<s>
The	O
Gauss	B-Algorithm
–	I-Algorithm
Legendre	I-Algorithm
algorithm	I-Algorithm
is	O
an	O
algorithm	O
to	O
compute	O
the	O
digits	O
of	O
.	O
</s>
<s>
It	O
is	O
notable	O
for	O
being	O
rapidly	O
convergent	O
,	O
with	O
only	O
25	O
iterations	B-Algorithm
producing	O
45	O
million	O
correct	O
digits	O
of	O
.	O
</s>
<s>
However	O
,	O
it	O
has	O
some	O
drawbacks	O
(	O
for	O
example	O
,	O
it	O
is	O
computer	O
memory-intensive	O
)	O
and	O
therefore	O
all	O
record-breaking	O
calculations	O
for	O
many	O
years	O
have	O
used	O
other	O
methods	O
,	O
almost	O
always	O
the	B-Algorithm
Chudnovsky	I-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
It	O
was	O
used	O
to	O
compute	O
the	O
first	O
206,158,430,000	O
decimal	O
digits	O
of	O
on	O
September	O
18	O
to	O
20	O
,	O
1999	O
,	O
and	O
the	O
results	O
were	O
checked	O
with	O
Borwein	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
The	O
first	O
three	O
iterations	B-Algorithm
give	O
(	O
approximations	O
given	O
up	O
to	O
and	O
including	O
the	O
first	O
incorrect	O
digit	O
)	O
:	O
</s>
<s>
The	O
algorithm	O
has	O
quadratic	O
convergence	O
,	O
which	O
essentially	O
means	O
that	O
the	O
number	O
of	O
correct	O
digits	O
doubles	O
with	O
each	O
iteration	B-Algorithm
of	O
the	O
algorithm	O
.	O
</s>
<s>
The	O
Gauss-Legendre	B-Algorithm
algorithm	I-Algorithm
can	O
be	O
proven	O
to	O
give	O
results	O
converging	O
to	O
π	O
using	O
only	O
integral	O
calculus	O
.	O
</s>
