5. Memory-Bandwidth Wall [15 marks] When a cache is used temporally, it acts as

ID: 3872923 • Letter: 5

Question

5. Memory-Bandwidth Wall [15 marks]

When a cache is used temporally, it acts as a bandwidth amplifier.

Specifically, the effective operand bandwidth reaching the pipeline is the

actual operand bandwidth reaching the processor divided by the miss rate.

Suppose we must deliver an actual operand bandwidth of 'n' words/second to

the processor to sustain a floating-point performance of 'n/m' flops/second,

where 'm' is the miss rate of the D-cache. Typically, we need a new word

from either the cache or the memory for each flop. By assumption, 'm' is

always 0.01. Today, the actual operand bandwidth delivered to the processor

is 8 * 10^7 words/second and the peak floating-point performance is 2 * 10^9

flops/second. If peak floating-point performance increases by a factor of

2.2 every year and memory bandwidth increases by a factor of 1.3 every year,

after how many years will the memory bandwidth be sufficient so that the

sustained floating-point performance equals the peak performance?

Answer: For the next 2 years

Currently the bandwidth is more than sufficient to serve processor to give peak performance in computing floating-point operations. Because,

Current year operand bandwidth(n) = 8 x 107 words/second and miss rate(m) = 0.01

So, we can serve processor with 8 x 109 flops/sercond which is equals to n/m value.

This value is greater than current year peak floating-point performance, which is 2 x 109 flops/second.

What floating-point performance, system can deliver What is peak floating-point performance in that year

Year 0(current year) : 8 x 109 flops/sercond 2 x 109 flops/sercond

Year 1(next year) : 10.4 x 109 flops/sercond 4.4 x 109 flops/sercond

Year 2 : 13.52 x 109 flops/sercond 9.68 x 109 flops/sercond

Year 3 : 17.576 x 109 flops/sercond 21.296 x 109 flops/sercond

In the year 3, system cannot satisfy processor to to achieve maximum performance in floating-point operations.

So, for next 2 years, system's bandwidth will be sufficient.

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