# 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:

#### Questions & Answers

find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
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.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
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
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele 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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