lisp/calc/calc-frac.el

   1 ;;; calc-frac.el --- fraction functions for Calc
   2
   3 ;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc.
   4
   5 ;; Author: David Gillespie <daveg@synaptics.com>
   6 ;; Maintainers: D. Goel <deego@gnufans.org>
   7 ;;              Colin Walters <walters@debian.org>
   8
   9 ;; This file is part of GNU Emacs.
  10
  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
  26 ;;; Commentary:
  27
  28 ;;; Code:
  29
  30 ;; This file is autoloaded from calc-ext.el.
  31 (require 'calc-ext)
  32
  33 (require 'calc-macs)
  34
  35 (defun calc-Need-calc-frac () nil)
  36
  37 (defun calc-fdiv (arg)
  38   (interactive "P")
  39   (calc-slow-wrapper
  40    (calc-binary-op ":" 'calcFunc-fdiv arg 1)))
  41
  42
  43 (defun calc-fraction (arg)
  44   (interactive "P")
  45   (calc-slow-wrapper
  46    (let ((func (if (calc-is-hyperbolic) 'calcFunc-frac 'calcFunc-pfrac)))
  47      (if (eq arg 0)
  48          (calc-enter-result 2 "frac" (list func
  49                                            (calc-top-n 2)
  50                                            (calc-top-n 1)))
  51        (calc-enter-result 1 "frac" (list func
  52                                          (calc-top-n 1)
  53                                          (prefix-numeric-value (or arg 0))))))))
  54
  55
  56 (defun calc-over-notation (fmt)
  57   (interactive
  58    (list
  59     (completing-read "Fraction separator: " (mapcar (lambda (s)
  60                                                       (cons s 0))
  61                                                     '(":" "::" "/" "//" ":/"))
  62                      nil t)))
  63   (calc-wrapper
  64    (if (string-match "\\`\\([^ 0-9][^ 0-9]?\\)[0-9]*\\'" fmt)
  65        (let ((n nil))
  66          (if (/= (match-end 0) (match-end 1))
  67              (setq n (string-to-int (substring fmt (match-end 1)))
  68                    fmt (math-match-substring fmt 1)))
  69          (if (eq n 0) (error "Bad denominator"))
  70          (calc-change-mode 'calc-frac-format (list fmt n) t))
  71      (error "Bad fraction separator format"))))
  72
  73 (defun calc-slash-notation (n)
  74   (interactive "P")
  75   (calc-wrapper
  76    (calc-change-mode 'calc-frac-format (if n '("//" nil) '("/" nil)) t)))
  77
  78
  79 (defun calc-frac-mode (n)
  80   (interactive "P")
  81   (calc-wrapper
  82    (calc-change-mode 'calc-prefer-frac n nil t)
  83    (message (if calc-prefer-frac
  84                 "Integer division will now generate fractions"
  85               "Integer division will now generate floating-point results"))))
  86
  87
  88 ;;;; Fractions.
  89
  90 ;;; Build a normalized fraction.  [R I I]
  91 ;;; (This could probably be implemented more efficiently than using
  92 ;;;  the plain gcd algorithm.)
  93 (defun math-make-frac (num den)
  94   (if (Math-integer-negp den)
  95       (setq num (math-neg num)
  96             den (math-neg den)))
  97   (let ((gcd (math-gcd num den)))
  98     (if (eq gcd 1)
  99         (if (eq den 1)
 100             num
 101           (list 'frac num den))
 102       (if (equal gcd den)
 103           (math-quotient num gcd)
 104         (list 'frac (math-quotient num gcd) (math-quotient den gcd))))))
 105
 106 (defun calc-add-fractions (a b)
 107   (if (eq (car-safe a) 'frac)
 108       (if (eq (car-safe b) 'frac)
 109           (math-make-frac (math-add (math-mul (nth 1 a) (nth 2 b))
 110                                     (math-mul (nth 2 a) (nth 1 b)))
 111                           (math-mul (nth 2 a) (nth 2 b)))
 112         (math-make-frac (math-add (nth 1 a)
 113                                   (math-mul (nth 2 a) b))
 114                         (nth 2 a)))
 115     (math-make-frac (math-add (math-mul a (nth 2 b))
 116                               (nth 1 b))
 117                     (nth 2 b))))
 118
 119 (defun calc-mul-fractions (a b)
 120   (if (eq (car-safe a) 'frac)
 121       (if (eq (car-safe b) 'frac)
 122           (math-make-frac (math-mul (nth 1 a) (nth 1 b))
 123                           (math-mul (nth 2 a) (nth 2 b)))
 124         (math-make-frac (math-mul (nth 1 a) b)
 125                         (nth 2 a)))
 126     (math-make-frac (math-mul a (nth 1 b))
 127                     (nth 2 b))))
 128
 129 (defun calc-div-fractions (a b)
 130   (if (eq (car-safe a) 'frac)
 131       (if (eq (car-safe b) 'frac)
 132           (math-make-frac (math-mul (nth 1 a) (nth 2 b))
 133                           (math-mul (nth 2 a) (nth 1 b)))
 134         (math-make-frac (nth 1 a)
 135                         (math-mul (nth 2 a) b)))
 136     (math-make-frac (math-mul a (nth 2 b))
 137                     (nth 1 b))))
 138
 139
 140 ;;; Convert a real value to fractional form.  [T R I; T R F] [Public]
 141 (defun calcFunc-frac (a &optional tol)
 142   (or tol (setq tol 0))
 143   (cond ((Math-ratp a)
 144          a)
 145         ((memq (car a) '(cplx polar vec hms date sdev intv mod))
 146          (cons (car a) (mapcar (function
 147                                 (lambda (x)
 148                                   (calcFunc-frac x tol)))
 149                                (cdr a))))
 150         ((Math-messy-integerp a)
 151          (math-trunc a))
 152         ((Math-negp a)
 153          (math-neg (calcFunc-frac (math-neg a) tol)))
 154         ((not (eq (car a) 'float))
 155          (if (math-infinitep a)
 156              a
 157            (if (math-provably-integerp a)
 158                a
 159              (math-reject-arg a 'numberp))))
 160         ((integerp tol)
 161          (if (<= tol 0)
 162              (setq tol (+ tol calc-internal-prec)))
 163          (calcFunc-frac a (list 'float 5
 164                                 (- (+ (math-numdigs (nth 1 a))
 165                                       (nth 2 a))
 166                                    (1+ tol)))))
 167         ((not (eq (car tol) 'float))
 168          (if (Math-realp tol)
 169              (calcFunc-frac a (math-float tol))
 170            (math-reject-arg tol 'realp)))
 171         ((Math-negp tol)
 172          (calcFunc-frac a (math-neg tol)))
 173         ((Math-zerop tol)
 174          (calcFunc-frac a 0))
 175         ((not (math-lessp-float tol '(float 1 0)))
 176          (math-trunc a))
 177         ((Math-zerop a)
 178          0)
 179         (t
 180          (let ((cfrac (math-continued-fraction a tol))
 181                (calc-prefer-frac t))
 182            (math-eval-continued-fraction cfrac)))))
 183
 184 (defun math-continued-fraction (a tol)
 185   (let ((calc-internal-prec (+ calc-internal-prec 2)))
 186     (let ((cfrac nil)
 187           (aa a)
 188           (calc-prefer-frac nil)
 189           int)
 190       (while (or (null cfrac)
 191                  (and (not (Math-zerop aa))
 192                       (not (math-lessp-float
 193                             (math-abs
 194                              (math-sub a
 195                                        (let ((f (math-eval-continued-fraction
 196                                                  cfrac)))
 197                                          (math-working "Fractionalize" f)
 198                                          f)))
 199                             tol))))
 200         (setq int (math-trunc aa)
 201               aa (math-sub aa int)
 202               cfrac (cons int cfrac))
 203         (or (Math-zerop aa)
 204             (setq aa (math-div 1 aa))))
 205       cfrac)))
 206
 207 (defun math-eval-continued-fraction (cf)
 208   (let ((n (car cf))
 209         (d 1)
 210         temp)
 211     (while (setq cf (cdr cf))
 212       (setq temp (math-add (math-mul (car cf) n) d)
 213             d n
 214             n temp))
 215     (math-div n d)))
 216
 217
 218
 219 (defun calcFunc-fdiv (a b)   ; [R I I] [Public]
 220   (if (Math-num-integerp a)
 221       (if (Math-num-integerp b)
 222           (if (Math-zerop b)
 223               (math-reject-arg a "*Division by zero")
 224             (math-make-frac (math-trunc a) (math-trunc b)))
 225         (math-reject-arg b 'integerp))
 226     (math-reject-arg a 'integerp)))
 227
 228 ;;; arch-tag: 89d65274-0b3b-42d8-aacd-eaf86da5b4ea
 229 ;;; calc-frac.el ends here