Question

Your company has a benchmark that is considered representative of your typical applications. One of the older-model workstations does not have a floating-point unit and must emulate each floating-point instruction by a sequence of integer instructions. This older-model workstation is rated at 120 MIPS on this benchmark. A 3rd -party vendor offers an attached processor that is intended to give a hardware accelerator to your workstation. The attached processor executes each floating-point instruction on a dedicated processor, without emulation. The workstation/attached processor rates 80 MIPS on the same benchmark. The following symbols are used to answer this exercise:

I – Number of integer instructions executed on the benchmark
F – Number of floating-point instructions executed on the benchmark
Y – Number of integer instructions to emulate a float-point instruction
W – Time to execute the benchmark on the processor alone
B – Time to execute the benchmark on the processor/coprocessor combination.

Required:
a. Write an equation for the MIPS rating of each configuration using the symbols above.
b. What is the value of B?
c. What is the MFLOPS rating of the system with the coprocessor?
d. Your colleague wants to purchase the coprocessor even though the MIPS rating for the configuration using the coprocessor is less than that of the processor alone. Is your colleague’s evaluation correct?

Answer 1

a-The equation for processor only configuration is
`120* 10^6=(I+YF)/(W)\\` while that for processor and co-processor configuration is
`80*10^6=(I+F)/(B)`.

b-The value of B is 1.1 second.

c-The value of MFLOPS for co-processor system in configuration 2 is 80 MFLOPS.

d-The evaluation of your colleague is correct.

Step-by-step explanation:

a

The MIPS rating equations are as follows

Configuration 01 (Processor only)

`120* 10^6=(I+YF)/(W)\\`

Configuration 02 (Processor + Co-processor)

`80*10^6=(I+F)/(B)`

b

From the equation, for processor and co-processor equation the value of B is calculated. For it to be calculated, the I value is calculated from the processor configuration with the following data F= 8 * 10^6 . Y= 50, W = 4 sec:

`I=120*10^6*W-YF\\I=(120*10^6*4)-(8*10^6*50)\\I=80*10^6 \text{instructions}`

Using this value of I gives

`B=(I+F)/(80*10^6)\\B=(80*10^6+8*10^6)/(80*10^6)\\B=(88*10^6)/(80*10^6)\\B=1.1\text{second}`

The value of B is 1.1 second.

c

The MFLOPS rating of configuration 2 is given as

`\text{MFLOPS}=(F)/(B-(I)/(MIPS_(proc+coproc)))\\\text{MFLOPS}=(8*10^6)/(1.1-(80*10^6)/(80*10^6))\\\text{MFLOPS}=(8*10^6)/(1.1-1)\\\text{MFLOPS}=(8*10^6)/(0.1)\\\text{Processor+Coprocessor MFLOPS}=80 \text{MFLOPS}`

So the value of MFLOPS for co-processor system in configuration 2 is 80 MFLOPS.

d

The value of W is 4 seconds while the value of B is 1.1 seconds. Despite being the configuration with lower MIPS, the co-processor configuration has a lower execution rate and thus the evaluation of your colleague is correct.