;;;; Programmer: Kevin M. Rosenberg
;;;; Date Started: Nov 2002
;;;;
-;;;; $Id: math.lisp,v 1.4 2003/06/06 21:59:29 kevin Exp $
+;;;; $Id$
;;;;
;;;; This file, part of KMRCL, is Copyright (c) 2002 by Kevin M. Rosenberg
;;;;
`(if (stringp ,obj)
(parse-integer ,obj)
,obj))
+
+(defun histogram (v n-bins &key min max)
+ (declare (fixnum n-bins))
+ (when (listp v)
+ (setq v (coerce v 'vector)))
+ (when (zerop (length v))
+ (return-from histogram (values nil nil nil)) )
+ (let ((n (length v))
+ (bins (make-array n-bins :element-type 'integer :initial-element 0))
+ found-min found-max)
+ (declare (fixnum n))
+ (unless (and min max)
+ (setq found-min (aref v 0)
+ found-max (aref v 0))
+ (loop for i fixnum from 1 to (1- n)
+ do
+ (let ((x (aref v i)))
+ (cond
+ ((> x found-max)
+ (setq found-max x))
+ ((< x found-min)
+ (setq found-min x)))))
+ (unless min
+ (setq min found-min))
+ (unless max
+ (setq max found-max)))
+ (let ((width (/ (- max min) n-bins)))
+ (setq width (+ width (* double-float-epsilon width)))
+ (dotimes (i n)
+ (let ((bin (nth-value 0 (truncate (- (aref v i) min) width))))
+ (declare (fixnum bin))
+ (when (and (not (minusp bin))
+ (< bin n-bins))
+ (incf (aref bins bin))))))
+ (values bins min max)))
+
+
+(defun fixnum-width ()
+ (nth-value 0 (truncate (+ (/ (log (1+ most-positive-fixnum)) (log 2)) .5))))
+
+(defun scaled-epsilon (float &optional (operation '+))
+ "Return the smallest number that would return a value different from
+ FLOAT if OPERATION were applied to FLOAT and this number. OPERATION
+ should be either + or -, and defauls to +."
+ (multiple-value-bind (significand exponent)
+ (decode-float float)
+ (multiple-value-bind (1.0-significand 1.0-exponent)
+ (decode-float (float 1.0 float))
+ (if (and (eq operation '-)
+ (= significand 1.0-significand))
+ (scale-float (typecase float
+ (short-float short-float-negative-epsilon)
+ (single-float single-float-negative-epsilon)
+ (double-float double-float-negative-epsilon)
+ (long-float long-float-negative-epsilon))
+ (- exponent 1.0-exponent))
+ (scale-float (typecase float
+ (short-float short-float-epsilon)
+ (single-float single-float-epsilon)
+ (double-float double-float-epsilon)
+ (long-float long-float-epsilon))
+ (- exponent 1.0-exponent))))))
+
+(defun sinc (x)
+ (if (zerop x)
+ 1d0
+ (let ((x (coerce x 'double-float)))
+ (/ (sin x) x))))
+
+
+(defun numbers-within-percentage (a b percent)
+ "Determines if two numbers are equal within a percentage difference."
+ (let ((abs-diff (* 0.01 percent 0.5 (+ (abs a) (abs b)))))
+ (< (abs (- a b)) abs-diff)))