Hi Federico,
On 11.05.2016 21:09, Federico Larroca wrote:
> Hello everyone,
> We are on the stage of optimizing our project (gr-isdbt).
Awesome!
> One of the most consuming blocks is OFDM synchronization, and in
> particular the equalization phase. This is simply the division between
> the input signal and the estimated channel gains (two modestly big
> arrays of ~5000 complexes for each OFDM symbol).
> Until now, this was performed by a for loop, so my plan was to change
> it for a volk function. However, there is no complex division in VOLK.
> So I've done a rather indirect operation using the property that a/b =
> a*conj(b)/|b|^2, resulting in six lines of code (a multiply conjugate,
> a magnitude squared, a deinterleave, a couple of float divisions and
> an interleave). Obviously the performance gain (measured with the
> Performance Monitor) is marginal (to be optimistic)...
I have to admit, I'd expect your "simple" for loop doing something like
void yourclass::normalize(std::complex<float> *a, std::complex<float> *b) {
for(size_t idx; idx < a_len; ++idx)
a[idx] /= b[idx];
}
to be neatly optimizable by the compiler, at least if it knows that a
and b aren't pointing at the same memory-
Your approach,
$\frac ab = a \cdot \frac{b^*}{|b|^2}= a \cdot \frac{b^*}{b\,b^*} = a
\cdot \frac 1b$
is correct; however, in C++ with std::complex<>
a/b
pretty much does that already (ugly std lib C++ ahead, from
/usr/include/c++/<version>/complex):
// XXX: This is a grammar school implementation.
template<typename _Tp>
template<typename _Up>
complex<_Tp>&
complex<_Tp>::operator/=(const complex<_Up>& __z)
{
const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag();
const _Tp __n = std::norm(__z);
_M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n;
_M_real = __r / __n;
return *this;
}
And the problem is that while doing that for every a and b separately
might mean you can't make full use of SIMD instructions to eg. do four
complex divisions at once, it avoids having to load and store original /
intermediate values from/to RAM. Basically, your CPU might not be the
bottleneck – RAM could be, and doing everything you need for a single
division at once, even if done without any optimization, might be faster
than incurring additional memory transfers. That's because your memory
controller pre-fetches whole cache lines worth of values when getting
the first elements of a and b, and working on values from cache is
significantly (read: factor > 50) than a single memory transfer.
So, my immediate recommendation really is to keep your loop as minimal
as possible, giving your compiler a solid chance to see the potential
for optimization. There might not be much you can do. Even hand-written
VOLK kernels aren't always faster than automatically generated optimized
machine code.
> Does anyone has a better idea? Implementing a new kernel is simply out
> of my knowledge scope.
Ha! But it would mean endless (additional) fame!
Soooo: look at the volk_32fc_x2_multiply_conjugate_32fc.h kernel source.
Specifically, at the SSE3 implementation,
volk_32fc_x2_multiply_conjugate_32fc_u_sse3(…).
You'll notice line 134:
z = _mm_complexconjugatemul_ps(x, y);
As you can see, there's a a "VOLK intrinsic",
_mm_complexconjugatemul_ps
which is defined in volk_intrinsics.h. That same file contains
_mm_magnitudesquared_ps_sse3 . Maybe you can make something clever out
of that :)
Best regards,
Marcus
[1] https://gcc.gnu.org/onlinedocs/gcc/Restricted-Pointers.html
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