Large discrepency between CPU and GPU with fftn and ifftn?
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Nathan Zechar
il 23 Mag 2020
Risposto: Andrea Picciau
il 26 Mag 2020
Hello,
I am using a GPU to compute multipul 3D FFTs. I've come across a problem where the output I am recieving from the GPU FFT is vastly different in terms of shape and values. I am unsure why this is the case and if there is any way to mitigate this problem.
I have included a small portion of code where data is generated, and the fftn and ifftn are applied to this data. Below the code are surface plots which show the difference in output. Is there a method that can be applied to where the output from the GPU FFT will be closer to the output of the CPU FFT?
N = 128;
x = (pi/4).*(0:N-1);
z = (3*pi/4).*(0:N-1);
tol = 1.0e-8;
kx = [tol 1:N/2 -N/2+1:-1].*2.*pi.*(1i)./N;
[X,Y,Z] = ndgrid(x,x,z);
X = cos(2.*pi.*X./(32*pi));
Y = cos(2.*pi.*Y./(32*pi));
Z = exp(-(Z-(48*pi)).^2./100./(96*pi));
A = 4.*Z.*(Y+1i.*X);
%% What the output should look like
A0 = A;
A0 = fftn(A0);
A0 = A0.*kx';
A0(1,:,:) = 0;
A0 = ifftn(A0);
A0 = real(A0);
A01 = squeeze(A0(:,:,64));
subplot(1,2,1)
surf(A01)
title('CPU')
%% GPU output is signigicantly different
A1 = gpuArray(A);
A1 = fftn(A1);
A1 = A1.*kx';
A1(1,:,:) = 0;
A1 = ifftn(A1);
A1 = real(A1);
A11 = squeeze(A1(:,:,64));
subplot(1,2,2)
surf(A11)
title('GPU')
%% Compares output of both
max(abs(A0-A1),[],'all')
2 Commenti
David Goodmanson
il 23 Mag 2020
Hi Nathan,
in your definition of A11, could you explain why you have VM on the right hand side in place of A1?
Risposta accettata
Andrea Picciau
il 26 Mag 2020
Hi Nathan,
The results differ for two related reasons:
- GPUs and CPUs have quite different architectures,
- the CPU and GPU algorithms are slightly different.
On my GPU, I'm getting a max abs error of 1.6584e-15, which is within the expected tolerance and our error analysis.
As a rule of thumb, you should (almost always) expect a discrepancy between the GPU and the CPU that goes from 1e-14 to 1e-15 for computations in double precision.
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