<s>
The	O
Library	B-Library
of	I-Library
Efficient	I-Library
Data	I-Library
types	I-Library
and	I-Library
Algorithms	I-Library
(	O
LEDA	O
)	O
is	O
a	O
proprietarily-licensed	B-Application
software	B-Library
library	I-Library
providing	O
C++	B-Language
implementations	O
of	O
a	O
broad	O
variety	O
of	O
algorithms	O
for	O
graph	O
theory	O
and	O
computational	O
geometry	O
.	O
</s>
<s>
The	O
Free	O
edition	O
is	O
freeware	B-License
,	O
with	O
source	O
code	O
access	O
available	O
for	O
purchase	O
.	O
</s>
<s>
Since	O
October	O
2017	O
,	O
LEDA	O
graph	O
algorithms	O
are	O
also	O
available	O
for	O
Java	B-Device
development	I-Device
environment	I-Device
.	O
</s>
<s>
LEDA	O
provides	O
four	O
additional	O
numerical	O
representations	O
alongside	O
those	O
built-in	O
to	O
C++	B-Language
:	O
integer	O
,	O
rational	O
,	O
bigfloat	O
,	O
and	O
real	O
:	O
</s>
<s>
LEDA	O
's	O
integer	O
type	O
offers	O
an	O
improvement	O
over	O
the	O
built-in	O
int	O
datatype	O
by	O
eliminating	O
the	O
problem	O
of	O
overflow	B-Error_Name
at	O
the	O
cost	O
of	O
unbounded	O
memory	O
usage	O
for	O
increasingly	O
large	O
numbers	O
.	O
</s>
<s>
It	O
follows	O
that	O
LEDA	O
's	O
rational	O
type	O
has	O
the	O
same	O
resistance	O
to	O
overflow	B-Error_Name
because	O
it	O
is	O
based	O
directly	O
on	O
the	O
mathematical	O
definition	O
of	O
rational	O
as	O
the	O
quotient	O
of	O
two	O
integers	O
.	O
</s>
<s>
The	O
bigfloat	O
type	O
improves	O
on	O
the	O
C++	B-Language
floating-point	B-Algorithm
types	O
by	O
allowing	O
for	O
mantissa	B-Algorithm
to	O
be	O
set	O
to	O
an	O
arbitrary	O
level	O
of	O
precision	O
instead	O
of	O
following	O
the	O
IEEE	O
standard	O
.	O
</s>
<s>
LEDA	O
makes	O
use	O
of	O
certifying	B-Error_Name
algorithms	I-Error_Name
to	O
demonstrate	O
that	O
the	O
results	O
of	O
a	O
function	O
are	O
mathematically	O
correct	O
.	O
</s>
<s>
LEDA	O
's	O
checker	O
programs	O
were	O
developed	O
in	O
Simpl	O
,	O
an	O
imperative	B-Application
programming	I-Application
language	I-Application
,	O
and	O
validated	O
using	O
Isabelle/HOL	B-Application
,	O
a	O
software	O
tool	O
for	O
checking	O
the	O
correctness	O
of	O
mathematical	O
proofs	O
.	O
</s>
<s>
This	O
provides	O
an	O
advantage	O
in	O
accuracy	O
over	O
floating-point	B-Algorithm
arithmetic	I-Algorithm
.	O
</s>
<s>
Algorithms	O
such	O
as	O
parametric	B-Algorithm
search	I-Algorithm
,	O
a	O
technique	O
for	O
solving	O
a	O
subset	O
of	O
optimization	O
problems	O
,	O
and	O
others	O
under	O
the	O
real	B-General_Concept
RAM	I-General_Concept
model	O
of	O
computation	O
rely	O
upon	O
real	O
number	O
parameters	O
to	O
produce	O
accurate	O
results	O
.	O
</s>
<s>
Boost	B-Language
and	O
LEMON	B-Language
are	O
potential	O
alternative	O
libraries	O
with	O
some	O
benefits	O
in	O
efficiency	O
due	O
to	O
different	O
implementations	O
of	O
fundamental	O
algorithms	O
and	O
data	O
structures	O
.	O
</s>
<s>
However	O
,	O
neither	O
employs	O
a	O
similar	O
set	O
of	O
correctness	O
checking	O
,	O
particularly	O
when	O
dealing	O
with	O
floating-point	B-Algorithm
arithmetic	I-Algorithm
.	O
</s>
