Why does .NET use banker's rounding as default?

278
votes

According to the documentation, the decimal.Round method uses a round-to-even algorithm which is not common for most applications. So I always end up writing a custom function to do the more natural round-half-up algorithm:

public static decimal RoundHalfUp(this decimal d, int decimals)
{
    if (decimals < 0)
    {
        throw new ArgumentException("The decimals must be non-negative", 
            "decimals");
    }

    decimal multiplier = (decimal)Math.Pow(10, decimals);
    decimal number = d * multiplier;

    if (decimal.Truncate(number) < number)
    {
        number += 0.5m;
    }
    return decimal.Round(number) / multiplier;
}

Does anybody know the reason behind this framework design decision?

Is there any built-in implementation of the round-half-up algorithm into the framework? Or maybe some unmanaged Windows API?

It could be misleading for beginners that simply write decimal.Round(2.5m, 0) expecting 3 as a result but getting 2 instead.

5
.netrounding
Rounding up is not "more natural." Nature has nothing to do with it. It's simply what you learned in gradeschool when you learned the concept of "rounding." Gradeschool lessons don't always paint a full picture. – Rob Kennedy
@Rob And that's why it is more natural, even though it ain't correct – Pacerier
I don't understand, @Pacerier. I explained why it's not natural, and you say that's in fact why it is natural. How does my argument work against my conclusion, which is the opposite of yours? Things you've grown accustomed to might feel natural, and sometimes we figuratively say that something is "second nature," but that doesn't make them natural. – Rob Kennedy
@Rob I'm saying it is natural, because it feels natural. You do know that there are 36 different objects with the same variable name natural right? – Pacerier
nature's defintely analogue so it's the wrong word to use; but this is being pedantic. Maybe 'usual' would be a better word to use.."what is the usual rounding that people do" > 0.5 goes to 1.0 – whytheq

5 Answers

443
votes

The other answers with reasons why the Banker's algorithm (aka round half to even) is a good choice are quite correct. It does not suffer from negative or positive bias as much as the round half away from zero method over most reasonable distributions.

But the question was why .NET use Banker's actual rounding as default - and the answer is that Microsoft has followed the IEEE 754 standard. This is also mentioned in MSDN for Math.Round under Remarks.

Also note that .NET supports the alternative method specified by IEEE by providing the MidpointRounding enumeration. They could of course have provided more alternatives to solving ties, but they choose to just fulfill the IEEE standard.

203
votes

Probably because it's a better algorithm. Over the course of many roundings performed, you will average out that all .5's end up rounding equally up and down. This gives better estimations of actual results if you are for instance, adding a bunch of rounded numbers. I would say that even though it isn't what some may expect, it's probably the more correct thing to do.

88
votes

While I cannot answer the question of "Why did Microsoft's designers choose this as the default?", I just want to point out that an extra function is unnecessary.

Math.Round allows you to specify a MidpointRounding:

  • ToEven - When a number is halfway between two others, it is rounded toward the nearest even number.
  • AwayFromZero - When a number is halfway between two others, it is rounded toward the nearest number that is away from zero.
22
votes

Decimals are mostly used for money; banker’s rounding is common when working with money. Or you could say.

It is mostly bankers that need the decimal type; therefore it does “banker’s rounding”

Bankers rounding have the advantage that on average you will get the same result if you:

  • round a set of “invoice lines” before adding them up,
  • or add them up then round the total

Rounding before adding up saved a lot of work in the days before computers.

(In the UK when we went decimal banks would not deal with half pence, but for many years there was still a half pence coin and shop often had prices ending in half pence – so lots of rounding)

0
votes

Use another overload of Round function like this:

decimal.Round(2.5m, 0,MidpointRounding.AwayFromZero)

It will output 3. And if you use

decimal.Round(2.5m, 0,MidpointRounding.ToEven)

you will get banker's rounding.