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Superdense Time

This article has examples in the following target languages:

Tag vs. Time

The model of time in Lingua Franca is a bit more sophisticated than we have hinted at. Specifically, a superdense model of time is used. In particular, instead of a timestamp, LF uses a tag, which consists of a logical time t and a microstep m.

A logical action may have a <min_delay> of zero, and the <offset> argument to the schedule() function may be zero. In this case, the call to schedule(>) appears to be requesting that the action trigger at the current logical time. Here is where superdense time comes in. The action will indeed trigger at the current logical time, but one microstep later. Consider the following example:

target C main reactor { state count: int = 1 logical action a reaction(startup, a) -> a {= printf("%d. Logical time is %lld. Microstep is %d.\n", self->count, lf_tag().time, lf_tag().microstep ); if (self->count++ < 5) { lf_schedule(a, 0); } =} }
Lingua Franca diagram: MicrostepsCreator: FreeHEP Graphics2D Driver Producer: de.cau.cs.kieler.klighd.piccolo.freehep.SemanticSVGGraphics2D Revision Source: Date: Sunday, April 10, 2022 at 9:19:33 AM Pacific Daylight TimeMicrostepsL

Executing this program will yield something like this:

1. Logical time is 1649607749415269000. Microstep is 0.
2. Logical time is 1649607749415269000. Microstep is 1.
3. Logical time is 1649607749415269000. Microstep is 2.
4. Logical time is 1649607749415269000. Microstep is 3.
5. Logical time is 1649607749415269000. Microstep is 4.

Notice that the logical time is not advancing, but the microstep is (the logical time, in this case, gives the number of nanoseconds that have elapsed since January 1, 1970). The general rule is that every call to schedule() advances the tag by at least one microstep.

Logical Simultaneity

Two events are logically simultaneous only if both the logical time and the microstep are equal. The following example illustrates this:

target C reactor Destination { input x: int input y: int reaction(x, y) {= printf("Time since start: %lld, microstep: %d\n", lf_time_logical_elapsed(), lf_tag().microstep ); if (x->is_present) { printf(" x is present.\n"); } if (y->is_present) { printf(" y is present.\n"); } =} } main reactor { logical action repeat d = new Destination() reaction(startup) -> d.x, repeat {= lf_set(d.x, 1); lf_schedule(repeat, 0); =} reaction(repeat) -> d.y {= lf_set(d.y, 1); =} }
Lingua Franca diagram: SimultaneousCreator: FreeHEP Graphics2D Driver Producer: de.cau.cs.kieler.klighd.piccolo.freehep.SemanticSVGGraphics2D Revision Source: Date: Sunday, April 10, 2022 at 9:31:53 AM Pacific Daylight TimeSimultaneousDestinationyx12L

The Destination reactor has two inputs, x and y, and it reports in a reaction to either input what is the logical time, the microstep, and which input is present. The main reactor reacts to startup by sending data to the x input of Destination. It then schedules a repeat action with an <offset> of zero. The repeat reaction is invoked strictly later, one microstep later. The output printed, therefore, will look like this:

Time since start: 0, microstep: 0
x is present.
Time since start: 0, microstep: 1
y is present.

The reported elapsed logical time has not advanced in the second reaction, but the fact that x is not present in the second reaction proves that the first reaction and the second are not logically simultaneous. The second occurs one microstep later.

Alignment of Logical and Physical Times

Recall that in Lingua Franca, logical time "chases" physical time, invoking reactions at a physical time close to their logical time. For that purpose, the microstep is ignored.