<s>
A	O
spigot	B-Algorithm
algorithm	I-Algorithm
is	O
an	O
algorithm	O
for	O
computing	O
the	O
value	O
of	O
a	O
transcendental	O
number	O
(	O
such	O
as	O
or	O
e	O
)	O
that	O
generates	O
the	O
digits	O
of	O
the	O
number	O
sequentially	O
from	O
left	O
to	O
right	O
providing	O
increasing	O
precision	B-Architecture
as	O
the	O
algorithm	O
proceeds	O
.	O
</s>
<s>
Spigot	B-Algorithm
algorithms	I-Algorithm
also	O
aim	O
to	O
minimize	O
the	O
amount	O
of	O
intermediate	O
storage	O
required	O
.	O
</s>
<s>
Spigot	B-Algorithm
algorithms	I-Algorithm
can	O
be	O
contrasted	O
with	O
algorithms	O
that	O
store	O
and	O
process	O
complete	O
numbers	O
to	O
produce	O
successively	O
more	O
accurate	O
approximations	O
to	O
the	O
desired	O
transcendental	O
.	O
</s>
<s>
Interest	O
in	O
spigot	B-Algorithm
algorithms	I-Algorithm
was	O
spurred	O
in	O
the	O
early	O
days	O
of	O
computational	O
mathematics	O
by	O
extreme	O
constraints	O
on	O
memory	O
,	O
and	O
such	O
an	O
algorithm	O
for	O
calculating	O
the	O
digits	O
of	O
e	O
appeared	O
in	O
a	O
paper	O
by	O
Sale	O
in	O
1968	O
.	O
</s>
<s>
The	O
name	O
"	O
spigot	B-Algorithm
algorithm	I-Algorithm
"	O
seems	O
to	O
have	O
been	O
coined	O
by	O
Stanley	O
Rabinowitz	O
and	O
Stan	O
Wagon	O
,	O
whose	O
algorithm	O
for	O
calculating	O
the	O
digits	O
of	O
is	O
sometimes	O
referred	O
to	O
as	O
"	O
the	O
spigot	B-Algorithm
algorithm	I-Algorithm
for	O
"	O
.	O
</s>
<s>
The	O
spigot	B-Algorithm
algorithm	I-Algorithm
of	O
Rabinowitz	O
and	O
Wagon	O
is	O
bounded	O
,	O
in	O
the	O
sense	O
that	O
the	O
number	O
of	O
terms	O
of	O
the	O
infinite	O
series	O
that	O
will	O
be	O
processed	O
must	O
be	O
specified	O
in	O
advance	O
.	O
</s>
<s>
A	O
variant	O
of	O
the	O
spigot	O
approach	O
uses	O
an	O
algorithm	O
which	O
can	O
be	O
used	O
to	O
compute	O
a	O
single	O
arbitrary	O
digit	O
of	O
the	O
transcendental	O
without	O
computing	O
the	O
preceding	O
digits	O
:	O
an	O
example	O
is	O
the	O
Bailey	B-Algorithm
–	I-Algorithm
Borwein	I-Algorithm
–	I-Algorithm
Plouffe	I-Algorithm
formula	I-Algorithm
,	O
a	O
digit	B-Algorithm
extraction	I-Algorithm
algorithm	I-Algorithm
for	O
which	O
produces	O
base	O
16	O
digits	O
.	O
</s>
<s>
The	O
precision	B-Architecture
of	O
calculations	O
and	O
intermediate	O
results	O
and	O
the	O
number	O
of	O
terms	O
taken	O
from	O
the	O
"	O
tail	O
"	O
sum	O
are	O
all	O
independent	O
of	O
n	O
,	O
and	O
only	O
depend	O
on	O
the	O
number	O
of	O
binary	O
digits	O
that	O
are	O
being	O
calculated	O
–	O
single	O
precision	B-Architecture
arithmetic	O
can	O
be	O
used	O
to	O
calculate	O
around	O
12	O
binary	O
digits	O
,	O
regardless	O
of	O
the	O
starting	O
position	O
.	O
</s>
