# 0.4 Streaming fft  (Page 12/19)

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## Example

[link] is a size-64 hard-coded leaf transform with size-16 leaves. The first function (lines 1–17) is a size-16 leaf sub-transform, while the second (lines 18–32) consists of two size-8 leaf sub-transforms in parallel. The main function (lines 36–46) invokes four leaf sub-transforms (lines 40, 41, 43 and 44), and two loops of body sub-transforms (lines 42 and 45).

The first parameter to the leaf functions (see lines 1 and 18) is a pointer into an array of precomputed indices for the input data array. At lines 41 and 43–44, the array is incremented before subsequent calls to the leaf functions, and at line 39 the pointer is reset to the base of the array so that the transform can be used repeatedly.

The function used for the body sub-transforms (lines 33–35) is a wrapper for a primitive that computes a radix-2/4 butterfly. The last parameter to this function is a pointer to a precomputed LUT of twiddle factors for a sub-transform of size $N$ (the second parameter).

## Improving memory locality in the leaves

 Size Input array addresses 16 {0, 64, 32, 96, 16, 80, 112, 48, 8, 72, 40, 104, 120, 56, 24, 88} 8(x2) {4, 68, 36, 100, 20, 84, 116, 52, 124, 60, 28, 92, 12, 76, 108, 44} 16 {2, 66, 34, 98, 18, 82, 114, 50, 10, 74, 42, 106, 122, 58, 26, 90} 16 {126, 62, 30, 94, 14, 78, 110, 46, 6, 70, 38, 102, 118, 54, 22, 86} 16 {1, 65, 33, 97, 17, 81, 113, 49, 9, 73, 41, 105, 121, 57, 25, 89} 8(x2) {5, 69, 37, 101, 21, 85, 117, 53, 125, 61, 29, 93, 13, 77, 109, 45} 16 {127, 63, 31, 95, 15, 79, 111, 47, 7, 71, 39, 103, 119, 55, 23, 87} 8(x2) {3, 67, 35, 99, 19, 83, 115, 51, 123, 59, 27, 91, 11, 75, 107, 43}

[link] lists the addresses of data loaded by each of the size-16 leaf nodes in a size-128 transform. It is difficult to improve the locality of accesses within a leaf sub-transform (doing so would require the use of expensive transposes), but the order of the leaf sub-transforms can be changed to yield better locality between sub-transforms.

 Size Input array addresses 16 {0, 64, 32, 96, 16, 80, 112, 48, 8, 72, 40, 104, 120, 56, 24, 88} 16 {1, 65, 33, 97, 17, 81, 113, 49, 9, 73, 41, 105, 121, 57, 25, 89} 16 {2, 66, 34, 98, 18, 82, 114, 50, 10, 74, 42, 106, 122, 58, 26, 90} 8(x2) {3, 67, 35, 99, 19, 83, 115, 51, 123, 59, 27, 91, 11, 75, 107, 43} 8(x2) {4, 68, 36, 100, 20, 84, 116, 52, 124, 60, 28, 92, 12, 76, 108, 44} 8(x2) {5, 69, 37, 101, 21, 85, 117, 53, 125, 61, 29, 93, 13, 77, 109, 45} 16 {126, 62, 30, 94, 14, 78, 110, 46, 6, 70, 38, 102, 118, 54, 22, 86} 16 {127, 63, 31, 95, 15, 79, 111, 47, 7, 71, 39, 103, 119, 55, 23, 87}

[link] is the list of nodes from [link] after the rows have been sorted according to the minimum address in each row. There are now three distinct groups in the list: the first three sub-transforms of size-16, the second three sub-transforms of 2x size-8, and the final two sub-transforms of size-16. The memory accesses are now linear between consecutive sub-transforms, though the second and third groups operate on a permuted ordering of the addresses.

what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
how did you get the value of 2000N.What calculations are needed to arrive at it
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Good
Berger describes sociologists as concerned with
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