# [Matroska-devel] timecode scale handling & sample precision

Moritz Bunkus m.bunkus at linet-services.de
Sun Aug 1 13:51:17 CEST 2004

```Hi,

until now I really didn't care all that much, but now that I'm
implementing sample precision I have to care. So I took the time to
study the current explanation for the timecode scale handling available
at http://www.matroska.org/technical/specs/notes.html#TimecodeScale

It is wrong.

Let's take the sample rate of 44100. A timecode scale parameter of
1000000000/44100 is 22675.736961. The example uses 22676 which results
in a precision that is LESS than the sample rate. There's no way to to
regenerate 44100 different sample numbers from < 44100 different values.
It must be 22675 - always _truncate_ the timecode scale factor.

The next thing is:
<quote>
To determine which sample that is,
(313450348 / 1000000000) * 44100 = ~13823.16
Check to see if the value is greater than the truncated version of
itself and if so, round up.
</quote>

A value is always at least as big as its truncated value! So this will
simply result in wrong values. You're throwing away up to nearly 1
sample of time. There's NO way a program can regenerate that from the
raw timecode and the timecode scale factor.

Here's how to use it right including a small demonstration application:

(I'll use \$var for a variable name because the text might be confusing
otherwise.)

Use the following timecode scale value:

\$tc_scale = (int64_t)(1000000000ll / \$sample_rate)

Let's assume we have a sample number \$sample, the sample rate
\$sample_rate and the timecode scale factor as given above. We further
need a function that can round a value to the nearest integer (in this
case the nearest 64bit integer). We can use a simple #define for this:

#define irnd(v) ((int64_t)((v) + 0.5) > (int64_t)(v) ? \
(int64_t)((v) + 0.5) : (int64_t)(v))

The 'original' timecode \$unscaled_timecode is the one the application
deals with. It is obviously just

\$unscaled_timecode = 1000000000ll * \$sample / \$sample_rate

Easy enough. Even better wound be using double precision and rounding,
but 1ns is WAY below any sensible \$sample_rate so we can live with the
imprecision of just truncating this value to the lower ns.

Next: the \$scaled_timecode is the one that is actually written to the
Matroska file. Other folks call this the 'raw' timecode. I'll use
'scaled' for timecodes whose unit is '1 \$tc_scale' and 'unscaled' for
timecodes whose unit is '1ns'.

--> Here we HAVE to round! <--

This timecode is

\$scaled_timecode = irnd((double)\$unscaled_timecode / (double)\$tc_scale)

Now we have a nice scaled timecode in our file. Another application
wants to read such a file, gets \$tc_scale from the header and reads a
block. Inside that file it finds \$scaled_timecode for that block. From
that it can calculated the 'unscaled' timecode on the reader's part:

\$rescaled_timecode = \$scaled_timecode * \$tc_scale

Easy. No rounding needed obviously because we multiply integers in the
first place. How does the application get the sample number from this?
Again this involves...

--> ROUNGIN! <--

\$recalculated_sample = irnd((double)\$rescaled_timecode * \$sample_rate /
1000000000.0l)

Et voila. That's it.

I've attached a small test application that demonstrates this for a
sample rate of 44100. It will output each of the four values along with
a string 'ok' or 'NOT OK!' if the \$sample is equal to or different from
the \$recalculated_sample. If you don't believe me just test it, redirect
the output to a file and search for 'NOT OK'. You won't find it.

I REALLY hope I'm not making a mistake here, but I'm pretty sure I
don't. So I'll overhaul the web page mentioned at the beginning with
this information and modify mkvmerge accordingly if no one objects.

Mosu

--
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