1 ;;; calc-frac.el --- fraction functions for Calc
3 ;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
4 ;; 2005, 2006, 2007, 2008, 2009, 2010, 2011 Free Software Foundation, Inc.
6 ;; Author: David Gillespie <daveg@synaptics.com>
7 ;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
9 ;; This file is part of GNU Emacs.
11 ;; GNU Emacs is free software: you can redistribute it and/or modify
12 ;; it under the terms of the GNU General Public License as published by
13 ;; the Free Software Foundation, either version 3 of the License, or
14 ;; (at your option) any later version.
16 ;; GNU Emacs is distributed in the hope that it will be useful,
17 ;; but WITHOUT ANY WARRANTY; without even the implied warranty of
18 ;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
19 ;; GNU General Public License for more details.
21 ;; You should have received a copy of the GNU General Public License
22 ;; along with GNU Emacs. If not, see <http://www.gnu.org/licenses/>.
28 ;; This file is autoloaded from calc-ext.el.
33 (defun calc-fdiv (arg)
36 (calc-binary-op ":" 'calcFunc-fdiv arg 1)))
39 (defun calc-fraction (arg)
42 (let ((func (if (calc-is-hyperbolic) 'calcFunc-frac 'calcFunc-pfrac)))
44 (calc-enter-result 2 "frac" (list func
47 (calc-enter-result 1 "frac" (list func
49 (prefix-numeric-value (or arg 0))))))))
52 (defun calc-over-notation (fmt)
53 (interactive "sFraction separator: ")
55 (if (string-match "\\`\\([^ 0-9][^ 0-9]?\\)[0-9]*\\'" fmt)
57 (if (/= (match-end 0) (match-end 1))
58 (setq n (string-to-number (substring fmt (match-end 1)))
59 fmt (math-match-substring fmt 1)))
60 (if (eq n 0) (error "Bad denominator"))
61 (calc-change-mode 'calc-frac-format (list fmt n) t))
62 (error "Bad fraction separator format"))))
64 (defun calc-slash-notation (n)
67 (calc-change-mode 'calc-frac-format (if n '("//" nil) '("/" nil)) t)))
70 (defun calc-frac-mode (n)
73 (calc-change-mode 'calc-prefer-frac n nil t)
74 (message (if calc-prefer-frac
75 "Integer division will now generate fractions"
76 "Integer division will now generate floating-point results"))))
81 ;;; Build a normalized fraction. [R I I]
82 ;;; (This could probably be implemented more efficiently than using
83 ;;; the plain gcd algorithm.)
84 (defun math-make-frac (num den)
85 (if (Math-integer-negp den)
86 (setq num (math-neg num)
88 (let ((gcd (math-gcd num den)))
94 (math-quotient num gcd)
95 (list 'frac (math-quotient num gcd) (math-quotient den gcd))))))
97 (defun calc-add-fractions (a b)
98 (if (eq (car-safe a) 'frac)
99 (if (eq (car-safe b) 'frac)
100 (math-make-frac (math-add (math-mul (nth 1 a) (nth 2 b))
101 (math-mul (nth 2 a) (nth 1 b)))
102 (math-mul (nth 2 a) (nth 2 b)))
103 (math-make-frac (math-add (nth 1 a)
104 (math-mul (nth 2 a) b))
106 (math-make-frac (math-add (math-mul a (nth 2 b))
110 (defun calc-mul-fractions (a b)
111 (if (eq (car-safe a) 'frac)
112 (if (eq (car-safe b) 'frac)
113 (math-make-frac (math-mul (nth 1 a) (nth 1 b))
114 (math-mul (nth 2 a) (nth 2 b)))
115 (math-make-frac (math-mul (nth 1 a) b)
117 (math-make-frac (math-mul a (nth 1 b))
120 (defun calc-div-fractions (a b)
121 (if (eq (car-safe a) 'frac)
122 (if (eq (car-safe b) 'frac)
123 (math-make-frac (math-mul (nth 1 a) (nth 2 b))
124 (math-mul (nth 2 a) (nth 1 b)))
125 (math-make-frac (nth 1 a)
126 (math-mul (nth 2 a) b)))
127 (math-make-frac (math-mul a (nth 2 b))
131 ;;; Convert a real value to fractional form. [T R I; T R F] [Public]
132 (defun calcFunc-frac (a &optional tol)
133 (or tol (setq tol 0))
136 ((memq (car a) '(cplx polar vec hms date sdev intv mod))
137 (cons (car a) (mapcar (function
139 (calcFunc-frac x tol)))
141 ((Math-messy-integerp a)
144 (math-neg (calcFunc-frac (math-neg a) tol)))
145 ((not (eq (car a) 'float))
146 (if (math-infinitep a)
148 (if (math-provably-integerp a)
150 (math-reject-arg a 'numberp))))
153 (setq tol (+ tol calc-internal-prec)))
154 (calcFunc-frac a (list 'float 5
155 (- (+ (math-numdigs (nth 1 a))
158 ((not (eq (car tol) 'float))
160 (calcFunc-frac a (math-float tol))
161 (math-reject-arg tol 'realp)))
163 (calcFunc-frac a (math-neg tol)))
166 ((not (math-lessp-float tol '(float 1 0)))
171 (let ((cfrac (math-continued-fraction a tol))
172 (calc-prefer-frac t))
173 (math-eval-continued-fraction cfrac)))))
175 (defun math-continued-fraction (a tol)
176 (let ((calc-internal-prec (+ calc-internal-prec 2)))
179 (calc-prefer-frac nil)
181 (while (or (null cfrac)
182 (and (not (Math-zerop aa))
183 (not (math-lessp-float
186 (let ((f (math-eval-continued-fraction
188 (math-working "Fractionalize" f)
191 (setq int (math-trunc aa)
193 cfrac (cons int cfrac))
195 (setq aa (math-div 1 aa))))
198 (defun math-eval-continued-fraction (cf)
202 (while (setq cf (cdr cf))
203 (setq temp (math-add (math-mul (car cf) n) d)
208 (defun calcFunc-fdiv (a b) ; [R I I] [Public]
210 ((Math-num-integerp a)
212 ((Math-num-integerp b)
214 (math-reject-arg a "*Division by zero")
215 (math-make-frac (math-trunc a) (math-trunc b))))
216 ((eq (car-safe b) 'frac)
217 (if (Math-zerop (nth 1 b))
218 (math-reject-arg a "*Division by zero")
219 (math-make-frac (math-mul (math-trunc a) (nth 2 b)) (nth 1 b))))
220 (t (math-reject-arg b 'integerp))))
221 ((eq (car-safe a) 'frac)
223 ((Math-num-integerp b)
225 (math-reject-arg a "*Division by zero")
226 (math-make-frac (cadr a) (math-mul (nth 2 a) (math-trunc b)))))
227 ((eq (car-safe b) 'frac)
228 (if (Math-zerop (nth 1 b))
229 (math-reject-arg a "*Division by zero")
230 (math-make-frac (math-mul (nth 1 a) (nth 2 b)) (math-mul (nth 2 a) (nth 1 b)))))
231 (t (math-reject-arg b 'integerp))))
233 (math-reject-arg a 'integerp))))
237 ;; arch-tag: 89d65274-0b3b-42d8-aacd-eaf86da5b4ea
238 ;;; calc-frac.el ends here