Square root

java-programmer, Square root What is the method of finding the square root of a number?

java-programmer >> Square root f2prateek wrote:

> What is the method of finding the square root of a number?

java.lang.Math.sqrt()

java-programmer >> Square root f2prateek wrote:
> What is the method of finding the square root of a number?
>

Here's one, that takes me back to high school:

http://www.qnet.fi/abehr/Achim/Calculators_SquareRoots.html

java-programmer >> Square root J. David Boyd wrote:
> f2prateek wrote:
>> What is the method of finding the square root of a number?
>>
>
> Here's one, that takes me back to high school:
>
> http://www.qnet.fi/abehr/Achim/Calculators_SquareRoots.html

I read about that algorithm when I was 11. I've never seen a computer implementation of it.

gtoomey

java-programmer >> Square root Gregory Toomey wrote:
> J. David Boyd wrote:
>> f2prateek wrote:
>>> What is the method of finding the square root of a number?
>>>
>>
>> Here's one, that takes me back to high school:
>>
>> http://www.qnet.fi/abehr/Achim/Calculators_SquareRoots.html
>
> I read about that algorithm when I was 11. I've never seen a computer
> implementation of it.
>
> gtoomey

Me either. But I didn't think the O.P. was looking for a computer
algorithm, just a method.

Dave

java-programmer >> Square root Gregory Toomey wrote:
> J. David Boyd wrote:
>> f2prateek wrote:
>>> What is the method of finding the square root of a number?
>>>
>>
>> Here's one, that takes me back to high school:
>>
>> http://www.qnet.fi/abehr/Achim/Calculators_SquareRoots.html
>
> I read about that algorithm when I was 11. I've never seen a computer
> implementation of it.

Of course not. The Newton-Raphson iteration is much faster.

However, in some cases, the use of a square root indicates that the
actual thing to be computed is a Pythagorean sum. That can be calculated
better.

/**
* Compute the Pythagorean Sum (I.E. what is the distance given Delta X,
* and Delta Y)
*
* Traditionally, this is done as sqrt(x*x+y*y), but this has the
* problem that the squared quantity can overflow long before the result
* would have.
*
* Cleve Moler and Donald Morrison show (as documented in their article
* in the IBM Journal of Research and Development, VOL27 No 6 NOV 83)
* that this can actually computed more directly.
*
* Advantages of this algorithm: It never squares X or Y, so it never
* overflows unless the answer does. It is very numerically stable. It
* is very fast.
*
* This code started life in MASM Assembley Language on a Univac. That
* code was then ported to Fortran IV, on a Univac. That code was then
* ported to C. That code was then ported to Ada. That code was then
* used as the base of this port. SO.. it has a lot of inherited uglies.
*/

public class PythagoreanSum {

/**
* Calculate a Pythagorean sum
*
* @param x
* @param y
* @return sqrt(x*x + y*y), calculated directly
*/
static public double sum(final double x, final double y) {
final double delta_x = Math.abs(x);
final double delta_y = Math.abs(y);
double guess, errval;
if (delta_x > delta_y) {
guess = delta_x;
errval = delta_y;
} else {
guess = delta_y;
errval = delta_x;
}
// The following code is the loop unrolling of:
// temp = error / guess;
// r = temp * temp;
// s = r / (r + 4.0);
// guess += 2.0 * s * guess;
// error *= s;
// The loop is unrolled because checking for convergence takes
// more time than the computation.
// 1 iteration gives 1 significant digits in the result.
// 2 iterations give 5 significant digits,
// 3 iterations give 20 significant digits,
// 4 iterations give 62 significant digits.
// Etc. (The number of significant decimal digits roughly
// triples with each iteration.)
// The loop invariant is that SQRT(GUESS**2+ERROR**2) is the
// Length with each iteration dramaticly shrinking ERROR.
// After this we have one significant figure in the result
double temp = errval / guess;
double r = temp * temp;
double s = r / (r + 4.0);
guess += 2.0 * s * guess;
// After this we have 6 significant digits in the result
errval *= s;
temp = errval / guess;
r = temp * temp;
s = r / (r + 4.0);
guess += 2.0 * s * guess;
// After this we have 20 significant digits in the result
errval *= s;
temp = errval / guess;
r = temp * temp;
s = r / (r + 4.0);
guess += 2.0 * s * guess;
return guess;
}

/**
* Tester
* @param args
*/
public static void main(String[] args) {
for (double i = 3.0, j = 4.0, k = 4.0;
i < 1000.0; i += 2.0, j += 4.0, k += j) {
System.out.println (i + '\t' + k + '\t' + sum(i, k));
}
}

}

--
John W. Kennedy
"The blind rulers of Logres
Nourished the land on a fallacy of rational virtue."
-- Charles Williams. "Taliessin through Logres: Prelude"

java-programmer >> Square root Gregory Toomey wrote:
> J. David Boyd wrote:
>> f2prateek wrote:
>>> What is the method of finding the square root of a number?
>>>
>>
>> Here's one, that takes me back to high school:
>>
>> http://www.qnet.fi/abehr/Achim/Calculators_SquareRoots.html
>
> I read about that algorithm when I was 11. I've never seen a computer
> implementation of it.

I did it once (in binary) for a integer square root routine.
A 256-place table of eight-bit approximations plus some scaling and
one or at most two Newton-Raphson iterations turned out to be faster,
though.

--
Eric Sosman
email***@***.com

java-programmer >> Square root I need to calculate the roots of a quadratic equation by formula.But
how do I use the math.sqrt thing?

java-programmer >> Square root
f2prateek wrote:
> I need to calculate the roots of a quadratic equation by formula.But
> how do I use the math.sqrt thing?

Do a google search on java math.sqrt The first link will give you the
class definition which you can use. Basically, this should be in the
comp.lang.java.help newsgroup as it is pretty much rank beginner stuff,
and that group is more for people just getting started with java.

However, giving you the fish as well as teaching you to fish, code
like:

double a, b, c, root1, root2;
a = 1;
b = 4;
c = 7; //picked random numbers
root1 = ((-1 * b) + (Math.sqrt((b * b) - (4 * a * c))) / (2 * a);
root2 = ...

java-programmer >> Square root thanks