CDFG for free HDL compiler as refenrece VCD file dumper Said Mchaalia Dortmund, September 2000

7/31/2019 CDFG for free HDL compiler as refenrece VCD file dumper Said Mchaalia Dortmund, September 2000

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FreeHDL Compiler Control Data Flow

Graph and its application in waveformcompression

Said Mchaalia

August 18, 2012

1 Intention of this document

In this document, we try to present an idea of using Control Data

Flow Graph (CDFG) to improve waveform compression.

A waveform file is a VCD (Value Change Dump) file, which is divided

in two parts: header that contains general information, which are

version, date,.. and kernel, which contains signal values belong to

each simulation step and simulation time.

Figure ?? describes a VCD file. Notice that each parameter is coded

with an ASCII code composed of 1 to 4 characters depending on the

number of parameters inside considered VHDL model. For eachVHDL model, the simulation time is written before the parameter val-

ues. For example: #0 and #100 represent the simulation times 10

and 100 us. The character b preceded parameter value describes

that this parameter value is a binary format. Thereby all parameter

values will be transformed to a binary format before that they will be

written in the VCD file.

To compress a VCD file, many techniques are developed. The basic

idea of these techniques is inspired from the Lempel-Ziv and the oth-

ers algorithms for data compression [4]. Mainly, five algorithms that

are Time-Value Separation, Time Compression Technique, Value

Compression Technique, Strength Reduction and Cross Signal StrengthReduction (see [1] and [2]) are developed to allow a suitable VCD file

compression.

The object of this work is to get out an idea of using CDFG for devel-

oping a new waveform compression algorithm. In following sections,

we will describe this idea and present its features.


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$date

Sep 26 2000 16:28:52

$end

$version

FREEHDL 0.1

$end

$timescale1 us

$end

$scope module struct $end

$var reg 8 ! qsig2[8:1] $end

$var reg 8 " qsig[8:1] $end

$var trireg 1 ? clk $end

$upscope $end

$enddefinitions $end

#0

$dumpvars

b110100 !b110100 "

b0 ?

#100

b110100 !

b1 ?

$end

Figure 1: VCD File

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2 An overview of waveform compression technique

The basic idea of waveform compression is finding a method that

reduces waveform file sizes in order to get more storage space for

further use.

The actual waveform compression techniques are described in [1]

and [2].

3 Control Data Flow description

The Control Data Flow Graph is a graphical representation, which

identifies each statement in a given program with a graph. A CDFG is

composed of edges, which represent data and/or control and nodes

that identify arithmetic and/or logic operations[3]. Figure ?? repre-sents a CFDG of VHDL model.

4 CDFG and its application in waveform compression

The object of using CDFG is to develop a compression algorithm

based on interpreted graphical information. In this section we detail

the different waveform compression cases in which the CDFG will be

used.

4.1 Dependency Schedules

In this section, we will deal with the dependency between signals

and/or variables and dependency between processes. This section

is divided in two main subsection: however the first section treats

the case of the dependencies between signals and/or variables, the

second one interests the dependency between processes.

4.1.1 Signal dependency schedules

We know that CDFG gives a knowledge a priori of relationships be-

tween signals and variables inside a given VHDL model. Due to this

information, we can minimize the data storage. For example let con-sider the VHDL model described in figure ??. We see, that the signal

c is depended on whether the signals a and/or b change values or

not. So, we can use such an information to reduce the stored infor-

mation belong to considered waveform. Thereby, we do not need to

store the c signal value and we should just store the a and b signal

values. In the other hand, notice that the signal d is depended on

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process(a,b)

begin

c


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Let us consider the new relation as follows:

c(n) = f(a(n1), b(n1)) (3)

where f(x, y) a logical function, which is defined as follows:

f(x, y) = x XOR y (4)

as the first relation between signals c, a and b.

d(n) = f(c(n1), a(n1)) (5)


f(x, y) = x AND y (6)

as the second relation between signal d, a and c.

Where n is the nth clock signal (clk) cycle.

4.1.2 Process dependency schedules

In this section, we will try to give an idea how the CDFG can solve

the dependencies between processes inside the same VHDL model

and how which information will be used in the waveform compression

techniques.

Let us look at the example of figure ??, we see that the three pro-cesses P1, P2, and P3 are depended each of the other. Based onthe CDFG of each process and on the knowledge that all processes

inside the same VHDL model have the same Read Signal and

Write Signal nodes, we can involve some relationships between

signals inside different processes to make a suitable optimization of

the waveform compression.

Figure ?? describes the CDFG of the VHDL model represented in

figure ??. We see that, the CDFGs allow us to get information about

the dependencies between signals inside theses processes and so

to achieve the needed optimization, which is the storage of signal a

and all relationships between considered signals such as:

b = f(a, 1) (7)


f(x, y) = x XOR y (8)

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P1: process(a)

begin

b


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S(n+1) = f(Si(n), Sj

(n))) (13)

Wheref(.,.,.)

represents a mathematical multi-variable func-

tion.

The more complex case is the case where each process hasits own clock signal. In this case, we must define a relation-

ship between all clock signals, and try to write the other clock

signals function of the first one for example. If we suppose

for example that the clock signal clkk is slower k times thanthe clock signal clk0, and the clock signal clkp is p times fasterthan signal clock clk0, we can write the following relationshipsbetween the distinguished clock signals:

clkk = k clk0 (14)

clkp = 1/p clk0 (15)

The relationships between signals inside theses processes will

be defined as follows:

Sl0(n) = f0(Si0

(n1), Sjk(E((n1)/k)), Shp

(p(n1))) (16)

Where E(x) is a function, which is defined as follows:

E(x) : IR > IN : x | > n such as : n 1 < x


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P1: process

begin

if clk0rising_edge then

b


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Suppose for example that:

clk1 = 3 clk0 (20)

and

clk2 = 0.5 clk0 (21)

To involve the relations between signals that are defined previously,

we can consider these equations:

b(n+1) = a(n) XOR 1 (22)

Where n is the nth clock signal clk0 cycle.

c(k+1) = b(k) N OR 1 (23)

Where k is the kth clock signal clk1 cycle.

d(m+1) = c(m) XOR 1 (24)

Where m is the mth clock signal clk2 cycle.

Indeed, we can use these equations to minimize data storage. Thereby,

we can just store the signal value a and these relations between dif-

ferent clock signals clk0, clk1 and clk2, and signals a, b, c and d.

Notice that these relations will be stored just only once a time dura-tion the VHDL model simulation.

4.2 CDFG and Waveform Decompression

In this section, we will describe how the CDFG will be used in the

complex cases to improve the waveform compression techniques.

4.2.1 Compromise between decompression and signal depen-

dencies

In the previous section, we treated the case of signal dependenciesand the involved solution based on the CDFG research. In section

4.1.1, we developed an algorithm that searches whether a signal will

be stored or not. Indeed, the storage of signal values needs a knowl-

edge a priori of the signal dependencies. Thereby, a signal value will

be stored only when this signal is independent from all other sig-

nals defined inside a given VHDL model. On the other hand, section

4.1.1 involves that only the relationship in their mathematical forms

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between signals will be stored, because this will be done just once

a time during a simulation process of waveform compression. Al-

though, it is hard to achieve this task during the decompression pro-

cess. Thereby, we do not know exactly the complexity of considered

mathematical functions, which link the signals to each other. In the

most case of complex VHDL models, we have mostly very complex

mathematical functions that belong a set of signals to a defined sig-

nal. This will make the process of decompression very complex and

it will take a great schedule time.

To solve this problem, we try to find an optimized solution for the

waveform compression techniques based on the signal dependen-

cies.

This solution is described as follows:

in the case of a signal that depends of a set of signals: find analgorithm that searches to store all needed signals based onoperation numbers that identify the signal values. Thereby, let

consider the signal Sk that depends on a set of signals. Thissignal will be written as follows:

Sk = fk(Sp0 ,...,Spi , Sj,...,Sn) (25)

where Sp0 ,...,Spi are independent or primery signals and Sj,..,Snare signals that depend of each other and the other signals.

For example, let consider the following signal dependencies:

Sj = fj(S1,..,Sl) (26)

Sm = fm(S3, S2) (27)

Sl = fl(S0) (28)

Sn = fn(S0, Sh, Sm) (29)

In section 4.1.1, we will just store the signals that do not de-

pend of any other signal. For example Sp0 ,...,Spi . There-fore, the decompression process complexity will depend on the

complexity of the functions f0(),...,fn(). Notice that these func-tions can be as complex as possible and so the decompression

task will be so complex. To solve this problem, we can precede

as follows:

first, store all independent signals.

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Figure 11: Complexity of dependency functions function of signal

numbers

secondly, in the case of dependent signals: see whetherthe dependency function fi() : i = 1...n and i kis complex or not. If it is simple then do not store the

corresponding dependent signal Si. Figure ?? representsthe graph of the complexity of dependency functions.

In figure ??, we see that the complexity Cij of dependencyfunction fi() depends on the number of signals j that are con-tained in this function. If this number is higher than the com-

plexity is lower and vice versa. This means that, in this case

of dependent signals, we must search the signal number to be

stored in order to reduce the complexity of the decompression

process. In the figure ??, we see that for a given dependencyfunctions that depend on m signal, we can find the suitablesignal number k such as k < m with which we can get anoptimized complexity of all considered dependency functions.

So, our object is to develop an algorithm that returns the signal

number k, which their values will be stored to allow a simplerestoration of the other signals and to identify the signals that

must be stored.

Thirdly, optimize the compromise between the storage space ofsignal values and the complexity of schedule time needed for

the decompression process. As, we describe above, we must

find the signal number k that allows a suitable complexity of allconsidered dependency functions inside a given VHDL model.

Although the research of this number is so complex and in the

most time we cannot find just a number but an interval. In this

case we must resolve the solution of finding this signal number

k based on other information, which is the reduction of neededstorage space of signal values. Throughout these information,

we must find a signal number k inside the considered intervaland which gives a less need of storage space of signal values.

Finally, store all needed signal and required dependency func-tions.

Problem formulation: The problem we are going to consider may

be formulated as follows:

For a given signal Sk, which is written in the form:

Sk = Fk(S0,...,Si)i = 0 n (30)

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minimize the dependency function complexity: Cki, which shouldbe written in the following form:

Ck =i Cki =

i,j iwiCij

(31)

where k, i = 0...n, n is the number maximal of signals, f(., .) afunction to define, and:

j is defined as follows:

j =

0 : Sj value not stored in DDB1 : otherwise

(32)

wi is the weight of operation i contained inside the dependencyfunction

fi(). It is defined as follows:

wi =

0 : Si independent1 : fi() = NOT2 : fi() = XOR

: so on(33)

Let consider the signal sets S = {S0, , Sn} as information model,which will be identified. It looks like that our VHDL model is a source

of signals, which will be produced each simulation time ti with distin-guished probabilities pi. These signals are dependent one of each

other and they are correlated between them. Where each signal Sirepresents an information to be stored or not. Thereby, our problem

will be considered as a Lossless Data Compression Problem that

searches to encode each signal Si with a number of bits and thenoptimizes the number of the signal values, which must be stored for

further use and that allows a suitable restoration of the all signals

during the decompression process.

On the other hand, for a given signal sets S = {S0, , Sn}, we con-sider the probability of a signal Si, i = 0 n, pi to be appear in theVCD file during a simulation process and the probability pi/j i j&i, j = 0

n as the probability of the dependency between signals

Si and Sj. The probability pi of signal Si. is defined as follows:

pi =i SSin

j=0j SSj

(34)

where i is the occurrence frequency of the signal Si and SSi isthe storage space needed for storing the signal Si. It means, when

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a signal Si appears just once a time during simulation process, iwill have the value one and so on. Although, the probability pi/jof dependency between the signals Si and Sj (or the conditionalprobability) is defined as follows:

pi/j = j SSj

i SSi =jSSj

pi nl=0

l

(35)

where j is the number of times in which the Sj belongs to signal Si.I.e. the number of times that the signal Sj is defined as a parameterof function fi().

The problem we are dealing with can be defined as an optimization

problem. So, mathematically, this problem will be written as follows:

OP :

minm ( 1mi,j

Cki)

minm

( 1mi

pi)(36)

From this optimization problem, we can say that the needed storage

space and the dependency function complexity are inversely (con-

versely) proportional. So, we can define a new space composed of

the complexity and the probability as shown in figure ??. This allows

us to consider the function to minimize as follows:

min

k

(1

k dim2) (37)

where dim is the distance between the points Xmin(pm, Ckm) andXi(pi, Cki):

dim = d(Xi, Xm) =

(pi pm

A)2 + (

Cki CkmB

)2 (38)

where A and B are constants for scaling, and the distance dm isdefined as follows:

dm = mini

(di) di =

(piA

)2 + (CkiB

)2 (39)

The Xmin(pm, Ckm) is chosen with the manner that Sm = fm(Sj)j {0 n} is composed of independent signals only. This means thatall Sj are independent.

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So, the problem we are dealing with can be written as follows:

minl

(1

l

(pi pm)2 + (Cki Ckm)2) (40)

This problem can be transformed to a quadratic optimization problemin the following form:

k {i h} Xk =

pi...

pkCik

...

Ckk

mink

(1

k(XTk MkXk + VkXk + Kk))(41)

where :

Mk =

1A2 0 00 1A2 0 0... . . . ...0 0 1A2

0 0

0 0

1B2 0 00 1B2 0 0... . . . ...0 0 1B2

the matrix of quadratic optimization. This matrix is (2k, 2k) di-mension. I.e Mk

R2k2k. We can demonstrate that the

matrix Mk is symmetric and positive definite, which meansMTk = Mk and x R2k1 : xTMkx > 0.

Vk = 2

pmA...

pmA

CmkB...

CkkB

, the vector of quadratic optimization.

The length of this vector is 2k.

Kk =

p2

iA2...p2k

A2C2km

B2...

C2kk

B2

is a constant vector. The length of this vector

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Figure 12: Considered Space

Figure 13: Variation of the chance of getting optimal solution

is 2k.

The solution of considered problem consists to find a set of signals

Xm = {Si}i{jm} where j < m < n, which satisfy the conditionbelow. Our object is to define the convenient signal sets with which

we have an optimal storage space that associates an optimal com-

plexity.

So, our new problem will be formulate as follows:

m

0

kfind Xm = Sii{jm}

j < m < n (42)

that succeeds:

m Xm = {Si}i{0m}

mink=0n

i=0n

( 1m

Cki) = (1m

Cki)opt

minm

( 1m

p(Si)) = (1m

pi)opt

(43)

To resolve this problem, we try to consider the optimal signal set

as Xopt, which has a length (number of signals inside) nopt such asnopt < n where n is the total signal number inside the consideredVCD file.

To search Xnopt, we need to consider a discrete probability problem,which is defined as follows:

for each m {0 k} we have a chance probability to geta solution of our OP problem. This solution can be writtenas follows: ( 1m

Cik,

1m

pi). Let associate to this solution a

chance probability qm that satisfies 0 < qm < 1.

we know that for our nopt we have the best chance to get theoptimal solution ( 1nopt

Cik,

1nopt

pi)of our OP solution. So,

m {0 k} we have the following condition to be verified :1 > qnopt qm > 0. The Figure ?? shows the variation of thechance to get an optimal solution function of the consideredsignal sets.

We can assume that the variation of the chance of getting an optimal

solution is a distribution. So, we can define this distribution, which

will identify the relationship between the chance probability to get an

optimal solution an the signal sets. This distribution can be written

as follows:

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q(Xi) = exp((Xi Xnopt)T(Xi Xnopt)

) + (44)

where , and are constants.We note that the peak of the chance is found at the point Xnopt .Although, we cannot demonstrate that the considered distribution or

density is not symmetric around Xnopt.

If we assume that this density is symmetric around Xnopt, we candemonstrate that it will be written as follows:

q(Xi) = fXnopt ,Mk(Xi) =1

(2)kdet(Mk)exp( (Xi Xnopt)

TM1k (Xi Xnopt)2

) (45)

Proof: to prove the equation above, just consider the case of the

p-variate normal distribution for multivariate with p = 2k [5].

So, we can use this equation as a constraint for the optimization

problem defined in equation (41). Always, we can fix the chance to

obtain an optimal solution of considered optimization problem, and

than search the corresponding signal sets which succeeds consid-

ered chance probability.

For example is we would like that the chance of getting an opti-

mal solution must be greater than 0.7, we can consider the followingquadratic optimization problem:

mink

( 1k (XTk MkXk + VkXk + Kk))

1

(2)kdet(Mk)

exp( (XkXnopt)TM1

k(XkXnopt)

2 ) 0.7(46)

where k represents the length of the vector Xk =

Si...

Sk

that must

be identified.

4.2.2 One signal restoration

In this section we try to treat the case of restoration of one signal from

a signal lists that have been compressed. We know that considered

signal is combination of a signal sets. So, to restore this signal we

need to calculate the function link this signal to all other signals. In-

deed the complexity of the restoration depends on the calculation of

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these signals. This can be so complex so possible. To reduce this

complexity, we need to reduce the complexities of the calculation of

all signal that are dependent of each other. This means that the

restoration depends on the operation number needed to calculate all

required signals.

Sn = Fn(S0, , Sn1) (47)

where

Si = Fi(S0, , Sk) i, k = 0 n 1 (48)

So, to calculate Fn() we need first to calculate Fi(). So, the com-plexity of the function Fn(), will be calculated based on the functioncomplexities Fi():

Cn =

ni=0

wiCi (49)

where wi represents the weight of the operation belong to signal Si

This problem can be transformed to an optimization problem, which

is

minn

(ni=0

wiCi) (50)

4.2.3 Data base optimization

In this section we try to give an overview about the case where the

same signal depends on itself for each clock cycle and/or on signal,

which depends on clock cycle. Although the simplicity of the sim-

ulation of the relationship between considered signal and the other

associated signal, we have to solve the problem of storage space

optimization.

Let look at the example of figure ??. We see that the signal a de-

pends on the clock signal. It changes value for each clock signal

cycle.

In the example of figure ??, we see that the signal a will change

value each cock signal cycle. So, if we like to store the signal a,

we will need more storage space. Mathematically, we can write the

following relation between the clock signal clk and the signal a

a(n) = a(n1) XOR 1 (51)

where n is the nth clock signal cycle.

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P: process

begin

if clkrising_edge then

a


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Figure 15: Software Design

needed for the restoration of signal value S(n). Arbitrary, we can

choose p as follows:

p IN : p 1 n10

p i = 1 9 (56)

Schedule time analyses: In this paragraph, we prove our choice

of the value of p. Let consider the case, when all values of the signala will be stored. So, we need (n 1) size(a) storage space tostore all values of signal a. However, if we store just the value of a

at the clock signal cycle 0, we will need (n 1) C0 schedule timeto restore the value of signal a at the clock signal cycle n. Indeed,if we apply the developed algorithm, we need just p C0 n10 C0schedule time to restore the a signal value at the clock signal cycle

n and just 9 size(a) storage space. So, we have to reduce thenumber of schedule time of 10 and the number of storage space of10 too.

4.3 Waveform Compression Software Design

In this section an overview of the developed software design is pre-

sented. Figure ?? represents the general aspect of this software.

FreeHDL Simulator: its task is to simulate a given VHDL designin order to create the VCD and DDB files for further use. CDFG Simulator: the CDFG simulator allows to create the

Control Data Flow Graph of considered VHDL model and write

it in a specific file.

Waveform Compressor: its task is the compression of the VCDfile based on the CDFG of considered model. The obtained file

will be stored for further use.

Waveform Decompressor: realizes the decompression of com-pressed VCD file to view it.

Waveform viewer: allows the viewing of the decompressedVCD file in order to get out the verification results of consid-

ered VDHL design.

Figure ?? represents the software module designs in detail.

Waveform Compressor: the waveform Compressor is com-posed of two basic modules:

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Waveform Compression module: this module interests the

compression techniques. Three compression modules

are employed:

Header file compression module: as it is describedabove, the compression of the VCD header file isdone independently of the Control Data Flow Graph.

Simulation Time Compression module: this moduleinterests the compression of the signal ids through-

out the knowledge of considered clock cycle and sig-

nal events. It returns the signal ids, which must be

compressed and stored.

Parameter value compression module: this modulerealizes the compression of considered parameter val-

ues inside the given VCD file based on the informa-

tion returned from Dependency Scheduler and VCDfile. It returns the signal values, which must be com-

pressed and stored.

Dependency Scheduler module: this module treats the

dependency of signals and processes based on the de-

veloped CDFG of the VHDL design. This module has to

control whether a given signal Id and value will be com-

pressed and stored or not. So, it controls the Parameter

Value Compression and the Simulation Time Compres-

sion modules. Thereby, it gives the needed information to

the Simulation Time module about which signal Ids that

must be compressed and these to the Parameter ValueCompression about which signal and variable values must

be compressed and stored. On the other hand, it returns

the dependency between signals and variables in math-

ematic forms to the Waveform Compression module to

be stored. Its input comes from the CDFG Scanner and

Parser.

CDFG Scanner and Parser module: this module translates theCDFG, which is written in a given file to a data base inside the

memory for further need. Its inputs are coming from the DDB

and CDFG files.

Viewer: the viewer has to get out the verification results of con-sidered VHDL model. Basically it consists of two modules :

Waveform Decompressor: it is composed of four mod-

ules, which are needed for the decompression of com-

pressed VCD file.

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Figure 16: Software Module Designs

Header File Decompression module: this module is

used to decompress the VCD header file.

Simulation Time Decompression module: this mod-ule allows the decompression of the Simulation Time

based on the information returned from the compressed

VCD file and the Dependency Simulator.

Parameter Value Decompression module: this mod-ule decompresses all parameter values based on the

information stored in the compressed VCD file and

those returned from the Dependency simulator.

Dependency Simulator module: this module allows to

simulate the stored dependencies between parame-ters and returns either the parameter value or the the

Simulation Time.

waveform viewer: simulates decompressed VCD file to

get out the Verification results of VHDL model.

5 Time Schedule

In this section we presents the needed time to achieve each module

of this software.

VCD header file compression: already done. Simulation time compression: one month. Parameter value compression: one month. Dependency scheduler: two months. CDFG scanner and parser: already done. VCD header file decompression: one month.

Simulation time decompression: two months.

Dependency simulator: three months. Parameter value decompression: two months. Waveform viewer: using Dinotrace. Already done.

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6 Conclusion

In this document, we presented an idea of using CDFG to improve

the developed waveform compression technique. Two cases for us-

ing CDFG in the waveform compression are developed: simple case,

which interests the signal and process dependencies, and complex

case that interests the other VHDL statements. We can conclude

that the CDFG advantages are to allow a rapid interpretation of the

information inside a VHDL model throughout a graphical represen-

tation.

7 Reference

[1] E. Naroska, A Novel Approach for Digital Waveform Compres-

sion.

[2] E. Naroska, Waveform Compression Technique.

[3] E. Naroska and S. Mchaalia, Control Data Flow Graph for Free-

HDL compiler.

[4] J. Ziv and A. Lempel,A Universal Algorithm for Sequential Data

Compression, IEEE Transaction on Information Theory, Vol. IT-23,

No.03, May 1997.

[5] The multivariate Normal Distribution, basic course.

List of Figures Figure ?? : VCD File. Figure ?? : VHDL Model 1. Figure ?? : CDFG of VHDL Model 1. Figure ?? : VHDL Model 2. Figure ??: VHDL Signal Assignment procedure. Figure ?? : CDFG of VHDL Model 2. Figure ?? : VHDL Model 3. Figure ?? : CDFG of VHDL Model3. Figure ?? : VHDL Model 4. Figure ?? : CDFG of VHDL Model 4. Figure ?? : Software Design. Figure ?? : Software Module Designs.

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CDFG for free HDL compiler as refenrece VCD file dumper Said Mchaalia Dortmund, September 2000

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