mirror of
https://git.savannah.gnu.org/git/emacs.git
synced 2024-11-27 07:37:33 +00:00
228 lines
6.3 KiB
EmacsLisp
228 lines
6.3 KiB
EmacsLisp
;;; calc-frac.el --- fraction functions for Calc
|
|
|
|
;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc.
|
|
|
|
;; Author: David Gillespie <daveg@synaptics.com>
|
|
;; Maintainer: Colin Walters <walters@debian.org>
|
|
|
|
;; This file is part of GNU Emacs.
|
|
|
|
;; GNU Emacs is distributed in the hope that it will be useful,
|
|
;; but WITHOUT ANY WARRANTY. No author or distributor
|
|
;; accepts responsibility to anyone for the consequences of using it
|
|
;; or for whether it serves any particular purpose or works at all,
|
|
;; unless he says so in writing. Refer to the GNU Emacs General Public
|
|
;; License for full details.
|
|
|
|
;; Everyone is granted permission to copy, modify and redistribute
|
|
;; GNU Emacs, but only under the conditions described in the
|
|
;; GNU Emacs General Public License. A copy of this license is
|
|
;; supposed to have been given to you along with GNU Emacs so you
|
|
;; can know your rights and responsibilities. It should be in a
|
|
;; file named COPYING. Among other things, the copyright notice
|
|
;; and this notice must be preserved on all copies.
|
|
|
|
;;; Commentary:
|
|
|
|
;;; Code:
|
|
|
|
;; This file is autoloaded from calc-ext.el.
|
|
(require 'calc-ext)
|
|
|
|
(require 'calc-macs)
|
|
|
|
(defun calc-Need-calc-frac () nil)
|
|
|
|
(defun calc-fdiv (arg)
|
|
(interactive "P")
|
|
(calc-slow-wrapper
|
|
(calc-binary-op ":" 'calcFunc-fdiv arg 1)))
|
|
|
|
|
|
(defun calc-fraction (arg)
|
|
(interactive "P")
|
|
(calc-slow-wrapper
|
|
(let ((func (if (calc-is-hyperbolic) 'calcFunc-frac 'calcFunc-pfrac)))
|
|
(if (eq arg 0)
|
|
(calc-enter-result 2 "frac" (list func
|
|
(calc-top-n 2)
|
|
(calc-top-n 1)))
|
|
(calc-enter-result 1 "frac" (list func
|
|
(calc-top-n 1)
|
|
(prefix-numeric-value (or arg 0))))))))
|
|
|
|
|
|
(defun calc-over-notation (fmt)
|
|
(interactive
|
|
(list
|
|
(completing-read "Fraction separator: " (mapcar (lambda (s)
|
|
(cons s 0))
|
|
'(":" "::" "/" "//" ":/"))
|
|
nil t)))
|
|
(calc-wrapper
|
|
(if (string-match "\\`\\([^ 0-9][^ 0-9]?\\)[0-9]*\\'" fmt)
|
|
(let ((n nil))
|
|
(if (/= (match-end 0) (match-end 1))
|
|
(setq n (string-to-int (substring fmt (match-end 1)))
|
|
fmt (math-match-substring fmt 1)))
|
|
(if (eq n 0) (error "Bad denominator"))
|
|
(calc-change-mode 'calc-frac-format (list fmt n) t))
|
|
(error "Bad fraction separator format"))))
|
|
|
|
(defun calc-slash-notation (n)
|
|
(interactive "P")
|
|
(calc-wrapper
|
|
(calc-change-mode 'calc-frac-format (if n '("//" nil) '("/" nil)) t)))
|
|
|
|
|
|
(defun calc-frac-mode (n)
|
|
(interactive "P")
|
|
(calc-wrapper
|
|
(calc-change-mode 'calc-prefer-frac n nil t)
|
|
(message (if calc-prefer-frac
|
|
"Integer division will now generate fractions"
|
|
"Integer division will now generate floating-point results"))))
|
|
|
|
|
|
;;;; Fractions.
|
|
|
|
;;; Build a normalized fraction. [R I I]
|
|
;;; (This could probably be implemented more efficiently than using
|
|
;;; the plain gcd algorithm.)
|
|
(defun math-make-frac (num den)
|
|
(if (Math-integer-negp den)
|
|
(setq num (math-neg num)
|
|
den (math-neg den)))
|
|
(let ((gcd (math-gcd num den)))
|
|
(if (eq gcd 1)
|
|
(if (eq den 1)
|
|
num
|
|
(list 'frac num den))
|
|
(if (equal gcd den)
|
|
(math-quotient num gcd)
|
|
(list 'frac (math-quotient num gcd) (math-quotient den gcd))))))
|
|
|
|
(defun calc-add-fractions (a b)
|
|
(if (eq (car-safe a) 'frac)
|
|
(if (eq (car-safe b) 'frac)
|
|
(math-make-frac (math-add (math-mul (nth 1 a) (nth 2 b))
|
|
(math-mul (nth 2 a) (nth 1 b)))
|
|
(math-mul (nth 2 a) (nth 2 b)))
|
|
(math-make-frac (math-add (nth 1 a)
|
|
(math-mul (nth 2 a) b))
|
|
(nth 2 a)))
|
|
(math-make-frac (math-add (math-mul a (nth 2 b))
|
|
(nth 1 b))
|
|
(nth 2 b))))
|
|
|
|
(defun calc-mul-fractions (a b)
|
|
(if (eq (car-safe a) 'frac)
|
|
(if (eq (car-safe b) 'frac)
|
|
(math-make-frac (math-mul (nth 1 a) (nth 1 b))
|
|
(math-mul (nth 2 a) (nth 2 b)))
|
|
(math-make-frac (math-mul (nth 1 a) b)
|
|
(nth 2 a)))
|
|
(math-make-frac (math-mul a (nth 1 b))
|
|
(nth 2 b))))
|
|
|
|
(defun calc-div-fractions (a b)
|
|
(if (eq (car-safe a) 'frac)
|
|
(if (eq (car-safe b) 'frac)
|
|
(math-make-frac (math-mul (nth 1 a) (nth 2 b))
|
|
(math-mul (nth 2 a) (nth 1 b)))
|
|
(math-make-frac (nth 1 a)
|
|
(math-mul (nth 2 a) b)))
|
|
(math-make-frac (math-mul a (nth 2 b))
|
|
(nth 1 b))))
|
|
|
|
|
|
;;; Convert a real value to fractional form. [T R I; T R F] [Public]
|
|
(defun calcFunc-frac (a &optional tol)
|
|
(or tol (setq tol 0))
|
|
(cond ((Math-ratp a)
|
|
a)
|
|
((memq (car a) '(cplx polar vec hms date sdev intv mod))
|
|
(cons (car a) (mapcar (function
|
|
(lambda (x)
|
|
(calcFunc-frac x tol)))
|
|
(cdr a))))
|
|
((Math-messy-integerp a)
|
|
(math-trunc a))
|
|
((Math-negp a)
|
|
(math-neg (calcFunc-frac (math-neg a) tol)))
|
|
((not (eq (car a) 'float))
|
|
(if (math-infinitep a)
|
|
a
|
|
(if (math-provably-integerp a)
|
|
a
|
|
(math-reject-arg a 'numberp))))
|
|
((integerp tol)
|
|
(if (<= tol 0)
|
|
(setq tol (+ tol calc-internal-prec)))
|
|
(calcFunc-frac a (list 'float 5
|
|
(- (+ (math-numdigs (nth 1 a))
|
|
(nth 2 a))
|
|
(1+ tol)))))
|
|
((not (eq (car tol) 'float))
|
|
(if (Math-realp tol)
|
|
(calcFunc-frac a (math-float tol))
|
|
(math-reject-arg tol 'realp)))
|
|
((Math-negp tol)
|
|
(calcFunc-frac a (math-neg tol)))
|
|
((Math-zerop tol)
|
|
(calcFunc-frac a 0))
|
|
((not (math-lessp-float tol '(float 1 0)))
|
|
(math-trunc a))
|
|
((Math-zerop a)
|
|
0)
|
|
(t
|
|
(let ((cfrac (math-continued-fraction a tol))
|
|
(calc-prefer-frac t))
|
|
(math-eval-continued-fraction cfrac)))))
|
|
|
|
(defun math-continued-fraction (a tol)
|
|
(let ((calc-internal-prec (+ calc-internal-prec 2)))
|
|
(let ((cfrac nil)
|
|
(aa a)
|
|
(calc-prefer-frac nil)
|
|
int)
|
|
(while (or (null cfrac)
|
|
(and (not (Math-zerop aa))
|
|
(not (math-lessp-float
|
|
(math-abs
|
|
(math-sub a
|
|
(let ((f (math-eval-continued-fraction
|
|
cfrac)))
|
|
(math-working "Fractionalize" f)
|
|
f)))
|
|
tol))))
|
|
(setq int (math-trunc aa)
|
|
aa (math-sub aa int)
|
|
cfrac (cons int cfrac))
|
|
(or (Math-zerop aa)
|
|
(setq aa (math-div 1 aa))))
|
|
cfrac)))
|
|
|
|
(defun math-eval-continued-fraction (cf)
|
|
(let ((n (car cf))
|
|
(d 1)
|
|
temp)
|
|
(while (setq cf (cdr cf))
|
|
(setq temp (math-add (math-mul (car cf) n) d)
|
|
d n
|
|
n temp))
|
|
(math-div n d)))
|
|
|
|
|
|
|
|
(defun calcFunc-fdiv (a b) ; [R I I] [Public]
|
|
(if (Math-num-integerp a)
|
|
(if (Math-num-integerp b)
|
|
(if (Math-zerop b)
|
|
(math-reject-arg a "*Division by zero")
|
|
(math-make-frac (math-trunc a) (math-trunc b)))
|
|
(math-reject-arg b 'integerp))
|
|
(math-reject-arg a 'integerp)))
|
|
|
|
;;; calc-frac.el ends here
|