math.lsp Version 1.021 11 June 2005, Minor documentation changes Version 1.02 02 June 2005, Commented out several never-used functions Version 1.01 21 May 2005, Minor bug fix, pick now handles empty list. Version 1.00 31 October 2004 Author Steven Jones Contact jones57@swbell.net include the word "nyquist" in subject line The contents of this file are released under the terms of the GNU General Public License. See the file LICENSE.txt Basic math functions, see also primes.lsp and nbase.lsp
function
(clamp v mn mx) Restrict value to given interval v - flonum. The value mn - flonum. The minimum result mx - flonum. The maximum result return - flonum. v | mn <= v <= mx
function
(range n [initial [increment [acc]]])
Generate arithmetic sequence
n - integer. Number of elements
initial - flonum. Initial value, default 0
increment - flonum. Common difference, default 1
acc - list. Used as part of recursive call but may be used by the
user to add static elements to the resulting list. Any elements
in acc will appear at the end of the resulting list.
return - list
function
(sqr x) Calculate square x - flonum. return - flonum. x^2
function
(log2 n) Determine the base 2 log of n n - flonum return - flonum
function
(log10 n) Determine the base 10 log of n n - flonum return - flonum
function
(rnd)
Generate random number
return - flonum. A random number to 5 decimal places in the
interval 0 <= (rnd) < 1
function
(rndr low high [fn])
Generate a random number in given interval
low - flonum. Minimum result
high - flonum. limit of maximum result
fn - closure. A random number function which returns a value in half-open
interval [0,1) Default #'rnd
return - flonum. A random number low <= (rndr low high) < high
function
(random-list n low high [fn])
Generate list of n random numbers.
n - integer. Number of elements.
low - flonum. Minimum result
high - flonum. Limit of maximum result
return - list. A list of n random values in half-open interval [low, high)
(defun random-list (n low high &optional (fn #'rnd))
(do ((index 0 (+ index 1))(acc '() (append acc (list (rndr low high fn)))))
((>= index n) acc)))
function
(pick lst) Pick an element of list at random lst - list return - any.
function
(permute lst) Create permutation of list lst - list return - list.
function
(mean [a [b [c ...]]]) Calculate mean of numeric values return - flonum
function
(fractional n) n - flonum. return - flonum. The fractional part of n (always positive)
function
(split-number n)
Split number into whole and fractional parts.
n - flonum.
return - cons. The result is a cons (w . f) where w is the whole number
part and f is the fractional part.
function
(polyn coeflst [x])
Evaluate polynomial.
coeflst - list. A list of coefficients (a0 a1 a2 ....an)
Where each ai is a real number.
x - flonum.
return - flonum. The result is the sum
a0*x^0 + a1*x^1 + a2*x^2 + ... + an*x^n
function
(about n [max])
Return a random number in the neighborhood of n
n - flonum. The center value
max - flonum. The maximum deviation from n as ratio of n.
Default 0.01 ~ 1%
return - flonum. The result is a random number in the interval
(n-n*max) <= result <= (n+n*max)
;; math.lsp
;; Version 1.021 11 June 2005, Minor documentation changes
;; Version 1.02 02 June 2005, Commented out several never-used functions
;; Version 1.01 21 May 2005, Minor bug fix, pick now handles empty list.
;; Version 1.00 31 October 2004
;;
;; Author Steven Jones
;;
;; Contact jones57@swbell.net include the word "nyquist" in subject line
;;
;; The contents of this file are released under the terms of the GNU General
;; Public License. See the file LICENSE.txt
;;
;; Basic math functions, see also primes.lsp and nbase.lsp
;;
(current-file "math")
(provide 'math)
;; @doc function clamp
;; (clamp v mn mx)
;; Restrict value to given interval
;;
;; v - flonum. The value
;; mn - flonum. The minimum result
;; mx - flonum. The maximum result
;; return - flonum. v | mn <= v <= mx
;;
(defun clamp (v mn mx)
(min (max v mn) mx))
;; --- Never used it ---
;; --- and not necessary ---
;;
;; -doc function mod
;; (mod a [b])
;; Calculate a modulo b
;; Unlike the standard XLISP rem function, mod only accepts two values either
;; of which may be flonum. In the case of a flonum argument the value is
;; "demoted" to an integer with the truncate function.
;;
;; a - flonum.
;; b - flonum. Default 1
;; return - integer
;;
;;(defun mod (a &optional (b 1))
;; (rem (truncate a) (truncate b)))
;; @doc function range
;; (range n [initial [increment [acc]]])
;; Generate arithmetic sequence
;;
;; n - integer. Number of elements
;; initial - flonum. Initial value, default 0
;; increment - flonum. Common difference, default 1
;; acc - list. Used as part of recursive call but may be used by the
;; user to add static elements to the resulting list. Any elements
;; in acc will appear at the end of the resulting list.
;; return - list
;;
(defun range (n &optional (initial 0)(increment 1.0)(acc ()))
(if (plusp n)
(cons initial (range (- n 1)(+ initial increment) increment acc))
acc))
;; --- Never used it ----
;; -doc function xrange
;; (xrange n [initial [ratio [acc]]])
;; Generate geometric sequence
;;
;; n - integer. Number of elements
;; initial - flonum. Initial value, default 1
;; ratio - flonum. Common ratio, default 2
;; acc - list. Used as part of recursive call but may be used by the
;; user to add static elements to the resulting list. Any elements
;; in acc will appear at the end of the resulting list.
;; return - list
;;
;;(defun xrange (n &optional (initial 1.0)(ratio 2)(acc ()))
;; (if (plusp n)
;; (cons initial (xrange (- n 1)(* initial ratio) ratio acc))
;; acc))
;; @doc function sqr
;; (sqr x)
;; Calculate square
;;
;; x - flonum.
;; return - flonum. x^2
;;
(defun sqr (x)
(* x x))
;; @doc function log2
;; (log2 n)
;; Determine the base 2 log of n
;; n - flonum
;; return - flonum
;;
(defun log2 (n)
(/ (log (float n)) +LOG2+))
;; @doc function log10
;; (log10 n)
;; Determine the base 10 log of n
;; n - flonum
;; return - flonum
;;
(defun log10 (n)
(/ (log (float n)) +LOG10+))
;; --- Never used it ---
;; -doc function logn
;; (logn n [b])
;; Determine the base b log of n
;; Note for bases 2 and 10 use log2 and log10 functions instead, they should
;; be a bit faster.
;;
;; n - flonum
;; b - flonum, default 10
;; return - flonum
;;
;;(defun logn (n &optional (base 10))
;; (/ (log (float n))(log (float base))))
;; @doc function rnd
;; (rnd)
;; Generate random number
;;
;; return - flonum. A random number to 5 decimal places in the
;; interval 0 <= (rnd) < 1
;;
(defun rnd ()
(/ (random 100000) 100000.0))
;; @doc function rndr
;; (rndr low high [fn])
;; Generate a random number in given interval
;;
;; low - flonum. Minimum result
;; high - flonum. limit of maximum result
;; fn - closure. A random number function which returns a value in half-open
;; interval [0,1) Default #'rnd
;; return - flonum. A random number low <= (rndr low high) < high
;;
(defun rndr (low high &optional (fn #'rnd))
(+ low (* (- high low) (funcall fn))))
;; --- Never used it ---
;; --- Code could be cleaner anyway ---
;; @doc function random-list
;; (random-list n low high [fn])
;; Generate list of n random numbers.
;;
;; n - integer. Number of elements.
;; low - flonum. Minimum result
;; high - flonum. Limit of maximum result
;; return - list. A list of n random values in half-open interval [low, high)
;;
;;(defun random-list (n low high &optional (fn #'rnd))
;; (do ((index 0 (+ index 1))(acc '() (append acc (list (rndr low high fn)))))
;; ((>= index n) acc)))
;; @doc function pick
;; (pick lst)
;; Pick an element of list at random
;;
;; lst - list
;; return - any.
;;
(defun pick (lst)
(if lst
(nth (random (length lst)) lst)
nil))
;; @doc function permute
;; (permute lst)
;; Create permutation of list
;;
;; lst - list
;; return - list.
;;
(defun permute (lst)
(if lst (let ((obj (pick lst)))
(cons obj (permute (remove obj lst))))
nil))
;; @doc function mean
;; (mean [a [b [c ...]]])
;; Calculate mean of numeric values
;; return - flonum
;;
(defun mean (&rest args)
(/ (apply #'+ args)(float (length args))))
;; --- Never used it ---
;; -doc function decimal->binary
;; Convert decimal value to binary. The binary value is represented as a
;; string. For negative values a '-' character is used as a prefix.
;; See also the file nbase.lsp
;;
;; n - integer
;; return - string.
;;
;;(defun decimal->binary (n)
;; (cond ((minusp n)
;; (strcat "-" (decimal->binary (d2b (abs n)))))
;; ((zerop n) "0")
;; (t (let ((acc ""))
;; (while (plusp n)
;; (setf acc (strcat (if (evenp n) "0" "1") acc))
;; (setf n (/ n 2)))
;; acc))))
;;
;; @doc function fractional
;; (fractional n)
;;
;; n - flonum.
;; return - flonum. The fractional part of n (always positive)
;;
(defun fractional (n)
(abs (- n (truncate n))))
;; @doc function split-number
;; (split-number n)
;; Split number into whole and fractional parts.
;;
;; n - flonum.
;; return - cons. The result is a cons (w . f) where w is the whole number
;; part and f is the fractional part.
;;
(defun split-number (n)
(cons (truncate n)(fractional n)))
;; @doc function polyn
;; (polyn coeflst [x])
;; Evaluate polynomial.
;;
;; coeflst - list. A list of coefficients (a0 a1 a2 ....an)
;; Where each ai is a real number.
;;
;; x - flonum.
;;
;; return - flonum. The result is the sum
;; a0*x^0 + a1*x^1 + a2*x^2 + ... + an*x^n
;;
(defun polyn (coeflst &optional (x 10))
(let (acc)
(setf acc 0)
(dotimes (i (length coeflst))
(setf acc (+ acc (* (nth i coeflst)(expt (float x) i)))))
acc))
;; @doc function about
;; (about n [max])
;; Return a random number in the neighborhood of n
;;
;; n - flonum. The center value
;; max - flonum. The maximum deviation from n as ratio of n.
;; Default 0.01 ~ 1%
;; return - flonum. The result is a random number in the interval
;; (n-n*max) <= result <= (n+n*max)
;;
(defun about (n &optional (maxratio 0.01))
(let ((range (* maxratio (float n))))
(+ n (- range (* range 2 (rnd))))))