code.delx.au - gnu-emacs/blob - 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 ;; Maintainer: Colin Walters <walters@debian.org>
   7
   8 ;; This file is part of GNU Emacs.
   9
  10 ;; GNU Emacs is distributed in the hope that it will be useful,
  11 ;; but WITHOUT ANY WARRANTY.  No author or distributor
  12 ;; accepts responsibility to anyone for the consequences of using it
  13 ;; or for whether it serves any particular purpose or works at all,
  14 ;; unless he says so in writing.  Refer to the GNU Emacs General Public
  15 ;; License for full details.
  16
  17 ;; Everyone is granted permission to copy, modify and redistribute
  18 ;; GNU Emacs, but only under the conditions described in the
  19 ;; GNU Emacs General Public License.   A copy of this license is
  20 ;; supposed to have been given to you along with GNU Emacs so you
  21 ;; can know your rights and responsibilities.  It should be in a
  22 ;; file named COPYING.  Among other things, the copyright notice
  23 ;; and this notice must be preserved on all copies.
  24
  25 ;;; Commentary:
  26
  27 ;;; Code:
  28
  29 ;; This file is autoloaded from calc-ext.el.
  30 (require 'calc-ext)
  31
  32 (require 'calc-macs)
  33
  34 (defun calc-Need-calc-frac () nil)
  35
  36 (defun calc-fdiv (arg)
  37   (interactive "P")
  38   (calc-slow-wrapper
  39    (calc-binary-op ":" 'calcFunc-fdiv arg 1)))
  40
  41
  42 (defun calc-fraction (arg)
  43   (interactive "P")
  44   (calc-slow-wrapper
  45    (let ((func (if (calc-is-hyperbolic) 'calcFunc-frac 'calcFunc-pfrac)))
  46      (if (eq arg 0)
  47          (calc-enter-result 2 "frac" (list func
  48                                            (calc-top-n 2)
  49                                            (calc-top-n 1)))
  50        (calc-enter-result 1 "frac" (list func
  51                                          (calc-top-n 1)
  52                                          (prefix-numeric-value (or arg 0))))))))
  53
  54
  55 (defun calc-over-notation (fmt)
  56   (interactive
  57    (list
  58     (completing-read "Fraction separator: " (mapcar (lambda (s)
  59                                                       (cons s 0))
  60                                                     '(":" "::" "/" "//" ":/"))
  61                      nil t)))
  62   (calc-wrapper
  63    (if (string-match "\\`\\([^ 0-9][^ 0-9]?\\)[0-9]*\\'" fmt)
  64        (let ((n nil))
  65          (if (/= (match-end 0) (match-end 1))
  66              (setq n (string-to-int (substring fmt (match-end 1)))
  67                    fmt (math-match-substring fmt 1)))
  68          (if (eq n 0) (error "Bad denominator"))
  69          (calc-change-mode 'calc-frac-format (list fmt n) t))
  70      (error "Bad fraction separator format"))))
  71
  72 (defun calc-slash-notation (n)
  73   (interactive "P")
  74   (calc-wrapper
  75    (calc-change-mode 'calc-frac-format (if n '("//" nil) '("/" nil)) t)))
  76
  77
  78 (defun calc-frac-mode (n)
  79   (interactive "P")
  80   (calc-wrapper
  81    (calc-change-mode 'calc-prefer-frac n nil t)
  82    (message (if calc-prefer-frac
  83                 "Integer division will now generate fractions"
  84               "Integer division will now generate floating-point results"))))
  85
  86
  87 ;;;; Fractions.
  88
  89 ;;; Build a normalized fraction.  [R I I]
  90 ;;; (This could probably be implemented more efficiently than using
  91 ;;;  the plain gcd algorithm.)
  92 (defun math-make-frac (num den)
  93   (if (Math-integer-negp den)
  94       (setq num (math-neg num)
  95             den (math-neg den)))
  96   (let ((gcd (math-gcd num den)))
  97     (if (eq gcd 1)
  98         (if (eq den 1)
  99             num
 100           (list 'frac num den))
 101       (if (equal gcd den)
 102           (math-quotient num gcd)
 103         (list 'frac (math-quotient num gcd) (math-quotient den gcd))))))
 104
 105 (defun calc-add-fractions (a b)
 106   (if (eq (car-safe a) 'frac)
 107       (if (eq (car-safe b) 'frac)
 108           (math-make-frac (math-add (math-mul (nth 1 a) (nth 2 b))
 109                                     (math-mul (nth 2 a) (nth 1 b)))
 110                           (math-mul (nth 2 a) (nth 2 b)))
 111         (math-make-frac (math-add (nth 1 a)
 112                                   (math-mul (nth 2 a) b))
 113                         (nth 2 a)))
 114     (math-make-frac (math-add (math-mul a (nth 2 b))
 115                               (nth 1 b))
 116                     (nth 2 b))))
 117
 118 (defun calc-mul-fractions (a b)
 119   (if (eq (car-safe a) 'frac)
 120       (if (eq (car-safe b) 'frac)
 121           (math-make-frac (math-mul (nth 1 a) (nth 1 b))
 122                           (math-mul (nth 2 a) (nth 2 b)))
 123         (math-make-frac (math-mul (nth 1 a) b)
 124                         (nth 2 a)))
 125     (math-make-frac (math-mul a (nth 1 b))
 126                     (nth 2 b))))
 127
 128 (defun calc-div-fractions (a b)
 129   (if (eq (car-safe a) 'frac)
 130       (if (eq (car-safe b) 'frac)
 131           (math-make-frac (math-mul (nth 1 a) (nth 2 b))
 132                           (math-mul (nth 2 a) (nth 1 b)))
 133         (math-make-frac (nth 1 a)
 134                         (math-mul (nth 2 a) b)))
 135     (math-make-frac (math-mul a (nth 2 b))
 136                     (nth 1 b))))
 137
 138
 139 ;;; Convert a real value to fractional form.  [T R I; T R F] [Public]
 140 (defun calcFunc-frac (a &optional tol)
 141   (or tol (setq tol 0))
 142   (cond ((Math-ratp a)
 143          a)
 144         ((memq (car a) '(cplx polar vec hms date sdev intv mod))
 145          (cons (car a) (mapcar (function
 146                                 (lambda (x)
 147                                   (calcFunc-frac x tol)))
 148                                (cdr a))))
 149         ((Math-messy-integerp a)
 150          (math-trunc a))
 151         ((Math-negp a)
 152          (math-neg (calcFunc-frac (math-neg a) tol)))
 153         ((not (eq (car a) 'float))
 154          (if (math-infinitep a)
 155              a
 156            (if (math-provably-integerp a)
 157                a
 158              (math-reject-arg a 'numberp))))
 159         ((integerp tol)
 160          (if (<= tol 0)
 161              (setq tol (+ tol calc-internal-prec)))
 162          (calcFunc-frac a (list 'float 5
 163                                 (- (+ (math-numdigs (nth 1 a))
 164                                       (nth 2 a))
 165                                    (1+ tol)))))
 166         ((not (eq (car tol) 'float))
 167          (if (Math-realp tol)
 168              (calcFunc-frac a (math-float tol))
 169            (math-reject-arg tol 'realp)))
 170         ((Math-negp tol)
 171          (calcFunc-frac a (math-neg tol)))
 172         ((Math-zerop tol)
 173          (calcFunc-frac a 0))
 174         ((not (math-lessp-float tol '(float 1 0)))
 175          (math-trunc a))
 176         ((Math-zerop a)
 177          0)
 178         (t
 179          (let ((cfrac (math-continued-fraction a tol))
 180                (calc-prefer-frac t))
 181            (math-eval-continued-fraction cfrac)))))
 182
 183 (defun math-continued-fraction (a tol)
 184   (let ((calc-internal-prec (+ calc-internal-prec 2)))
 185     (let ((cfrac nil)
 186           (aa a)
 187           (calc-prefer-frac nil)
 188           int)
 189       (while (or (null cfrac)
 190                  (and (not (Math-zerop aa))
 191                       (not (math-lessp-float
 192                             (math-abs
 193                              (math-sub a
 194                                        (let ((f (math-eval-continued-fraction
 195                                                  cfrac)))
 196                                          (math-working "Fractionalize" f)
 197                                          f)))
 198                             tol))))
 199         (setq int (math-trunc aa)
 200               aa (math-sub aa int)
 201               cfrac (cons int cfrac))
 202         (or (Math-zerop aa)
 203             (setq aa (math-div 1 aa))))
 204       cfrac)))
 205
 206 (defun math-eval-continued-fraction (cf)
 207   (let ((n (car cf))
 208         (d 1)
 209         temp)
 210     (while (setq cf (cdr cf))
 211       (setq temp (math-add (math-mul (car cf) n) d)
 212             d n
 213             n temp))
 214     (math-div n d)))
 215
 216
 217
 218 (defun calcFunc-fdiv (a b)   ; [R I I] [Public]
 219   (if (Math-num-integerp a)
 220       (if (Math-num-integerp b)
 221           (if (Math-zerop b)
 222               (math-reject-arg a "*Division by zero")
 223             (math-make-frac (math-trunc a) (math-trunc b)))
 224         (math-reject-arg b 'integerp))
 225     (math-reject-arg a 'integerp)))
 226
 227 ;;; calc-frac.el ends here