lavfi/vf_libplacebo: set time_base/frame_rate dynamically

Use the gcd of all input timebases to ensure PTS accuracy. For the
framerate, just pick the highest of all the inputs, under the assumption
that we will render frames with approximately this frequency. Of course,
this is not 100% accurate, in particular if the input frames are badly
misaligned. But this field is informational to begin with.

Importantly, it covers the "common" case of combining high FPS and low
FPS streams with aligned frames.

libavfilter/vf_libplacebo.c

@@ -1158,6 +1158,11 @@ static int libplacebo_config_input(AVFilterLink *inlink)
     return 0;
 }
 
+static inline AVRational max_q(AVRational a, AVRational b)
+{
+    return av_cmp_q(a, b) < 0 ? b : a;
+}
+
 static int libplacebo_config_output(AVFilterLink *outlink)
 {
     int err;
@@ -1198,6 +1203,16 @@ static int libplacebo_config_output(AVFilterLink *outlink)
     if (s->fps.num) {
         outlink->frame_rate = s->fps;
         outlink->time_base = av_inv_q(s->fps);
+    } else {
+        outlink->frame_rate = avctx->inputs[0]->frame_rate;
+        outlink->time_base = avctx->inputs[0]->time_base;
+        for (int i = 1; i < s->nb_inputs; i++) {
+            outlink->frame_rate = max_q(outlink->frame_rate,
+                                        avctx->inputs[i]->frame_rate);
+            outlink->time_base = av_gcd_q(outlink->time_base,
+                                          avctx->inputs[i]->time_base,
+                                          AV_TIME_BASE / 2, AV_TIME_BASE_Q);
+        }
     }
 
     /* Static variables */