Small numerical error when calculating Weight Average - c++

Question

Here is a part in a Physics engine.
The simplified function centerOfMass calculates 1D-center-of-mass of two rigid bodies (demo) :-
#include <iostream>
#include <iomanip>
float centerOfMass(float pos1,float m1, float pos2,float m2){
return (pos1*m1+pos2*m2)/(m1+m2);
}
int main(){
float a=5.55709743f;
float b= centerOfMass(a,50,0,0);
std::cout << std::setprecision(9) << a << '\n'; //5.55709743
std::cout << std::setprecision(9) << b << '\n'; //5.55709696
}
I need b to be precisely = 5.55709743.
The tiny difference can, sometimes (my real case = 5%), introduces a nasty Physics divergence.
There are some ways to solve it e.g. heavily do some conditional checking.
However, it is very error-prone for me.
Question: How to solve the calculation error while keep the code clean, fast, and still easily to be maintained?
By the way, if it can't be done elegantly, I would probably need to improve the caller to be more resistant against such numerical error.
Edit
(clarify duplicate question)
Yes, the cause is the precision error from the storage/computing format (mentioned in Is floating point math broken?).
However, this question asks about how to neutralize its symptom in a very specific case.

Answer 1

You are trying to get 9 decimal digits of precision , but the datatype float has a precision of about 7 decimal digits.
Use double instead. (demo)

Answer 2

Use double, not float. IEEE 754 double has about 16 decimal places of precision.
#include <iostream>
#include <iomanip>
double centerOfMass(double pos1, double m1, double pos2, double m2) {
return (pos1*m1 + pos2 * m2) / (m1 + m2);
}
int main() {
double a = 5.55709743;
double b = centerOfMass(a, 50, 0, 0);
std::cout << std::setprecision(16) << a << '\n'; //5.55709743
std::cout << std::setprecision(16) << b << '\n'; //5.55709743
std::cout << std::setprecision(16) << (b - a) << '\n'; // 0
}
For the example given, centerOfMass(a, 50, 0, 0), the following will give exact results for all values of a, but of course the example does not look realistic.
double centerOfMass(double pos1, double m1, double pos2, double m2) {
double divisor = m1 + m2;
return pos1*(m1/divisor) + pos2*(m2/ divisor);
}