A Novel Approach of Caching Direct Mapping using Cubic Approach

A Novel Approach Of Caching
Direct Mapping Using Cubic
Approach
Guidance
Professor Chandrasegar .T
Site,vit university Vellore
Team Member
Kamlesh Asati 11MCA0133
Aakansha Soni 11MCA0080
Harikesh Dwivedi 11MCA0083
04SETMCAO056

Aim
 A novel approach of caching direct mapping
using cubic approach appreciate to improve
system efficiency without losses the data.
 It means that decrease the data access time
with using sufficient memory but that’s not
enough while we are implement these things
with minimum time complexity and high
level security.
04SETMCAO056

Objective Scope
 Increase the system performs.
 Decrease the process execution time and find
the method in which time complexity in this
approach is minimum.
 Try to produce accurate result without data
losses.
04SETMCAO056

Abstract
 In the last few decades there is lot of research
works carried out for the improvement of c p u.
 Caching address mapping technique plays a
vital role for the system improvement.
 Based on the number of hits occurred on the
caching leads to the effective utilization of
processor.
 in general when the caching memory size
increases then the number of page faults
/misses is going to get decreases between the
processor and the system memory.
 In this concept the proposed work is to deal with
caching direct mapping and to secure the data in
a random and cubic based combinatorial
approach.
04SETMCAO056

Introduction
Cache Memory Mapping
 The memory system has to quickly determine if a
given address is in the cache.
 Caching address mapping techniques plays a vital
role for the system improvement. Based on the no
of hits occurred on the caching leads to the
effective utilization of processor.
There are three popular methods
1) Fully associative mapping
2) Set associative mapping
3) Direct mapping
04SETMCAO056

Direct Mapping
 This is the most popular technique for
cache memory mapping.
 If each block from main memory has only
one place it can appear in the cache, the
cache is said to be direct mapped.
 Since a data block from ram can only be on
space line in the cache , it must always
replace the one block that was already
there.
04SETMCAO056

 Address Splits into two part address
S w
 Least significant w bits identify unique word
in block.
 Most significant s bits specify one memory
block.
 s bits divided into two parts tag line
s
a) Cache line address field r bits.
b) Tag field of s-r most significant bit.
S-r r
04SETMCAO056

Cubic Approach
 In cubic approach for Mapping we map the
data in random and cubic base approach.
 For this we use the formula of cubic equation.
F(x)= ax3+bx2+cx+d
04SETMCAO056

Existing System
 In direct mapping, mapping is done with the linear approach.
For this we use hashing concept, If data is consist of n integers
and we have k number of cells then the address where in data
stored or retrieved is the ordinary hash function is Hash = n%k
H (k, i) = (h (k) + ci) modm
 Think how linear mapping works then the answer is if the first
location is not free, then it will go to the next location and
check if the location is free or not, and so on until it finds
empty blocks or can’t find at all. For retrieving the data, hash
function and rehash function is used, retrieving is done by
using the hash function to find the key and check if the data
would coincide to the data needed. If not then rehash would
be needed. Until such time the correct location is found or an
empty space is encountered which shows the data does not
exists. In linear approach the searching takes so much time
because in linear mapping it searches in all blocks of memory
therefore the speed is slow.
04SETMCAO056

Literature Review
According to Zhenghong Wang and Ruby B. Lee ,
Caches ideally should have low miss rates and short
access times, and should be power efficient to system
at the same time.
 Sincerely finding on efficient hits based on
information losses in caches have also moves the
security issue for it. finally this concept shows that
the cache architecture has low Miss Rates
comparable to a highly associative cache and short
access times and power efficiency close to that of a
direct-mapped cache.
 Additional benefits that the include cache
architecture can bring, like fault method and hot-spot
revolution techniques.
04SETMCAO056

According to Mark D. Hill , cache is used to
improve the system cost, which have large
memory but using the cache memory we
increase the access time of the system.
Cache is small in size so it holds some data at a
time .cache memory hold that data which are
frequently used by the processor. For storing
cache retained the recent referenced
information.
Caches are successful due to temporal and
spatial locality. Temporal locality means future
references are likely to be made to the same
locations as recent references, while spatial
locality suggests that future references are also
likely to be made to locations near recent
references.
 Caches take advantage of temporal locality by
retaining recently referenced Information.
04SETMCAO056

Methodology
Now we are trying to use our cubic approach to
map the memory. The family of cubic equation is
f(x) =ax3+bx2+cx+d.We use the function
h(x) = (ax 3+bx 2+cx+d) mod y
For finding the key element in cache memory .in
this formula we take the value of x between 0 to 15
and map the memory into cache between 0 to 15.
For finding the solution we gives the value of x
from 0 to 15 and change the values of a, b, c, d and
calculate the function value y= ax3+bx2+cx+d and
for the value of key element we calculate the value
y modmheremis 16.
04SETMCAO056

In this table we
observe this cubic
formula
F(x)=(ax3+bx2+cx+)
mody gives the
value which is
repeated in the
column (ymod16),it
means for that
value of a,b,c,d
it maps some
memory address
which is same.so
this is not a
correct mapping.
X a b c d y Mod y
0 2 3 3 1 1 1
1 2 3 3 1 9 9
2 2 3 3 1 35 3
3 2 3 3 1 91 11
4 2 3 3 1 189 13
5 2 3 3 1 341 5
6 2 3 3 1 559 15
7 2 3 3 1 855 7
8 2 3 3 1 1241 9
9 2 3 3 1 1729 1
10 2 3 3 1 2331 11
11 2 3 3 1 3069 3
12 2 3 3 1 3925 5
13 2 3 3 1 4941 13
14 2 3 3 1 6119 7
04SETMCA56 15 2 3 3 1 7471 15

State diagram
Start
0,2,4,6,8 0,2,4,6,8 1,3,5,7,9
1,3,5,7,9
1,3,5,7,9 0,2,4,6,8
0 to 9
a
Final/
hit
b
miss
c d
04SETMCAO056

 We notice that the function
 F(x)= (ax3+bx2+cx+d)mod y
 give unique value
when we choose the value of a b & c such
that a & b must be even and c must be odd
but d consist any value between 0 to 9.
above given state diagram shows how the
function will work.
04SETMCAO056

Result
 Using this approach we decrease the time
complexity of the direct mapping which is
good and complexity is o(n) , its also help the
decrease the process execution time.
input(0-15) output(0-15)
 The proposed work is to deal with caching and
to secure the data in a random and cubic base
approach.
04SETMCAO056
Cubic remapping
system
f(x) =ax3+bx2+cx+d

 So we are using the cubic approach which
maps the function more speedily than linear.
In linear approach power consumption is also
high using this approach we can also reduce
the power consumption.
 Using cubic approach we get the time
complexity is o(n) .
04SETMCAO056

Consider this snapshot as sample
output ...
04SETMCAO056

Conclusion
 A cache is to improve system cost performance by
providing the capacity of the large, slow memory
with an access time close to that of the small, fast
cache.
 This simple approach implements a form of by
passing the different address value.
We develop a cubic approach to evaluate the
performance of the proposed direct mapped caching
algorithm our method enhances the reuse behavior of
the temporal data while improving the reuse of the no
temporal data by cubic associativity.
 From our experimental results, we see that our
method is both fast and accurate.
04SETMCAO056

Future Enhancement
 Future reaches issue can give better solution
for this system , provided it overcomes the
problems like replacement strategy that can
better adopt to user access pattern and improve
the cache space utilization , security issue.
04SETMCAO056

A Novel Approach of Caching Direct Mapping using Cubic Approach

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