arnesi

Rounding functions 

(defun round-down (number &optional (precision *precision*))
  "Round towards 0."
  (if (minusp number)
      (round-ceiling number precision)
      (round-floor   number precision)))

(defun round-half-up (number &optional (precision *precision*))
  "Round towards the nearest value allowed with the current
precision. If the current value is exactly halfway between two logal[...]
values round away from 0."
  (multiple-value-bind (value discarded)
      (floor (* number precision))
    (if (<= 1/2 discarded)
	(/ (1+ value) precision)
        (/ value precision))))

(defun round-half-even (number &optional (precision *precision*))
  "Round towards the nearest value allowed with the current
precision. If the current value is exactly halfway between two legal[...]
values round towards the nearest even value."
  (multiple-value-bind (value discarded)
      (floor (* number precision))
    (cond
     ((< discarded 1/2) ;; down
      (/ value precision))
     ((= discarded 1/2) ;; goto even
      (if (evenp value)
	  (/ value precision)
	  (/ (1+ value) precision)))
     (t ;; (>= discarded 1/2)
      (/ (1+ value) precision)))))

(defun round-ceiling (number &optional (precision *precision*))
  "Round towards positive infintity"
  (/ (ceiling (* number precision)) precision))

(defun round-floor (number &optional (precision *precision*))
  "Round towards negative infinity."
  (/ (floor (* number precision)) precision))

(defun round-half-down (number &optional (precision *precision*))
  "Round towards the nearest legal value. If the current value is
exactly half way between two legal values round towards 0."[...]
  (multiple-value-bind (value discarded)
      (floor number)
    (if (< 1/2 discarded)
	(/ (1+ value) precision)
        (/ value precision))))

(defun round-up (number &optional (precision *precision*))
  "Round away from 0."
  (if (minusp number)
      (round-floor number precision)
      (round-ceiling number precision)))