# ROUNDing

```    Date: Thu, 27 Jun 1991 05:29 EDT
From: kddlab!atr-la.atr.co.jp!myers@uunet.UU.NET (John K. Myers)

What is the rationale for having ROUND round to the nearest
even integer on a .5 boundary, instead of rounding down in every case?
Does it make it easier to implement?  Not rounding down
creates beat frequencies in my numeric representations.
I'd vote for having the standard changed next time.
Unless, is there a graphics application or something that likes
having ROUND wobble?
--John Myers

Rounding to the nearest even number is standard for numeric analysis,
independent of computers.  I remember learning that rule in elementary
school.

I believe the justification is that rounding in the same direction all
the time would introduce a bias.  Consider the first 20 multiples of .1:

.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

If ROUND always went the same way, 12 of them would round down, while
only 8 of them would round up.  By rounding to even, 10 round up and 10
round down.

barmar

```

• References:
• ROUNDing
• From: kddlab!atr-la.atr.co.jp!myers@uunet.UU.NET (John K. Myers)