Re: [RFC PATCH] clk: fractional-divider: Correct max_{m,n} handed over to rational_best_approximation()

[Andy Shevchenko]

On Thu, Jul 15, 2021 at 8:51 AM Liu Ying <victor.liu@xxxxxxx> wrote:
> On Wed, 2021-07-14 at 13:46 +0300, Andy Shevchenko wrote:
> > On Wed, Jul 14, 2021 at 01:38:22PM +0300, Andy Shevchenko wrote:
> > > On Wed, Jul 14, 2021 at 06:10:46PM +0800, Liu Ying wrote:
> > > > On Wed, 2021-07-14 at 12:12 +0300, Andy Shevchenko wrote:
> > > > > On Wed, Jul 14, 2021 at 02:41:29PM +0800, Liu Ying wrote:
> > >
> > > ...
> > >
> > > > > > /*
> > > > > >  * Get rate closer to *parent_rate to guarantee there is no overflow
> > > > > >  * for m and n. In the result it will be the nearest rate left shifted
> > > > > >  * by (scale - fd->nwidth) bits.
> > > > > >  */
> > > > >
> > > > > I don't know how to rephrase above comment better.
> > > > >
> > > > > > scale = fls_long(*parent_rate / rate - 1);
> > > > > > if (scale > fd->nwidth)
> > > > > >       rate <<= scale - fd->nwidth;
> > > > >
> > > > > This takes an advantage of the numbers be in a form of
> > > > >
> > > > >         n = k * 2^m, (1)
> > > > >
> > > > > where m will be scale in the snippet above. Thus, if n can be represented by
> > > > > (1), we opportunistically reduce amount of bits needed for it by shifting right
> > > > > by m bits.
> > > > > Does it make sense?
> > > >
> > > > Thanks for your explaination.
> > > > But, sorry, Jacky and I still don't understand this.
> >
> > It seems I poorly chose the letters for (1). Let's rewrite above as
> >
> > This takes an advantage of the numbers be in a form of
> >
> >       a = k * 2^b, (1)
> >
> > where b will be scale in the snippet above. Thus, if a can be represented by
> > (1), we opportunistically reduce amount of bits needed for it by shifting right
> > by b bits.
> >
> > Also note, "shifting right" here is about the result of n (see below).
> >
> > > Okay, We have two values in question:
> > >  r_o (original rate of the parent clock)
> > >  r_u (the rate user asked for)
> > >
> > > We have a pre-scaler block which asks for
> > >  m (denominator)
> > >  n (nominator)
> > > values to be provided to satisfy the (2)
> > >
> > >     r_u ~= r_o * m / n, (2)
> > >
> > > where we try our best to make it "=" instead of "~=".
> > >
> > > Now, m and n have the limitation by a range, e.g.
> > >
> > >     n >= 1, n < N_lim, where N_lim = 2^nlim. (3)
> > >
> > > Hence, from (2) and (3), assuming the worst case m = 1,
> > >
> > >     ln2(r_o / r_u) <= nlim. (4)
> > >
> > > The above code tries to satisfy (4).
> > >
> > > Have you got it now?
>
> I'm afraid I haven't, sorry. Jacky, what about you?

You may take a pen and paper and model different cases. After all it's
not rocket science, just arithmetics :-)

> Is that snippet really needed?

Yes. The (4)  shows why.

> Without that snippet, it seems that rational_best_approximation() is
> able to offer best_numerator and best_denominator without the risk of
> overflow for m and n, since max_numerator and max_denominator are
> already handed over to rational_best_approximation()?

No.

> Does rational_best_approximation() always offer best_numerator by the
> range of [1, max_numerator] and best_denominator [1, max_denominator]?

Of course not, when it goes out of the range.

> > > > > The code looks good to me, btw, although I dunno if you need to call the newly
> > > > > introduced function before or after the above mentioned snippet.
> > > >
> > > > Assuming that snippet is fully orthogonal to this patch, then it
> > > > doesn't matter if it's before or after.
> > >
> > > Please, double check this. Because you play with limits, while we expect them
> > > to satisfy (3).


-- 
With Best Regards,
Andy Shevchenko