suppose you have three different core designs which you can use to build a heterogeneous multi$-$core system.

$\backslash (>\backslash )$ An Out$-$of$-$Order core $(\backslash (\backslash$mathrm$\{$O$\}\_\{0\}\backslash$mathrm$\{$O$\}\backslash )-$Fixed$)$ that can execute instructions out$-$of$-$order.

$\backslash (>\backslash )$ An in$-$order core $($IO$-$Fixed$)$ that can execute instructions in order. The area of IO$-$Fixed is $\backslash (1/4\backslash )$ the size of OoO$-$Fixed.

$>$ Morphy core: a hybrid core which can dynamically switch between two modes of execution: out$-$of$-$order with a single thread $($OoO$-$Morphy$)$ and in$-$order with $4$ threads $($IO$-$Morphy$).$

The implementations of out$-$of$-$order execution in OoO$-$Morphy and OoO$-$Fixed are the same, except OoO$-$Morphy requires the ability to switch between out$-$of$-$order and in$-$order modes. Likewise, the implementations of in$-$order execution in IO$-$Morphy and IO$-$Fixed are the same except for the ability to switch modes.

Answer the following:

a$)$ Could the peak single$-$threaded performance of OoO$-$Morphy mode be less than the peak single$-$thread performance of OoO$-$Fixed. Explain your reasoning.

b$)$ Imagine a heterogeneous multi$-$core system Fixed with $12$ IO$-$Fixed cores and $1$ OoO$-$Fixed core, and a homogeneous multi$-$core system Morphy with four Morphy cores.

Suppose we want to accelerate critical sections on both systems using an OoO core:

When could the same critical section that is accelerated run faster on System Fixed than on System Morphy; and when could the same critical section that is accelerated run faster on System Morphy than on System Fixed? Explain.

Question $6[20$ Marks$]$

David Patterson states that "the recent switch to parallel microprocessors is a milestone in history of computing. Industry has laid out a roadmap for multicore designs that preserve the programming paradigm of the past via binary$-$compatibility and cache$-$coherence. Conventional wisdom is now to double the number of cores on a chip with each silicon generation. $[...]$ Investigations into the future opportunities led to the following recommendations which are more revolutionary than what industry plans to do:

$1.$ The target should be $1000$ s of cores per chip.

$2.$ Maximize application efficiency, programming models should support a wide range of data types and successful models of parallelism: data$-$level parallelism, independent task parallelism, and instruction$-$level parallelism.

$3.$ Should play a larger role than conventional compilers in translating parallel programs.

Page $4$ of $5$