<s>
Gravity	B-Device
Pipe	I-Device
(	O
abbreviated	O
GRAPE	B-Device
)	O
is	O
a	O
project	O
which	O
uses	O
hardware	B-General_Concept
acceleration	I-General_Concept
to	O
perform	O
gravitational	O
computations	O
.	O
</s>
<s>
Integrated	O
with	O
Beowulf-style	O
commodity	O
computers	O
,	O
the	O
GRAPE	B-Device
system	O
calculates	O
the	O
force	O
of	O
gravity	O
that	O
a	O
given	O
mass	O
,	O
such	O
as	O
a	O
star	O
,	O
exerts	O
on	O
others	O
.	O
</s>
<s>
The	O
GRAPE	B-Device
hardware	B-General_Concept
acceleration	I-General_Concept
component	O
"	O
pipes	O
"	O
the	O
force	O
computation	O
to	O
the	O
general-purpose	O
computer	O
serving	O
as	O
a	O
node	O
in	O
a	O
parallelized	B-Operating_System
cluster	I-Operating_System
as	O
the	O
innermost	O
loop	O
of	O
the	O
gravitational	O
model	O
.	O
</s>
<s>
Its	O
shortened	O
name	O
,	O
GRAPE	B-Device
,	O
was	O
chosen	O
as	O
an	O
intentional	O
reference	O
to	O
the	O
Apple	O
Inc	O
.	O
line	O
of	O
computers	O
.	O
</s>
<s>
The	O
primary	O
calculation	O
in	O
GRAPE	B-Device
hardware	O
is	O
a	O
summation	O
of	O
the	O
forces	O
between	O
a	O
particular	O
star	O
and	O
every	O
other	O
star	O
in	O
the	O
simulation	O
.	O
</s>
<s>
Several	O
versions	O
(	O
GRAPE-1	O
,	O
GRAPE-3	O
and	O
GRAPE-5	O
)	O
use	O
the	O
logarithmic	O
number	O
system	O
(	O
LNS	O
)	O
in	O
the	O
pipeline	O
to	O
calculate	O
the	O
approximate	O
force	O
between	O
two	O
stars	O
and	O
take	O
the	O
antilogarithms	O
of	O
the	O
x	O
,	O
y	O
and	O
z	O
components	O
before	O
adding	O
them	O
to	O
their	O
corresponding	O
total	O
.	O
</s>
<s>
The	O
GRAPE-2	O
,	O
GRAPE-4	O
and	O
GRAPE-6	O
use	O
floating-point	B-Algorithm
arithmetic	I-Algorithm
for	O
more	O
accurate	O
calculation	O
of	O
such	O
forces	O
.	O
</s>
<s>
The	O
advantage	O
of	O
the	O
logarithmic-arithmetic	O
versions	O
is	O
that	O
they	O
allow	O
more	O
and	O
faster	O
parallel	O
pipes	O
for	O
a	O
given	O
hardware	O
cost	O
because	O
all	O
but	O
the	O
sum	O
portion	O
of	O
the	O
GRAPE	B-Device
algorithm	O
(	O
1.5	O
power	O
of	O
the	O
sum	O
of	O
the	O
squares	O
of	O
the	O
input	O
data	O
divided	O
by	O
the	O
input	O
data	O
)	O
is	O
easy	O
to	O
perform	O
with	O
LNS	O
.	O
</s>
<s>
GRAPE-DR	O
consists	O
of	O
a	O
large	O
number	O
of	O
simple	O
processors	O
,	O
all	O
operating	O
in	O
the	O
SIMD	B-Device
fashion	O
.	O
</s>
<s>
GRAPE	B-Device
computes	O
approximate	O
solutions	O
to	O
the	O
historically	O
intractable	O
n-body	O
problem	O
,	O
which	O
is	O
of	O
interest	O
in	O
astrophysics	O
and	O
celestial	O
mechanics	O
.	O
</s>
<s>
GRAPE	B-Device
assists	O
in	O
calculations	O
of	O
interactions	O
between	O
particles	O
where	O
the	O
interaction	O
scales	O
as	O
r−2	O
.	O
</s>
<s>
These	O
problems	O
include	O
the	O
evolution	O
of	O
galaxies	B-Application
(	O
gravitation	O
force	O
scales	O
as	O
r−2	O
)	O
.	O
</s>
<s>
This	O
simulation	O
used	O
the	O
GRAPE-4	O
system	O
.	O
</s>
<s>
The	O
LNS-based	O
GRAPE-5	O
architecture	O
won	O
the	O
Price	O
Performance	O
category	O
of	O
the	O
Gordon	O
Bell	O
Prize	O
in	O
1999	O
,	O
at	O
about	O
$7	O
per	O
MegaFLOPS	O
.	O
</s>
<s>
The	O
particular	O
implementation	O
"	O
Grape-6	O
"	O
also	O
won	O
prizes	O
in	O
2000	O
and	O
2001	O
(	O
see	O
external	O
links	O
)	O
.	O
</s>
<s>
Grape-DR	O
was	O
ranked	O
first	O
in	O
the	O
June	O
2010	O
Little	O
Green500	O
List	O
,	O
a	O
ranking	O
of	O
supercomputer	B-Architecture
's	O
performance	O
per	O
unit	O
power	O
consumption	O
published	O
by	O
the	O
Green500.org	O
.	O
</s>
