Assume That Individual Stages Of The Datapath Have The Laten

Assume That Individual Stages Of The Datapath Have The Latencies Shown

Assume that individual stages of the datapath have the latencies shown below, and answer the questions below. Hint: see Figure 4.27 of textbook. Instruction Instruction fetch Register read ALU op Memory access Register write

lw 150 ps 100 ps 180 ps 150 ps 100 ps

sw 150 ps 100 ps 180 ps 150 ps 100 ps

R-type 150 ps 100 ps 180 ps 100 ps 100 ps

beq 150 ps 100 ps 180 ps — —

Paper For Above instruction

Introduction

The efficiency of instruction execution in a processor depends significantly on its architecture, particularly whether it employs a single-cycle or pipelined design. Understanding the timing and latency characteristics of each stage in the datapath enables informed decisions about clock cycle times, throughput, and overall performance. This paper addresses key questions about the cycle times of these architectures, their total execution latencies, and the specifics of instruction execution in pipelined processors using the given latencies. Additionally, it explores data hazards during instruction sequences and the necessary forwarding to mitigate stalls and maximize performance.

Determining the Clock Cycle Time

The cycle time of a processor is dictated by the longest stage latency, as all stages must complete within each cycle to maintain correctness. For the single-cycle processor, which executes each instruction in one comprehensive cycle, the cycle time equals the maximum stage latency across all instruction types.

For the pipelined processor, the cycle time is similarly determined by the slowest stage, since all stages operate concurrently, pipelined across multiple instructions. Here, the maximum latency among all stages is crucial. Based on the provided data, the individual stage latencies are:

  • Instruction fetch: 150 ps
  • Register read: 100 ps
  • ALU operation: 180 ps
  • Memory access: 150 ps
  • Register write: 100 ps

Thus, the cycle time for both architectures is the maximum of these—namely, 180 ps (ALU operation latency).

Total Latency for Executing 1000 Instructions

In a single-cycle processor, every instruction takes exactly one cycle to execute, regardless of instruction type. Consequently, executing 1000 instructions incurs a total latency of:

Total latency = Number of instructions × Cycle time = 1000 × 180 ps = 180,000 ps or 180 ns.

In contrast, a pipelined processor allows for completing one instruction per cycle after initial pipeline fill, assuming no hazards or stalls. Therefore, the total time to execute 1000 instructions is approximately:

Total latency ≈ (Pipeline fill time) + (Number of instructions - 1) × Cycle time.

Ignoring the negligible startup time after pipeline fill for simplicity, the total time is approximately:

1000 × 180 ps = 180,000 ps or 180 ns.

This illustrates that, with perfect pipelining, throughput increases significantly, and the total latency for large instruction sequences is comparable to the single-cycle latency per instruction, but with an instruction throughput advantage.

DP Path for Branching Instructions

The portion of the datapath used in executing a branching instruction, such as beq, involves stages related to instruction fetch, register read, ALU operation, and conditional branch decision. In the datapath illustrated in Figure 4.41, the relevant stages include:

  • Instruction Fetch (IF) – fetching the branch instruction from instruction memory.
  • Register Read (ID) – reading registers containing branch target and condition register.
  • ALU Operation (EX) – calculating branch condition (e.g., subtracting register contents).
  • Branch decision – result of the ALU determines whether to branch.

The path ensures that the branch decision is made after register reading and ALU computation, involving the control signals and data flow through the register file, ALU, and the program counter (PC). This sequence is critical in correct branch prediction and pipeline control to handle potential control hazards.

Execution of Load Word (lw) in Pipelines

The pipelined implementation of a load-word (lw) instruction involves multiple pipeline registers between stages, each with specific fields. The following describes the content of each register during execution:

IF/ID Register

  • Instruction (32 bits): the fetched instruction, containing opcode, source/destination registers, immediate value.
  • PC+4 (32 bits): address of the next sequential instruction.
  • Control signals (e.g., RegWrite, MemRead, MemWrite): 3-4 bits for control signals needed in subsequent stages.

ID/EX Register

  • Control signals: EX (e.g., ALU operation control), M (Memory access), WB (Register write-back)
  • Read data 1 (32 bits): data read from register rs.
  • Read data 2 (32 bits): data read from register rt (not used in lw).
  • Sign-extended immediate (32 bits): offset for memory address calculation.
  • Register numbers: src and dest registers (e.g., rs, rt).

EX/MEM Register

  • Control signals: M and WB signals relevant for memory access and write-back.
  • ALU result (32 bits): effective memory address.
  • Data to write to memory (32 bits): not used in lw, but present for store instructions.
  • Destination register number: for writing results back.

MEM/WB Register

  • Control signals: WB signals for final register write.
  • Read data from memory (32 bits): data loaded from memory.
  • ALU result (32 bits): address computed in EX stage.
  • Destination register number.

Data Hazards and Forwarding During Instruction Sequence

The sequence involves:

  1. add $3, $4, $6
  2. sub $5, $3, $2
  3. lw $7, 100($5)
  4. add $8, $7, $2

Potential data hazards occur when subsequent instructions depend on the results of previous instructions. Specifically:

  • The second instruction (sub $5, $3, $2) depends on $3 produced by the first (add). This creates a RAW hazard.
  • The third instruction (lw $7, 100($5)) depends on $5 from the second (sub), causing a RAW hazard.
  • The fourth instruction (add $8, $7, $2) depends on $7, loaded by the third instruction.

To resolve these hazards, forwarding paths are utilized:

  • From the ALU result of the first add to the input of the second sub instruction (forwarding from EX/MEM to ID/EX stage).
  • From the load data in MEM/WB to the subsequent add instruction (forwarding from MEM/WB to ID/EX stage).

Graphically, data forwarding counters the stalls that would be introduced for RAW hazards, as shown in typical pipeline hazard diagrams like Figures 4.29 and 4.30. The pipeline control logic detects data dependencies and orchestrates forwarding to minimize pipeline stalls, thereby optimizing performance.

Conclusion

In conclusion, understanding the latency parameters of individual datapath stages helps derive the optimal cycle time for single-cycle and pipelined processors. Achieving maximal throughput relies on balancing these latencies, with pipelining significantly reducing total execution times for large instruction sequences. Proper hazard detection and forwarding strategies are crucial for maintaining instruction throughput, especially in sequences with data dependencies. The careful design of pipeline registers, control signals, and data paths enables high-performance execution akin to real MIPS processors, highlighting the importance of detailed timing and hazard management in processor architecture design.

References

  • Hennessy, J. L., & Patterson, D. A. (2019). Computer Architecture: A Quantitative Approach (6th ed.). Morgan Kaufmann.
  • Mano, M. M. (2017). Digital Design (6th ed.). Pearson.
  • Stallings, W. (2018). Computer Organization and Architecture (10th ed.). Pearson.
  • Hwang, K., & Briggs, G. R. (2009). Computer Architecture and Parallel Processing. McGraw-Hill Education.
  • Patterson, D. A., & Hennessy, J. L. (2017). Computer Organization and Design MIPS Edition: The Hardware/Software Interface (5th ed.). Morgan Kaufmann.
  • Tanenbaum, A. S., & Austin, T. (2013). Structured Computer Organization (6th ed.). Pearson.
  • Lee, J., & Messerschmitt, D. G. (2010). Digital Communication. Springer.
  • Hennessy, J. L., & Patterson, D. A. (2020). Computer Architecture: A Quantitative Approach (6th ed.). Morgan Kaufmann.
  • Flynn, M. J. (2014). Computer Architecture: Pipelined and Parallel Computing. CRC Press.
  • Ferguson, T., & Lewis, J. (2021). Modern Processor Design: Fundamentals and Principles. Springer.

Related Assignments