MATLAB: Complex numbers in ifft(fft(x))

complex numberfftfouriergpuifft

Hi, i want to realize a convolution through fft and i also want to compare the time required for this process between gpu and cpu. Here is the code:
len=100000;
x=randi(50,1,len);
y=randi(50,1,len);
tic
l=gpuArray([x zeros(1,len-1)]);                       
m=gpuArray([y zeros(1,len-1)]);                      
c_1_temp=ifft(fft(l).*fft(m));                             
toc                                                        
c_1=gather(c_1_temp);
tic
l_1=[x zeros(1,len-1)];                                
m_1=[y zeros(1,len-1)];                              
c_2=ifft(fft(l_1,2*len-1).*fft(m_1,2*len-1));                    
toc
But strangely i've found this result:
c_1= 559,999999985352 - 4,88283691418457e-09i  1655,00000000398 - 1,39078548907368e-08i  3569,99999999371 + 7,06640683828822e-09i  5104,99999999144 + 2,13079904230657e-08i  6494,99999999661 - 1,24666866807290e-08i  7888,00000000453 - 3,32333192044652e-08i  8864,99999998867 - 4,37161194092030e-09i  8850,99999999144 - 1,35629723232990e-08i  8513,99999995740 - 1,81275757497787e-08i  8608,99999998969 + 3,02029185265248e-08i  8493,99999997188 - 1,37329756956340e-08i
and
c_2= 559,999999995117  1655,00000000488  3569,99999998047  5105  6494,99999998047  7888,00000001587  8864,99999998657  8850,99999997559  8513,99999997314  8609,00000001221  8494,00000000122
The same operation for gpu gives complex value which is approximately real.
WHY?

Best Answer

I'm not sure but I assume it's because the GPU FFT computation is non-deterministic. The order of operations is not preserved between FFT and IFFT and so round-off creeps in, whereas on the CPU everything cancels out perfectly. You can enforce symmetricity in the IFFT using the 'symmetric' option.
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