Multicore Systems on Chip - Signal Processing Systems - page 515

Instructions

CPI SLE CycleTime SHE

CPI SLE
issue

∝ + β

ET SHE
ET MP =

Instructions P + γ

CycleTime MP .

(6)

( ∝ CPI SLE + β CPI SLE )

If one considers that in the model of the multiprocessor environment, a single
low end processor is not capable of exploiting instruction level parallelism, and
then ∝ =

0, one can reduce the Eq. ( 6 ) to:

Instructions

CPI SLE CycleTime SHE

CPI SLE

∝

issue + β

ET SHE
ET MP =

Instructions P + γ

CycleTime MP ,

(7)

( 0 ∗ CPI SLE + 1 ∗ CPI SLE )

and, by simplifying ( 7 ) , one gets

Instructions

CPI SLE CycleTime SHE

CPI SLE
issue

+ β

∝

ET SHE
ET MP =

Instructions P + γ

CycleTime MP .

(8)

( CPI SLE )

We are also considering that, as a homogeneous multiprocessor design is
composed of several low-end processors with a very simple organization, those
processors could run at much higher frequencies than a single and complex high-end
processor. Therefore, we will assume that

1
CycleTime MP

1
CycleTime SHE

= K ∗ , (9)

where K is the frequency adjustment factor to equal the power consumption of the
homogeneous multiprocessor with the high-end single processor.
By merging and simplifying Eqs. ( 8 ) and( 9 ) , one gets:

1
P + γ

K

CPI SLE

∝

issue + β

CPI SLE
CPI SLE

ET SHE
ET MP =

. (10)

According to Eq. ( 10 ) , a machine based on a high-end single core will be faster

than a multiprocessor-based machine if ET SHE

ET MP

1. This equation also shows that,
although the multiprocessor architecture with low-end simple processors could have
a faster cycle time (by a factor of K ), that factor alone is not enough to define
performance, as demonstrated in the second term between brackets in Eq. ( 10 ) .
Because the high-end processor can execute many instructions in parallel, better
performance improvements can be obtained, as long as ILP is the dominant factor,
instead of TLP.
To better illustrate this point, let us imagine the extreme case: P

<

, meaning
that infinite processors are available. In addition, if one considers that the multipro-

= ∞