# Metrics and Evaluations/Problem04

Your company currently uses the “High RISC” processor by RISCy Solutions. It is a 2GHz processor with an average cpi of 1.5. RISCy solutions has just come out with two new processors which you are to compare and select the best performer.

1. “Triple the RISC” is a three pipelined machine that also runs at 2GHz, and maintains the same cpi as the High RISC. It is estimated that one third of your code can use all three pipelines and another third can use two pipelines. For an n- pipelined processor, the ideal speedup is n.

2. “RISCily Fast” is a 5GHz single processor, that due to its speed encounters a larger memory penalty. When the cache misses (5% of the time) on memory accesses (40% of all instructions), it incurs a penalty of 50 cycle more than the original High RISC processor. In all other ways it is identical to the High RISC.

Solution

Using the following equation for speedup:

The speedup for the "Triple the RISK" processor:

`````` S = 1 / [ ( 1 - [ 1/3 + 1/3 ] + [ ( 1 / 3 ) / 2 + ( 1 / 3 ) / 3 ] ) ]

S = 1 / ( 1/3 + 1/6 + 1 / 9)

S = 18 / 11 = 1.637
``````

To determine the speedup for the "RISCily Fast" processor we look at the keywords “penalties of x cycles”. We still have to figure out speedup, so we use the CPI version of speedup.

`````` S = Old Time * Old CPI  New Time * New CPI

S = New Freq * Old CPI /  Old Freq * New CPI
``````

New CPI = Old CPI + penalty * frequency = 1.5 + 50 [ (0.05) (0.4) ] = 2.5

`````` S = 5 GHz * 1.5 / ( 2 GHz * 2.5)
S = 1.5
``````

I would recommend using Triple the RISC.

This problem is adapted from a midterm given by Schubert at CSUSB