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c++rounding-error
Freesnöw
Freesnöw

Reputation: 32133

Preventing Rounding Errors

I was just reading about rounding errors in C++. So, if I'm making a math intense program (or any important calculations) should I just drop floats all together and use only doubles or is there an easier way to prevent rounding errors?

Upvotes: 3

Views: 6741

Answers (3)

zawy
zawy

Reputation: 391

This might work if your highest number is less than 10 billion and you're using C++ double precision.

if ( ceil(10000*(x + 0.00001)) > ceil(100000*(x - 0.00001))) { 
    x = ceil(10000*(x + 0.00004)) / 10000; 
}

This should allow at least the last digit to be off +/- 9. I'm assuming dividing by 1000 will always just move a decimal place. If not, then maybe it could be done in binary.

You would have to apply it after every operation that is not +, -, *, or a comparison. For example, you can't do two divisions in the same formula because you'd have to apply it to each division.

If that doesn't work, you could work in integers by scaling the numbers up and always use integer division. If you need advanced functions maybe there is a package that does deterministic integer math. Integer division is required in a lot of financial settings because of round off error being subject to exploit like in the movie "The Office".

Upvotes: 0

Mihai Maruseac
Mihai Maruseac

Reputation: 21435

Obligatory lecture: What Every Programmer Should Know About Floating-Point Arithmetic.

Also, try reading IEEE Floating Point standard.

You'll always get rounding errors. Unless you use an infinite arbitrary precision library, like gmplib. You have to decide if your application really needs this kind of effort.

Or, you could use integer arithmetic, converting to floats only when needed. This is still hard to do, you have to decide if it's worth it.

Lastly, you can use float or double taking care not to make assumption about values at the limit of representation's precision. I'd wish this Valgrind plugin was implemented (grep for float)...

Upvotes: 8

Puppy
Puppy

Reputation: 146910

The rounding errors are normally very insignificant, even using floats. Mathematically-intense programs like games, which do very large numbers of floating-point computations, often still use single-precision.

Upvotes: 1

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