[MPlayer-dev-eng] [PATCH] MPEG-2 TS 60000/1001 FPS Conversion Error in mencoder

[Uoti Urpala]

On Sun, 2006-11-26 at 15:58 -0500, Eric Lammerts wrote:
> When you go from a rational number to floating point and then back to a 
> rational number you'll lose precision. It is unavoidable.

It's avoidable if there's a limit on the numerator/denominator sizes of
the rationals and the floats have enough precision compared to that. The
difference of two rationals a/b and p/q is at least 1/bq; thus if you
have a limit M then converting a float point number approximating a/b
back to the closest possible rational gives a/b as long as the floating
point number has enough precision to tell it's closer to a/b than to
(a/b +- 1/bM)=(a*M +- 1)/bM. About log2(M**2) == 2log2(M) bits of
precision is enough to convert any rational within that limit to
floating point and back without any loss of precision.

> So we should either fix that and make the fps numbers rationals, or (as a 
> dirty workaround) make everything after such conversions less picky about 
> exact matches (e.g., in find_frame_rate_index() change the "if(dmin)" to 
> "if(dmin > 1)").

Just using doubles instead of single precision floats should be enough
as long as the frame rates do not have numerators or denominators in the
tens of millions.