blob: 0847f0756cb0b402f0c995c98ea0f470e9dfeac4 (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
|
;;; calc-frac.el --- fraction functions for Calc
;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc.
;; Author: David Gillespie <daveg@synaptics.com>
;; Maintainers: D. Goel <deego@gnufans.org>
;; 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
|
