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;;; numbers.lisp
;;;
;;; Copyright (C) 2003-2006 Peter Graves
;;; $Id$
;;;
;;; This program is free software; you can redistribute it and/or
;;; modify it under the terms of the GNU General Public License
;;; as published by the Free Software Foundation; either version 2
;;; of the License, or (at your option) any later version.
;;;
;;; This program is distributed in the hope that it will be useful,
;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
;;; GNU General Public License for more details.
;;;
;;; You should have received a copy of the GNU General Public License
;;; along with this program; if not, write to the Free Software
;;; Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
;;;
;;; As a special exception, the copyright holders of this library give you
;;; permission to link this library with independent modules to produce an
;;; executable, regardless of the license terms of these independent
;;; modules, and to copy and distribute the resulting executable under
;;; terms of your choice, provided that you also meet, for each linked
;;; independent module, the terms and conditions of the license of that
;;; module. An independent module is a module which is not derived from
;;; or based on this library. If you modify this library, you may extend
;;; this exception to your version of the library, but you are not
;;; obligated to do so. If you do not wish to do so, delete this
;;; exception statement from your version.
;;; Adapted from CMUCL/SBCL.
(in-package "SYSTEM")
(defun signum (number)
"If NUMBER is zero, return NUMBER, else return (/ NUMBER (ABS NUMBER))."
(if (zerop number)
number
(if (rationalp number)
(if (plusp number) 1 -1)
(/ number (abs number)))))
(defun round (number &optional (divisor 1))
"Rounds number (or number/divisor) to nearest integer.
The second returned value is the remainder."
(multiple-value-bind (tru rem) (truncate number divisor)
(if (zerop rem)
(values tru rem)
(let ((thresh (/ (abs divisor) 2)))
(cond ((or (> rem thresh)
(and (= rem thresh) (oddp tru)))
(if (minusp divisor)
(values (- tru 1) (+ rem divisor))
(values (+ tru 1) (- rem divisor))))
((let ((-thresh (- thresh)))
(or (< rem -thresh)
(and (= rem -thresh) (oddp tru))))
(if (minusp divisor)
(values (+ tru 1) (- rem divisor))
(values (- tru 1) (+ rem divisor))))
(t (values tru rem)))))))
(defun ffloor (number &optional (divisor 1))
"Same as FLOOR, but returns first value as a float."
(multiple-value-bind (tru rem) (ftruncate number divisor)
(if (and (not (zerop rem))
(if (minusp divisor)
(plusp number)
(minusp number)))
(values (1- tru) (+ rem divisor))
(values tru rem))))
(defun fceiling (number &optional (divisor 1))
"Same as CEILING, but returns first value as a float."
(multiple-value-bind (tru rem) (ftruncate number divisor)
(if (and (not (zerop rem))
(if (minusp divisor)
(minusp number)
(plusp number)))
(values (+ tru 1) (- rem divisor))
(values tru rem))))
(defun fround (number &optional (divisor 1))
"Same as ROUND, but returns first value as a float."
(multiple-value-bind (res rem)
(round number divisor)
(values (float res (if (floatp rem) rem 1.0)) rem)))
;;; FIXME
(defun rationalize (number)
(rational number))
(defun gcd (&rest integers)
(cond ((null integers)
0)
((null (cdr integers))
(let ((n (car integers)))
(if (integerp n)
(abs n)
(error 'type-error :datum n :expected-type 'integer))))
(t
(do ((gcd (car integers) (gcd-2 gcd (car rest)))
(rest (cdr integers) (cdr rest)))
((null rest) gcd)))))
;;; From discussion on comp.lang.lisp and Akira Kurihara.
(defun isqrt (natural)
"Returns the root of the nearest integer less than natural which is a perfect
square."
(unless (and (integerp natural) (not (minusp natural)))
(error 'simple-type-error
:format-control "The value ~A is not a non-negative real number."
:format-arguments (list natural)))
(if (and (fixnump natural) (<= natural 24))
(cond ((> natural 15) 4)
((> natural 8) 3)
((> natural 3) 2)
((> natural 0) 1)
(t 0))
(let* ((n-len-quarter (ash (integer-length natural) -2))
(n-half (ash natural (- (ash n-len-quarter 1))))
(n-half-isqrt (isqrt n-half))
(init-value (ash (1+ n-half-isqrt) n-len-quarter)))
(loop
(let ((iterated-value
(ash (+ init-value (truncate natural init-value)) -1)))
(unless (< iterated-value init-value)
(return init-value))
(setq init-value iterated-value))))))
;; FIXME Need to add support for denormalized floats!
;; "FLOAT-PRECISION returns the number of significant radix b digits present in
;; FLOAT; if FLOAT is a float zero, then the result is an integer zero."
;; "For normalized floats, the results of FLOAT-DIGITS and FLOAT-PRECISION are
;; the same, but the precision is less than the number of representation digits
;; for a denormalized or zero number.
(defun float-precision (float)
(if (floatp float)
(cond ((zerop float)
0)
((typep float 'single-float)
24)
((typep float 'double-float)
53)
(t
;; Shouldn't get here!
(aver nil)))
(error 'simple-type-error
:format-control "~S is not of type FLOAT."
:format-arguments (list float))))
(defun decode-float (float)
(cond
((typep float 'single-float)
(decode-float-single float))
((typep float 'double-float)
(decode-float-double float))
(t
(error 'simple-type-error
:format-control "~S is neither SINGLE-FLOAT nor DOUBLE-FLOAT."
:format-arguments (list float)))))
(defun decode-float-single (float)
;; TODO memoize
(let ((float-precision-single (float-precision 1f0)))
(multiple-value-bind (significand exponent sign)
(integer-decode-float float)
(values (coerce (/ significand (expt 2 float-precision-single)) 'single-float)
(+ exponent float-precision-single)
(if (minusp sign) -1f0 1f0)))))
(defun decode-float-double (float)
;; TODO memoize
(let ((float-precision-double (float-precision 1d0)))
(multiple-value-bind (significand exponent sign)
(integer-decode-float float)
(values (coerce (/ significand (expt 2 float-precision-double)) 'double-float)
(+ exponent float-precision-double)
(if (minusp sign) -1d0 1d0)))))
(defun conjugate (number)
(etypecase number
(complex
(complex (realpart number) (- (imagpart number))))
(number
number)))
(defun phase (number)
"Returns the angle part of the polar representation of a complex number.
For complex numbers, this is (atan (imagpart number) (realpart number)).
For non-complex positive numbers, this is 0. For non-complex negative
numbers this is PI."
(etypecase number
(rational
(if (minusp number)
(coerce pi 'single-float)
0.0f0))
(single-float
(if (minusp (float-sign number))
(coerce pi 'single-float)
0.0f0))
(double-float
(if (minusp (float-sign number))
(coerce pi 'double-float)
0.0d0))
(complex
(if (zerop (realpart number))
(coerce (* (/ pi 2) (signum (imagpart number)))
(if (typep (imagpart number) 'double-float)
'double-float 'single-float))
(atan (imagpart number) (realpart number))))))
