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In K&B book, page 371 following definition is given for Math.round():

The round() method returns the integer closest to the argument. The algorithm is to add 0.5 to the argument and truncate to the nearest integer equivalent.

Going by the above definition: round(8.2) = Nearest integer to (8.2 + 0.5 = 8.7) = 8 round(8.7) = Nearest integer to (8.7 + 0.5 = 9.2) = 9 round(-8.2) = Nearest integer to (-8.2 + 0.5 = -7.7) = -7 //?? (Ans: -8) round(-8.7) = Nearest integer to (-8.7 + 0.5 = -8.2) = -8 //?? (Ans: -9)

But, for negative numbers, if I subtract 0.5 instead of adding, we get the right answers. So, I think it should be add 0.5 to +ve numbers and subtract 0.5 from negative numbers. Also, I don't think 'nearest integer' are the right words to use. I think it should be add 0.5 to +ve numbers or subtract 0.5 from negative numbers and 'discard decimal portion'. Does anyone have a different opinion on this?

I think that we have to add 0.5 to the given number and take its floor value, regardless of whether the number is positive or negative. e.g. Math.round(-8.2) = Math.floor(-8.2+0.5)=Math.floor(-7.7)=-8

I don't know about what the book says, but the correct method is to add 0.5, then take the floor - i.e. find the first integer smaller than whatever value you have.

so:

round(8.2) = floor of (8.2 + 0.5) = floor of (8.7) = 8 round(8.7) = floor of (8.7 + 0.5) = floor of (9.2) = 9 round(-8.2) = floor of (-8.2 + 0.5) = floor of (-7.7) = -8 (-7 is bigger) round(-8.7) = floor of (-8.7 + 0.5) = floor of (-8.2) = -9 (-8 is bigger)

[corrected cut'n'paste goof] [ July 01, 2005: Message edited by: fred rosenberger ]

There are only two hard things in computer science: cache invalidation, naming things, and off-by-one errors

The K&B book also says that when if a number's fraction is less than 0.5 then round will work like Math.floot(); When the number's fraction is equal to or greater than 0.5 then round will work like Math.ceil().

When dealing with negative numbers think of them like this: