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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, |
09ea57ea | 4 | ;; 2005, 2006 Free Software Foundation, Inc. |
136211a9 | 5 | |
12f1951a | 6 | ;; Author: David Gillespie <daveg@synaptics.com> |
3ccef44f | 7 | ;; Maintainer: Jay Belanger <belanger@truman.edu> |
136211a9 | 8 | |
a2cdc7f9 PJ |
9 | ;; This file is part of GNU Emacs. |
10 | ||
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11 | ;; GNU Emacs is distributed in the hope that it will be useful, |
12 | ;; but WITHOUT ANY WARRANTY. No author or distributor | |
13 | ;; accepts responsibility to anyone for the consequences of using it | |
14 | ;; or for whether it serves any particular purpose or works at all, | |
15 | ;; unless he says so in writing. Refer to the GNU Emacs General Public | |
16 | ;; License for full details. | |
17 | ||
18 | ;; Everyone is granted permission to copy, modify and redistribute | |
19 | ;; GNU Emacs, but only under the conditions described in the | |
20 | ;; GNU Emacs General Public License. A copy of this license is | |
21 | ;; supposed to have been given to you along with GNU Emacs so you | |
22 | ;; can know your rights and responsibilities. It should be in a | |
23 | ;; file named COPYING. Among other things, the copyright notice | |
24 | ;; and this notice must be preserved on all copies. | |
25 | ||
12f1951a | 26 | ;;; Commentary: |
136211a9 | 27 | |
12f1951a | 28 | ;;; Code: |
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29 | |
30 | ;; This file is autoloaded from calc-ext.el. | |
136211a9 | 31 | |
3ccef44f | 32 | (require 'calc-ext) |
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33 | (require 'calc-macs) |
34 | ||
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35 | (defun calc-fdiv (arg) |
36 | (interactive "P") | |
37 | (calc-slow-wrapper | |
bf77c646 | 38 | (calc-binary-op ":" 'calcFunc-fdiv arg 1))) |
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39 | |
40 | ||
41 | (defun calc-fraction (arg) | |
42 | (interactive "P") | |
43 | (calc-slow-wrapper | |
44 | (let ((func (if (calc-is-hyperbolic) 'calcFunc-frac 'calcFunc-pfrac))) | |
45 | (if (eq arg 0) | |
46 | (calc-enter-result 2 "frac" (list func | |
47 | (calc-top-n 2) | |
48 | (calc-top-n 1))) | |
49 | (calc-enter-result 1 "frac" (list func | |
50 | (calc-top-n 1) | |
bf77c646 | 51 | (prefix-numeric-value (or arg 0)))))))) |
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52 | |
53 | ||
54 | (defun calc-over-notation (fmt) | |
97d83988 | 55 | (interactive "sFraction separator: ") |
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56 | (calc-wrapper |
57 | (if (string-match "\\`\\([^ 0-9][^ 0-9]?\\)[0-9]*\\'" fmt) | |
58 | (let ((n nil)) | |
59 | (if (/= (match-end 0) (match-end 1)) | |
d227f871 | 60 | (setq n (string-to-number (substring fmt (match-end 1))) |
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61 | fmt (math-match-substring fmt 1))) |
62 | (if (eq n 0) (error "Bad denominator")) | |
63 | (calc-change-mode 'calc-frac-format (list fmt n) t)) | |
12f1951a | 64 | (error "Bad fraction separator format")))) |
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65 | |
66 | (defun calc-slash-notation (n) | |
67 | (interactive "P") | |
68 | (calc-wrapper | |
bf77c646 | 69 | (calc-change-mode 'calc-frac-format (if n '("//" nil) '("/" nil)) t))) |
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70 | |
71 | ||
72 | (defun calc-frac-mode (n) | |
73 | (interactive "P") | |
74 | (calc-wrapper | |
75 | (calc-change-mode 'calc-prefer-frac n nil t) | |
76 | (message (if calc-prefer-frac | |
12f1951a CW |
77 | "Integer division will now generate fractions" |
78 | "Integer division will now generate floating-point results")))) | |
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79 | |
80 | ||
81 | ;;;; Fractions. | |
82 | ||
83 | ;;; Build a normalized fraction. [R I I] | |
84 | ;;; (This could probably be implemented more efficiently than using | |
85 | ;;; the plain gcd algorithm.) | |
86 | (defun math-make-frac (num den) | |
87 | (if (Math-integer-negp den) | |
88 | (setq num (math-neg num) | |
89 | den (math-neg den))) | |
90 | (let ((gcd (math-gcd num den))) | |
91 | (if (eq gcd 1) | |
92 | (if (eq den 1) | |
93 | num | |
94 | (list 'frac num den)) | |
95 | (if (equal gcd den) | |
96 | (math-quotient num gcd) | |
bf77c646 | 97 | (list 'frac (math-quotient num gcd) (math-quotient den gcd)))))) |
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98 | |
99 | (defun calc-add-fractions (a b) | |
100 | (if (eq (car-safe a) 'frac) | |
101 | (if (eq (car-safe b) 'frac) | |
102 | (math-make-frac (math-add (math-mul (nth 1 a) (nth 2 b)) | |
103 | (math-mul (nth 2 a) (nth 1 b))) | |
104 | (math-mul (nth 2 a) (nth 2 b))) | |
105 | (math-make-frac (math-add (nth 1 a) | |
106 | (math-mul (nth 2 a) b)) | |
107 | (nth 2 a))) | |
108 | (math-make-frac (math-add (math-mul a (nth 2 b)) | |
109 | (nth 1 b)) | |
bf77c646 | 110 | (nth 2 b)))) |
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111 | |
112 | (defun calc-mul-fractions (a b) | |
113 | (if (eq (car-safe a) 'frac) | |
114 | (if (eq (car-safe b) 'frac) | |
115 | (math-make-frac (math-mul (nth 1 a) (nth 1 b)) | |
116 | (math-mul (nth 2 a) (nth 2 b))) | |
117 | (math-make-frac (math-mul (nth 1 a) b) | |
118 | (nth 2 a))) | |
119 | (math-make-frac (math-mul a (nth 1 b)) | |
bf77c646 | 120 | (nth 2 b)))) |
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121 | |
122 | (defun calc-div-fractions (a b) | |
123 | (if (eq (car-safe a) 'frac) | |
124 | (if (eq (car-safe b) 'frac) | |
125 | (math-make-frac (math-mul (nth 1 a) (nth 2 b)) | |
126 | (math-mul (nth 2 a) (nth 1 b))) | |
127 | (math-make-frac (nth 1 a) | |
128 | (math-mul (nth 2 a) b))) | |
129 | (math-make-frac (math-mul a (nth 2 b)) | |
bf77c646 | 130 | (nth 1 b)))) |
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131 | |
132 | ||
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133 | ;;; Convert a real value to fractional form. [T R I; T R F] [Public] |
134 | (defun calcFunc-frac (a &optional tol) | |
135 | (or tol (setq tol 0)) | |
136 | (cond ((Math-ratp a) | |
137 | a) | |
138 | ((memq (car a) '(cplx polar vec hms date sdev intv mod)) | |
139 | (cons (car a) (mapcar (function | |
140 | (lambda (x) | |
141 | (calcFunc-frac x tol))) | |
142 | (cdr a)))) | |
143 | ((Math-messy-integerp a) | |
144 | (math-trunc a)) | |
145 | ((Math-negp a) | |
146 | (math-neg (calcFunc-frac (math-neg a) tol))) | |
147 | ((not (eq (car a) 'float)) | |
148 | (if (math-infinitep a) | |
149 | a | |
150 | (if (math-provably-integerp a) | |
151 | a | |
152 | (math-reject-arg a 'numberp)))) | |
153 | ((integerp tol) | |
154 | (if (<= tol 0) | |
155 | (setq tol (+ tol calc-internal-prec))) | |
156 | (calcFunc-frac a (list 'float 5 | |
157 | (- (+ (math-numdigs (nth 1 a)) | |
158 | (nth 2 a)) | |
159 | (1+ tol))))) | |
160 | ((not (eq (car tol) 'float)) | |
161 | (if (Math-realp tol) | |
162 | (calcFunc-frac a (math-float tol)) | |
163 | (math-reject-arg tol 'realp))) | |
164 | ((Math-negp tol) | |
165 | (calcFunc-frac a (math-neg tol))) | |
166 | ((Math-zerop tol) | |
167 | (calcFunc-frac a 0)) | |
168 | ((not (math-lessp-float tol '(float 1 0))) | |
169 | (math-trunc a)) | |
170 | ((Math-zerop a) | |
171 | 0) | |
172 | (t | |
173 | (let ((cfrac (math-continued-fraction a tol)) | |
174 | (calc-prefer-frac t)) | |
bf77c646 | 175 | (math-eval-continued-fraction cfrac))))) |
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176 | |
177 | (defun math-continued-fraction (a tol) | |
178 | (let ((calc-internal-prec (+ calc-internal-prec 2))) | |
179 | (let ((cfrac nil) | |
180 | (aa a) | |
181 | (calc-prefer-frac nil) | |
182 | int) | |
183 | (while (or (null cfrac) | |
184 | (and (not (Math-zerop aa)) | |
185 | (not (math-lessp-float | |
186 | (math-abs | |
187 | (math-sub a | |
188 | (let ((f (math-eval-continued-fraction | |
189 | cfrac))) | |
190 | (math-working "Fractionalize" f) | |
191 | f))) | |
192 | tol)))) | |
193 | (setq int (math-trunc aa) | |
194 | aa (math-sub aa int) | |
195 | cfrac (cons int cfrac)) | |
196 | (or (Math-zerop aa) | |
197 | (setq aa (math-div 1 aa)))) | |
bf77c646 | 198 | cfrac))) |
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199 | |
200 | (defun math-eval-continued-fraction (cf) | |
201 | (let ((n (car cf)) | |
202 | (d 1) | |
203 | temp) | |
204 | (while (setq cf (cdr cf)) | |
205 | (setq temp (math-add (math-mul (car cf) n) d) | |
206 | d n | |
207 | n temp)) | |
bf77c646 | 208 | (math-div n d))) |
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209 | |
210 | ||
211 | ||
212 | (defun calcFunc-fdiv (a b) ; [R I I] [Public] | |
213 | (if (Math-num-integerp a) | |
214 | (if (Math-num-integerp b) | |
215 | (if (Math-zerop b) | |
216 | (math-reject-arg a "*Division by zero") | |
217 | (math-make-frac (math-trunc a) (math-trunc b))) | |
218 | (math-reject-arg b 'integerp)) | |
bf77c646 | 219 | (math-reject-arg a 'integerp))) |
136211a9 | 220 | |
3ccef44f JB |
221 | (provide 'calc-frac) |
222 | ||
ab5796a9 | 223 | ;;; arch-tag: 89d65274-0b3b-42d8-aacd-eaf86da5b4ea |
bf77c646 | 224 | ;;; calc-frac.el ends here |