Dealing with accuracy problems in floating-point numbers

Question

I was wondering if there is a way of overcoming an accuracy problem that seems to be the result of my machine's internal representation of floating-point numbers:

For the sake of clarity the problem is summarized as:

// str is "4.600";   atof( str ) is 4.5999999999999996  
double mw = atof( str )  

// The variables used in the columns calculation below are:   
//  
//                    mw = 4.5999999999999996  
//                    p = 0.2  
//                    g = 0.2  
//                    h = 1 (integer)  

int columns = (int) ( ( mw - ( h * 11 * p ) ) / ( ( h * 11 * p ) + g ) ) + 1;

Prior to casting to an integer type the result of the columns calculation is 1.9999999999999996; so near yet so far from the desired result of 2.0.

Any suggestions most welcome.

Answer 1

A very simple and effective way to round a floating point number to an integer:

int rounded = (int)(f + 0.5);

Note: this only works if f is always positive. (thanks j random hacker)

Answer 2

There's no accurracy problem.

The result you got (1.9999999999999996) differed from the mathematical result (2) by a margin of 1E-16. That's quite accurate, considering your input "4.600".

You do have a rounding problem, of course. The default rounding in C++ is truncation; you want something similar to Kip's solution. Details depend on your exact domain, do you expect round(-x)== - round(x) ?

Answer 3

Use decimals: decNumber++