Alessandro Gabrielli

Davide Falchieri

Enzo Gandolfi

Massimo Masetti

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   Design of Very High  Speed  CMOS  Fuzzy Processors for
Applications in  High Energy Physics Experiments
Davide Falchieri, Alessandro Gabrielli, Enzo Gandolfi, Massimo Masetti
Istituto Nazionale di Fisica Nucleare - Università di Bologna
via Berti Pichat 6/2 - 40127 Bologna Italy
Email: masetti@bo.infn.it
Abstract
We faced the problem of VLSI fuzzy chip design because the
processing rate of the fuzzy chips available on the market is
too low for trigger applications in High Energy Physics
Experiments. When we started, three years ago, we chose the
0.7 micron  ES2 technology because it was the fastest one
available at an accessible price.  The paper describes chip
architectures where each rule is processed in one clock
period: 20 ns. Our goal was a processing rate of  few
hundred  ns: it was possible to reach such a result only when
the number of  the inputs is less or equal to four: for two
inputs the processing rate is 80 ns while for four inputs 320
ns because only the active rules are processed. For more
inputs a genetic rule generator is used because it allows to
have a fuzzy system with a very low number of rules: for most
applications the number of rules is about 10. The architec-
ture of a 10 input fuzzy chip able to process a "genetic fuzzy
system" is described. The above chips have been constructed
and now we have redesigned the two input fuzzy chip using
the 0 .35 µm technology  of the Alcatel Mietec to reach a
higher processing rate.
1. Introduction
Neural chips are now used in trigger devices for HEPE [1].
Four years ago we faced the problem of using also fuzzy chip
microprocessors [2], because a fuzzy system can work as a
neural system and is more flexible [3]. We made then a
comparison between the neural and fuzzy approaches reach-
ing the following conclusions:
- fuzzy chips running at a speed suitable for trigger devices
are not available on the market [4],  [5], therefore one has
to design its own VLSI chip while, for the neural solution,
one can use commercial chips;
- to develop the fuzzy system, that is the rules and the
Membership Functions (MF) related to an application,
there are two possibilities: an expert can develop it or SW
tools can be used. These are called Rule Generators and are
able to develop a fuzzy system related to a specific appli-
cation by means of Neural Network (NN) [6] and/or
Genetic Algorithms (GA)  [7];
- the fuzzy solution is more flexible because you know its
knowledge basis that is the fuzzy system and you can
improve on-line the performances by changing the rules.
That is not completely true when a fuzzy system is obtained
by a rule generator.
To design a very high speed fuzzy chip we have:
- to select a very advanced CMOS technology: three years
ago we used the 0.7 µm CMOS technology and the ES2
foundry standard cells;
- to design a pipeline architecture: 20 ns delay for each
pipeline stage with a 50 MHz clock;
- to implement very fast algorithms like the Sugeno infer-
ence and defuzzification method [8] that is the final
division process, see figure 1, which takes place in parallel
to the pipeline stages.
To further improve the processing rate we followed two
different solutions:
- for a fuzzy processor with no more than 4 inputs and each
input with no more than 7 fuzzy sets (FS) it is possible to
process only the active rules. Following this approach we
designed and constructed a two input fuzzy processor
running at a rate of 80 ns [9], with a 14 square millimetre
area and a 4 input fuzzy processor running at a rate of 320
ns, with a 60 square millimetre area [10];
- for more than 4 inputs we designed a 10 input fuzzy
processor matched to a fuzzy system obtained by a genetic
rule generator where the  number of the rules of the fuzzy
system is very low. The processing rate is 20 ns times the
number of the rules of the fuzzy system to be processed.
The chip area is 80 square millimetres. The above realisa-
tions can match the processing rate of a second level trigger
but now new CMOS technologies, that is 0.5, 0.35 micron
by Alcatel Mietec and 0.25 micron by SGS Thomson are
available. With these new technologies we are starting to
redesign (the previous designs have been made using the
VHDL) the above chips with a clock up to 150 - 200 MHz,
- maximum overlapping of the input MFs no more than 2;
- 128 crisp MFs for the output variable;
- 4 bits both for the predicates and the premise degree of
truth, called respectively α and θ value;
- T-norm implemented by Minimum, (MIN), or Product
to obtain the θ value;
- Sugeno order zero [3] inference and defuzzification
method;
- 50 Mega Fuzzy Inferences per Second with a 50 MHz
clock.
With these features we obtain the following performances:
- any mathematical function can be approxi-
mated with an error of 1%;
- each  rule is processed in one clock period. The
total processing time is:
- number of active rules times the clock period:
16 x 20 = 320 ns  plus
- two delays that are due to the number of
pipeline stages, 12 x 20 = 240 ns,   and to the
time required by the division process: 90 ns.
The main chip architecture is reported in figure 1. The ARS
selects the active rules related to the actual values of the
input variables; to do that it generates the related addresses
for the rule and the MFs shape memories. Then the
fuzzification process starts.
The design of the chip has been carried out using the Cadence
DFWII Software obtained via Europractice and using the
therefore they can match the processing rate required by a
first trigger level; for example the two input fuzzy chip will
run at a rate less than 27 ns with further improvements while
the "genetic" fuzzy chip will have a processing rate of less
than 7 ns times the number of rules. These chips will be sent
to the Alcatel Mietec foundry by the end of this year. In this
paper the architecture of the chips are described.
2. The four Input Fuzzy Processor
Here is described, see figure 1, the four input fuzzy
processor; the two input fuzzy processor has a similar
architecture. The innovative feature of this design is the
independence of the processing rate from the fuzzy system.
This is obtained in the following way:
- any fuzzy system is converted into a new one where all
the rules are present and then loaded in the rule and MF
memories,
- an Active Rule Selector (ARS) identifies, without chang-
ing the processing rate, the active rules related to each
input data set which are to be processed.
The chip architecture involves 12 pipeline stages and each
stage takes 20 ns. The main features of the 0.7 micron
CMOS fuzzy processor are here summarized:
- four 7 bit inputs, one 7 bit output;
- 7 FSs for each of the 4 input variables, only trapezoidal
shapes are allowed;
Figure 1. The fuzzy chip architecture
Figure 2. An input data set and the the related MFs
VHDL language. The block diagram of the chip layout is
reported in figure 3 a), while the chip actual layout is reported
in figure 3 b).
2.1. The selection of the active fuzzy rules
To understand what an active rule is let us suppose to have
a fuzzy system with 2 input variables, 3 FSs for each input
with overlapping of the MFs not higher than 2. A typical
fuzzy rule for the above fuzzy system is like:
if (X0 is Low) and (X1 is Medium) then (Z is High).
You can see in figure 2 that only the four rules where X0 is
related to L or M FSs and/or X1 to M or H FSs give a non
zero contribution to the final result, that is the α values are
different from 0: these rules are called active rules. In figure
2 is sketched the α value which is the degree of truth of the
predicate X0 is Low. If we have N input variables, K  FSs
for each input variable, only t-norm operator for the rules
and at most an overlap of 2, the active rules are  2N while all
the possible fuzzy rules are  KN. Therefore, for the above
example, we can process only 4 rules instead of 9 for a fuzzy
system made of all the rules.
Our 4 input fuzzy processor is able to process only the
active rules,  which are 16, between all the possible ones,
which are 2401; to obtain this result our solution requires:
- to store a fuzzy system made of all the possible rules in
the fuzzy chip;
- to use the address code to identify the rule premise.
Then  we store the rules starting from the address 0000
where it is stored the rule if (X0 is Low) and (X1 is Low) and
(X2 is Low) and (X3 is Low) then (Z is ...) and at the address
0001 the rule if (X0 is Low) and (X1 is Low) (X1 is Low)
and (X2 is Low) and (X3 is Medium ) then (Z is ...) and so
on. The rule code consists of two parts: the first one, related
to the premise, where zero means that the related variable
is not present in the rule while 1 means the vice versa and
the second one, related to the consequent, reports the crisp
output fuzzy set. In this way  the rule address defines the
fuzzy sets of the premise while the rule code confirms or not
if the rule was present in the initial fuzzy system (the one
without all the rules) and which input variables and output
FSs were involved. In figure 1 the premise code 0110 means
that the active rule involved comes from a rule in the former
fuzzy system where only X
2
 and X
3
 are involved while the
consequent code identifies the crisp value of the output FS.
If we had 0000, as a premise code, it would mean that there
is not a corresponding rule in the initial fuzzy system,
therefore its contribution is zero.
2.2. The chip architecture
The input data set has to be loaded, see the input register in
figure 1, into the chip  according to the input synchroniza-
tion handshake signals. The input data set can be ready at
any time depending on the external device that generates it:
the inputs can be loaded at a maximum rate of 320 ns. The
chip architecture is made of the following blocks:
2.2.1. The MF Memory and the Active Rule Selector. In
this block there are four memories where the beginning and
ending points of the 7 MFs related to the FSs for each
variable are stored. Then the ARS can select the two
involved MFs related to each input variable. As soon as
these FSs are identified another circuit is able to compute
the address code where are stored the MF shapes - four
points for each trapezoidal MF - and the related active rules.
These two addresses are sent to the fuzzification and rule
memory blocks.
2.2.2. The Fuzzification Process. In this block there are
four memories where are stored the four points related to
each MF (the MF shape is trapezoidal) and a  MF generator
creates the shape in such a way that a four bit α value can
be computed for each input value. This circuit receives both
the addresses related to all the active MFs and the input data
set then computes the related α values. This four values are
sent to an operator to compute the related premise grade of
truth θ as the MIN (minimum) or Product of the α values.
2.2.3. The Inference and Defuzzification block. This
block receives the θ value and, from the rule memory, the
consequent code, that is the crisp 7 bit Z
i
 value and it
computes the Σ θ
i
 and Σ θ
i 
Z
i
 operations. After the last rule
is  processed a new input data set can enter the chip and the
division process starts in order to compute, in parallel to the
pipeline processing,  the Z
o 
output value:
Z
o
 = Σ  Z
i
θ
i 
 /Σ θ
i
3. The pipeline timing
We will describe now what elaboration takes place, clock
by clock, in each pipeline stage, see table 1, where two
processing  steps are computed in parallel:
- at the first clock a new input data set is loaded in the input
register, this process is off line to the pipeline processing;
- the ARS requires one clock to generate the code of the
active MFs to be sent to the fuzzification process and two
clocks to compute the premise and consequent code of the
Figure 3 b). The chip actual layout
- the defuzzification block requires one clock to compute
the Σ θ
i 
and the Sugeno multiplication Z
i 
θ
i
  operations and
another clock to compute  the Σ Z
i 
θ
i 
operation: pipeline
steps 11 and 12.
- the division process takes place when the last rule has been
processed and runs in parallel to the pipeline stages. It
takes 90 ns.
Pipe # 2 Parallel pipelines: processing goals
Off pipe Input Data Set Read Parallel pipeline processing
1 Selection of the active MF for each input
variable on the base of the input data set
2 MF memories address generation
3 MF memories read cycle Rule memory address generation
4 - 5 - 6 α computations for the 4 input variables Rule memory cycle: Z and Premise Rule Code
7 Selection/Rejection of the α on the base Z Shift Process
of the Premise Rule Code
8 - 9 α Minimum and Product computation Z Shift process
10 Selection of the θ value between Z Shift process
Minimum and Product computation
11 Σ θi computation θ*Z multiplication
12 Σ Zi θi computation
Off pipe: Computation of the output value: Zo = Σ Zi θi / Σ θi
Table 1. Pipelines and off line computation steps
active rule: pipeline steps from 1 to 3, see table 1;
- the fuzzification block requires four clock periods to
compute the α values: pipeline steps from 4 to 7;
- the MIN block requires three clocks to compute the θ
value, there are three identical circuits which perform the
same operation on two input variables:  pipeline steps
from 8 to 10;
Figure 3 a). The block diagram
 of the chip layout
These 4 small blocks are the 4
MF memories
4. The 10 input fuzzy chip matched  to a genetic
fuzzy system
The rule structure of a genetic fuzzy system, that is obtained
by a genetic rule generator, is completely different from the
one of the traditional fuzzy system as each rule has its
membership functions. Therefore the fuzzy processor archi-
tecture is different: in the previous fuzzy chips we had a rule
memory and a MF memory for each input variable, here we
only have one  rule memory where, in each rule, are coded
the related MFs. There is another difference concerning the
shape of the MFs which are taken into account. In figure 4 is
presented a fuzzy system composed of four rules and the MFs
related to each rule are sketched. As a genetic fuzzy system
can be made of few rules, our rule memory capacity is made
of 60 rules and it is possible to store more than one fuzzy
system related to the same input data: our application fore-
sees to have up to four different fuzzy systems that can be
selected on line to process the input data. In the figure 4 are
shown the input MF shapes that will be approximated by a
trapezoidal symmetric shape and the crisp output MFs. The
fuzzy processor architecture has been designed according to
the following considerations:
- to improve the processing  rate it has no meaning to select
the active rules because most of the rules are active;
- the number of rules of the genetic fuzzy system is much
smaller than the number of rules written by an expert;
- the number of FSs for each variable is equal to the number
of rules of the fuzzy system.
The main features of the 0.7  micron CMOS genetic fuzzy
processor are:
- maximum number of rules of the fuzzy system: 60 rules;
- up to four different fuzzy systems can process the same
input data set (this is required by our application);
- 10 inputs, each of 9 bits, and one 9 bit output;


Design of Very High Speed CMOS Fuzzy Processors for Applications in High Energy Physics Experiments

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Design of Very High Speed CMOS Fuzzy Processors for Applications in High Energy Physics Experiments

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