Mark: 14 revision(s)

2008-11-03T05:19:47Z

14 revision(s)

New page

==task1==
<pre>
Entropy Chi Square mean pi% Correlation
Buzhash low 7.98550 99.00% 125.825 1.26% -0.000047
Buzhash typical 7.97970 25.00% 127.177 1.95% -0.007153
Buzhashn low 7.98214 50.00% 127.589 2.10% 0.000600
Buzhashn typical 7.98214 50.00% 127.589 2.10% 0.000600
hash crc low 4.85247 0.01% 99.261 26.10% -0.285059
hash crc typical 7.77880 0.01% 123.087 1.11% -0.002250
base256 low 0.00000 0.01% 97.000 27.32% undefined
base256 typical 3.90309 0.01% 107.987 27.32% 0.079032
object low 2.00000 0.01% 77.000 27.32% -0.521556
object typical 4.97364 0.01% 54.918 27.32% -0.021550
integer low 4.11606 0.01% 32.385 27.32% -0.217081
integer typical 4.11606 0.01% 32.385 27.32% -0.217081
string low 7.99463 99.99% 127.867 1.95% 0.009136
string typical 7.89301 0.01% 126.009 1.42% -0.021360
rand low 7.93533 0.01% 112.054 10.82% -0.066125
rand typical 7.93951 0.01% 111.686 10.82% -0.060458
high rand low 7.98301 75.00% 127.541 0.42% 0.001185
high rand typical 7.98338 75.00% 128.211 1.49% -0.014177
</pre>
====rand vs high rand====
high rand has higher entropy and better chi square compare to rand . The mean of high rand is much closer to 127.5 than rand. Also high rand's pi% and Correlation are much closer to zero compare to rand. Over all high rand has higher randomness than rand.
-----------------------------------------------------------------------------------------------

Entropy: the closer the value is to 8 bits per byte, the more random the numbers returned by the function must be. in this case the entropy of string low is closer to 8bits per bytes.
i don't know why my string low has the higher entropy. Because when i look at some other people's outputs their Buzhash lows have the highest entropy.

====Ranking based on ehtropy====
<pre>
string low 7.99463
Buzhash low 7.98550
high rand typical 7.98338
high rand low 7.98301
Buzhashn low 7.98214
Buzhashn typical 7.98214
Buzhash typical 7.97970
</pre>

Chi Square: The number of times the values would exceed the random variable obtained gives an indication of how random the numbers must be. Values close to 50% have the highest randomness.
the Buzhashn low and typical have the highest randomness{50%}.
====Ranking Based on chi square====
<pre>
Buzhashn low 50.00%
Buzhashn typical 50.00%
high rand low 75.00%
high rand typical 75.00%
Buzhash typical 25.00%
</pre>

Arithmetic mean: The expected mean for a set of random numbers is always the centre between the highest value and the lowest value. For this set of tests, 127.5 is the expected mean. High rand low has 125.541 which is much closer than the others to the expected mean.
====Ranking based on mean====
<pre>
high rand low 127.541
Buzhashn low 127.589
Buzhashn typical 127.589
string low 127.867
Buzhash typical 127.177
</pre>

pi%: the numbers are plotted on a 2D grid containing a circle. The percentage of points inside the circle and the percentage of points outside the circle should be the same. The error indicates by how much the two differ. Hence, the closer the error is to 0, the more random the numbers generated must be. the high rand low has 0.42% of the error
====ranking based on pi%====
<pre>
high rand low 0.42%
hash crc typical 1.11%
Buzhash low 1.26%
string typical 1.42%
high rand typical 1.49%
string low 1.95%
Buzhash typical 1.95%
Buzhashn low 2.10%
Buzhashn typical 2.10%
</pre>

Serial Correlation: Values close to 0 show that the relationship between the numbers is fairly non-existant (and hence must be random).
====why is the Correlation for base256 low is undefined?====
====Ranking based on Correlation====
<pre>
Buzhash low -0.000047
Buzhashn low 0.000600
Buzhashn typical 0.000600
Buzhash typical -0.007153
string low 0.009136
</pre>
------------------------------------------------------------------------------------

Over all Buzhash has highest randomness compare to all the other hush functions.

==task2==
<pre>
Buzhash low 100/1000: llps = 2, expecting 2.13803
Buzhash typical 100/1000: llps = 1, expecting 2.13803
CRC low 100/1000: llps = 2, expecting 2.13803
CRC typical 100/1000: llps = 3, expecting 2.13803
base256 low 100/1000: llps = 100, expecting 2.13803
base256 typical 100/1000: llps = 4, expecting 2.13803
Object low 100/1000: llps = 100, expecting 2.13803
Object typical 100/1000: llps = 3, expecting 2.13803
string low 100/1000: llps = 1, expecting 2.13803
String typical 100/1000: llps = 2, expecting 2.13803
</pre>

Rearranged :

<pre>
String typical 100/1000: llps = 2, expecting 2.13803
Buzhash low 100/1000: llps = 2, expecting 2.13803
CRC low 100/1000: llps = 2, expecting 2.13803
Buzhash typical 100/1000: llps = 1, expecting 2.13803
string low 100/1000: llps = 1, expecting 2.13803
Object typical 100/1000: llps = 3, expecting 2.13803
CRC typical 100/1000: llps = 3, expecting 2.13803
base256 typical 100/1000: llps = 4, expecting 2.13803
base256 low 100/1000: llps = 100, expecting 2.13803
Object low 100/1000: llps = 100, expecting 2.13803
</pre>
---------------------------------------------------------------
String typical ,Buzhash low and CRC low have the best actual performance compare to all the others.
---------------------------------------------------------------
Buzhash has the best performance in both theoretical and actual situation.
hash crc low has the best performance in actual situation. (But in the theoretical situation CRC low had an entropy of 4.85247 which is not close to 8 bits per byte. Also it has a chi square of 0.01% which is not close to 50%.The mean of CRC low is 99.261 which is much lower than the expected mean(127.5). the %pi is much greater than 0 . over all theoretical performance of CRC low is not as good as the theoretical performance of Buzhash .

SE250:lab-5:hlin079 - Revision history

Mark: 14 revision(s)