<s>
In	O
mathematics	O
,	O
binary	B-Algorithm
splitting	I-Algorithm
is	O
a	O
technique	O
for	O
speeding	O
up	O
numerical	O
evaluation	O
of	O
many	O
types	O
of	O
series	O
with	O
rational	O
terms	O
.	O
</s>
<s>
Binary	B-Algorithm
splitting	I-Algorithm
requires	O
more	O
memory	O
than	O
direct	O
term-by-term	O
summation	O
,	O
but	O
is	O
asymptotically	O
faster	O
since	O
the	O
sizes	O
of	O
all	O
occurring	O
subproducts	O
are	O
reduced	O
.	O
</s>
<s>
Additionally	O
,	O
whereas	O
the	O
most	O
naive	O
evaluation	O
scheme	O
for	O
a	O
rational	O
series	O
uses	O
a	O
full-precision	O
division	O
for	O
each	O
term	O
in	O
the	O
series	O
,	O
binary	B-Algorithm
splitting	I-Algorithm
requires	O
only	O
one	O
final	O
division	O
at	O
the	O
target	O
precision	O
;	O
this	O
is	O
not	O
only	O
faster	O
,	O
but	O
conveniently	O
eliminates	O
rounding	O
errors	O
.	O
</s>
<s>
To	O
take	O
full	O
advantage	O
of	O
the	O
scheme	O
,	O
fast	O
multiplication	O
algorithms	O
such	O
as	O
Toom	B-Algorithm
–	I-Algorithm
Cook	I-Algorithm
and	O
Schönhage	B-Algorithm
–	I-Algorithm
Strassen	I-Algorithm
must	O
be	O
used	O
;	O
with	O
ordinary	O
O(n2 )	O
multiplication	O
,	O
binary	B-Algorithm
splitting	I-Algorithm
may	O
render	O
no	O
speedup	O
at	O
all	O
or	O
be	O
slower	O
.	O
</s>
<s>
Since	O
all	O
subdivisions	O
of	O
the	O
series	O
can	O
be	O
computed	O
independently	O
of	O
each	O
other	O
,	O
binary	B-Algorithm
splitting	I-Algorithm
lends	O
well	O
to	O
parallelization	B-Operating_System
and	O
checkpointing	B-General_Concept
.	O
</s>
<s>
In	O
a	O
less	O
specific	O
sense	O
,	O
binary	B-Algorithm
splitting	I-Algorithm
may	O
also	O
refer	O
to	O
any	O
divide	B-Algorithm
and	I-Algorithm
conquer	I-Algorithm
algorithm	I-Algorithm
that	O
always	O
divides	O
the	O
problem	O
in	O
two	O
halves	O
.	O
</s>
