<s>
The	O
LINPACK	B-Device
Benchmarks	I-Device
are	O
a	O
measure	O
of	O
a	O
system	O
's	O
floating-point	B-Algorithm
computing	O
power	O
.	O
</s>
<s>
The	O
latest	O
version	O
of	O
these	O
benchmarks	O
is	O
used	O
to	O
build	O
the	O
TOP500	B-Operating_System
list	O
,	O
ranking	O
the	O
world	O
's	O
most	O
powerful	O
supercomputers	B-Architecture
.	O
</s>
<s>
Nevertheless	O
,	O
the	O
LINPACK	B-Device
benchmark	I-Device
performance	O
can	O
provide	O
a	O
good	O
correction	O
over	O
the	O
peak	O
performance	O
provided	O
by	O
the	O
manufacturer	O
.	O
</s>
<s>
The	O
performance	O
measured	O
by	O
the	O
LINPACK	B-Device
benchmark	I-Device
consists	O
of	O
the	O
number	O
of	O
64-bit	O
floating-point	B-Algorithm
operations	O
,	O
generally	O
additions	O
and	O
multiplications	O
,	O
a	O
computer	O
can	O
perform	O
per	O
second	O
,	O
also	O
known	O
as	O
FLOPS	O
.	O
</s>
<s>
However	O
,	O
a	O
computer	O
's	O
performance	O
when	O
running	O
actual	O
applications	O
is	O
likely	O
to	O
be	O
far	O
behind	O
the	O
maximal	O
performance	O
it	O
achieves	O
running	O
the	O
appropriate	O
LINPACK	B-Device
benchmark	I-Device
.	O
</s>
<s>
The	O
name	O
of	O
these	O
benchmarks	O
comes	O
from	O
the	O
LINPACK	B-Application
package	O
,	O
a	O
collection	O
of	O
algebra	O
Fortran	B-Application
subroutines	O
widely	O
used	O
in	O
the	O
1980s	O
,	O
and	O
initially	O
tightly	O
linked	O
to	O
the	O
LINPACK	B-Device
benchmark	I-Device
.	O
</s>
<s>
The	O
LINPACK	B-Application
package	O
has	O
since	O
been	O
replaced	O
by	O
other	O
libraries	O
.	O
</s>
<s>
The	O
LINPACK	B-Device
benchmark	I-Device
report	O
appeared	O
first	O
in	O
1979	O
as	O
an	O
appendix	O
to	O
the	O
LINPACK	B-Application
user	O
's	O
manual	O
.	O
</s>
<s>
LINPACK	B-Application
was	O
designed	O
to	O
help	O
users	O
estimate	O
the	O
time	O
required	O
by	O
their	O
systems	O
to	O
solve	O
a	O
problem	O
using	O
the	O
LINPACK	B-Application
package	O
,	O
by	O
extrapolating	O
the	O
performance	O
results	O
obtained	O
by	O
23	O
different	O
computers	O
solving	O
a	O
matrix	O
problem	O
of	O
size	O
100	O
.	O
</s>
<s>
10,000	O
floating-point	B-Algorithm
entries	O
from	O
-1	O
to	O
1	O
are	O
randomly	O
generated	O
to	O
fill	O
in	O
a	O
general	O
,	O
dense	O
matrix	O
,	O
</s>
<s>
then	O
,	O
LU	O
decomposition	O
with	O
partial	B-Algorithm
pivoting	I-Algorithm
is	O
used	O
for	O
the	O
timing	O
.	O
</s>
<s>
Parallel	O
processing	O
was	O
also	O
introduced	O
in	O
the	O
LINPACK	B-Application
Parallel	O
benchmark	O
in	O
the	O
late	O
1980s	O
.	O
</s>
<s>
solving	O
problems	O
of	O
arbitrary	O
size	O
,	O
enabling	O
high	B-Architecture
performance	I-Architecture
computers	I-Architecture
(	O
HPC	O
)	O
to	O
get	O
near	O
to	O
their	O
asymptotic	O
performance	O
.	O
</s>
<s>
Two	O
years	O
later	O
this	O
benchmark	O
was	O
used	O
for	O
measuring	O
the	O
performance	O
of	O
the	O
first	O
TOP500	B-Operating_System
list	O
.	O
</s>
<s>
LINPACK	B-Application
100	O
is	O
very	O
similar	O
to	O
the	O
original	O
benchmark	O
published	O
in	O
1979	O
along	O
with	O
the	O
.	O
</s>
<s>
The	O
solution	O
is	O
obtained	O
by	O
Gaussian	B-Algorithm
elimination	I-Algorithm
with	O
partial	B-Algorithm
pivoting	I-Algorithm
,	O
with	O
2/3n³	O
+	O
2n²	O
floating-point	B-Algorithm
operations	O
where	O
n	O
is	O
100	O
,	O
the	O
order	O
of	O
the	O
dense	O
matrix	O
A	O
that	O
defines	O
the	O
problem	O
.	O
</s>
<s>
LINPACK	B-Application
1000	O
can	O
provide	O
a	O
performance	O
nearer	O
to	O
the	O
machine	O
's	O
limit	O
because	O
in	O
addition	O
to	O
offering	O
a	O
bigger	O
problem	O
size	O
,	O
a	O
matrix	O
of	O
order	O
1000	O
,	O
changes	O
in	O
the	O
algorithm	O
are	O
possible	O
.	O
</s>
<s>
The	O
previous	O
benchmarks	O
are	O
not	O
suitable	O
for	O
testing	O
parallel	O
computers	O
,	O
and	O
the	O
so-called	O
Linpack	B-Application
's	O
Highly	O
Parallel	O
Computing	O
benchmark	O
,	O
or	O
HPLinpack	O
benchmark	O
,	O
was	O
introduced	O
.	O
</s>
<s>
Use	O
of	O
the	O
Strassen	B-Algorithm
algorithm	I-Algorithm
is	O
not	O
allowed	O
because	O
it	O
distorts	O
the	O
real	O
execution	O
rate	O
.	O
</s>
<s>
These	O
results	O
are	O
used	O
to	O
compile	O
the	O
TOP500	B-Operating_System
list	O
twice	O
a	O
year	O
,	O
with	O
the	O
world	O
's	O
most	O
powerful	O
computers	O
.	O
</s>
<s>
TOP500	B-Operating_System
measures	O
these	O
in	O
double-precision	O
floating-point	B-Algorithm
format	I-Algorithm
(	O
FP64	O
)	O
.	O
</s>
<s>
or	O
Java	B-Language
.	O
</s>
<s>
HPL	O
is	O
a	O
portable	O
implementation	O
of	O
HPLinpack	O
that	O
was	O
written	O
in	O
C	B-Language
,	O
originally	O
as	O
a	O
guideline	O
,	O
but	O
that	O
is	O
now	O
widely	O
used	O
to	O
provide	O
data	O
for	O
the	O
TOP500	B-Operating_System
list	O
,	O
though	O
other	O
technologies	O
and	O
packages	O
can	O
be	O
used	O
.	O
</s>
<s>
It	O
requires	O
installed	O
implementations	O
of	O
MPI	B-Application
and	O
either	O
BLAS	B-Application
or	O
VSIPL	O
to	O
run	O
.	O
</s>
<s>
The	O
LINPACK	B-Device
benchmark	I-Device
is	O
said	O
to	O
have	O
succeeded	O
because	O
of	O
the	O
scalability	O
of	O
HPLinpack	O
,	O
the	O
fact	O
that	O
it	O
generates	O
a	O
single	O
number	O
,	O
making	O
the	O
results	O
easily	O
comparable	O
and	O
the	O
extensive	O
historical	O
data	O
base	O
it	O
has	O
associated	O
.	O
</s>
<s>
However	O
,	O
soon	O
after	O
its	O
release	O
,	O
the	O
LINPACK	B-Device
benchmark	I-Device
was	O
criticized	O
for	O
providing	O
performance	O
levels	O
"	O
generally	O
unobtainable	O
by	O
all	O
but	O
a	O
very	O
few	O
programmers	O
who	O
tediously	O
optimize	O
their	O
code	O
for	O
that	O
machine	O
and	O
that	O
machine	O
alone	O
"	O
,	O
because	O
it	O
only	O
tests	O
the	O
resolution	O
of	O
dense	O
linear	O
systems	O
,	O
which	O
are	O
not	O
representative	O
of	O
all	O
the	O
operations	O
usually	O
performed	O
in	O
scientific	O
computing	O
.	O
</s>
<s>
Jack	O
Dongarra	O
,	O
the	O
main	O
driving	O
force	O
behind	O
the	O
LINPACK	B-Device
benchmarks	I-Device
,	O
said	O
that	O
,	O
while	O
they	O
only	O
emphasize	O
"	O
peak	O
"	O
CPU	O
speed	O
and	O
number	O
of	O
CPUs	O
,	O
not	O
enough	O
stress	O
is	O
given	O
to	O
local	O
bandwidth	O
and	O
the	O
network	O
.	O
</s>
<s>
Thom	O
Dunning	O
,	O
Jr.	O
,	O
director	O
of	O
the	O
National	B-General_Concept
Center	I-General_Concept
for	I-General_Concept
Supercomputing	I-General_Concept
Applications	I-General_Concept
,	O
had	O
this	O
to	O
say	O
about	O
the	O
LINPACK	B-Device
benchmark	I-Device
:	O
"	O
The	O
Linpack	B-Device
benchmark	I-Device
is	O
one	O
of	O
those	O
interesting	O
phenomena	O
--	O
almost	O
anyone	O
who	O
knows	O
about	O
it	O
will	O
deride	O
its	O
utility	O
.	O
</s>
<s>
According	O
to	O
Dongarra	O
,	O
"	O
the	O
organizers	O
of	O
the	O
Top500	B-Operating_System
are	O
actively	O
looking	O
to	O
expand	O
the	O
scope	O
of	O
the	O
benchmark	O
reporting	O
"	O
because	O
"	O
it	O
is	O
important	O
to	O
include	O
more	O
performance	O
characteristic	O
and	O
signatures	O
for	O
a	O
given	O
system	O
"	O
.	O
</s>
<s>
One	O
of	O
the	O
possibilities	O
that	O
is	O
being	O
considered	O
to	O
extend	O
the	O
benchmark	O
for	O
the	O
TOP500	B-Operating_System
is	O
the	O
HPC	B-Application
Challenge	I-Application
Benchmark	I-Application
Suite	O
.	O
</s>
<s>
With	O
the	O
advent	O
of	O
petascale	B-General_Concept
computers	I-General_Concept
,	O
traversed	B-Operating_System
edges	I-Operating_System
per	I-Operating_System
second	I-Operating_System
have	O
started	O
to	O
emerge	O
as	O
a	O
complementary	O
metric	O
to	O
FLOPS	O
measured	O
by	O
LINPACK	B-Application
.	O
</s>
<s>
Another	O
such	O
metric	O
is	O
the	O
HPCG	B-Operating_System
benchmark	I-Operating_System
,	O
proposed	O
by	O
Dongarra	O
.	O
</s>
