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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:

Questions & Answers

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
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
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
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket 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, High performance computing. OpenStax CNX. Aug 25, 2010 Download for free at http://cnx.org/content/col11136/1.5
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