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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

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
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Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
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
NANO
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
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
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Cied
what is biological synthesis of nanoparticles
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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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