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12f1951a CW |
1 | ;;; calc-frac.el --- fraction functions for Calc |
2 | ||
58ba2f8f | 3 | ;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004, |
8b72699e | 4 | ;; 2005, 2006, 2007, 2008 Free Software Foundation, Inc. |
136211a9 | 5 | |
12f1951a | 6 | ;; Author: David Gillespie <daveg@synaptics.com> |
e8fff8ed | 7 | ;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com> |
136211a9 | 8 | |
a2cdc7f9 PJ |
9 | ;; This file is part of GNU Emacs. |
10 | ||
662c9c64 | 11 | ;; GNU Emacs is free software: you can redistribute it and/or modify |
7c671b23 | 12 | ;; it under the terms of the GNU General Public License as published by |
662c9c64 GM |
13 | ;; the Free Software Foundation, either version 3 of the License, or |
14 | ;; (at your option) any later version. | |
7c671b23 | 15 | |
136211a9 | 16 | ;; GNU Emacs is distributed in the hope that it will be useful, |
7c671b23 GM |
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. | |
20 | ||
21 | ;; You should have received a copy of the GNU General Public License | |
662c9c64 | 22 | ;; along with GNU Emacs. If not, see <http://www.gnu.org/licenses/>. |
136211a9 | 23 | |
12f1951a | 24 | ;;; Commentary: |
136211a9 | 25 | |
12f1951a | 26 | ;;; Code: |
136211a9 EZ |
27 | |
28 | ;; This file is autoloaded from calc-ext.el. | |
136211a9 | 29 | |
3ccef44f | 30 | (require 'calc-ext) |
136211a9 EZ |
31 | (require 'calc-macs) |
32 | ||
136211a9 EZ |
33 | (defun calc-fdiv (arg) |
34 | (interactive "P") | |
35 | (calc-slow-wrapper | |
bf77c646 | 36 | (calc-binary-op ":" 'calcFunc-fdiv arg 1))) |
136211a9 EZ |
37 | |
38 | ||
39 | (defun calc-fraction (arg) | |
40 | (interactive "P") | |
41 | (calc-slow-wrapper | |
42 | (let ((func (if (calc-is-hyperbolic) 'calcFunc-frac 'calcFunc-pfrac))) | |
43 | (if (eq arg 0) | |
44 | (calc-enter-result 2 "frac" (list func | |
45 | (calc-top-n 2) | |
46 | (calc-top-n 1))) | |
47 | (calc-enter-result 1 "frac" (list func | |
48 | (calc-top-n 1) | |
bf77c646 | 49 | (prefix-numeric-value (or arg 0)))))))) |
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50 | |
51 | ||
52 | (defun calc-over-notation (fmt) | |
97d83988 | 53 | (interactive "sFraction separator: ") |
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54 | (calc-wrapper |
55 | (if (string-match "\\`\\([^ 0-9][^ 0-9]?\\)[0-9]*\\'" fmt) | |
56 | (let ((n nil)) | |
57 | (if (/= (match-end 0) (match-end 1)) | |
d227f871 | 58 | (setq n (string-to-number (substring fmt (match-end 1))) |
136211a9 EZ |
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)) | |
12f1951a | 62 | (error "Bad fraction separator format")))) |
136211a9 EZ |
63 | |
64 | (defun calc-slash-notation (n) | |
65 | (interactive "P") | |
66 | (calc-wrapper | |
bf77c646 | 67 | (calc-change-mode 'calc-frac-format (if n '("//" nil) '("/" nil)) t))) |
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68 | |
69 | ||
70 | (defun calc-frac-mode (n) | |
71 | (interactive "P") | |
72 | (calc-wrapper | |
73 | (calc-change-mode 'calc-prefer-frac n nil t) | |
74 | (message (if calc-prefer-frac | |
12f1951a CW |
75 | "Integer division will now generate fractions" |
76 | "Integer division will now generate floating-point results")))) | |
136211a9 EZ |
77 | |
78 | ||
79 | ;;;; Fractions. | |
80 | ||
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) | |
87 | den (math-neg den))) | |
88 | (let ((gcd (math-gcd num den))) | |
89 | (if (eq gcd 1) | |
90 | (if (eq den 1) | |
91 | num | |
92 | (list 'frac num den)) | |
93 | (if (equal gcd den) | |
94 | (math-quotient num gcd) | |
bf77c646 | 95 | (list 'frac (math-quotient num gcd) (math-quotient den gcd)))))) |
136211a9 EZ |
96 | |
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)) | |
105 | (nth 2 a))) | |
106 | (math-make-frac (math-add (math-mul a (nth 2 b)) | |
107 | (nth 1 b)) | |
bf77c646 | 108 | (nth 2 b)))) |
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109 | |
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) | |
116 | (nth 2 a))) | |
117 | (math-make-frac (math-mul a (nth 1 b)) | |
bf77c646 | 118 | (nth 2 b)))) |
136211a9 EZ |
119 | |
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)) | |
bf77c646 | 128 | (nth 1 b)))) |
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129 | |
130 | ||
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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)) | |
134 | (cond ((Math-ratp a) | |
135 | a) | |
136 | ((memq (car a) '(cplx polar vec hms date sdev intv mod)) | |
137 | (cons (car a) (mapcar (function | |
138 | (lambda (x) | |
139 | (calcFunc-frac x tol))) | |
140 | (cdr a)))) | |
141 | ((Math-messy-integerp a) | |
142 | (math-trunc a)) | |
143 | ((Math-negp a) | |
144 | (math-neg (calcFunc-frac (math-neg a) tol))) | |
145 | ((not (eq (car a) 'float)) | |
146 | (if (math-infinitep a) | |
147 | a | |
148 | (if (math-provably-integerp a) | |
149 | a | |
150 | (math-reject-arg a 'numberp)))) | |
151 | ((integerp tol) | |
152 | (if (<= tol 0) | |
153 | (setq tol (+ tol calc-internal-prec))) | |
154 | (calcFunc-frac a (list 'float 5 | |
155 | (- (+ (math-numdigs (nth 1 a)) | |
156 | (nth 2 a)) | |
157 | (1+ tol))))) | |
158 | ((not (eq (car tol) 'float)) | |
159 | (if (Math-realp tol) | |
160 | (calcFunc-frac a (math-float tol)) | |
161 | (math-reject-arg tol 'realp))) | |
162 | ((Math-negp tol) | |
163 | (calcFunc-frac a (math-neg tol))) | |
164 | ((Math-zerop tol) | |
165 | (calcFunc-frac a 0)) | |
166 | ((not (math-lessp-float tol '(float 1 0))) | |
167 | (math-trunc a)) | |
168 | ((Math-zerop a) | |
169 | 0) | |
170 | (t | |
171 | (let ((cfrac (math-continued-fraction a tol)) | |
172 | (calc-prefer-frac t)) | |
bf77c646 | 173 | (math-eval-continued-fraction cfrac))))) |
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174 | |
175 | (defun math-continued-fraction (a tol) | |
176 | (let ((calc-internal-prec (+ calc-internal-prec 2))) | |
177 | (let ((cfrac nil) | |
178 | (aa a) | |
179 | (calc-prefer-frac nil) | |
180 | int) | |
181 | (while (or (null cfrac) | |
182 | (and (not (Math-zerop aa)) | |
183 | (not (math-lessp-float | |
184 | (math-abs | |
185 | (math-sub a | |
186 | (let ((f (math-eval-continued-fraction | |
187 | cfrac))) | |
188 | (math-working "Fractionalize" f) | |
189 | f))) | |
190 | tol)))) | |
191 | (setq int (math-trunc aa) | |
192 | aa (math-sub aa int) | |
193 | cfrac (cons int cfrac)) | |
194 | (or (Math-zerop aa) | |
195 | (setq aa (math-div 1 aa)))) | |
bf77c646 | 196 | cfrac))) |
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197 | |
198 | (defun math-eval-continued-fraction (cf) | |
199 | (let ((n (car cf)) | |
200 | (d 1) | |
201 | temp) | |
202 | (while (setq cf (cdr cf)) | |
203 | (setq temp (math-add (math-mul (car cf) n) d) | |
204 | d n | |
205 | n temp)) | |
bf77c646 | 206 | (math-div n d))) |
136211a9 EZ |
207 | |
208 | ||
209 | ||
210 | (defun calcFunc-fdiv (a b) ; [R I I] [Public] | |
211 | (if (Math-num-integerp a) | |
212 | (if (Math-num-integerp b) | |
213 | (if (Math-zerop b) | |
214 | (math-reject-arg a "*Division by zero") | |
215 | (math-make-frac (math-trunc a) (math-trunc b))) | |
216 | (math-reject-arg b 'integerp)) | |
bf77c646 | 217 | (math-reject-arg a 'integerp))) |
136211a9 | 218 | |
3ccef44f JB |
219 | (provide 'calc-frac) |
220 | ||
cbee283d | 221 | ;; arch-tag: 89d65274-0b3b-42d8-aacd-eaf86da5b4ea |
bf77c646 | 222 | ;;; calc-frac.el ends here |