1 ;;; calc-frac.el --- fraction functions for Calc
3 ;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc.
5 ;; Author: David Gillespie <daveg@synaptics.com>
6 ;; Maintainer: Jay Belanger <belanger@truman.edu>
8 ;; This file is part of GNU Emacs.
10 ;; GNU Emacs is distributed in the hope that it will be useful,
11 ;; but WITHOUT ANY WARRANTY. No author or distributor
12 ;; accepts responsibility to anyone for the consequences of using it
13 ;; or for whether it serves any particular purpose or works at all,
14 ;; unless he says so in writing. Refer to the GNU Emacs General Public
15 ;; License for full details.
17 ;; Everyone is granted permission to copy, modify and redistribute
18 ;; GNU Emacs, but only under the conditions described in the
19 ;; GNU Emacs General Public License. A copy of this license is
20 ;; supposed to have been given to you along with GNU Emacs so you
21 ;; can know your rights and responsibilities. It should be in a
22 ;; file named COPYING. Among other things, the copyright notice
23 ;; and this notice must be preserved on all copies.
29 ;; This file is autoloaded from calc-ext.el.
34 (defun calc-fdiv (arg)
37 (calc-binary-op ":" 'calcFunc-fdiv arg 1)))
40 (defun calc-fraction (arg)
43 (let ((func (if (calc-is-hyperbolic) 'calcFunc-frac 'calcFunc-pfrac)))
45 (calc-enter-result 2 "frac" (list func
48 (calc-enter-result 1 "frac" (list func
50 (prefix-numeric-value (or arg 0))))))))
53 (defun calc-over-notation (fmt)
54 (interactive "sFraction separator: ")
56 (if (string-match "\\`\\([^ 0-9][^ 0-9]?\\)[0-9]*\\'" fmt)
58 (if (/= (match-end 0) (match-end 1))
59 (setq n (string-to-int (substring fmt (match-end 1)))
60 fmt (math-match-substring fmt 1)))
61 (if (eq n 0) (error "Bad denominator"))
62 (calc-change-mode 'calc-frac-format (list fmt n) t))
63 (error "Bad fraction separator format"))))
65 (defun calc-slash-notation (n)
68 (calc-change-mode 'calc-frac-format (if n '("//" nil) '("/" nil)) t)))
71 (defun calc-frac-mode (n)
74 (calc-change-mode 'calc-prefer-frac n nil t)
75 (message (if calc-prefer-frac
76 "Integer division will now generate fractions"
77 "Integer division will now generate floating-point results"))))
82 ;;; Build a normalized fraction. [R I I]
83 ;;; (This could probably be implemented more efficiently than using
84 ;;; the plain gcd algorithm.)
85 (defun math-make-frac (num den)
86 (if (Math-integer-negp den)
87 (setq num (math-neg num)
89 (let ((gcd (math-gcd num den)))
95 (math-quotient num gcd)
96 (list 'frac (math-quotient num gcd) (math-quotient den gcd))))))
98 (defun calc-add-fractions (a b)
99 (if (eq (car-safe a) 'frac)
100 (if (eq (car-safe b) 'frac)
101 (math-make-frac (math-add (math-mul (nth 1 a) (nth 2 b))
102 (math-mul (nth 2 a) (nth 1 b)))
103 (math-mul (nth 2 a) (nth 2 b)))
104 (math-make-frac (math-add (nth 1 a)
105 (math-mul (nth 2 a) b))
107 (math-make-frac (math-add (math-mul a (nth 2 b))
111 (defun calc-mul-fractions (a b)
112 (if (eq (car-safe a) 'frac)
113 (if (eq (car-safe b) 'frac)
114 (math-make-frac (math-mul (nth 1 a) (nth 1 b))
115 (math-mul (nth 2 a) (nth 2 b)))
116 (math-make-frac (math-mul (nth 1 a) b)
118 (math-make-frac (math-mul a (nth 1 b))
121 (defun calc-div-fractions (a b)
122 (if (eq (car-safe a) 'frac)
123 (if (eq (car-safe b) 'frac)
124 (math-make-frac (math-mul (nth 1 a) (nth 2 b))
125 (math-mul (nth 2 a) (nth 1 b)))
126 (math-make-frac (nth 1 a)
127 (math-mul (nth 2 a) b)))
128 (math-make-frac (math-mul a (nth 2 b))
132 ;;; Convert a real value to fractional form. [T R I; T R F] [Public]
133 (defun calcFunc-frac (a &optional tol)
134 (or tol (setq tol 0))
137 ((memq (car a) '(cplx polar vec hms date sdev intv mod))
138 (cons (car a) (mapcar (function
140 (calcFunc-frac x tol)))
142 ((Math-messy-integerp a)
145 (math-neg (calcFunc-frac (math-neg a) tol)))
146 ((not (eq (car a) 'float))
147 (if (math-infinitep a)
149 (if (math-provably-integerp a)
151 (math-reject-arg a 'numberp))))
154 (setq tol (+ tol calc-internal-prec)))
155 (calcFunc-frac a (list 'float 5
156 (- (+ (math-numdigs (nth 1 a))
159 ((not (eq (car tol) 'float))
161 (calcFunc-frac a (math-float tol))
162 (math-reject-arg tol 'realp)))
164 (calcFunc-frac a (math-neg tol)))
167 ((not (math-lessp-float tol '(float 1 0)))
172 (let ((cfrac (math-continued-fraction a tol))
173 (calc-prefer-frac t))
174 (math-eval-continued-fraction cfrac)))))
176 (defun math-continued-fraction (a tol)
177 (let ((calc-internal-prec (+ calc-internal-prec 2)))
180 (calc-prefer-frac nil)
182 (while (or (null cfrac)
183 (and (not (Math-zerop aa))
184 (not (math-lessp-float
187 (let ((f (math-eval-continued-fraction
189 (math-working "Fractionalize" f)
192 (setq int (math-trunc aa)
194 cfrac (cons int cfrac))
196 (setq aa (math-div 1 aa))))
199 (defun math-eval-continued-fraction (cf)
203 (while (setq cf (cdr cf))
204 (setq temp (math-add (math-mul (car cf) n) d)
211 (defun calcFunc-fdiv (a b) ; [R I I] [Public]
212 (if (Math-num-integerp a)
213 (if (Math-num-integerp b)
215 (math-reject-arg a "*Division by zero")
216 (math-make-frac (math-trunc a) (math-trunc b)))
217 (math-reject-arg b 'integerp))
218 (math-reject-arg a 'integerp)))
222 ;;; arch-tag: 89d65274-0b3b-42d8-aacd-eaf86da5b4ea
223 ;;; calc-frac.el ends here