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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

How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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.
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
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
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
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
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
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.
is Bucky paper clear?
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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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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