;;;; Programmer: Kevin M. Rosenberg
;;;; Date Started: Nov 2002
;;;;
-;;;; $Id$
-;;;;
;;;; This file, part of KMRCL, is Copyright (c) 2002 by Kevin M. Rosenberg
;;;;
;;;; KMRCL users are granted the rights to distribute and use this software
(defun deriv (f dx)
#'(lambda (x)
(/ (- (funcall f (+ x dx)) (funcall f x))
- dx)))
+ dx)))
(defun sin^ (x)
(funcall (deriv #'sin 1d-8) x))
(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)
+ (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))
+ 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)))))
+ 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))
+ (setq min found-min))
(unless max
- (setq max found-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))))))
+ (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)))