add TimestampNumerator/TimestampDenominator to override the value of TimestampScale

This allows sample precision of each timestamp is some cases, mostly single track files.

Wherever TimestampScale was used, if this fraction is found, it should be used
instead.

Author: robUx4

ebml_matroska.xml

@@ -88,11 +88,18 @@ The format depends on the ChapProcessCodecID used; see (#chapprocesscodecid-elem
     <documentation lang="en" purpose="definition">Timestamp scale in nanoseconds (1.000.000 means all timestamps in the Segment are expressed in milliseconds).</documentation>
     <extension type="libmatroska" cppname="TimecodeScale"/>
   </element>
-  <!-- <element name="TimestampScaleDenominator" parent="/Segment/Info" level="2" id="0x2AD7B2" type="uinteger" minOccurs="1" maxOccurs="1" minver="4" default="1000000000">
-    <documentation lang="en">Timestamp scale numerator; see <a href="https://www.matroska.org/technical/elements.html#TimestampScale">TimestampScale</a>.</documentation>
-TimestampScale When combined with <a href="https://www.matroska.org/technical/elements.html#TimestampScaleDenominator">TimestampScaleDenominator</a> the Timestamp scale is given by the fraction TimestampScale/TimestampScaleDenominator in seconds.-->
+
+  <element name="TimestampNumerator" path="\Segment\Tracks\TrackEntry\TimestampNumerator" id="0x2AF6A9" type="uinteger" range="not 0" maxOccurs="1" minver="4">
+    <documentation lang="en" purpose="definition">Timestamp numerator to apply instead of the TimestampScale, when the TimestampDenominator is present as well.</documentation>
+    <extension webm="0"/>
+  </element>
+  <element name="TimestampDenominator" path="\Segment\Tracks\TrackEntry\TimestampDenominator" id="0x2AF6AA" type="uinteger" range="not 0" maxOccurs="1" minver="4">
+    <documentation lang="en" purpose="definition">Timestamp denominator to apply instead of the TimestampScale, when the TimestampNumerator is present as well.</documentation>
+    <extension webm="0"/>
+  </element>
+
   <element name="Duration" path="\Segment\Info\Duration" id="0x4489" type="float" range="&gt; 0x0p+0" maxOccurs="1">
-    <documentation lang="en" purpose="definition">Duration of the Segment in nanoseconds based on TimestampScale.</documentation>
+    <documentation lang="en" purpose="definition">Duration of the Segment in nanoseconds based on TimestampScale or TimestampNumerator/TimestampDenominator.</documentation>
   </element>
   <element name="DateUTC" path="\Segment\Info\DateUTC" id="0x4461" type="date" maxOccurs="1">
     <documentation lang="en" purpose="definition">The date and time that the Segment was created by the muxing application or library.</documentation>
@@ -113,7 +120,7 @@ TimestampScale When combined with <a href="https://www.matroska.org/technical/el
     <documentation lang="en" purpose="definition">The Top-Level Element containing the (monolithic) Block structure.</documentation>
   </element>
   <element name="Timestamp" path="\Segment\Cluster\Timestamp" id="0xE7" type="uinteger" minOccurs="1" maxOccurs="1">
-    <documentation lang="en" purpose="definition">Absolute timestamp of the cluster (based on TimestampScale).</documentation>
+    <documentation lang="en" purpose="definition">Absolute timestamp of the cluster (based on TimestampScale or TimestampNumerator/TimestampDenominator).</documentation>
     <extension type="libmatroska" cppname="ClusterTimecode"/>
   </element>
   <element name="SilentTracks" path="\Segment\Cluster\SilentTracks" id="0x5854" type="master" maxOccurs="1">
@@ -175,7 +182,7 @@ If BlockAddIDType of the corresponding block is 0, this value is also the value
     <extension type="webmproject.org" webm="1"/>
   </element>
   <element name="BlockDuration" path="\Segment\Cluster\BlockGroup\BlockDuration" id="0x9B" type="uinteger" maxOccurs="1">
-    <documentation lang="en" purpose="definition">The duration of the Block (based on TimestampScale).
+    <documentation lang="en" purpose="definition">The duration of the Block (based on TimestampScale or TimestampNumerator/TimestampDenominator). 
 The BlockDuration Element can be useful at the end of a Track to define the duration of the last frame (as there is no subsequent Block available),
 or when there is a break in a track like for subtitle tracks.</documentation>
     <implementation_note note_attribute="minOccurs">BlockDuration **MUST** be set (minOccurs=1) if the associated TrackEntry stores a DefaultDuration value.</implementation_note>
@@ -206,7 +213,7 @@ This information **SHOULD** always be referenced by a seek entry.</documentation
 The duration of DiscardPadding is not calculated in the duration of the TrackEntry and **SHOULD** be discarded during playback.</documentation>
     <extension type="webmproject.org" webm="1"/>
   </element>
-  <element name="Slices" path="\Segment\Cluster\BlockGroup\Slices" id="0x8E" type="master" maxOccurs="1">
+  <element name="Slices" path="\Segment\Cluster\BlockGroup\Slices" id="0x8E" type="master" maxver="1" maxOccurs="1">
     <documentation lang="en" purpose="definition">Contains slices description.</documentation>
     <extension type="webmproject.org" webm="0"/>
     <extension type="divx.com" divx="0"/>

notes.md

@@ -577,6 +577,32 @@ Some general notes for a program:
    that it started with. Using a slightly lower timestamp scale factor can help here in
    that it removes the need for proper rounding in the conversion from sample number to `Raw Timestamp`.
 
+## Rational Number and Nanoseconds
+
+Historically timestamps in Matroska were stored in nanoseconds precision.
+The `TimestampScale` would reduce the size of each value stored in the file by dividing each real timestamps by a certain value.
+For many sampling frequencies, that means rounding the values and losing precision.
+There are `TimestampNumerator` and `TimestampDenominator` to fix this precision loss.
+They override the value of `TimestampScale` in all places it is used. 
+
+This formula remains but there is no rounding involved anymore:
+
+    (a + b) * c
+
+    a = `Block`'s Timestamp
+    b = `Cluster`'s Timestamp
+    c = `TimestampScale`
+
+For compatibility with older readers that don't understand these elements, the `TimestampScale` value *MUST*
+be the rounded values of `TimestampNumerator` divided by `TimestampDenominator` in nanoseconds.
+
+This fraction may not be usable in most cases. It works well with files having a single Track.
+It only works when Tracks have a sampling frequency which is highly divisible.
+For example even a video track of 1/25000 (PAL) with audio of 1/48000 (DAT) doesn't work well. The reduced fraction gives 25/48.
+A `TimestampNumerator` of 1 and `TimestampDenominator` of 25\*48000 would give ticks that hit on each clock.
+But the amount of samples possible in a Block/SimpleBlock is stored on 16 bits or 65536 values. So the duration possible in a Cluster would be 65536 / (25\*48000) or 54.6 ms. Which is not enough to be efficient storage.
+It would only work if audio samples were packed with a multiple of 25 samples, which is usually not the case.
+
 ## TrackTimestampScale
 
 The `TrackTimestampScale Element` is used align tracks that would otherwise be played at