Re: [Discuss-gnuradio] the block “complex to Arg” in gnuradio

[Marcus Müller]

Hi Johannes, Hi xd,

complex_to_arg uses GNU Radio's fast_atan2f function, which is an approximation [1].
Between the 255 values of the lookup table, it uses linear interpolation, hence your 0.4 error factor.

As Johannes said, that's not really surprising for a look up table-based approach.
I do think using this approximation is justified, but I also think that the codebase it uses has been obsolete for a bit now:
gr::fast_atan2 could be replaced by volk's volk_32fc_s32f_atan2_32f, which has been around since 2012, but hasn't seen any use in GNU Radio, as far as I can tell.

Now, I went ahead and had a benchmark [2] which showed that gr::fast_atan2 is actually quite fast -- but that's only twice as fast as the standard been-around-forever libc implementation and the volk implementation (which, admittedly, also does a multiplication with 1.0, and by the way: the generic volk kernel (which does libc atan2 + multiplication) is exactly as fast as the SSE4 one on my machine), and everything is pretty much in the same range as C++ <complex>'s std::arg :

For 2²⁵ complex numbers, of which at least half have small angles:

1: .fast:
1:  0.397261s wall, 0.370000s user + 0.020000s system = 0.390000s CPU (98.2%)
1:
1: .volk:  0.780515s wall, 0.760000s user + 0.020000s system = 0.780000s CPU (99.9%)
1:
1: .libc:  0.777738s wall, 0.760000s user + 0.020000s system = 0.780000s CPU (100.3%)
1:
1: .c++ complex arg:  0.815700s wall, 0.780000s user + 0.030000s system = 0.810000s CPU (99.3%)

But: this is on an Intel i7. Things might look different on your average android phone or even worse, your raspberry Pi (so if you wanna test, [2] ).

Conclusion: If you're after small angles, the current complex_to_arg's factor 2 speedup might not be what your after.
That is probably not the case if you use complex_to_arg in an quadrature_demod inside an FM audio receiver running on an embedded device -- small angle errors don't make the least difference here.
The question is, like it was with gr::random, whether we still prefer performance over preciseness, or if we excercise exactness.

Also, I was pretty amazed how fast fast_atan2 really is –  its dependence on branching suggests it's pretty hard to vectorize and optimize as a compiler.

Best regards,
Marcus

[1] https://gnuradio.org/doc/doxygen/group__misc.html#ga6c1470346a3524989b7a8a3639aa79a7
[2]
On 10.11.2015 10:45, Johannes Demel wrote:

Hi,

Could you extend a test case for this block with Python? This might
reveal issues with the implementation more easily. Also, others might
benefit from it.
For your specific problem, I guess the GR block result is as close as
it gets for a LUT-based calculation. And it's not off by a lot but by
some 10^-x.

Cheers
Johannes

On 10.11.2015 10:29, w xd wrote:
> Hi all,

> Thank you very much in advance.

> I find the result of the block "complex to Arg" is same to the
> result in matlab most of the time,while sometimes the results is
> different from the result in matlab.

> For example, a=1.646236600879293e+03 + 8.043715071772031e+00i I use
> the command  atan2 or angle to calculate the result. It return
> 0.004886084452240.

> While i calculate the result using the gnuradio. It return
> 0.002944485750049.

> Can someone explain it?

> The version of gnuradio:3.7.5. Best regards, xd



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