# 3.5 Classical optimizations  (Page 3/4)

 Page 3 / 4
``` REAL X,Y Y = X**2J = K*2```

For the exponentiation operation on the first line, the compiler generally makes an embedded mathematical subroutine library call. In the library routine, `X` is converted to a logarithm, multiplied, then converted back. Overall, raising `X` to a power is expensive — taking perhaps hundreds of machine cycles. The key is to notice that `X` is being raised to a small integer power. A much cheaper alternative would be to express it as `X*X` , and pay only the cost of multiplication. The second statement shows integer multiplication of a variable `K` by 2. Adding `K+K` yields the same answer, but takes less time.

There are many opportunities for compiler-generated strength reductions; these are just a couple of them. We will see an important special case when we look at induction variable simplification. Another example of a strength reduction is replacing multiplications by integer powers of two by logical shifts.

## Variable renaming

In [link] , we talked about register renaming. Some processors can make runtime decisions to replace all references to register 1 with register 2, for instance, to eliminate bottlenecks. Register renaming keeps instructions that are recycling the same registers for different purposes from having to wait until previous instructions have finished with them.

The same situation can occur in programs — the same variable (i.e., memory location) can be recycled for two unrelated purposes. For example, see the variable `x` in the following fragment:

``` x = y * z; q = r + x + x;x = a + b;```

When the compiler recognizes that a variable is being recycled, and that its current and former uses are independent, it can substitute a new variable to keep the calculations separate:

``` x0 = y * z; q = r + x0 + x0;x = a + b;```

Variable renaming is an important technique because it clarifies that calculations are independent of each other, which increases the number of things that can be done in parallel.

## Common subexpression elimination

Subexpressions are pieces of expressions. For instance, `A+B` is a subexpression of `C*(A+B)` . If `A+B` appears in several places, like it does below, we call it a common subexpression :

``` D = C * (A + B) E = (A + B)/2.```

Rather than calculate `A + B` twice, the compiler can generate a temporary variable and use it wherever `A + B` is required:

``` temp = A + B D = C * tempE = temp/2.```

Different compilers go to different lengths to find common subexpressions. Most pairs, such as `A+B` , are recognized. Some can recognize reuse of intrinsics, such as `SIN(X)` . Don’t expect the compiler to go too far though. Subexpressions like `A+B+C` are not computationally equivalent to reassociated forms like `B+C+A` , even though they are algebraically the same. In order to provide predictable results on computations, FORTRAN must either perform operations in the order specified by the user or reorder them in a way to guarantee exactly the same result. Sometimes the user doesn’t care which way `A+B+C` associates, but the compiler cannot assume the user does not care.

Address calculations provide a particularly rich opportunity for common subexpression elimination. You don’t see the calculations in the source code; they’re generated by the compiler. For instance, a reference to an array element `A(I,J)` may translate into an intermediate language expression such as:

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
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
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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 ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
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
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
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
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Got questions? Join the online conversation and get instant answers!