Question Regarding fft_step_size (int k) in 'tuneup.c' in GMP

[Lingchuan Meng]

Hi all,

I've been studying and twisting the tuneup program in GMP4.2.4 recently. And
I got a question about the fft_step_size().

mp_size_t
fft_step_size (int k)
{
  mp_size_t  step;

  *step = MAX ((mp_size_t) 1 << (k-1), BITS_PER_MP_LIMB) /
BITS_PER_MP_LIMB;  //what's the special purpose of this line?*
*  step *= (mp_size_t) 1 << k;  //** Is it not good enough just to set step
to 2^k?                             *
  ...
  return step;
}

In addition, I noticed that if I half the step size in fft_step_size(), I
can gain better performance around the point where Toom3 is replaced by SSA.
A plot is provided in attachment, where you can see the threshold generated
by default tuning program (green line) causes a loss since it sets the fft
threshold greater than what it actually is. The one labeled 'tune2' is what
I got by halving the step size. All the values in labels correspond to FFT
thresholds in each case.

-- 
Best regards,

Lingchuan Meng
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