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the difference LT and AT

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Well, usually this describes the simulation timing behavior of a system. Approximately-timed models breakdown communication protocols into the subsquent phases with attached time points and durations. The components of a system adhere to a common or global time base - they execute in sync. In loosly-timed models part of the system are allowed to stick to their own time base which might deviate from the  global time base by a given amount (the quantum). Communication transactions a handled as a single transaction with annoteted time points so that the components can react acccordingly.

As a simple example let's have a look at an instruction set simulator (ISS). In AT mode it would execute one machine instruction, do all the bus transactions at the correct points in time (related to the global time base). Thus interactions in the system (triggering interrupts, writing GPIO pins etc.) are fairly correct from a timing point of few. But it inccurs quite some overhead as the execution (in the simulation) switches very often from the model to kernel and back (so called context switches). In LT mode the ISS is allowed to execute a whole bunch of instructions without returning the control to the simulation kernel. Usuallay this implies that communication transaction are executed in a blocking fashion without wait() calls. To be able to run-ahead and still have time passing the ISS has to maintain a local time base (the local quantum). In the case of simple memory read and writes this has no effect on the entire system but it saves a lot context switches so it boosts the performance. To make sure that the functionality get not sacrificed each interaction with the system carries an annotated delay so that the reciever of the transaction (e.g. a timer) can decide to stop the ISS execution simulation thread and let the rest of the simulation catch up - it breaks the quantum.

In practice you will find mostly mixtures of the 2 apporaches but I hope this gives you an idea.

Cheers

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