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Team Members

1. Yehoshua Ghitis, Stuff
2. Boris Bershadsky, Prime generator
3. Ozal Islam, Precision of Pi

oaislam1@myseneca.ca, bbershadsky@myseneca.ca?subject=dps901-gpu610 Email All

Progress

Assignment 1

Precision of Pi

Calculation of Pi:

The number of miliseconds required to complete the function for computing the precision of Pi takes longer if the number of iterations is increased by 10 exponentially.

If GPU was used to compute the function then the number of miliseconds could be drastically reduced with high number of iterations.

Test runs with number of iterations:

oaislam1@matrix:~/Ozal/GPU610/a1> time a1 100
Compute pi - took - 0 millisecs
3.131592903558551910236928961239755153656005859375

real    0m0.137s
user    0m0.004s
sys     0m0.008s
oaislam1@matrix:~/Ozal/GPU610/a1> time a1 5000
Compute pi - took - 0 millisecs
3.14139265359178754266622490831650793552398681640625

real    0m0.145s
user    0m0.004s
sys     0m0.004s
oaislam1@matrix:~/Ozal/GPU610/a1> time a1 10000
Compute pi - took - 1 millisecs
3.141492653590030936783250581356696784496307373046875

real    0m0.143s
user    0m0.000s
sys     0m0.012s
oaislam1@matrix:~/Ozal/GPU610/a1> time a1 100000
Compute pi - took - 12 millisecs
3.14158265358971622305261917063035070896148681640625

real    0m0.141s
user    0m0.012s
sys     0m0.012s
oaislam1@matrix:~/Ozal/GPU610/a1> time a1 1000000
Compute pi - took - 139 millisecs
3.141591653589779209454491137876175343990325927734375

real    0m0.269s
user    0m0.140s
sys     0m0.008s
oaislam1@matrix:~/Ozal/GPU610/a1> time a1 1000000000
Compute pi - took - 178576 millisecs
3.14159265258789854868837210233323276042938232421875

real    2m58.717s
user    2m58.315s
sys     0m0.040s

Sample GProf profile:

Flat profile:

Each sample counts as 0.01 seconds.
%   cumulative   self              self     total
time   seconds   seconds    calls  Ts/call  Ts/call  name
100.00     10.05    10.05                             compute_pi(int)
0.00     10.05     0.00        1     0.00     0.00  _GLOBAL__sub_I__Z10compute_pii

Calculation of prime numbers

Prime numbers are essential in the science of cryptography and are a good test of computational capacity of computers. The bigger the number, the more exponentially the hardware must work to calculate the next prime number.

Calculation of prime numbers is a very simple objective with a simple double for loop:

for (int i = 2; i<100; i++) for (int j = 2; j*j <= i; j++) { if (i % j == 0) break; else if (j + 1 > sqrt(i)) { std::cout << i << " "; } }

However, this serial processing is extremely inefficient when the numbers become extremely large. For the range of 1-1,000,000 the results are as follows:

real 0m4.982s user 0m3.644s sys 0m0.072s

Flat profile:

Each sample counts as 0.01 seconds.

 %   cumulative   self              self     total           
time   seconds   seconds    calls  Ts/call  Ts/call  name    

100.00 3.63 3.63 genPrime(unsigned long long, unsigned long long)

 0.00      3.63     0.00        1     0.00     0.00  _GLOBAL__sub_I__Z8genPrimeyy

There are 78496 prime numbers in the calculated range. Splitting the for loop between several cores to handle each subrange separately can yield extremely high performance gains.

Console output:

\\CPD S4\GPU610\a1\a1Boris\Debug>a1Boris 5000

• • • Team /dev/null GPU610 PRIME NUMBER GENERATOR***

No range given (or bad input), using preset values Generating from range (0~5000)

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