clk: imx: improve precision of AV PLL to 1 Hz

clk: imx: improve precision of AV PLL to 1 Hz

The audio and video PLLs are designed to have a precision of 1 Hz if some
conditions are met. The current implementation only allows a precision that
depends on the rate of the parent clock. E.g., if the parent clock is 24
MHz, the precision will be 24 Hz; or more generally the precision will be

    p / 10^6 Hz

where p is the parent clock rate. This comes down to how the register
values for the PLL's fractional loop divider are chosen.

The clock rate calculation for the PLL is

    PLL output frequency = Fref * (DIV_SELECT + NUM / DENOM)

or with a shorter notation

    r = p * (d + a / b)

In addition to all variables being integers, we also have the following
conditions:

    27 <= d <= 54

    -2^29 <= a <= 2^29-1
     0    <  b <= 2^30-1
    |a| < b

Here, d, a and b are register values for the fractional loop divider. We
want to chose d, a and b such that f(p, r) = p, i.e. f is our round_rate
function. Currently, d and b are chosen as

    d = r / p
    b = 10^6

hence we get the poor precision. And a is defined in terms of r, d, p and
b:

    a = (r - d * p) * b / p

I propose that if p <= 2^30-1 (i.e., the max value for b), we chose b as

    b = p

We can do this since

    |a| < b

    |(r - d * p) * b / p| < b

    |r - d * p| < p

Which have two solutions, one of them is when p < 0, so we can skip that
one. The other is when p > 0 and

    p * (d - 1) < r < p * (d + 1)

Substitute d = r / p:

    (r - p) < r < (r + p)  <=>  p > 0

So, as long as p > 0, we can chose b = p. This is a good choise for b since

    a = (r - d * p) * b / p
      = (r - d * p) * p / p
      = r - d * p

    r = p * (d + a / b)
      = p * d + p * a / b
      = p * d + p * a / p
      = p * d + a

and if d = r / p:

    a = r - d * p
      = r - r / p * p
      = 0

    r = p * d + a
      = p * d + 0
      = p * r / p
      = r

I reckon this is the intention by the design of the clock rate formula.

Signed-off-by: Emil Lundmark <emil@limesaudio.com>
Reviewed-by: Fabio Estevam <fabio.estevam@nxp.com>
Acked-by: Shawn Guo <shawnguo@kernel.org>
Signed-off-by: Stephen Boyd <sboyd@codeaurora.org>