Fini e S a e Machines Wi h Inpu Mul iplexing: A Pe o mance S udy
Ignacio Ga cia-Va gas and Raou Senhadji-Na a o
Abs ac —Fini e s a e machines wi h inpu mul iplexing (FSMIMs)
ha e been p oposed in p e ious wo ks as a echnique o e icien
mapping FSMs in o ROM memo y. In his pape , we p opose a new
a chi ec u e o implemen ing FSMIMs, called FSMIM wi h s a e-based
inpu selec ion, whose goal is o achie e a u he educ ion in memo y
usage. This pape also desc ibes in de ail he algo i hms o gene a -
ing FSMIMs used by he ool FSMIM-Gen, which has been de eloped
and made a ailable on he In e ne o ee public use. A compa a-
i e s udy in e ms o speed and a ea be ween FSMIM app oaches
and o he ield p og ammable ga e a ay-based echniques is p e-
sen ed. The esul s show ha he FSMIM app oaches ob ain huge
educ ions in he look-up able (LUT) usage by using a small num-
be o embedded memo y blocks. In addi ion, speed imp o emen s
o e con en ional LUT-based implemen a ions ha e been ob ained in
many cases.
Index Te ms—Embedded memo y blocks (EMBs), ini e s a e
machine (FSM), ield p og ammable ga e a ay (FPGA), logic
syn hesis, ROM.
I. INTRODUCTION
In he las decade, he numbe o embedded memo y
blocks (EMBs) a ailable in ield p og ammable ga e a ays (FPGAs)
has inc eased g ea ly. The de elopmen o e icien echniques o
implemen ing ini e s a e machines (FSMs) using EMBs is a g ea
challenge [1]–[6]. The epo ed ad an ages o ROM-based FSM
implemen a ions make i an in e es ing al e na i e o he con en ional
LUT-based implemen a ions. Fi s ly, he use o EMBs ees look-
up ables (LUTs) ha can be used o o he gene al pu poses [5].
Secondly, speed imp o emen s ha e been ob ained by he ac
ha EMBs ha e a ixed access memo y ime independen ly o i s
con en [6]. Finally, a conside able powe consump ion educ ion can
be achie ed by disabling EMBs du ing he idle s a es [4].
Mos o he app oaches o enhancing he pe o mance o ROM-
based FSM implemen a ions ely on a unc ional decomposi ion
o he memo y componen in o wo elemen s: 1) a combina ional
add ess modi ie and 2) a smalle memo y componen [1], [5], [7].
Senhadji-Na a o e al. [8] p esen ed he undamen als o a new
app oach called FSM wi h inpu mul iplexing (FSMIM) whose
main goal is o educe he ROM memo y dep h. This app oach
includes op imiza ion echniques and an a chi ec u e, he eina e
called FSMIM wi h ansi ion-based inpu selec ion (FSMIM-T),
which uses a mul iplexe bank as add ess modi ie . In [6], signi i-
can speed imp o emen s and a ea educ ions ha e been ob ained by
FSMIM implemen a ions on FPGAs due o he ollowing wo ac s:
1) ypically, a s a e ansi ion in ol es many don’ ca e inpu s [9]
and 2) cu en FPGAs allow e y e icien implemen a ions o wide
mul iplexe s by using dedica ed mul iplexe s [10].
In his pape , we ha e made se e al new con ibu ions wi h
espec o hose p esen ed in [6]and [8]. Fi s ly, we desc ibe in de ail
The au ho s a e wi h he Depa amen o de A qui ec u a y Tecnología de
Compu ado es, Uni e sidad de Se illa, E.T.S. Ingenie ía In o má ica,
Se illa 41012, Spain (e-mail: [email p o ec ed]).
he op imiza ion p ocess in ol ed in he FSMIM implemen a ions.
Secondly, we p opose a new a chi ec u e o implemen FSMIMs,
called FSMIM wi h s a e-based inpu selec ion (FSMIM-S), wi h he
aim o u he educing he size o he ROM memo y. Finally, we
p esen a compa a i e s udy be ween FSMIM and o he s echniques.
A ool called FSMIM-Gen o gene a ing FSMIMs om FSMs ha e
been de eloped and dis ibu ed as open-sou ce [11].
II. CONVENTIONAL ROM-BASED IMPLEMENTATION
The ansi ion and ou pu unc ions o an FSM can be implemen ed
using memo y [12]. In his pape , we assume Mealy machines wi h
synch onous ou pu s because he EMBs a ailable in cu en FPGAs
a e synch onous. Fig. 1(a) shows he e e ence a chi ec u e o ROM-
based implemen a ions o Mealy machines. The ROM s o es he FSM
ou pu s and he nex s a e o each FSM ansi ion. The ROM size in
bi s is
CROM =2m|S|(n+p)≤2m+p(n+p)(1)
whe e Sis he se o s a es, mis he numbe o inpu s, nis he
numbe o ou pu s, and p=log2|S|is he numbe o s a e encod-
ing bi s. The memo y usage g ows exponen ially wi h he numbe
o inpu s and he numbe o s a e encoding bi s [12]. The speed is
deg aded due o ou ing o e head when a la ge numbe o EMBs
is equi ed. Mo eo e , i he memo y dep h exceeds he maximum
dep h o he EMBs, hen he speed is u he educed because some
LUTs a e used o implemen ing he mul iplexe s equi ed o join
he EMBs.
III. FSMIM
The FSMIM app oach ies o educe he dep h o he ROM mem-
o y by educing bo h he mand |S| alues in (1). Le us de ine he
e ec i e inpu s o a s a e sas he subse o FSM inpu s ha a e
ele an o de e mine he s a e ansi ions o s. Fo any gi en s a e,
he ROM could be add essed using only he e ec i e inpu s o he
s a e ins ead o all FSM inpu s. I he maximum numbe o e ec i e
inpu s pe s a e (deno ed by m)isless hanm, hen he ROM dep h
can be educed om 2m|S| o 2m|S|. Fo his pu pose, a combina-
ional componen called inpu selec o bank (ISB) is used o selec
he e ec i e inpu s o each s a e. The ISB is composed by mele-
men s called inpu selec o s. Fo each s a e, each inpu selec o selec s
one di e en e ec i e inpu o he s a e om a subse o he FSM
inpu s. The ISB selec s minpu s no ma e how many e ec i e inpu s
he p esen s a e has. Fo hose s a es ha ha e less e ec i e inpu s
han m, only pa o he selec ed inpu s a e e ec i e; he es a e
don’ ca e alues o he s a e. We will e e o hem as don’ ca e
selec ed inpu s (DCSIs). DCSIs can be exploi ed o o m g oups o
s a es ha can be encoded wi h he same code. So, i all s a es a e
g ouped in o Ng oups, hen he ROM dep h can be educed o 2mN
wi h N≤|S|. This allows o educe he dep h e en in FSMs wi h
s a es sensi i e o all inpu s (i.e., m=m).
An op imiza ion p ocess is used o ans o m FSMs in o FSMIMs
which can be implemen ed e icien ly using bo h he FSMIM-S and
FSMIM-T a chi ec u es.
Fig. 1. ROM-based FSM a chi ec u es. (a) Con en ional. (b) FSMIM-T.
(c) FSMIM-S.
(a)
S a e
S2S1S0
S0 000
S1 001
S2 010
S3 011
S4 100
S5 101
(b)
(c)
G oup
G1G0
g0 00
g123 01
g45 10
(d)
S2S1S0
G1G0
000 00
001 01
010 01
011 01
100 10
101 10
110 --
111 --
(e) (g) ( )
S2S1S0 Ou pu
000 x5
001 x5
010 0
011 1
100 x4
101 x4
110 --
111 --
00
01
10
11
0
1
Fig. 2. Example o FSMIM gene a ion. (a) ISS. (b) S a e encoding. (c) SG.
(d) G oup encoding. (e) T u h able o he GE o FSMIM-S. ( ) T u h able o
he second inpu selec o o ASG
3 o FSMIM-S. (g) Second inpu selec o
o ASG
3 o FSMIM-T (R1
2and R0
2a e selec ion bi s).
A. Op imiza ion P ocess
Be o e desc ibing he op imiza ion p ocess, we in oduce he inpu
selec ion ma ix (ISM), which ep esen s he ela ionship be ween
s a es and e ec i e inpu s. Each ow o he ISM con ains he e ec i e
inpu s o a s a e and each column con ains he FSM inpu s connec ed
o an inpu selec o . Le S={s1,s2,...,sq}and X={x1,x2,...,xm}
be he se s o s a es and inpu s, espec i ely. Le us de ine an ISM
as a ma ix A=aij∈Mq×m,whe eaij ∈X∪{0,1,−} ep e-
sen s he inpu selec ed by he j h inpu selec o o he s a e si.The
alues 0 and 1 indica e ha he inpu selec o selec s he cons an
alue 0 and 1, espec i ely, ins ead o an FSM inpu . Fo cla i y,
he ISM ma ix includes an addi ional column o ep esen ing ei he
he s a e sio he g oup o which sibelongs. Fig. 2(a) shows he
ISM o a FSMIM wi h six s a es and h ee inpu selec o s (see he
ma ix A).
The op imiza ion p ocess s a s wi h he inpu selec o simpli ica-
ion (ISS) p ocedu e, which educes he complexi y o he ISB. In
gene al e ms, inpu selec o s wi h less numbe o inpu s ha e be -
e pe o mance in e ms o speed and a ea. As he ISB is in
he c i ical pa h, he speed o he FSMIM implemen a ion can be
enhanced by he ISS p ocedu e. The p oposed algo i hm is based on
he classical dynamic-p og amming-based solu ion o he Knapsack
p oblem [13]. We ha e modi ied his algo i hm in o de o include
con lic s be ween i ems so ha wo i ems wi h con lic s canno be
s o ed in he Knapsack. We will e e o i as Knapsack wi h con-
lic s (KC) p oblem. Unlike he classical algo i hm, he KC p oblem
does no gua an y an op imal solu ion. Ini ially, each i em ep esen s
an FSM inpu . Two inpu s ha e a con lic i hey a e e ec i e inpu s
o he same s a e. Fo example, in Fig. 2(a), he inpu s x1,x5,andx6
ha e a con lic because hey a e e ec i e inpu s o he s a e s0.The
p o i o each i em (i.e., each FSM inpu ) is equal o i s weigh .
The weigh ep esen s he numbe o s a es o which he inpu is
e ec i e. A di e en Knapsack is equi ed o each inpu selec o
(o ISM column), so he ISS p ocedu e equi es mins ances o he
KC p oblem. The subse o inpu s assigned o each inpu selec o is
de e mined by sol ing i s co esponding KC p oblem. In each s ep
o he algo i hm, one ins ance o he KC p oblem is sol ed. In he i h
s ep, he i ems no s o ed in he p e ious s eps (0,1,...,i−1) a e
used o he cu en KC p oblem. I i is no possible o include all
o he i ems in mKnapsacks, hen an i em is selec ed o be pa i-
ioned in o wo di e en i ems which a e ea ed as di e en inpu s
al hough ep esen he same o iginal inpu . So, he weigh s o he
new i ems a e educed and some con lic s could be elimina ed. Fo
example, in Fig. 2(a), he inpu x1can be pa i ioned in o he i ems
x1
1( he e ec i e inpu x1o he s a e s0)andx2
1( he e ec i e inpu x1
o s a es s1and s2). So, x1
1and x2
1ha e a weigh o 1 and 2, espec-
i ely; and he e a e no con lic be ween x6and x2
1. The algo i hm
selec s he pa i ioning ha emo es he g ea es numbe o con lic s,
upda es he weigh s and he con lic ela ion, and ies again o sol e
he mins ances o he KC p oblem.
Fig. 2(a) shows an example o he ISS p ocedu e. The ma ix A
is he ini ial ISM, which has six s a es and h ee inpu selec o s
(wi h i e, h ee, and wo inpu signals). The ma ix AISS is he ISM
ob ained a e he ISS p ocedu e. The algo i hm o he KC p oblem
has been applied h ee imes (one o each inpu selec o ). In he i s
ound, he inpu s x1,x2,andx3ha e been assigned o he i s inpu
selec o ( i s column). The weigh s o x1,x2,andx3a e3,2,and1,
espec i ely; his makes a o al weigh o 6 o he Knapsack ela ed
o he i s column (no e ha 6 is he maximum alue). In addi ion,
x1,x2,andx3do no ha e con lic s be ween hem. Simila ly, he
algo i hm ies o alloca e he es o he i ems (x4,x5,andx6)in he
es o he columns (one by one). In his example, no pa i ion has
been equi ed. As a esul o he ISS p ocedu e, he inpu selec o s
ha e h ee, wo, and one inpu signals.
A e he ISS p ocedu e, he s a e g ouping (SG) p ocedu e is
applied o u he educe he memo y dep h which can also esul
in speed imp o emen s [12]. A g oup o s a es can be encoded wi h
he same encoding bi s i exis s an assignmen o alues 0 and 1 o
he DCSIs ha allows o alloca e he ansi ions o hese s a es in
di e en wo ds o he ROM. We will e e o hese g oups o s a es
simply as g oups. The cons an alues 0 and 1 mus be selec ed by he
ISB in he same way ha he FSM inpu s (no e ha he ISM include
hese alues). Fo example, he s a es s2and s3o AISS [see Fig. 2(a)]
ha e been iden i ied by he same g oup g23 due o he second inpu
selec o selec s 0 o s2and1 o s3[see ASG
1in Fig. 2(c)]. Le us
say ha he s a es s2and s3ha e been g ouped in o he g oup g23.
So, in he FSM ansi ions, he nex s a es s2and s3a e eplaced by
he nex g oup g23 wi h he inpu selec ions (x1,0,−)and(x2,1,−),
espec i ely.
Gi en an ISM, he SG p ocedu e can be summa ized as ollows.
The algo i hm p ocesses he di e en columns o he ISM one by
one. The DCSIs o each column a e se o 0 o 1 in o de o c ea e
new g oups. The ISM is upda ed be o e he nex column is p ocessed.
Bo h he o de in which he columns a e p ocessed and he o de in
which he g oups a e c ea ed ha e in luence in he inal numbe o
g oups ob ained. FSMIM-Gen uses di e en so ing s a egies and
selec s he bes solu ion. The dis ibu ion o he DCSIs in he ISM
de e mines he minimum numbe o g oups ha can be ob ained.
Howe e , he dis ibu ion o he DCSIs is ob ained by he ISS p oce-
du e and i is no changed by he SG p ocedu e o a oid inc easing
he complexi y o he ISB.
Fig. 2(c) shows an example o he SG p ocedu e applied o AISS
[see Fig. 2(a)]. Ini ially, he numbe o g oups is equal o he numbe
o FSM s a es (G={s0,s1,s2,s3,s4,s5}). In he i s s ep, s2and
s3a e g ouped in o g23 by ixing he DCSIs o he second column
(see ASG
1). Nex , g23 and s1a e g ouped in o g123 by ixing he
ela edDCSIs o0and1(seeASG
2). Finally, s4and s5a e g ouped
in o g45 (see ASG
3). The SG p ocedu e educes he numbe o g oups
om 6 o 3 (G={s0,g123,g45}). So, he numbe o encoding bi s
is educed om 3 o 2.
B. FSMIM-T A chi ec u e
The FSMIM-T a chi ec u e is shown in Fig. 1(b). In his a chi-
ec u e, he ISB is a mul iplexe bank. The bi s used o con ol he
mul iplexe s, called selec ion bi s, a e s o ed in he ROM memo y.
Fig. 2(g) shows he inpu selec o o he second column o ASG
3[see
Fig. 2(c)]. Fo each FSM ansi ion, he ROM con ains he FSM ou -
pu s, he nex g oup, and he selec ion bi s o he nex s a e. The
ROM size in bi s is
CFSMIM−T=2m|G|n+p+ ≤2m+pn+p+ (2)
whe e Gis he se o g oups, p=log2|G|is he numbe o g oup
encoding bi s, and is he numbe o selec ion bi s. In Fig. 2(c),
=6 o ASG
3. Each s a e encoding bi sa ed by g ouping s a es
equi es he alues 0 and 1 o be assigned o a leas one di e en
ISM column. Mo eo e , a column wi h cons an s needs a leas wo
selec ion bi s [e.g., in Fig. 2(c), he hi d column o ASG
3 equi es wo
selec ion bi s o selec 0, 1, o x6]. So, p+ >p(i.e., he ROM wid h
inc eases). Howe e , he wid h inc emen has less in luence on he
speed and size o he ROM han he dep h educ ion [12]. The goal o
he FSMIM-T a chi ec u e is o use a e y e icien implemen a ion o
he ISB in e ms o speed and a ea. This is achie ed by using mul i-
plexe s, which can be implemen ed e icien ly in cu en FPGAs [10].
The inclusion o he selec ion bi s in he ROM allows o each he
objec i e a he expense o inc easing he ROM wid h wi h espec
o he con en ional ROM-based implemen a ions (CONV-ROMs).
C. FSMIM-S A chi ec u e
The FSMIM-S a chi ec u e is shown in Fig. 1(c). This a chi ec u e
has been p oposed o allow he implemen a ion o FSMIM wi h less
memo y esou ces han hose equi ed by FSMIM-T. The add ess
modi ie is composed by wo combina ional componen s: he ISB
and he g oup encode (GE). Unlike he ISB o FSMIM-T, he ISB
o FSMIM-S is con olled by he p esen s a e encoding bi s. GE is
a combina ional componen wi h pinpu s and pou pu s ha gene a e
he encoding bi s o he g oup o which he p esen s a e belongs.
The pe o mance o ISB and GE depends on he s a e and g oup
encoding. Fig. 2shows he u h ables o he GE [see Fig. 2(e)] and
o he second inpu selec o [see Fig. 2( )]. Bo h a e ob ained om
ASG
3[see Fig. 2(c)] by using he encoding o s a es and g oups shown
in Fig. 2(b) and (d), espec i ely.
TABLE I
PARAMETERS OF THE FSMSUSED IN THE EXPERIMENTS
Like in he con en ional ROM-based a chi ec u e, each wo d o
he ROM s o es he FSM nex s a e and ou pu s. So, his a chi ec u e
can educe he dep h o he ROM wi h espec o he con en ional
ROM-based a chi ec u e wi hou inc easing he wid h. The ROM size
in bi s is
CFSMIM−S=2m|G|(n+p)≤2m+p(n+p). (3)
F om (1) o(3), i can be seen ha CFSMIM−S≤
min{CFSMIM−T,CROM}. This memo y educ ion is achie ed a
expense o inc easing he numbe o used LUTs due o he implemen-
a ion o a mo e complex add ess modi ie . So, FSMIM-S is usually
slowe han FSMIM-T.
IV. EXPERIMENTAL RESULTS
In his pape , we ha e used Xilinx ISE Design Sui e 13.4 and he
xc6slx75-3 FPGA de ice (Vi ex-6). This de ice includes 172 EMBs
o 18 Kbi s which can be con igu ed as wo independen EMBs
o 9 Kbi s. The echniques CONV-ROM, ISE LUT-based imple-
men a ion (LUT-ISE), ISE EMB-based implemen a ion (EMB-ISE),
FSMIM-T implemen a ion, and FSMIM-S implemen a ion ha e been
compa ed. The FSMIM echnique can be applied o a FSM i m<m
and/o i wo o mo e s a es can be g ouped a e he ISS p ocedu e
(i.e., he e is a leas one ISM column wi h a leas wo DCSIs).
We ha e used MCNC benchma ks [14] and 150 FSMs gene a ed by
BenGen ool [15]. We ha e disca ded he cases in which he FSMIM
canno be applied and he cases whose CONV-ROM equi es only one
9 Kbi s EMB (i.e., no u he educ ion can be ob ained). The inal
numbe o FSMs used in he expe imen s was 73. Howe e , en o
hese cases canno be implemen ed in he a ge FPGA de ice using
CONV-ROM and/o EMB-ISE due o hei high esou ce equi e-
men s. These cases ha e been excluded om he ables o allow
a p ope compa ison (we will e e o hem as unsuccess ul cases).
Table Ishows he mean, s anda d de ia ion, minimum alue, qua -
iles, and maximum alue o he a chi ec u al pa ame e s and o he
speed and a ea esul s o he e e ence echniques (i.e., CONV-ROM
and ISE-LUT). When a esidual 9 Kbi s EMB is used by ISE, i
is compu ed as 0.5 EMB. The pa ame e s o FSMIM a e shown
no malized wi h espec o he co esponding pa ame e s o he FSM.
Fi s ly, we compa e he speed inc emen o each echnique wi h
espec o LUT-ISE because i is he s anda d echnique and i does
no use EMBs (see Table II). The s a is ic measu es shown in his
and o he simila ables a e: mean, s anda d de ia ion, minimum
alue, qua iles, and maximum alue. Bo h FSMIM-T and CONV-
ROM achie e a posi i e a e age inc emen . Al hough CONV-ROM
ob ains he bes esul s, he pe cen age o he cases whe e each
echnique is as e han LUT-ISE is sligh ly g ea e o FSMIM-T
(see “Hi ” column). In ac , FSMIM-T achie es he highes ope a -
ing equency in he 11% o he cases. As expec ed, FSMIM-S ge s
TABLE II
SPEED INCREMENT WITH RESPECT TO LUT-ISE (%)
Fig. 3. Speed inc emen in pe cen age o he ROM-based echniques wi h
espec o CONV-ROM e sus he ROM dep h o CONV-ROM.
TABLE III
REDUCTION OF THE NUMBER OF USED EMBSWITH
RESPECT TO CONV-ROM (%)
wo se esul s han FSMIM-T because he add ess modi ie is mo e
complex. Despi e his, FSMIM-S is as e han LUT-ISE in he 38%
o he cases ( he inc emen is g ea e han o equal o 15% o he 25%
o he cases). Clea ly, he wo s esul s a e ob ained by EMB-ISE.
Compa ed o CONV-ROM, he FSMIM-S and FSMIM-T ech-
niques a e as e in 13% and 30% o he cases, espec i ely. In
addi ion, as shown in Fig. 3, he speed inc emen o he FSMIM-based
a chi ec u es wi h espec o CONV-ROM ends o inc ease wi h he
inc easing o he ROM dep h o CONV-ROM. This shows he impac
o he ROM dep h educ ion on speed. In ac , o he i e cases in
which he ROM dep h is g ea e han he maximum EMB dep h, he
a e age speed inc emen o FSMIM-S and FSMIM-T a e 115% and
131%, espec i ely. In he unsuccess ul cases, he ROM dep h a e
always g ea e han 105; so, in a la ge a ge de ice, i is expec ed
u he inc emen s.
Le us now p esen a compa ison o a ea be ween he di e en
echniques. Fi s , we analyze he EMB educ ion o he di e en
ROM-based echniques wi h espec o CONV-ROM (see Table III).
Again, he wo s echnique is EMB-ISE. FSMIM implemen a ions
use much less memo y han he o he echniques (in he hal o he
cases, he EMB educ ion is g ea e han o equal o 50% o bo h
FSMIM-based a chi ec u es). As expec ed, FSMIM-S always uses
a numbe o EMBs less han o equal o FSMIM-T. We highligh
ha , in six o he unsuccess ul cases, CONV-ROM equi es mo e
EMBs han hose a ailable in any de ice o he Vi ex-6 amily while
FSMIM-S and FSMIM-T equi e only 2.9 and 5.6 EMBs on a e age,
espec i ely.
In o de o e alua e he numbe o LUTs sa ed in he implemen-
a ion o FSMs by using EMBs, we ha e calcula ed he educ ion o
he numbe o used LUTs wi h espec o LUT-ISE (see Table IV).
The wo s echnique is EMB-ISE, which uses mo e LUTs han
LUT-ISE on a e age despi e he ac ha i uses a conside able
numbe o EMBs. The a e age educ ion is g ea e han 80% o
TABLE IV
REDUCTION OF THE NUMBER OF USED LUTSWITH
RESPECT TO LUT-ISE (%)
TABLE V
NUMBER OF SAVED LUTSPERUSED EMB
TABLE VI
COMPARATIVE OF FSMIM-S RESULTS WITH
RESPECT TO FSMIM-T (%)
CONV-ROM and FSMIM-based echniques. The e o e, in hese ech-
niques, he use o EMBs allows a huge educ ion o he LUT usage.
As expec ed, CONV-ROM ob ains he bes esul s. Howe e , he a e -
age educ ion o FSMIM-T is e y close o ha o CONV-ROM
despi e he ac ha CONV-ROM do no include any add ess mod-
i ie . We ha e also calcula ed he numbe o sa ed LUTs pe used
EMB o each echnique (see Table V). Al hough bo h FSMIM imple-
men a ions achie e be e esul s han CONV-ROM, FSMIM-S is he
mos e ec i e echnique o sa ing LUTs.
Table VI shows a compa ison be ween FSMIM-S and FSMIM-T.
We ha e used he cases in which FSMIM-T equi es mo e han
one 9 Kbi s EMB ( he unsuccess ul cases ha e also been included).
FSMIM-S educes signi ican ly he numbe o EMBs a expense o
a li le speed educ ion. Al hough he ela i e LUT inc emen o
FSMIM-S is high, he numbe o used LUTs (22 on a e age) is no
signi ican compa ed o he numbe o sa ed LUTs (446 on a e age).
The numbe o sa ed LUTs o FSMIM-S is only 12% less han
FSMIM-T on a e age; howe e , i is impo an o highligh ha
FSMIM-S sa es 45% mo e LUTs pe used EMB.
V. CONCLUSION
Rega ding he a ea esul s, he s udied echniques could be so ed
in ascending o de o EMB usage and descending o de o LUT usage
as ollows: LUT-ISE, FSMIM-S, FSMIM-T, and CONV-ROM. The
possibili y o exploi ing all kinds o esou ces a ailable in FPGAs
allows o i he design in o a smalle (and cheape ) de ice. FSMIM-
based a chi ec u es allow o ind an adequa e adeo be ween LUT
and EMB usage. In ac , hey ob ain huge educ ions in he LUT
u iliza ion by using a easonable numbe o EMBs. The p oposed
FSMIM-S a chi ec u e ex ends he numbe o a ailable al e na i es
o sa is ying he a ea cons ain s. FSMIM-S is he bes design op ion
when he numbe o unused EMBs is limi ed. O he wise, FSMIM-T
is a be e op ion i he speed is c i ical. Al hough CONV-ROMs
wi h small ROM dep h a e as e on a e age han FSMIM imple-
men a ions, his end is e e sed when he ROM dep h inc eases.
We hink ha FSMIM-Gen is a use ul ool o in eg a ing he use o
EMBs in he con en ional design low.
In u u e wo k, we plan o enhance he pe o mance o he FSMIM
echnique. Recen ly, we ha e modeled he ISS op imiza ion p ob-
lem as a new gene aliza ion o he classical hi ing se p oblem,
and p oposed an in ege linea p og amming o mula ion [16]. We
plan o in eg a e his o mula ion in o FSMIM-Gen. Mo eo e , we
will s udy he in luence o he s a e and g oup encoding on he pe -
o mance o he ISB and GE o FSMIM-S-based implemen a ions.
We plan o in eg a e an algo i hm o inding e icien encoding in o
FSMIM-Gen.
ACKNOWLEDGMENT
The au ho s would like o hank P o . L. Józwiak o p o iding us
a benchma k se gene a ed by he BenGen ool.
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