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[link] shows that SFFT is easily faster than FFTW on both devices. This contradicts Frigo and Johnson's claim that the performance of FFTW is portable, and tends to support the idea that it is possible to write fast and portable code without exhaustive searches through the configuration space of all possible FFTs.

A considerable amount of effort was needed to work around several problems that were encountered when targeting ARM NEON with Apple clang 3.0, and many of SFFT's primitive macros for NEON were written in inline assembly code. Among the problems encountered when targeting ARM NEON with Apple clang 3.0:

  1. There is no way of explicitly specifying memory alignment when using vector intrinsics;
  2. Fused multiply-add/subtract intrinsics do not currently compile to the correct instructions because of a bug in clang;
  3. Clang's inline assembly front-end lacks the syntax and semantics to properly address the dual-size aliased vector registers.

The above problems affect all FFT libraries equally, and it seems that portability depends critically on the quality of the machine specific code and macros.

Accuracy

SSE, single-precision
SSE, double-precision
Accuracy of FFTs on an Intel Core i7-2600. SFFT, FFTW and SPIRAL were compiled for x86_64 with icc

The accuracy of each FFT was measured as per the methods in Benchmark methods . The accuracy of single and double precision FFTs on an Intel Core i7-2600 is plotted in [link] , and shows that the relative RMS error for FFTW, SFFT and SPIRAL is within an acceptable range. Graphs for all other machines are similar.

Setup time

SSE, single-precision
SSE, double-precision
Setup times of FFTs on an Intel Core i7-2600. SFFT, FFTW and SPIRAL were compiled for x86_64 with icc

[link] shows that FFTW, in patient mode, requires several orders of magnitude more time to initialize as it searches for a fast FFT configuration. SPIRAL has a very fast setup time, because it is entirely statically elaborated and needs no dynamic initialization. The setup time for SFFT is comparable to FFTW in estimate mode, though SFFT's setup time begins to increase for transforms larger than 8192 points. This is likely because of repeated calls to the complex exponential function as twiddle factor LUTs are elaborated; no effort was made to optimize this setup code, and it is likely that it would be much faster if the calls to the complex exponential function were optimized.

Graphs for all other machines are similar.

Binary size

Compared to other libraries, SFFT produced larger binaries for the benchmarks, because there is currently no optimization performed between transforms contained in the same library. For 64-bit single precision binaries on OS X with AVX, the size of the SFFT benchmark was approximately 2.8 megabytes while the size of the FFTW benchmark was 1.8 megabytes.

Predicting performance

For each size of transform on a particular machine, SFFT chooses the fastest configuration from a set of up to eight possible configurations. Small transforms have only one option, which is a fully hard-coded transform, while larger transforms have up to eight, which could include the four-step transform, and several variants of the hard-coded leaf transform, where each variant corresponds to a particular size of leaf sub-transform and size of body sub-transform, and for size-16 leaf sub-transforms, a streaming store variant is included too. The decision of exactly which configuration to use depends on the size of transform, the compiler, and the characteristics of the host machine.

Questions & Answers

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
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
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
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.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
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
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
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.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
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
Prasenjit Reply
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.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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