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Split format complex multiplication

  typedef struct _reg_t {     __m128 re, im;  } reg_t;    static inline reg_t MUL_SPLIT(reg_t a, reg_t b) {     reg_t r;    r.re = _mm_sub_ps(_mm_mul_ps(a.re,b.re),_mm_mul_ps(a.im,b.im));     r.im = _mm_add_ps(_mm_mul_ps(a.re,b.im),_mm_mul_ps(a.im,b.re));    return r;   }
SSE multiplication with split complex data

The function in [link] takes complex data in two structs of SSE registers, performs the complex multiplication of each element of the vectors, and returns the result in a struct of SSEregisters. Each struct is composed of a register containing the real parts of four complex numbers, and another register containing the imaginary parts – sothe function in [link] is effectively operating on vectors twice as long as the function in [link] . The benefit of operating in split format is obvious: the shuffle operations that wererequired in [link] are avoided because the real and imaginary parts can be implicitly swapped at the instruction level, rather thanby awkwardly manipulating SIMD registers at the data level of abstraction. Thus, [link] computes complex multiplication for vectors twice as long while using one less SSE instruction – not to mention otheradvantages such as reducing chains of dependent instructions. The only disadvantage to the split format approach is that twice as many registers areneeded to compute a given operation – this might preclude the use of a larger radix or force register paging for some kernels of computation.

Fast interleaved format complex multiplication

[link] is fast method of interleaved complex multiplication that may be used in situations where one of the operands can beunpacked prior to multiplication – in such cases the instruction count is reduced from 7 instructions to 4 instructions (cf. [link] ). This method of complex multiplication lends itself especially well to the conjugate-pair algorithm where the same twiddlefactor is used twice – by doubling the size of the twiddle factor LUT, the multiplication instruction count is reduced from 14 instructions to 8instructions. Furthermore, large chains of dependent instructions are reduced,and in practice the actual performance gain can be quite impressive.

Operand a in [link] has been replaced with two operands in [link] : re and im – these operands have been unpacked, as was done in lines 3 and 5 of [link] . Furthermore, line 8 of [link] is also avoided by performing the selective negation during unpacking.

  static inline __m128   MUL_UNPACKED_INTERLEAVED(__m128 re, __m128 im, __m128 b) {    re = _mm_mul_ps(re, b);     im = _mm_mul_ps(im, b);    im = _mm_shuffle_ps(im,im,_MM_SHUFFLE(2,3,0,1));     return _mm_add_ps(re, im);  }
SSE multiplication with partially unpacked interleaved data

Vectorized loops

The performance of the FFTs in the previous sections can be increased by explicitly vectorizing the loops. The Macbook Air 4,2 used to compile and runthe previous examples has a CPU that implements SSE and AVX, but for the purposes of simplicity, SSE intrinsics are used in thefollowing examples. The loop of the radix-2 implementation is used as an example in [link] .

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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