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Other vector lengths

If V L > 1 , the list of nodes that results from the elaborate function in [link] is vectorized. Broadly speaking, CNodeLoad objects that operate on adjacent memory locations are collected together and computed in parallel. After each such computation, each position in a vector register contains an element that belongs to a different node. Transposes are then used to transform sets of vector registers such that each register contains elements from one node. Finally, the CNodeBfly objects can be easily computed in parallel, as they were with VL-1 because the elements in each vector register correspond to one node.

Overview

[link] lists the nodes that represent a VL-1 size-16 transform. A VL of 2 implies that each vector register contains 2 complex words, and load operations on each of the 4 addresses in the first row of [link] will also load the complex words in the adjacent memory locations. Note that the complex words that would be incidentally loaded in the upper half of the VL-2 registers are the complex words that the third CNodeLoad object at row 5 would have loaded. This is exploited to load and compute the first and third CNodeLoad objects in parallel.

VL-1 size-16 conjugate-pair transform nodes
Type Size Addresses Registers Twiddle
CNodeLoad 4 {0,8,4,12} {0,1,2,3}
CNodeLoad 2(x2) {2,10,14,6} {4,5,6,7}
CNodeBfly 4 {0,2,4,6} ω 16 0
CNodeBfly 4 {1,3,5,7} ω 16 2
CNodeLoad 4 {1,9,5,13} {8,9,10,11}
CNodeLoad 4 {15,7,3,11} {12,13,14,15}
CNodeBfly 4 {0,4,8,12} ω 16 0
CNodeBfly 4 {1,5,9,13} ω 16 1
CNodeBfly 4 {2,6,10,14} ω 16 2
CNodeBfly 4 {3,7,11,15} ω 16 3
VL-2 size-16 conjugate-pair transform nodes
Type Sizes Addresses Registers Twiddles
Load {4,4} {{0,1},{8,9},{4,5},{12,13}} {{0,1},{2,3},{8,9},{10,11}}
Load {2(x2),4} {{2,3},{10,11},{14,15},{6,7}} {{4,5},{6,7},{14,15},{12,13}}
Bfly {4,4} {{0,1},{2,3},{4,5},{6,7}} { ω 16 0 , ω 16 2 }
Bfly {4,4} {{0,1},{4,5},{8,9},{12,13}} { ω 16 0 , ω 16 1 }
Bfly {4,4} {{2,3},{6,7},{10,11},{14,15}} { ω 16 2 , ω 16 3 }

The second CNodeLoad object computes two size-2 leaf transforms in parallel, while the last CNodeLoad object computes a size-4 leaf transform. Because the size-4 transform is composed of two size-2 transforms, and memory addresses of the fourth CNodeLoad are adjacent (although permuted), some of the computation can be computed in parallel.

If the CNodeLoad objects at rows 1 and 5 are computed in parallel, the output will be four VL-2 registers: {{0,8}, {1,9}, {2,10}, {3,11}} – i.e., the first register contains what would have been register 0 in the lower half, and what would have been register 8 in the top half etc. Similarly, computing rows 2 and 6 in parallel would yield four VL-2 registers: {{4,14}, {5,15}, {6,12}, {7,13}} – note the permutation of the upper halves in this case. These registers are transposed to {{0,1}, {2,3}, {8,9}, {10,11}} and {{4,5}, {6,7}, {14,15}, {12,13}}, as in row 1 and 2 of [link] .

With the transposed VL-2 registers, it is now possible to compute CNodeBfly nodes in parallel. For example, rows 2 and 3 of [link] can be computed in parallel on four VL-2 registers represented by {{0,1}, {2,3}, {4,5}, {6,7}}, as in row 3 of [link] .

Implementation

[link] is a C++ implementation of the vectorize_loads function. This function modifies a topological ordering of nodes (the class member variable ns ) and uses two other functions: find_parallel_loads , which searches forward from the current node to find another CNodeLoad that shares adjacent memory addresses; and merge_loads(a,b) , which adds the addresses, registers and type of b to a . Type introspection is used at lines 7 and 36 (and in other Listings), to differentiate between the two types of object.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
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biomolecules are e building blocks of every organics and inorganic materials.
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research.net
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sciencedirect big data base
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Introduction about quantum dots in nanotechnology
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nano basically means 10^(-9). nanometer is a unit to measure length.
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Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
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what is fullerene does it is used to make bukky balls
Devang Reply
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
Abhijith Reply
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
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s. Reply
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.
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in general
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Source:  OpenStax, Computing the fast fourier transform on simd microprocessors. OpenStax CNX. Jul 15, 2012 Download for free at http://cnx.org/content/col11438/1.2
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