Cycles per instruction

In computer architecture, cycles per instruction (aka clock cycles per instruction, clocks per instruction, or CPI) is one aspect of a processor's performance: the average number of clock cycles per instruction for a program or program fragment.^[1] It is the multiplicative inverse of instructions per cycle.

Definition

Cycles Per Instruction is defined by the following:

$CPI = \frac{\Sigma (IIC)(CCI) }{IC}$

Where IIC is the number of instructions for a given instruction type, CCI is the clock-cycles for a given instruction type, IC is the total instruction count. The summation sums over all instruction types for a given benchmarking process.

Explanation

Let us assume a classic RISC pipeline, with the following 5 stages:

Instruction fetch cycle (IF)
Instruction decode/Register fetch cycle (ID)
Execution/Effective address cycle (EX)
Memory access (MEM)
Write-back cycle (WB)

Each stage requires one clock cycle and an instruction passes through the stages sequentially. Without pipelining, a new instruction is fetched in stage 1 only after the previous instruction finishes at stage 5. Therefore without pipelining the number of cycles it takes to execute an instruction is 5. This is the definition of CPI.

With pipelining we can improve the CPI by exploiting instruction level parallelism. For example, what if an instruction is fetched every cycle? We could theoretically have 5 instructions in the 5 pipeline stages at once (one instruction per stage). In this case, a different instruction would complete stage 5 in every clock cycle, and therefore on average we have one clock cycle per instruction (CPI = 1).

With a single-issue processor, the best CPI attainable is 1. However with multiple-issue processors, we may achieve even better CPI values. For example a processor that issues two instructions per clock cycle (see Superscalar) can achieve a CPI of 0.5 when two instructions are completing every clock cycle.

Examples

Example 1

For the multi-cycle MIPS, there are 5 types of instructions:

Load (5 cycles)
Store (4 cycles)
R-type (4 cycles)
Branch (3 cycles)
Jump (3 cycles)

If a program has:

50% R-type instructions
15% load instructions
25% store instructions
8% branch instructions
2% jump instructions

then, the CPI is:

$\text{CPI} = \frac{4 \times 50 + 5 \times 15 + 4 \times 25 + 3 \times 8 + 3 \times 2}{100} = 4.05$

Example 2

^[2] A 400-MHz processor was used to execute a benchmark program with the following instruction mix and clock cycle count:

Instruction type	Instruction count	Clock cycle count
Integer arithmetic	45000	1
Data transfer	32000	2
Floating point	15000	2
Control transfer	8000	2

Determine the effective CPI, MIPS rate, and execution time for this program.

Total instruction count = 100000

$\text{CPI} = \frac{45000 \times 1 + 32000 \times 2 + 15000 \times 2 + 8000 \times 2}{100000} = \frac{155000}{100000} = 1.55$

$\text{Effective processor performance} = \text{MIPS} = \frac{\text{clock frequency}}{\text{CPI} \times 1000000} = \frac{400 \times 1000000}{1.55 \times 1000000} = 258 \, \text{MIPS}$

Therefore:

$\text{Execution time}(T) = \text{CPI} \times \text{Instruction count} \times \text{clock time} = \frac{\text{CPI} \times \text{Instruction Count}}{\text{frequency}} = \frac{1.55 \times 100000}{400 \times 1000000} = \frac{1.55}{4000} = 0.387 \, \text{ms}$

References

↑ Patterson, David A.; Hennessy, John L. Computer Organization and Design: The Hardware/Software Interface.
↑ Advanced Computer Architecture by Kai Hwang, Chapter 1, Exercise Problem 1.1