1. Functional-Level Hardware Simulation with Pull-Model Data Flow George Riley Brian Hayes Elizabeth Lynch

2. Overview Discrete Event Simulation of Digital Devices The Little Computer 3 (LC3) The Pull-Model Approach Performance Comparison Conclusions

3. Discrete Event Simulation Create a computer-based model of the behavior of some particular real-world phenomenon – Airports Events are aircraft arrival, departure, taxiing, waiting – Computer Network Events are packets arrivals, queuing, dropping, departing, application actions – Digital Logic Events are input level changed, speed of light/capacitance delays Common approach in all cases – Maintain sorted (by timestamp) list of things known to happen in the future (an aircraft will be arriving at a particular time) – Find earliest event, remove from sorted list, advance the time to the timestamp of that event, and process the event. Note runway busy while aircraft landing, increment count of aircraft at the airport, schedule a taxi event to occur after the landing

4. Gate-Level Hardware Simulation Each level change on an input schedules a new input changed event in the future (speed of light) for any directly connected device – Level change on A changes input to the inverter, which changes the input to the AND gate, which changes input to the OR gate, which changes the SUM value.

5. Functional Level Hardware Simulation Do not model state of individual gates Rather, model the device as a black box, with known outputs for every possible set of inputs. Include rise-time and processing time delay within the device Four Bit Adder A input, bits 0-3 B input, bits 0-3 Carry Out Sum, bits 0 - 3 Carry In

6. Instruction-Level Simulation Model the effects of each instruction – LD R2,1000 – Maintain state of each of the registers, program counter, result flags, memory, etc. An extreme form of functional-level simulation, where the black box is the entire CPU/Memory of the computer Clearly, significantly more efficient than either functional-level or gate level Generally does not model simulation time – Instructions or clock ticks

7. Synchronous vs. Asynchronous Devices Asynchronous devices change their output values immediately (within rise-time and speed of light delays) upon any change in an input – Adders, multiplexers, sign extenders, ALU, tri-state buffers Synchronous devices only change outputs or observe inputs at specific clock ticks – Latch (observe and store internally) inputs on rising edge – Change outputs on falling edge – Registers, Memory, Finite State Machine

8. Asynchronous Loops in Logic Design Async 1 Async 4Async 3 Async 2 Not likely to be the desired behavior Inputs and outputs continuously change at speed of light

9. Synchronous Loops in Logic Design Async 1 Sync 4Async 3 Async 2 Output to Async 1 only changes on falling edge clock Synchronous device latches input from Async 3 on rising edge clock Clock Effects of synchronous output changes must propagate in one-half clock cycle

10. The Little Computer 3 Yale Patt Textbook

11. The LC3 Finite State Machine Fetch State – Substates: LDMAR, LDMDR, LDMDR2, LDIR, DELAY Decode State Evaluate Address State – Substates: GET_BASE, COMP_ADDR, LDMDR, LDMDR2 Operand Fetch State – Substates: NORM, GETSR Execute State – Substates: NORM, DELAY Store Result State

12. The LC3 Finite State Machine Outputs The LC3 FSM has 23 outputs: – OutAluControl, OutSR2MuxSel, OutGateALU, OutGatePC, OutGateMARMux, OutGateMDR, OutMARMuxSel, OutAddr1MuxSel, OutAddr2MuxSel, OutPCMuxSel, OutLdIR, OutLdMDR1, OutLdMDR2, OutLdMAR, OutLdReg, OutLdPC, OutLdCC, OutSR1, OutSR2, OutDr, OutMemEnable, OutMemRW

13. The Traditional Push-Model Approach On each clock falling edge tick, all synchronous devices produce new output (which might be inputs to other asynchronous devices), and schedule future events to notify those devices of new input values. When processing these input changed events, these asynchronous devices further propagate their changed outputs to the corresponding inputs. For example, on the FETCH state of the FSM, substate LDMAR, the following outputs are set – PCMuxSel = 2 – LdPC = 1 – OutGatePC = 1 – LdMAR = 1 All other FSM outputs are zero. This results in nearly all devices in the LC3 design receiving input changed events, depending on the prior value of the individual FSM outputs. Significant wasted computation for signals not of value at any point

14. The New Pull-Model Approach Devices need not notify other devices of changed inputs Rather, devices ask for input values only when needed. The querying of input values might recursively propagate to several levels, but stops at a synchronous device. Needless computation not performed For example, if GateMARMux is zero, the output of the tri-state device is not used, and therefore the inputs (the output of the MARMUX device) are not needed. For example, if LD.PC is one, the PC register asks the PCMUX device for the current value. – The PCMUX asks the FSM the value of the PCMUX.SEL selector – If the value is 2 (for example) then the PCMux asks the +1 adder for the current output, which in turn asks the PC register for the current (latched) output. – No other computation is done (in this case)

15. Pull-Model One downside is that there is no mechanism to account for speed of light and rise time delays We simply assume that one-half clock cycle is sufficient for all propagation through asynchronous devices Interestingly, this approach results in no future events at all, other than clock ticks. Further, the order that synchronous devices receive the tick events is not relevant – The device will work the same regardless of the order of the ticks – This is of course the case, as in actual circuits the clock inputs for the synchronous devices are varying distance from the clock source, resulting in random ordering of the ticks.

16. Performance Comparison Simple LC3 assembly language program, with two nested loops. Short Version, 2^16 iterations Medium Version, 2^20 iterations Long Version, 2^24 iterations Implemented as two simple nested loops, with 2^16 inner loop, varying output loop count Also implemented instruction-level simulation for performance comparison.

17. Performance Results

18. Summary Pull Model is substantially more efficient – Nearly a factor of 80 – No loss in accuracy, assuming the one-half clock tick rule We are looking into methods to include speed-of-light and rise-time delays in the pull model We expect that more complex CPU/datapath designs will continue to enjoy significant speedup compared to the push-model, but doubt it will be as significant as the simple LC3 design. – Instruction level parallelism utilizes more parts of the entire circuit during clock tick