<s>
A	O
torus	B-Operating_System
interconnect	I-Operating_System
is	O
a	O
switch-less	O
network	B-Architecture
topology	I-Architecture
for	O
connecting	O
processing	O
nodes	O
in	O
a	O
parallel	B-Operating_System
computer	I-Operating_System
system	O
.	O
</s>
<s>
While	O
this	O
is	O
a	O
general	O
definition	O
in	O
geometry	O
,	O
the	O
topological	O
properties	O
of	O
this	O
type	O
of	O
shape	O
describes	O
the	O
network	B-Architecture
topology	I-Architecture
in	O
its	O
essence	O
.	O
</s>
<s>
To	O
better	O
illustrate	O
the	O
concept	O
,	O
and	O
understand	O
what	O
the	O
topology	B-Architecture
means	O
in	O
network	O
interconnect	O
,	O
we	O
give	O
3	O
examples	O
of	O
parallel	O
interconnected	O
nodes	O
using	O
torus	O
topology	B-Architecture
.	O
</s>
<s>
At	O
one	O
dimension	O
,	O
a	O
torus	O
topology	B-Architecture
is	O
equivalent	O
to	O
a	O
ring	B-Architecture
interconnect	I-Architecture
network	O
,	O
of	O
a	O
shape	O
of	O
a	O
circle	O
.	O
</s>
<s>
Torus	B-Operating_System
interconnect	I-Operating_System
is	O
a	O
switch-less	O
topology	B-Architecture
that	O
can	O
be	O
seen	O
as	O
a	O
mesh	B-Architecture
interconnect	I-Architecture
with	O
nodes	O
arranged	O
in	O
a	O
rectilinear	O
array	O
of	O
N	O
=	O
2	O
,	O
3	O
,	O
or	O
more	O
dimensions	O
,	O
with	O
processors	O
connected	O
to	O
their	O
nearest	O
neighbors	O
,	O
and	O
corresponding	O
processors	O
on	O
opposite	O
edges	O
of	O
the	O
array	O
connected	O
.	O
</s>
<s>
This	O
topology	B-Architecture
got	O
the	O
name	O
from	O
the	O
fact	O
that	O
the	O
lattice	O
formed	O
in	O
this	O
way	O
is	O
topologically	O
homogeneous	O
to	O
an	O
N-dimensional	O
torus	O
.	O
</s>
<s>
The	O
first	O
3	O
dimensions	O
of	O
torus	B-Operating_System
network	I-Operating_System
topology	I-Operating_System
are	O
easier	O
to	O
visualize	O
and	O
are	O
described	O
below	O
:	O
</s>
<s>
1D	O
Torus	O
is	O
same	O
as	O
ring	B-Architecture
interconnection	I-Architecture
.	O
</s>
<s>
A	O
number	O
of	O
supercomputers	B-Architecture
on	O
the	O
TOP500	B-Operating_System
list	O
use	O
three-dimensional	O
torus	O
networks	O
,	O
e.g.	O
</s>
<s>
Fujitsu	O
's	O
K	B-Device
computer	I-Device
and	O
the	O
PRIMEHPC	O
FX10	O
use	O
a	O
proprietary	O
three-dimensional	O
torus	O
3D	O
mesh	B-Architecture
interconnect	I-Architecture
called	O
Tofu	O
.	O
</s>
<s>
The	O
model	O
is	O
used	O
in	O
the	O
K	B-Device
computer	I-Device
and	O
Fugaku	B-Device
.	O
</s>
<s>
In	O
a	O
4×4	O
mesh	B-Architecture
interconnect	I-Architecture
,	O
the	O
longest	O
distance	O
between	O
nodes	O
is	O
from	O
upper	O
left	O
corner	O
to	O
lower	O
right	O
corner	O
.	O
</s>
<s>
While	O
long	O
wrap-around	O
links	O
may	O
be	O
the	O
easiest	O
way	O
to	O
visualize	O
the	O
connection	O
topology	B-Architecture
,	O
in	O
practice	O
,	O
restrictions	O
on	O
cable	O
lengths	O
often	O
make	O
long	O
wrap-around	O
links	O
impractical	O
.	O
</s>
