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Re^2: How to calculate the sum of columns to be equal to 100?by Laurent_R (Monsignor) 
on Aug 15, 2013 at 13:14 UTC ( #1049586=note: print w/ replies, xml )  Need Help?? 
One floatingpoint technique that is sometimes used is called banker’s rounding,” which rounds evenending numbers one way, oddending numbers the other. (I don’t rightly recall if Perl implements it.) Yes, Perl implements it, because it uses C libraries which implement the rounding recommended by IEEE. The idea is the following. Suppose, to take a simple case, that you want to round to the unit numbers which have only one decimal digit. Any number where the decimal digit is less than 5 will be rounded down and any number where the decimal digit is larger than 5 is rounded up. But what do you do if the decimal part is exactly 5? Say, for example, how do you round 3.5? The most usual method rounds such a number up. But bankers claim that this introduces a bias towards rounding up: out of ten possible decimal digits, one will not be rounded (0), 4 will be rounded down (1, 2, 3 and 4) and 5 will be rounded up (5 to 9). This can make a difference if you add a long series of numbers. So they decided that the rounding of the 5 decimal digit will be rounded up or down, depending on whether the previous digit is odd or even. This is what you can see in the somewhat strange output of a Perl oneliner below:
I actually once had to write a special rounding module just because my client considered the above to be simply wrong and wanted 2.5 to be rounded to 3.
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