How to achieve higher precision?

[PrydeRage]

Hello everyone.
I am writing a program to calculate the Speed of an object according to Einstein's Special Relativity.
The formula is really easy to implement into C++ and I'll share my approach here:

#include <math.h>
#include <iostream>
#include <cstdio>

using namespace std;
int main()
{
	int mySpeed = 10; //units in metres per second
	int speedOfLight = 299792458;
	double changeFactor = sqrt(1 - (pow(mySpeed,2) / pow(speedOfLight,2)));
	double newSpeed = mySpeed - changeFactor;
	cout << "I am traveling at " << newSpeed << " metres per second!" << endl;
	getchar();
}

The result should be smaller than 10, however, when I run the program in VS2012, the program says relativeSpeed = 9 which can't be correct. (I'm expecting a very long 9.99999999 somewhat sequence)

I am pretty sure that my formula is correct, but how do I get C++ to calculate the correct floating point number?

[TheIdeasMan]

cout defaults to 6 dp, so try using setprecsion - look it up in the reference section.

[MiiNiPaa]

Looks legit: http://gm4.in/i/dn9.png
It rounds to 9 because of precision issues.
I suggest to look into changeFactor calculation. You might made mistake there: result of division of two powers is very close to 0, 1-<result> close to one and sqrt(<>) is even closer.

[TheIdeasMan]

Yeah, now I think about it - you need to set a much higher MySpeed - relativity is only noticeably at very high speed.

Edit: It was MiiNiPaa's comment that made me think about it properly.

[MiiNiPaa]

Hmm. changeFactor always will be in [0;1]. And that Factor part of the name... I'm sure that you should multiply mySpeed with changeFactor, not substract.

Also include <iomanip> and add << std::setprecision(16) before outputting newSpeed.

I am traveling at 9.999999999999995 metres per second!

[UldisK]

Actualy, the problem here is that,

(pow(mySpeed,2) / pow(speedOfLight,2))

will always return 0 if mySpeed<speedOfLight.

[MiiNiPaa]

Nope, pow() always returns floating point values. No integer division here.

[UldisK]

Jeah ... my mistake. Just checked the reference and there isn't pow(int,int).

[PrydeRage]

Thanks for all your replies.

cout.precision(16);
has worked for me, but I've reopened VS to check my code again and now cout.precision doesnt work anymore (also setprecision in iomanip doesnt work)

[PrydeRage]

Nevermind, as TheIdeasMan said, 10 metres/second were too slow to make any difference.
Thanks everyone :)