# 0.4 Streaming fft  (Page 2/19)

 Page 2 / 19

## Vector length 1

A VL of 1 implies that the computation is essentially scalar, and only one complex element can fit in a vector register. An example of such a scenario is when using interleaved double-precision floating-point arithmetic on an SSE2 machine: one 128-bit XMM register is used to store two 64-bit floats that represent the real and imaginary parts of a complex number.

When $VL=1$ , the process of generating a program for a hard-coded FFT is as follows:

1. Elaborate a topological ordering of nodes, where each node represents either a computation at the leaves of the transform, or a computation in the body of the transform (i.e., where smaller sub-transforms are combined into a larger transform);
2. Write the program header to output, including a list of variables that correspond to registers used by the nodes;
3. Traverse the list of nodes in order, and for each node, emit a statement that performs the computation represented by the given node. If a node is the last node to use a variable, a statement storing the variable to its corresponding location in memory is also emitted;
4. Write the program footer to output.

## Elaborate

[link] is a function, written in C++, that performs the first task in the process. As mentioned earlier, elaborating a topological ordering of nodes with a depth-first recursive structure is much likeactually computing an FFT with a depth-first recursive program (cf. Listing 3 in Appendix 2 ). [link] lists the nodes contained in the list  ns ' after elaborating a size-8 transform by invoking elaborate(8, 0, 0, 0) .

  CSplitRadix::elaborate(int N, int ioffset, int offset, int stride) {     if(N > 4) {       elaborate(N/2, ioffset, offset, stride+1);      if(N/4 >= 4) {         elaborate(N/4, ioffset+(1<<stride), offset+(N/2), stride+2);         elaborate(N/4, ioffset-(1<<stride), offset+(3*N/4), stride+2);       }else{        CNodeLoad *n = new CNodeLoad(this, 4, ioffset, stride, 0);         ns.push_back(assign_leaf_registers(n));      }       for(int k=0;k<N/4;k++) {         CNodeBfly *n = new CNodeBfly(this, 4, k, stride);        ns.push_back(assign_body_registers(n,k,N);       }    }else if(N==4) {       CNodeLoad *n = new CNodeLoad(this, 4, ioffset, stride, 1);      ns.push_back(assign_leaf_registers(n));     }else if(N==2) {      CNodeLoad *n = new CNodeLoad(this, 2, ioffset, stride, 1);       ns.push_back(assign_leaf_registers(n));    }   } Elaborate function for hard-coded conjugate-pair FFT `

A transform is divided into sub-transforms with recursive calls at lines 4, 6 and 7, until the base cases of size 2 or size 4 are reached at the leaves of the elaboration. As well as the size-2 and size-4 base cases, which are handled at lines 20-21 and 17-18 (respectively), there is a special case where two size-2 base cases are handled in parallel at lines 9-10. This special case of handling two size-2 base cases as a larger size-4 node ensures that larger transforms are composed of nodes that are homogeneous in size – this is of little utility when emitting $VL=1$ code, but it is exploited in "Other vector lengths" where the topological ordering of nodes is vectorized. The second row of [link] is just such a special case, since two size-2 leaf nodes are being computed, and thus the size is listed as 2(x2).

can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
im not good at math so would this help me
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!