# 0.2 Implementation details  (Page 6/9)

 Page 7 / 9

## 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] .

how can chip be made from sand
is this allso about nanoscale material
Almas
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Got questions? Join the online conversation and get instant answers!