<s>
isl	O
(	O
integer	B-Language
set	I-Language
library	I-Language
)	O
is	O
a	O
portable	O
C	B-Language
library	B-Library
for	O
manipulating	O
sets	O
and	O
relations	O
of	O
integer	O
points	O
bounded	B-Algorithm
by	O
linear	O
constraints	B-Application
.	O
</s>
<s>
It	O
also	O
includes	O
an	O
ILP	B-Algorithm
solver	O
based	O
on	O
generalized	O
basis	O
reduction	O
,	O
transitive	O
closures	O
on	O
maps	B-Algorithm
(	O
which	O
may	O
encode	O
infinite	O
graphs	O
)	O
,	O
dependence	O
analysis	O
and	O
bounds	O
on	O
piecewise	B-Algorithm
step-polynomials	O
.	O
</s>
<s>
All	O
computations	O
are	O
performed	O
in	O
exact	O
integer	O
arithmetic	O
using	O
GMP	B-Application
or	O
imath	O
.	O
</s>
<s>
The	O
integers	O
typically	O
represent	O
iterations	O
of	O
a	O
loop	O
nest	O
or	O
elements	O
of	O
an	O
array	B-Data_Structure
.	O
</s>
<s>
isl	O
uses	O
parametric	O
integer	B-Algorithm
programming	I-Algorithm
to	O
obtain	O
an	O
explicit	O
representation	O
in	O
terms	O
of	O
integer	O
divisions	O
.	O
</s>
