Improvement of segment timeline $Time$ accuracy (#706)

Fix incorrect timeReplacement when large timescale

The current code essentially does this

    timeReplacement =
	(startTime / timescale + presentationTimeOffset) * timescale

When timescale is large enough (e.g. 10 MHz in order to support MS
Smooth Streaming as well), "startTime / timescale * timescale" may not
always be exactly "startTime" because of floating point precision,
which could produce incorrect segment URLs.

Keep startTime and presentationTimeOffset unchanged in the timeline
just to avoid the multiply/divide dance.

Closes #690

CONTRIBUTORS

@@ -26,6 +26,7 @@ Andy Hochhaus <[email protected]>
 Chad Assareh <[email protected]>
 Costel Madalin Grecu <[email protected]>
 Donato Borrello <[email protected]>
+Duc Pham <[email protected]>
 Esteban Dosztal <[email protected]>
 Itay Kinnrot <[email protected]>
 Jacob Trimble <[email protected]>

lib/dash/mpd_utils.js

@@ -44,6 +44,7 @@ shaka.dash.MpdUtils.GAP_OVERLAP_TOLERANCE_SECONDS = 1 / 15;
 /**
  * @typedef {{
  *   start: number,
+ *   unscaledStart: number,
  *   end: number
  * }}
  *
@@ -52,6 +53,8 @@ shaka.dash.MpdUtils.GAP_OVERLAP_TOLERANCE_SECONDS = 1 / 15;
  *
  * @property {number} start
  *   The start time of the range.
+ * @property {number} unscaledStart
+ *   The start time of the range in representation timescale units.
  * @property {number} end
  *   The end time (exclusive) of the range.
  */
@@ -64,6 +67,7 @@ shaka.dash.MpdUtils.TimeRange;
  *   segmentDuration: ?number,
  *   startNumber: number,
  *   presentationTimeOffset: number,
+ *   unscaledPresentationTimeOffset: number,
  *   timeline: Array.<shaka.dash.MpdUtils.TimeRange>
  * }}
  *
@@ -78,6 +82,8 @@ shaka.dash.MpdUtils.TimeRange;
  *   The start number of the segments; 1 or greater.
  * @property {number} presentationTimeOffset
  *   The presentationTimeOffset of the representation, in seconds.
+ * @property {number} unscaledPresentationTimeOffset
+ *   The presentationTimeOffset of the representation, in timescale units.
  * @property {Array.<shaka.dash.MpdUtils.TimeRange>} timeline
  *   The timeline of the representation, if given.  Times in seconds.
  */
@@ -269,8 +275,12 @@ shaka.dash.MpdUtils.createTimeline = function(
 
     for (var j = 0; j <= repeat; ++j) {
       var endTime = startTime + d;
-      timeline.push(
-          {start: (startTime / timescale), end: (endTime / timescale)});
+      var item = {
+        start: startTime / timescale,
+        end: endTime / timescale,
+        unscaledStart: startTime
+      };
+      timeline.push(item);
 
       startTime = endTime;
       lastEndTime = endTime;
@@ -398,6 +408,7 @@ shaka.dash.MpdUtils.parseSegmentInfo = function(context, callback) {
     segmentDuration: segmentDuration,
     startNumber: startNumber,
     presentationTimeOffset: pto,
+    unscaledPresentationTimeOffset: Number(presentationTimeOffset),
     timeline: timeline
   };
 };

lib/dash/segment_template.js

@@ -114,6 +114,7 @@ shaka.dash.SegmentTemplate.createStream = function(
  *   segmentDuration: ?number,
  *   startNumber: number,
  *   presentationTimeOffset: number,
+ *   unscaledPresentationTimeOffset: number,
  *   timeline: Array.<shaka.dash.MpdUtils.TimeRange>,
  *   mediaTemplate: ?string,
  *   indexTemplate: ?string
@@ -131,6 +132,8 @@ shaka.dash.SegmentTemplate.createStream = function(
  *   The start number of the segments; 1 or greater.
  * @property {number} presentationTimeOffset
  *   The presentationTimeOffset of the representation, in seconds.
+ * @property {number} unscaledPresentationTimeOffset
+ *   The presentationTimeOffset of the representation, in timescale units.
  * @property {Array.<shaka.dash.MpdUtils.TimeRange>} timeline
  *   The timeline of the representation, if given.  Times in seconds.
  * @property {?string} mediaTemplate
@@ -174,6 +177,7 @@ shaka.dash.SegmentTemplate.parseSegmentTemplateInfo_ = function(context) {
     timescale: segmentInfo.timescale,
     startNumber: segmentInfo.startNumber,
     presentationTimeOffset: segmentInfo.presentationTimeOffset,
+    unscaledPresentationTimeOffset: segmentInfo.unscaledPresentationTimeOffset,
     timeline: segmentInfo.timeline,
     mediaTemplate: media,
     indexTemplate: index
@@ -357,16 +361,16 @@ shaka.dash.SegmentTemplate.createFromTimeline_ = function(context, info) {
   var references = [];
   for (var i = 0; i < info.timeline.length; i++) {
     var start = info.timeline[i].start;
+    var unscaledStart = info.timeline[i].unscaledStart;
     var end = info.timeline[i].end;
 
     // Note: i = k - 1, where k indicates the k'th segment listed in the MPD.
     // (See section 5.3.9.5.3 of the DASH spec.)
     var segmentReplacement = i + info.startNumber;
 
     // Consider the presentation time offset in segment uri computation
-    var timeReplacement = (start + info.presentationTimeOffset) *
-        info.timescale;
-
+    var timeReplacement = unscaledStart +
+        info.unscaledPresentationTimeOffset;
     var createUris = (function(
             template, repId, bandwidth, baseUris, segmentId, time) {
           var mediaUri = MpdUtils.fillUriTemplate(