Problem 1: Delayed Principles (25 points)

1.1

Fill in the following table regarding the latencies and initiation intervals of each functional unit. Each correct value is worth one point.

Unit	Latency	Initiation Interval
INT ALU	0	1
FP ADD	7	1
FP MULT	17	1
FP DIV	59	66 (not pipelined!)

1.2

Using the information in the FU table and the pipeline structure, determine the latencies in the MMM-MIPS for potentially dependent pairs of ALU instructions in the table below.

For example, the value 0 corresponds to the latency between an INT ALU instruction producing a result that another INT ALU instruction needs. Each correct value is worth (1) point.

Hint: for each dependent instruction pair, identify which stage of the producer instruction is the ``source'' of the value that must be ``received'' by the consumer instruction.

Producer	Consumer	Latency
Instruction	Instruction
INT ALU	INT ALU	0
INT ALU	INT LOAD	0
INT ALU	BNEZ	1
INT Load	INT ALU	1
FP ADD	FP ALU	7
FP MUL	FP ALU	17
FP Load	FP ALU	1

Instruction Latency Table

Answer:

To see where the numbers in the instruction latency table came from, write down two instructions that satisfy the consumer/producer roles above. Then, track their execution on the pipelike pipe, under the assumptions above, and determine how many stalls are required to clear the data hazard.

The tricky one is the one with the BNEZ in it.

DADD R5, R5, R5 F D X M W
BNEZ R5, dump F S D X M W

1.3

Answer: As in the previous problem, you needed to determine the latencies associated with the pairs of operations given below. To verify these, write out two instructions satisfying the producer/consumer instruction definition and count the stalls needed to have the data hazard clear. Notice that it's impossible to have to related instructions of the types noted as independent below.

That is, a FP ALU instruction has no use for a result from an INT ALU instruction; so, the latency is zero because they are independent. Similarly, an instruction that stores a value has no output! So, the latency of any instruction following it is always zero, because it is impossible for the first instruction to affect the values in the 2nd.

Producer	Consumer	Latency
Instruction	Instruction
INT ALU	INT Store	0
INT ALU	FP Load	0
INT ALU	FP Store	0
INT ALU	FP ALU	0 (Independent)
FP ALU	INT ALU	0
FP ALU	FP Load	(# FP unit stages - 1)
FP ALU	FP Store	(# FP unit stages - 2)
FP Load	FP ALU	1
FP Store	FP ALU	0 (Independent)

Instruction Latency Table for Problem 1.3

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