<s>
In	O
computer	B-General_Concept
architecture	I-General_Concept
,	O
speedup	B-Operating_System
is	O
a	O
number	O
that	O
measures	O
the	O
relative	O
performance	O
of	O
two	O
systems	O
processing	O
the	O
same	O
problem	O
.	O
</s>
<s>
The	O
notion	O
of	O
speedup	B-Operating_System
was	O
established	O
by	O
Amdahl	B-Operating_System
's	I-Operating_System
law	I-Operating_System
,	O
which	O
was	O
particularly	O
focused	O
on	O
parallel	B-Operating_System
processing	I-Operating_System
.	O
</s>
<s>
However	O
,	O
speedup	B-Operating_System
can	O
be	O
used	O
more	O
generally	O
to	O
show	O
the	O
effect	O
on	O
performance	O
after	O
any	O
resource	O
enhancement	O
.	O
</s>
<s>
Speedup	B-Operating_System
can	O
be	O
defined	O
for	O
two	O
different	O
types	O
of	O
quantities	O
:	O
latency	O
and	O
throughput	O
.	O
</s>
<s>
ρ	O
is	O
the	O
execution	O
density	O
(	O
e.g.	O
,	O
the	O
number	O
of	O
stages	O
in	O
an	O
instruction	B-General_Concept
pipeline	I-General_Concept
for	O
a	O
pipelined	O
architecture	O
)	O
;	O
</s>
<s>
A	O
is	O
the	O
execution	O
capacity	O
(	O
e.g.	O
,	O
the	O
number	O
of	O
processors	B-General_Concept
for	O
a	O
parallel	B-Operating_System
architecture	I-Operating_System
)	O
.	O
</s>
<s>
Speedup	B-Operating_System
is	O
dimensionless	O
and	O
defined	O
differently	O
for	O
each	O
type	O
of	O
quantity	O
so	O
that	O
it	O
is	O
a	O
consistent	O
metric	O
.	O
</s>
<s>
Speedup	B-Operating_System
in	O
latency	O
is	O
defined	O
by	O
the	O
following	O
formula	O
:	O
</s>
<s>
Slatency	O
is	O
the	O
speedup	B-Operating_System
in	O
latency	O
of	O
the	O
architecture	O
2	O
with	O
respect	O
to	O
the	O
architecture	O
1	O
;	O
</s>
<s>
Speedup	B-Operating_System
in	O
latency	O
can	O
be	O
predicted	O
from	O
Amdahl	B-Operating_System
's	I-Operating_System
law	I-Operating_System
or	O
Gustafson	B-Operating_System
's	I-Operating_System
law	I-Operating_System
.	O
</s>
<s>
Speedup	B-Operating_System
in	O
throughput	O
is	O
defined	O
by	O
the	O
formula	O
:	O
</s>
<s>
Sthroughput	O
is	O
the	O
speedup	B-Operating_System
in	O
throughput	O
of	O
the	O
architecture	O
2	O
with	O
respect	O
to	O
the	O
architecture	O
1	O
;	O
</s>
<s>
Our	O
new	O
branch	O
predictor	O
has	O
provided	O
a	O
1.5x	O
speedup	B-Operating_System
over	O
the	O
original	O
.	O
</s>
<s>
We	O
can	O
also	O
measure	O
speedup	B-Operating_System
in	O
cycles	O
per	O
instruction	O
(	O
CPI	O
)	O
which	O
is	O
a	O
latency	O
.	O
</s>
<s>
We	O
can	O
also	O
measure	O
speedup	B-Operating_System
in	O
instructions	O
per	O
cycle	O
(	O
IPC	O
)	O
,	O
which	O
is	O
a	O
throughput	O
and	O
the	O
inverse	O
of	O
CPI	O
.	O
</s>
<s>
We	O
achieve	O
the	O
same	O
1.5x	O
speedup	B-Operating_System
,	O
though	O
we	O
measured	O
different	O
quantities	O
.	O
</s>
<s>
Let	O
S	O
be	O
the	O
speedup	B-Operating_System
of	O
execution	O
of	O
a	O
task	O
and	O
s	O
the	O
speedup	B-Operating_System
of	O
execution	O
of	O
the	O
part	O
of	O
the	O
task	O
that	O
benefits	O
from	O
the	O
improvement	O
of	O
the	O
resources	O
of	O
an	O
architecture	O
.	O
</s>
<s>
Linear	B-Operating_System
speedup	I-Operating_System
or	O
ideal	B-Operating_System
speedup	I-Operating_System
is	O
obtained	O
when	O
.	O
</s>
<s>
When	O
running	O
a	O
task	O
with	O
linear	B-Operating_System
speedup	I-Operating_System
,	O
doubling	O
the	O
local	O
speedup	B-Operating_System
doubles	O
the	O
overall	O
speedup	B-Operating_System
.	O
</s>
<s>
As	O
this	O
is	O
ideal	O
,	O
it	O
is	O
considered	O
very	O
good	O
scalability	B-Architecture
.	O
</s>
<s>
Programs	O
with	O
linear	B-Operating_System
speedup	I-Operating_System
and	O
programs	O
running	O
on	O
a	O
single	O
processor	O
have	O
an	O
efficiency	O
of	O
1	O
,	O
while	O
many	O
difficult-to-parallelize	O
programs	O
have	O
efficiency	O
such	O
as	O
1/ln	O
( s	O
)	O
that	O
approaches	O
0	O
as	O
the	O
number	O
of	O
processors	B-General_Concept
increases	O
.	O
</s>
<s>
all	O
of	O
the	O
area	O
in	O
the	O
graph	O
is	O
useful	O
(	O
whereas	O
in	O
speedup	B-Operating_System
curves	O
half	O
of	O
the	O
space	O
is	O
wasted	O
)	O
;	O
</s>
<s>
there	O
is	O
no	O
need	O
to	O
plot	O
a	O
"	O
perfect	O
speedup	B-Operating_System
"	O
curve	O
.	O
</s>
<s>
In	O
marketing	O
contexts	O
,	O
speedup	B-Operating_System
curves	O
are	O
more	O
often	O
used	O
,	O
largely	O
because	O
they	O
go	O
up	O
and	O
to	O
the	O
right	O
and	O
thus	O
appear	O
better	O
to	O
the	O
less-informed	O
.	O
</s>
<s>
Sometimes	O
a	O
speedup	B-Operating_System
of	O
more	O
than	O
A	O
when	O
using	O
A	O
processors	B-General_Concept
is	O
observed	O
in	O
parallel	B-Operating_System
computing	I-Operating_System
,	O
which	O
is	O
called	O
super-linear	O
speedup	B-Operating_System
.	O
</s>
<s>
Super-linear	O
speedup	B-Operating_System
rarely	O
happens	O
and	O
often	O
confuses	O
beginners	O
,	O
who	O
believe	O
the	O
theoretical	O
maximum	O
speedup	B-Operating_System
should	O
be	O
A	O
when	O
A	O
processors	B-General_Concept
are	O
used	O
.	O
</s>
<s>
One	O
possible	O
reason	O
for	O
super-linear	O
speedup	O
in	O
low-level	O
computations	O
is	O
the	O
cache	B-General_Concept
effect	I-General_Concept
resulting	O
from	O
the	O
different	O
memory	B-General_Concept
hierarchies	I-General_Concept
of	O
a	O
modern	O
computer	O
:	O
in	O
parallel	B-Operating_System
computing	I-Operating_System
,	O
not	O
only	O
do	O
the	O
numbers	O
of	O
processors	B-General_Concept
change	O
,	O
but	O
so	O
does	O
the	O
size	O
of	O
accumulated	O
caches	O
from	O
different	O
processors	B-General_Concept
.	O
</s>
<s>
With	O
the	O
larger	O
accumulated	O
cache	O
size	O
,	O
more	O
or	O
even	O
all	O
of	O
the	O
working	B-General_Concept
set	I-General_Concept
can	O
fit	O
into	O
caches	O
and	O
the	O
memory	O
access	O
time	O
reduces	O
dramatically	O
,	O
which	O
causes	O
the	O
extra	O
speedup	B-Operating_System
in	O
addition	O
to	O
that	O
from	O
the	O
actual	O
computation	O
.	O
</s>
<s>
An	O
analogous	O
situation	O
occurs	O
when	O
searching	O
large	O
datasets	O
,	O
such	O
as	O
the	O
genomic	O
data	O
searched	O
by	O
BLAST	B-Application
implementations	O
.	O
</s>
<s>
Super-linear	O
speedups	O
can	O
also	O
occur	O
when	O
performing	O
backtracking	B-Algorithm
in	O
parallel	O
:	O
an	O
exception	O
in	O
one	O
thread	O
can	O
cause	O
several	O
other	O
threads	O
to	O
backtrack	O
early	O
,	O
before	O
they	O
reach	O
the	O
exception	O
themselves	O
.	O
</s>
<s>
Super-linear	O
speedups	O
can	O
also	O
occur	O
in	O
parallel	O
implementations	O
of	O
branch-and-bound	O
for	O
optimization	O
:	O
the	O
processing	O
of	O
one	O
node	O
by	O
one	O
processor	O
may	O
affect	O
the	O
work	O
other	O
processors	B-General_Concept
need	O
to	O
do	O
for	O
the	O
other	O
nodes	O
.	O
</s>
