<s>
The	O
Fastest	B-Application
Fourier	I-Application
Transform	I-Application
in	I-Application
the	I-Application
West	I-Application
(	O
FFTW	B-Application
)	O
is	O
a	O
software	B-Library
library	I-Library
for	O
computing	O
discrete	B-Algorithm
Fourier	I-Algorithm
transforms	I-Algorithm
(	O
DFTs	O
)	O
developed	O
by	O
Matteo	O
Frigo	O
and	O
Steven	O
G	O
.	O
Johnson	O
at	O
the	O
Massachusetts	O
Institute	O
of	O
Technology	O
.	O
</s>
<s>
FFTW	B-Application
is	O
one	O
of	O
the	O
fastest	O
free	B-Application
software	I-Application
implementations	O
of	O
the	O
fast	O
Fourier	O
transform	O
(	O
FFT	O
)	O
.	O
</s>
<s>
FFTW	B-Application
expeditiously	O
transforms	O
data	O
by	O
supporting	O
a	O
variety	O
of	O
algorithms	O
and	O
choosing	O
the	O
one	O
(	O
a	O
particular	O
decomposition	O
of	O
the	O
transform	O
into	O
smaller	O
transforms	O
)	O
it	O
estimates	B-Algorithm
or	O
measures	O
to	O
be	O
preferable	O
in	O
the	O
particular	O
circumstances	O
.	O
</s>
<s>
To	O
decompose	O
transforms	O
of	O
composite	O
sizes	O
into	O
smaller	O
transforms	O
,	O
it	O
chooses	O
among	O
several	O
variants	O
of	O
the	O
Cooley	B-Algorithm
–	I-Algorithm
Tukey	I-Algorithm
FFT	I-Algorithm
algorithm	I-Algorithm
(	O
corresponding	O
to	O
different	O
factorizations	O
and/or	O
different	O
memory-access	O
patterns	O
)	O
,	O
while	O
for	O
prime	O
sizes	O
it	O
uses	O
either	O
Rader	O
's	O
or	O
Bluestein	O
's	O
FFT	O
algorithm	O
.	O
</s>
<s>
Once	O
the	O
transform	O
has	O
been	O
broken	O
up	O
into	O
subtransforms	O
of	O
sufficiently	O
small	O
sizes	O
,	O
FFTW	B-Application
uses	O
hard-coded	O
unrolled	B-Operating_System
FFTs	O
for	O
these	O
small	O
sizes	O
that	O
were	O
produced	O
(	O
at	O
compile	B-Application
time	I-Application
,	O
not	O
at	O
run	B-Library
time	I-Library
)	O
by	O
code	B-Application
generation	I-Application
;	O
these	O
routines	O
use	O
a	O
variety	O
of	O
algorithms	O
including	O
Cooley	O
–	O
Tukey	O
variants	O
,	O
Rader	O
's	O
algorithm	O
,	O
and	O
prime-factor	O
FFT	O
algorithms	O
.	O
</s>
<s>
For	O
a	O
sufficiently	O
large	O
number	O
of	O
repeated	O
transforms	O
it	O
is	O
advantageous	O
to	O
measure	O
the	O
performance	O
of	O
some	O
or	O
all	O
of	O
the	O
supported	O
algorithms	O
on	O
the	O
given	O
array	O
size	O
and	O
platform	B-Device
.	O
</s>
<s>
FFTW	B-Application
has	O
a	O
"	O
guru	O
interface	O
"	O
that	O
intends	O
"	O
to	O
expose	O
as	O
much	O
as	O
possible	O
of	O
the	O
flexibility	O
in	O
the	O
underlying	O
FFTW	B-Application
architecture	O
"	O
.	O
</s>
<s>
FFTW	B-Application
has	O
limited	O
support	O
for	O
out-of-order	O
transforms	O
(	O
using	O
the	O
Message	B-Application
Passing	I-Application
Interface	I-Application
(	O
MPI	O
)	O
version	O
)	O
.	O
</s>
<s>
FFTW	B-Application
is	O
licensed	O
under	O
the	O
GNU	B-License
General	I-License
Public	I-License
License	I-License
.	O
</s>
<s>
It	O
is	O
also	O
licensed	O
commercially	O
(	O
for	O
a	O
cost	O
of	O
up	O
to	O
$	O
12,500	O
)	O
by	O
MIT	O
and	O
is	O
used	O
in	O
the	O
commercial	O
MATLAB	B-Language
matrix	O
package	O
for	O
calculating	O
FFTs	O
.	O
</s>
<s>
FFTW	B-Application
is	O
written	O
in	O
the	O
C	B-Language
language	I-Language
,	O
but	O
Fortran	B-Application
and	O
Ada	B-Language
interfaces	O
exist	O
,	O
as	O
well	O
as	O
interfaces	O
for	O
a	O
few	O
other	O
languages	O
.	O
</s>
<s>
While	O
the	O
library	B-Library
itself	O
is	O
C	B-Language
,	O
the	O
code	O
is	O
actually	O
generated	O
from	O
a	O
program	O
called	O
'	O
genfft	O
 '	O
,	O
which	O
is	O
written	O
in	O
OCaml	B-Language
.	O
</s>
<s>
In	O
1999	O
,	O
FFTW	B-Application
won	O
the	O
J	O
.	O
H	O
.	O
Wilkinson	O
Prize	O
for	O
Numerical	O
Software	O
.	O
</s>
