<s>
In	O
computing	O
,	O
especially	O
computational	O
geometry	O
,	O
a	O
real	B-General_Concept
RAM	I-General_Concept
(	O
random-access	B-Application
machine	I-Application
)	O
is	O
a	O
mathematical	O
model	O
of	O
a	O
computer	O
that	O
can	O
compute	O
with	O
exact	O
real	O
numbers	O
instead	O
of	O
the	O
binary	O
fixed	O
point	O
or	O
floating	B-Algorithm
point	I-Algorithm
numbers	I-Algorithm
used	O
by	O
most	O
actual	O
computers	O
.	O
</s>
<s>
The	O
real	B-General_Concept
RAM	I-General_Concept
was	O
formulated	O
by	O
Michael	O
Ian	O
Shamos	O
in	O
his	O
1978	O
Ph.D.	O
dissertation	O
.	O
</s>
<s>
The	O
"	O
RAM	O
"	O
part	O
of	O
the	O
real	B-General_Concept
RAM	I-General_Concept
model	O
name	O
stands	O
for	O
"	O
random-access	B-Application
machine	I-Application
"	O
.	O
</s>
<s>
It	O
consists	O
of	O
a	O
stored	O
program	O
,	O
a	O
computer	B-General_Concept
memory	I-General_Concept
unit	O
consisting	O
of	O
an	O
array	O
of	O
cells	O
,	O
and	O
a	O
central	B-General_Concept
processing	I-General_Concept
unit	I-General_Concept
with	O
a	O
bounded	O
number	O
of	O
registers	B-General_Concept
.	O
</s>
<s>
Under	O
the	O
control	O
of	O
the	O
program	O
,	O
the	O
real	B-General_Concept
RAM	I-General_Concept
can	O
transfer	O
real	O
numbers	O
between	O
memory	O
and	O
registers	B-General_Concept
,	O
and	O
perform	O
arithmetic	O
operations	O
on	O
the	O
values	O
stored	O
in	O
the	O
registers	B-General_Concept
.	O
</s>
<s>
The	O
reason	O
for	O
avoiding	O
integer	O
rounding	O
and	O
modulus	O
operations	O
is	O
that	O
allowing	O
these	O
operations	O
could	O
give	O
the	O
real	B-General_Concept
RAM	I-General_Concept
unreasonable	O
amounts	O
of	O
computational	O
power	O
,	O
enabling	O
it	O
to	O
solve	O
PSPACE-complete	O
problems	O
in	O
polynomial	O
time	O
.	O
</s>
<s>
When	O
analyzing	O
algorithms	O
for	O
the	O
real	B-General_Concept
RAM	I-General_Concept
,	O
each	O
allowed	O
operation	O
is	O
typically	O
assumed	O
to	O
take	O
constant	O
time	O
.	O
</s>
<s>
Software	B-Library
libraries	I-Library
such	O
as	O
LEDA	B-Library
have	O
been	O
developed	O
which	O
allow	O
programmers	O
to	O
write	O
computer	O
programs	O
that	O
work	O
as	O
if	O
they	O
were	O
running	O
on	O
a	O
real	B-General_Concept
RAM	I-General_Concept
.	O
</s>
<s>
These	O
libraries	O
represent	O
real	O
values	O
using	O
data	B-General_Concept
structures	I-General_Concept
which	O
allow	O
them	O
to	O
perform	O
arithmetic	O
and	O
comparisons	O
with	O
the	O
same	O
results	O
as	O
a	O
real	B-General_Concept
RAM	I-General_Concept
would	O
produce	O
.	O
</s>
<s>
For	O
example	O
,	O
In	O
LEDA	B-Library
,	O
real	O
numbers	O
are	O
represented	O
using	O
the	O
leda_real	O
datatype	O
,	O
which	O
supports	O
k-th	O
roots	O
for	O
any	O
natural	O
number	O
k	O
,	O
rational	O
operators	O
,	O
and	O
comparison	O
operators	O
.	O
</s>
<s>
The	O
real	B-General_Concept
RAM	I-General_Concept
closely	O
resembles	O
the	O
later	O
Blum	B-Application
–	I-Application
Shub	I-Application
–	I-Application
Smale	I-Application
machine	I-Application
.	O
</s>
<s>
However	O
,	O
the	O
real	B-General_Concept
RAM	I-General_Concept
is	O
typically	O
used	O
for	O
the	O
analysis	O
of	O
concrete	O
algorithms	O
in	O
computational	O
geometry	O
,	O
while	O
the	O
Blum	B-Application
–	I-Application
Shub	I-Application
–	I-Application
Smale	I-Application
machine	I-Application
instead	O
forms	O
the	O
basis	O
for	O
extensions	O
of	O
the	O
theory	O
of	O
NP-completeness	O
to	O
real-number	O
computation	O
.	O
</s>
<s>
An	O
alternative	O
to	O
the	O
real	B-General_Concept
RAM	I-General_Concept
is	O
the	O
word	B-Application
RAM	I-Application
,	O
in	O
which	O
both	O
the	O
inputs	O
to	O
a	O
problem	O
and	O
the	O
values	O
stored	O
in	O
memory	O
and	O
registers	B-General_Concept
are	O
assumed	O
to	O
be	O
integers	O
with	O
a	O
fixed	O
number	O
of	O
bits	O
.	O
</s>
<s>
The	O
word	B-Application
RAM	I-Application
model	O
can	O
perform	O
some	O
operations	O
more	O
quickly	O
than	O
the	O
real	B-General_Concept
RAM	I-General_Concept
;	O
for	O
instance	O
,	O
it	O
allows	O
fast	O
integer	B-Algorithm
sorting	I-Algorithm
algorithms	O
,	O
while	O
sorting	O
on	O
the	O
real	B-General_Concept
RAM	I-General_Concept
must	O
be	O
done	O
with	O
slower	O
comparison	B-Algorithm
sorting	I-Algorithm
algorithms	O
.	O
</s>
