# 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.

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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