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Chapter 3 Pipelining

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3.1 Pipeline Model n Terminology –task –subtask –stage –staging register n Total processing time for each task. –T pl =, where t i is the processing time, d i is the delay by the staging register, and k is the number of stages

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3.1 Pipeline Model (continued) n Total processing time for each task. –T seq = n pipeline cycle time, t max = Max(t i +d i ), 1 I k n clock frequency = 1/ t max n pipeline cycle time t cyc can be denoted by T seq /k + d n speedup, S =,where N is the number of tasks.

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3.1 Pipeline Model (continued) n If staging register delay is ignored and the processing times of the stages are same, t cyc = T seq / k. Therefore, S ideal becomes n If

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3.1 Pipeline Model (continued) n The total cost of the pipeline is given by C= L.k + Cp where Cp = and L is the cost of each staging register. n To minimize the composite cost per the computation rate, k =

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3.1 Pipeline Model (continued) n In practice, making the delays of pipeline stages equal is a complicated and time-consuming process –It is essential to maximum performance that the stages be close to balanced. –It is done for commercial processors, although it is not easy and cheap to do n Another problem with pipelines is the overhead in term of handling exception or interrupts. –A deep pipeline increases the interrupt handling overhead.

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Pipeline Types n Pipeline Types(Handler’s classification) –Instruction pipelines n FI, DI, CA, FO, EX, ST –arithmetic pipelines –processor pipelines: a cascade of processors each executing a specific module in the application program.

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Instruction pipeline n reservation table –Row : stages –Column : pipeline cycles n The cycle time of instruction pipelines is often determined by the stages requiring memory access.

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Control Hazard n Conditional branch instructions –The target address of branch will be known only after the evaluation of the condition. n The ways to solve control hazards –The pipeline is frozen –The pipeline predicts that the branch will not be taken. – It would be to start fetching the target instruction sequence into a buffer while the nonbranch sequence is being fed into the pipeline.

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Arithmetic pipelines n Floating point addition –Consider S = A + B, where A=(Ea,Ma), B=(Eb, Mb), and S=(Es,Ms) –Addition steps (Figure 3.5) n Equalize the exponents n Add mantissas n Normalize Ms and adjust Es for the sum normalization n Round Ms n Renormalize Ms and adjust Es –Modified floating point add pipeline (Figure 3.6 & 3.7)

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Arithmetic pipelines(cont.) n floating point multiplication –Consider P= A x B, where A=(Ea,Ma), B=(Eb, Mb), and P=(Ep,Mp) –Multiplication steps (Figure 3.8) n Add exponents n Multiply mantissas n Normalize Mp and adjust Ep n Round Mp n Renormalize Mp and adjust Ep –Modified floating point add pipeline (Figure 3.9)

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Arithmetic pipelines(cont.) n Multifunction pipeline –To perform more than one operation –A control input is needed for proper operation of the multifunction pipeline. –Figure 3.10 : floating point add/multiplier

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Classification scheme by Ramamoorthy and Li n Functionality –unifunctional – multifunctional n Configuration –static –dynamic n Mode of operation: –scalar – vector

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3.2 Pipeline control and Performance n To provide the max. possible throughput, it must be kept full and flowing smoothly. n Two conditions of smooth flow of a pipeline: –the rate of input of data –data interlocks between the stages n Example 3.1 : the pipeline completes one operation per cycle(once it is full) n Example 3.2 : non-linear pipeline

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Structural hazard n Due to the non-availability of appropriate hardware n One obvious way of avoiding structural hazard is to insert additional hardware into the pipeline.

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Example 3.3 n Figure 3.12 depicts the operation of the pipeline –In cycle 3, 4, 5, and 6, simultaneous accesses are needed. – If we assume that the machine has separate data and instruction caches, in cycles 5 and 6 the problems are solved. – One way to solve the problem in cycle 4 is to stall the ADD instruction (Figure 3.13) n The stalling process results in a degradation of pipeline performance.

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Collision vectors n Initiation : launching of an operation into the pipeline n Latency: the number of cycles that elapse between two initiation. n Latency sequence: the latencies between successive initiations n Collision: it occurs if a stage in the pipeline is required to perform more than one task at any time.

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Collision vectors(cont.) n Forbidden set: the set of all possible column distances between two entries on some row of RT. n Collision vector can be derived from forbidden set F and can be utilized to control the initiation of operations in the pipelines. –CV = (v n-1,v n-2,…,v 2,v 1 ) –V i =1 if i is in the forbidden set

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Examples Example 3.4 (a)Overlapped RT (b)Collision Vector(CV) Example 3.5 & 3.6 Collision case and no collision case

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Control n How to control the initiation of pipeline using CV. –Place the CV in a shift reg. –If the LSB of the shift reg. Is 1, do not initiate an operation at that cycle; shift the CV right once, inserting 0 at the vacant MSB position –If the LSB of the shift reg. Is 0, initiate a new operation at that cycle; shift the CV right once, inserting 0 at the vacant MSB position. In order to reflect the superposing status due to the new initiation over the original one, perform a bit-by-bit OR of the original CV with the content of the shift reg.

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3.2.3 Performance n Figure 3.15(a) – The CV of Figure 3.11 : (00111) – Figure 3.15(a) shows the state transitions.

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3.2.3 Performance n Average latency n simple cycle n greedy cycle n MAL(Minimum average Latency)

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3.2.4 Multifunction Pipelines n Figure 3.17 n Vxx, Vxy, Vyx, Vyy

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3.3 Other Pipeline Problems n Data Interlock: due to the sharing of resources. Data hazard n data forwarding n internal forwarding –write-read forwarding –read-read forwarding –write-write forwarding n load/store architectures versus memory/memory architectures

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3.3 Other Pipeline Problems (continued) n Conditional Branches –branch prediction –delayed branch –branch-prediction buffer –branch history –multiple instruction buffers n Interrupts –precise interrupt scheme

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3.4 Dynamic Pipelines n Instruction deferral –scoreboard n Tomosulo’s algorithm n Performance evaluation –maximizing the total number of initiations per unit time –minimizing the total time required to handle a specific sequences of initiation table types

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3.5 Example systems n CDC Star-100 n CDC 6600 n MIPS R-4000

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3.6 Summaries n Three approaches have been tried to improve the performance beyond the ideal CPI case: –superpipeline –superscalar –VLIW(Very Long Instruction Word)

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End of Chapter 3

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PIPELINING AND VECTOR PROCESSING

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