square root algorithm for c++?

Question

0.00/5 (No votes)

See more:

i needed a pretty much efficient way to calculate square roots upto 100 decimal places(and 100% correct).i have been searching for square root algorithms on the internet.actually, i want a c++ adaptation of long division method that we learn in high school.by far,it seems most promising to me.but it's too much for my programming skills(i know only very basic c++,actually,i want to test the mathematical formula i made using a computer so that it produces high values.i even tested the method in which a value is estimated and average is taken,but it fails after only 10 digits).

Posted 22-May-12 1:19am

utkarshs

Add a Solution

4 solutions

Add a Solution

Add your solution here

Treat my content as plain text, not as HTML

Preview 0

…

Existing Members

Sign in to your account

...or Join us

Download, Vote, Comment, Publish.

Your Email
Password
Forgot your password?

Your Email
This email is in use. Do you need your password?
Optional Password

I have read and agree to the Terms of Service and Privacy Policy
Please subscribe me to the CodeProject newsletters

When answering a question please:

Read the question carefully.
Understand that English isn't everyone's first language so be lenient of bad spelling and grammar.
If a question is poorly phrased then either ask for clarification, ignore it, or edit the question and fix the problem. Insults are not welcome.
Don't tell someone to read the manual. Chances are they have and don't get it. Provide an answer or move on to the next question.

Let's work to help developers, not make them feel stupid.

This content, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)

Aescleal · Answer 1 · 2012-05-22T06:47:00

You've got two choices here - one is to roll your own using a single digit method (as shown on the page Richard mentioned) but from what you've said you're not that experienced and implementing it looks a bit fiddly if not fundamentally difficult.

Another option would be to use an arbitrary precision arithmetic library. This page [^] has some you might like to consider. As you're not that experienced with C++ you could end up thinking you've changed the problem from "How do I calculate a high precision square root" to "how do I build and use this sodding library?"

If you want to keep using C++ then working out how to use libraries is probably a better bet. If you want to keep numerical programming in the language then rolling your own might be better for now.

And... (final point that might make the whole thing redundant) does it have to be C++? A fair number of languages have support for arbitrary numbers built in. Python, for example, has a class (Decimal) that can can crank you square roots out to an arbitrary precision. It might be worth learning enough Python so you can use that rather than fighting with C++.

Richard MacCutchan · Answer 2 · 2012-05-22T01:46:00

Solution 1

My suggestion would be to work out the algorithm first (without worrying about code) and get the steps written down in natural language. Only when you have that done and you understand each step can you turn it into code.

Posted 22-May-12 1:46am

Richard MacCutchan

Comments

utkarshs 22-May-12 7:54am

thanks for your answer but i already tried it.i gets VERY complex,much dues to the fact that every number must be broken down into pairs of digits,and then acted on.i tried using arrays for it,but it gets too complex

Richard MacCutchan 22-May-12 8:16am

Sounds like you need to work on something simpler.

utkarshs 22-May-12 9:06am

any ideas?

utkarshs 22-May-12 9:20am

is there no way to use this method in c++,even with advanced functions or something?

Richard MacCutchan 22-May-12 9:51am

Like I said above, forget C++, until you have worked out what the algorithm should be. This is a question of mathematics rather than programming.

Richard MacCutchan 22-May-12 9:58am

There is a good description of the algorithm here in WikiPedia. Once you have studied that and understand it clearly, it should be a reasonably easy exercise to convert it into a program. You may also try further Google searches for existing samples.

utkarshs 22-May-12 16:18pm

hey! i found the solution! please see the ANSWER 3 AND 4!

utkarshs 22-May-12 14:23pm

the main problem is bringing the digits in pairs,rest of it is easy

Wendelius 22-May-12 15:15pm

OP's comment:
@Richard MacCutchan, thanks!!i think i have found the solution .i have to deal with set of numbers from 1 to 2.so,first i'll take an int named pair,and put the number equal to it.the pair would contain integral value to the number x(the number to be square rooted),and i will find the first digit of answer(a).then i will put x=(x-pair)*100,and pair=x,which would give me next pair.continuing the calculation,i would calculate the answer and put a=(10*a)+ans

utkarshs · Answer 3 · 2012-05-22T08:49:00

@Richard MacCutchan, thanks!!i think i have found the solution .i have to deal with set of numbers from 1 to 2.so,first i'll take an int named pair,and put the number equal to it.the pair would contain integral value to the number x(the number to be square rooted),and i will find the first digit of answer(a).then i will put x=(x-pair)*100,and pair=x,which would give me next pair.continuing the calculation,i would calculate the answer and put a=(10*a)+ans

utkarshs · Answer 4 · 2012-05-22T10:22:00

#include<iostream.h>
#include<iomanip.h>
#include<math.h>
#include<stdlib.h>
int trt;
	int pair(double y,int k){
	y=y*pow(10,(k-1)*2);
	int n=y;
	y=y-n;
	y=y*100;
	n=y;
	return n;
}
int scal2(int s,int f){
	f=f*20;
	for(int j=9;j>=0;j--)
	{
		if((j*(j+f))<s){>
		return(s-(j*(j+f)));
		break;
		}
	}
}
int sqcalc(int g,int h){
	h=h*20;
	for(int j=9;j>=0;j--)
	{
		if((j*(j+h))<g){>
		return j;
		break;
		}
	}
}
double sqroot(double x,double res){
double ans;
int r,a;
	r=sqrt(x);
	ans=r;
	r=x-ans;
	
		for(int i=1;i<=res;i++){
		r=(r*100)+pair(x,i);
		double d=scal2(r,ans);
		ans=(ans*10)+sqcalc(r,ans);
		r=d;
	}	
		
		ans=ans/(pow(10,res));
		return ans;
}	
	int main(){
	cout << setprecision(10)<< sqroot(2,5);
	return(0);
}</stdlib.h></math.h></iomanip.h></iostream.h>

here sqroot(a,b) returns value of square root of a upto b decimal places.there is an another problem.for root 2 it works upto 5 places,but after that it goes to 60!what do you think could be the cause?(please help me i am a novice programmer,maybe even worse!)

square root algorithm for c++?

4 solutions

Solution 2

Solution 1

Solution 3

Solution 4

Add your solution here

Preview 0