Make live HLS default start position at least 2*target duration from live edge

Issue:#6360
PiperOrigin-RevId: 267615050

library/hls/src/main/java/com/google/android/exoplayer2/source/hls/HlsMediaSource.java

@@ -414,8 +414,18 @@ public final class HlsMediaSource extends BaseMediaSource
           playlist.hasEndTag ? offsetFromInitialStartTimeUs + playlist.durationUs : C.TIME_UNSET;
       List<HlsMediaPlaylist.Segment> segments = playlist.segments;
       if (windowDefaultStartPositionUs == C.TIME_UNSET) {
-        windowDefaultStartPositionUs = segments.isEmpty() ? 0
-            : segments.get(Math.max(0, segments.size() - 3)).relativeStartTimeUs;
+        windowDefaultStartPositionUs = 0;
+        if (!segments.isEmpty()) {
+          int defaultStartSegmentIndex = Math.max(0, segments.size() - 3);
+          // We attempt to set the default start position to be at least twice the target duration
+          // behind the live edge.
+          long minStartPositionUs = playlist.durationUs - playlist.targetDurationUs * 2;
+          while (defaultStartSegmentIndex > 0
+              && segments.get(defaultStartSegmentIndex).relativeStartTimeUs > minStartPositionUs) {
+            defaultStartSegmentIndex--;
+          }
+          windowDefaultStartPositionUs = segments.get(defaultStartSegmentIndex).relativeStartTimeUs;
+        }
       }
       timeline =
           new SinglePeriodTimeline(