Information Technology Reference
In-Depth Information
In its given form, Amdahl's law accounts for cases whereby improvement can be
applied to the instruction execution time. However, sometimes it may be possible to
achieve performance enhancement for only a fraction of time,
. In this case a new
formula has to be developed in order to relate the speedup, SU
D
due to an enhance-
ment for a fraction of time
D
to the speedup due to an overall enhancement, SU
o
.
This relationship can be expressed as
D
1
SU
o
¼
(1
D
)
þ
(
D
=
SU
D
)
It should be noted that when
1, that is, when enhancement is possible at all
times, then SU
o
¼
SU
D
, as expected.
Consider, for example, a machine for which a speedup of 30 is possible after
applying an enhancement. If under certain conditions the enhancement was only
possible for 30% of the time, what is the speedup due to this partial application
of the enhancement?
D ¼
1
1
1
SU
o
¼
D
=
SU
D
)
¼
¼
01
¼
1
:
4
0
3
30
:
(1
D
)
þ
(
0
:
7
þ
0
:
(1
0
:
3)
þ
It is interesting to note that the above formula can be generalized as shown below to
account for the case whereby a number of different independent enhancements can
be applied separately and for different fractions of the time,
D
1
,
D
2
,
,
D
n
, thus
...
leading respectively to the speedup enhancements SU
D
1
, SU
D
2
,
, SU
D
n
.
...
1
SU
o
¼
D
1
þ
D
2
þþ
D
n
)
(SU
D
1
þ
SU
D
2
þþ
SU
D
n
)
(
½
1
(
D
1
þ
D
2
þþ
D
n
)
þ
1.5. SUMMARY
In this chapter, we provided a brief historical background for the development of
computer systems, starting from the first recorded attempt to build a computer,
the Z1, in 1938, passing through the CDC 6600 and the Cray supercomputers,
and ending up with today's modern high-performance machines. We then provided
a discussion on the RISC versus CISC architectural styles and their impact on
machine performance. This was followed by a brief discussion on the technological
development and its impact on computing performance. Our coverage in this chapter
was concluded with a detailed treatment of the issues involved in assessing the per-
formance of computers. In particular, we have introduced a number of performance
measures such as CPI, MIPS, MFLOPS, and Arithmetic
Geometric performance
means, none of them defining the performance of a machine consistently. Possible
/
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