player: add ability to speed up based on delay

Added the following command-line options:
 --rt-catchup: enables the new feature
 --rt-catchup-multiplier: (double) sets a constant speed multiplier
 --rt-catchup-max-delay: (double) sets the maximum delay before speedup

If --rt-catchup is enabled, when the player falls a number of seconds
exceeding the value given by --rt-catchup-max-delay, playback speed is
multiplied by the sum of 1 and the square of the product of the value
given by --rt-catchup-multiplier and the current delay in excess of the
delay given by --rt-catchup-max-delay in seconds.

The speed multiplier is applied in addition to the playback speed
multiplier set by the user.

This feature is introduced to help prevent falling behind real-time
sources such as live streams.

DOCS/man/options.rst

@@ -216,6 +216,21 @@ Playback Control
     speed higher than normal automatically inserts the ``scaletempo2`` audio
     filter.
 
+``--rt-catchup``
+    Enable the player to speed up by a factor equal to the sum of 1, and the
+    square of the product of how many seconds behind the the delay given by
+    ``--rt-catchup-max-delay`` the player has fallen and the value given by
+    ``--rt-catchup-multiplier`` unless the delay does not exceed the delay
+    given by ``--rt-catchup-max-delay``.
+
+``--rt-catchup-max-delay=<0.0..>``
+    The maximum delay in seconds behind the media source the player may reach
+    before it starts speeding up, if ``--rt-catchup`` is enabled.
+
+``--rt-catchup-multiplier=<0.0..>``
+    A coefficient applied during the speed multiplier calculation according to
+    ``--rt-catchup`` and ``--rt-catchup-max-delay``
+
 ``--pause``
     Start the player in paused state.
 

options/options.c

@@ -568,6 +568,13 @@ static const m_option_t mp_opts[] = {
     // set a-v distance
     {"audio-delay", OPT_FLOAT(audio_delay)},
 
+    // set live/realtime catch-up parameters
+    {"rt-catchup", OPT_FLAG(realtime_catchup)},
+    {"rt-catchup-multiplier", OPT_DOUBLE(realtime_catchup_speed_multiplier),
+        M_RANGE(0, DBL_MAX)},
+    {"rt-catchup-max-delay", OPT_DOUBLE(realtime_catchup_max_delay),
+        M_RANGE(0, DBL_MAX)},
+
 // ------------------------- codec/vfilter options --------------------
 
     {"af-defaults", OPT_SETTINGSLIST(af_defs, &af_obj_list),

options/options.h

@@ -224,6 +224,9 @@ typedef struct MPOpts {
     int hr_seek_framedrop;
     float audio_delay;
     float default_max_pts_correction;
+    int realtime_catchup;
+    double realtime_catchup_speed_multiplier;
+    double realtime_catchup_max_delay;
     int autosync;
     int frame_dropping;
     int video_latency_hacks;

player/audio.c

@@ -174,9 +174,29 @@ void audio_update_volume(struct MPContext *mpctx)
     ao_set_gain(ao_c->ao, gain);
 }
 
+// Calculate a speed multiplier proportional to the delay between the current
+// playback time and the media source. This multiplier is used to keep up with a
+// real-time source such as a live stream.
+static double calc_realtime_catchup_speed(struct MPContext *mpctx)
+{
+    double max_delay = mpctx->opts->realtime_catchup_max_delay;
+    double delay = get_time_length(mpctx) - get_playback_time(mpctx);
+
+    if (delay > max_delay) {
+        double multiplier = mpctx->opts->realtime_catchup_speed_multiplier;
+        return 1.0 + powf((delay - max_delay) * multiplier, 2.0);
+    } else {
+        return 1.0;
+    }
+}
+
 // Call this if opts->playback_speed or mpctx->speed_factor_* change.
 void update_playback_speed(struct MPContext *mpctx)
 {
+    if (mpctx->opts->realtime_catchup) {
+        mpctx->opts->playback_speed = calc_realtime_catchup_speed(mpctx);
+    }
+
     mpctx->audio_speed = mpctx->opts->playback_speed * mpctx->speed_factor_a;
     mpctx->video_speed = mpctx->opts->playback_speed * mpctx->speed_factor_v;