4
(
Externer Speicher
Globale Steuerung
INIT
FIND BM
ADAPT
CALC Dist
data cache
alpha cache
result FIFO
PE
PE
PE
ProzessorfeldLokale Steuerung
Lokale Daten
SOM SPE
Schnittstelle
zur
Applikation
INIT
FIND BM
ADAPT
CALC Dist
data cache
alpha cache
result FIFO
PE
PE
PE
ProzessorfeldLokale Steuerung
Lokale Daten
SOM SPE
data FIFO
alpha FIFO
result FIFO
INIT
FIND BM
ADAPT
CALC Dist
Steuerung
(O 2 983
141 !4A 8 #
! 1 8 7 24
! 11 * 8A ; 2
4 7= <25 ! / 3 ( !
2A 4
2!4 4 3 ' #1
74 ! ! 8 ;P
8& . 7.
A 1 ! 4; 1 #8 8
7 < 8 2! 4; &!
#A ' 8 ? 4
2!4 1 4! ' 8 -
1 @# <25 7. #
0 1 !E
.635%
+ ! 4; 1 , .4
A . 1 # 8 F
G 8 EA ,
A ! F 3 #!G
> #& O . !
; !
dm
# 8 F
Q 1 !8 1
m
.
> #
2(w+1)
3GA 8& 8 . 4
2(w+1)+dm
; &! . !4&
2!
7 3 & 1A 8 <& 4
7. F G
+
7 . <
•
1 A # .
8 ;A 8 2 L 5
F $ =G
•
! # :8 .
8 F$29G ' .!. ; 1
A 94 . 8 1
!B! 4; 8 7 #
7. 8 4; ; 1
5lA
1 ,A 8
5+rh
1A 8
rh
@ L441 A
lA
! !
. LA
lA∝r2
h
•
F?G ! . ! !8
@4!#1 #8 8
<1 4; 1. . < 8
4 , 1 F 2!4G # 8A
. !A 88 @ 4 &
! 8 7 < 8 !& 1! <1&
.4 O
•
1
3 7 8 ! :
1 . A @4!#1
mi
A 2
:48 ! , 2:4!
8 . & A
> 4; 7 . <
8 !& 2! F-A*G
!8 1 .
•
1
3 !8 @4
! #1
mi
!8
x(t)
8 . <
#1 8 ; 1A 8&
@4!#1 1 . 8 8
8 !
p=1
1 !
;!
p=2
F Q1A G 7
1. . < 8
. #1 ! ;
4 4 ,
•
(1
7 . < 8
3 4;A ! ,
("
neuronen-
komponenten-
parallel
MUL
z
-2
SUB
z
-0
ADD
z
-0
ALPHA
z
-1
SUM
z
-1
LRAM
z
-1
SELECT
z
-1
z
-2
1
neuronen-
parallel
-1
MUL
z
-2
SUB
z
-0
ADD
z
-0
z
-2
1
-1
addr a
we a
addr b
dout bdin a
RND
Steuersignale
Busse
Signale
+O .4 !8 1. .
1
8 ? F@$ 3 3 G !
1 !A
2 2! 2!4 8
1 8 4; .& . , 3
1. . 4 !
4 ,
•
1
>& 1. . <
4 5 #8 ! .*1#
L .8 # 1 !8 8A
4 :8 . < #O 4;
. , .> 8 94 $29 .
2 ! 8 ;
2!4 ! 2 1 3
# ! ! 8
! !8 1 4;
. 7 & 8 .8
αi
; 1A 8& >
(
H 1
cdec
F@ G 1 8 > >
L A 8 .8 #
. . 4 > ,
.>
rh+2
1A 8
rh
3 .<1
< .41 8 # 4; 3
! ! #8 ' >&
8 ! 4, 7
F "G A 1 ! 1
4, 7 F "G
•
1
! 8 <&
#1 ; 1A E! !8
@4! 8
α
.!
' 11 > # F >
#
[0..2n−1]
8 #
2n
3A .1 4
n
3 ,G > 8 4 .;
mi,j
.; .
•
1
94 1 1 . #
- % / !8 8 L 1
1 1 4 .
$34 A 8 # 1 .
, 8 ' 1 . 4
8A 8 8 4; $ 4;
FG 1
F G 1
8 . 1 4; B! L! 1
!. 8 4 #
2! ,' ! # LT. A
.*1# 8 . @4!#1
Q . 2! Q
4 4; ! , $!
1 1 . 2! !A
,' 8 1, & # . 4
!
vnp =Speichertiefe
dm+2
F.G F)G
vnkp =Speichertiefe
dm
F
$
1. .G FG
(
0 112 2
1 223 3
2 334 4
1 223 3
2 334 4
0 114 4
1 225 5
4 558 8
1 225 5
4 558 8
?
"O 81 !' 4 < .41
# . 2! 8 .4
8 81A ? !8 # 1
!&! 1 ,A .
. < 8 1.-O # 2 L ;
1 . 8 -
, ,
PE
1
2(v−
2
)
!EA 8
2 ! 2!
v
! # L
0#!$ %)(
! 4 2!4 >
A ; 4; 1.
. 4 <1 4 2!4 #
8 8 . 1 !
H8 4; 5.. # 2! FB 3
G A 8 1
8 .. 2! <1A
3 L F # LG 4;
1, <; !8 ,
4O 8 8 8 A 4
8A 8 . #8 <;
; $! <& 4 8 8 F
G
(
PE
(0,0)
Prozessorfeld neuronenparallel
PE
(0,1)
PE
(0,2)
PE
(1,0)
PE
(1,1) PE
(2,1)
PE
(2,0)
PE
(1,2) PE
(2,2)
Daten + Adressen
Steuersignale
Ergebnisse Suche d. Erregungszentrums
Prozessorfeld neuronen- und komponentenparallel
Daten + Adressen
Steuersignale
Ergebnisse
PE
(0,0,0)
PE
(0,0,1)
PE
(0,0,2)
+ +
PE
(0,1,0)
PE
(0,1,1)
PE
(0,1,2)
+
PE
(1,0,1)
PE
(1,0,0)
PE
(1,0,2)
min
O 2!4 1 B 3
! <1.. A L
. < 2!
4A ; 4 2!4 1 8 , 1
! 8 7 8
4 8 11
! 4 # #1 &Q# 4A
>O 8& . <
. #1 A 8 4;
. 3 . 1. .
< . . ! ,
> A 8 ! H 2!4 1
.A &4 ; R
&4 8 F<A <
G A :E 4 / 4
! 4 < .O
•
1
. ! 8 .!4& >
# F G 8
7 . < # ! 2
L 5
•
=1
!# . : 1
8A 8 2 $# !.
•
(1
8 ! ! #1
2 L !
#1 8 <7<.A
! # 2!4 4 8 1
•
( C !1
3 7. 8
&
= 3 !
()
•
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$
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0
0 20 40 60 80 100
0
1000
2000
3000
4000
5000
6000
7000
Anzahl Prozessorelemente
Gesamtlatenz [s]
Neuro.−Par., Bitseriell
Neuro.−Par., Baumsuche
Komp.−Par., Baumsuche
Tmin = 128.3406s, 97 PEs, Komp.−Par., Baumsuche
"#$ #
#
0
10
20
30
40
50
010 20
30 40 50
0
1000
2000
3000
4000
Anzahl Komponenten
Anzahl Neuronen
Gesamtlatenz [s]
Latenz [s]
Tmin = 124.5006 s, 50 N, 2 K;
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0 20 40 60 80 100
14
14.5
15
15.5
16
16.5
17
17.5
18
18.5
19
Anzahl Prozessorelemente
Flächenbedarf [mm²]
Neuro.−Par., Bitseriell
Neuro.−Par., Baumsuche
Komp.−Par., Baumsuche
Amin = 14.0526mm², 2 PEs, Komp.−Par., Baumsuche
"#$ #
#
010 20 30 40 50
0
20
40
60
14
16
18
20
22
24
Anzahl Komponenten
Anzahl Neuronen
Flächenbedarf [mm²]
Flächenbedarf [mm²]
Amin = 14.2645 mm², 2 N, 2 K;
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10
15
20
25 0.5 11.5 22.5
102
103
104
Leistungsaufnahme [W]
Fläche [mm2]
Latenz [s]
Mögliche Implementierungen
Pareto optimale Implementierungen, Neuro.−Par., Baumsuche
Pareto optimale Implementierungen, Komp.−Par., Baumsuche
Pareto optimale Implementierungen, Neuro.−Komp.−Par., Baumsuche
<##
0 20 40 60 80 100
0
10
20
30
40
50
60
70
80
90
100
PE neuronenparallel
PE komponentenparallel
Pareto optimale Implementierungen, Neuro.−Par., Baumsuche
Pareto optimale Implementierungen, Komp.−Par., Baumsuche
Pareto optimale Implementierungen, Neuro.−Komp.−Par., Baumsuche
PEn ⋅ PEc=100
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0 20 40 60 80 100
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Anzahl Prozessorelemente
Ressourceneffizienz
Neuro.−Par., Bitseriell
Neuro.−Par., Baumsuche
Komp.−Par., Baumsuche
REmax = 0.3413, 97 PEs, Komp.−Par., Baumsuche
"#$ #
#
010 20 30 40 50
0
20
40
60
0
0.1
0.2
0.3
0.4
Anzahl Komponenten
Anzahl Neuronen
Ressourceneffizienz
Ressourceneffizienz
REmax = 0.32659, 2N, 49K
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0 20 40 60 80 100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Anzahl Prozessorelemente
Ressourceneffizienz mit skalierter Versorgungsspannung
Neuro.−Par., Bitseriell
Neuro.−Par., Baumsuche
Komp.−Par., Baumsuche
REmax = 0.77572, 97 PEs, Komp.−Par., Baumsuche
"#$ #
#
010 20 30 40 50
0
20
40
60
0
0.2
0.4
0.6
0.8
Anzahl Komponenten
Anzahl Neuronen
Ressourceneffizienz mit skalierter Versorgungsspannung
Ressourceneffizienz mit skalierter Versorgungsspannung
REmax = 0.74889, 2N, 49K
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0.7
0.8
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Ausgänge berechnen
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Simulation beenden
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Simulationsschleife
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mdlUpdate()
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wb
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Simulation
ADS_N
VAL_N
ADR
DATA
RDY_N
CLK
W_N_R
n+1n+2n+3n+4n+5n+6 n+1n+2n+3n+4n+5n+6
Takt #
Ereignisbasierte Übertragung HiLDE-DUT
lokales
Signal
externes
Signal
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wb
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Simulation
Busteilnehmer
Busteilnehmer
Busteilnehmer
Software Transaktor
HiL-DUT
Busteilnehmer
Busteilnehmer
Busteilnehmer
Hardware Transaktor
)6O 1 ; 4; 3
Simulation
Komplettierte Anfrage startet
Transaktion am DUT
Ergebnis der Anfrage
wird übertragen
Transaktions-Beginn verzögert
Taktfortschaltung am DUT
ADS_N
VAL_N
ADR
DATA
RDY_N
CLK
W_N_R
n+1n+2n+3 n+4n+5n+6 n+1 n+2n+3n+4n+5n+6
Takt #
Sim-Transaktor DUT-Transaktor HiLDE-DUT
lokales
Signal
externes
Signal
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5,00E+03
1,00E+04
1,50E+04
2,00E+04
2,50E+04
3,00E+04
3,50E+04
12345678910111213
A
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d
e
r
G
a
t
t
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r
ä
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n
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Anzahl der Zähler (j eweils ein Ein- und Ausga ng) im Entwurf
Zähler
HiLDE Adapter Standard
B** B@6 + $
n
6
n
+5
0,00E+00
2,00E+03
4,00E+03
6,00E+03
8,00E+03
1,00E+04
1,20E+04
1,40E+04
1,60E+04
1,80E+04
12345678910111213
A
n
z
a
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l
d
e
r
G
a
t
t
e
r
ä
q
u
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a
l
e
n
t
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Anzahl der Z ä hler (jeweils ein Ein- und Ausgang) im Entwurf
HiL DE Adapte r Standard
HiLDE Adapter Ereignisbasiert
0 B** 6 C
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0 10 20 30 40 50 60 70 80 90 100
0
50
100
150
Anzahl 32 Bit Datenworte
Round−Trip−Frequenz [KHz]
DMA SGL−Transfer
DMA Blocktransfer
PIO
)+O - 4Q!
Fsim
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Parameter FiFo
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we
re
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Timer
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Parameter 3
Parameter 2
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A
D
Aktoren
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Eingang 2
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Ausgang 2
Echtzeit-
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Event
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RAPTOR2000
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re
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we
we
we
62
we
data 0
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we
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+1
we
we
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we
we
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+1
data 1
data 2
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we
re
data
FiFo
we
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SDRAM in FiFo
FiFo
we
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ODER
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X-NICHT
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n
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vMAGIC Bibliothek
VHDL-Datei Angepasste
VHDL-Datei
Token Stream
Lexer
Parser
Abstract
Syntax Tree
(AST)
Java
Metaklassen
(G)UI
Angepasster
AST
String-
Templates
Anforderungs
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Hierarchie
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0
200
400
600
800
1000
1200
1400
Anzahl Komponenten
Leistung [MCUPS]
Messung Netto (nur Prozessorfeld)
Messung Brutto (ohne PC Kommunikation)
Messung Brutto (mit PC Kommunikation)
Messung Brutto (mit FPGA Konfiguration)
Berechnung ohne Kommunikation mit PC
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Berechnung: 13,25 W
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Initialisierung: 5,5 W Datenabruf: 5,5 W
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20 mA/Div @ 3,3V
Berechnung: 330 mW
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Initialisierung: 336 mW
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0 50 100 150 200
0
50
100
150
200
250
300
350
400
Dimension der Referenzvektoren dm
Lernleistung PC,l [MCUPS]
l = 200, 1 Kern(e)
l = 800, 1 Kern(e)
l = 3200, 1 Kern(e)
l = 200, 2 Kern(e)
l = 800, 2 Kern(e)
l = 3200, 2 Kern(e)
@ <$ )#*# # <#2# /DD >B2 $ B.
0 50 100 150 200
0
500
1000
1500
2000
2500
Dimension der Referenzvektoren dm
Lernleistung PC,l [MCUPS]
l = 200, 1 Kern(e)
l = 800, 1 Kern(e)
l = 3200, 1 Kern(e)
l = 200, 2 Kern(e)
l = 800, 2 Kern(e)
l = 3200, 2 Kern(e)
l = 200, 4 Kern(e)
l = 800, 4 Kern(e)
l = 3200, 4 Kern(e)
l = 200, 8 Kern(e)
l = 800, 8 Kern(e)
l = 3200, 8 Kern(e)
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0 50 100 150 200
101
102
103
104
105
Komponenten
Lernleistung [MCUPS]
ASIC (a) eingebettet
ASIC (b) eingebettet
FPGA eingebettet
ASIC (a) PC
ASIC (b) PC
FPGA PC
CPU
@
0 50 100 150 200
100
101
102
103
104
105
Komponenten
Energie [Ws]
ASIC (a) eingebettet
ASIC (b) eingebettet
FPGA eingebettet
ASIC (a) PC
ASIC (b) PC
FPGA PC
CPU
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1995 2000 2005 2010 2015 2020 2025
108
109
1010
1011
1012
Jahre
Lernleistung PC,l [MCUPS]
ASIC 50N4K
ASIC 25N4K
ASIC 10N4K
FPGA
CPU
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