ROUNDing

[jpg@allegheny.scrc.symbolics.com (Jeffrey P. Golden)]

    Date: Thu, 27 Jun 91 17:21 PDT
    From: rsl@MAX-FLEISCHER.SF.Dialnet.ILA.COM (Richard Lamson)

	Date: Thu, 27 Jun 1991 11:44-0400
	From: JGA@alderaan.scrc.symbolics.com (John G. Aspinall)

	    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?

	The behaviour of ROUND is determined by the IEEE standard on
	floating-point operations.  The rationale behind the standard is, in
	turn, that rounding should be unbiased in a statistical sense.

    Also, if you genuinely want to round down in all cases, you can always
    say
  
      (FLOOR (+ X 0.5))	; Or (+ x 0.5d0) or (+ X 1/2), as appropriate.

That's round up.  Round down is (CEILING (- X 0.5)) .
You may want to send a correction.

    or
      (TRUNCATE (+ X 0.5))

    as appropriate.