I'm using the vDSP framework for a real-time audio application based on FFT computation.
After having lots of problems trying to figure out why the algorithm was producing incorrect results, I found out the following comment on the official vDSP FFT help code (DemonstrateFFT.c, lines 242, 416, 548)
/* Zero the signal before timing because repeated FFTs on non-zero
data can cause abnormalities such as infinities, NaNs, and
subnormal numbers.
*/
In order to reproduce the error, just comment line 247 (no zero the signal) and add something similar to the following line at line 273 (just after the vDSP_fft_zrip method)
if (isnan(Observed.realp[0])) printf("Iteration %lu: NaN\n",i); // it would work with any of the components of Observed
It is interesting to observe that reducing N (i.e. increasing the amount of FFTs per time unit) makes the zrip algorithm to fail before, which kinds of makes sense since the comment advices about performing repeated FFTs.
The behavior is also observed with the vDSP_fft_zrop algorithm.
I'm really wondering what's the point about performing FFTs of "zero data" as advised on the comment. Either I'm missing something important, or definitely the vDSP framework is not suited at all for real-time audio processing.
Normal 16 and 24-bit "real time" audio samples will not see this issue.
But benchmarks can create bigger and smaller numbers that can exceed the range of double precision floats when iterated enough times, and when using many functions, not just FFTs. Try iterating exp() fed back to itself, that will blow up even faster. It's a problem one encounters using any finite precision computer arithmetic (not just the ARM and x86 CPUs that vDSP uses).