lisp/calc/calc-frac.el

   1 ;;; calc-frac.el --- fraction functions for Calc
   2
   3 ;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
   4 ;;   2005, 2006, 2007, 2008 Free Software Foundation, Inc.
   5
   6 ;; Author: David Gillespie <daveg@synaptics.com>
   7 ;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
   8
   9 ;; This file is part of GNU Emacs.
  10
  11 ;; GNU Emacs is free software; you can redistribute it and/or modify
  12 ;; it under the terms of the GNU General Public License as published by
  13 ;; the Free Software Foundation; either version 3, or (at your option)
  14 ;; any later version.
  15
  16 ;; GNU Emacs is distributed in the hope that it will be useful,
  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
  22 ;; along with GNU Emacs; see the file COPYING.  If not, write to the
  23 ;; Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
  24 ;; Boston, MA 02110-1301, USA.
  25
  26 ;;; Commentary:
  27
  28 ;;; Code:
  29
  30 ;; This file is autoloaded from calc-ext.el.
  31
  32 (require 'calc-ext)
  33 (require 'calc-macs)
  34
  35 (defun calc-fdiv (arg)
  36   (interactive "P")
  37   (calc-slow-wrapper
  38    (calc-binary-op ":" 'calcFunc-fdiv arg 1)))
  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)
  51                                          (prefix-numeric-value (or arg 0))))))))
  52
  53
  54 (defun calc-over-notation (fmt)
  55   (interactive "sFraction separator: ")
  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))
  60              (setq n (string-to-number (substring fmt (match-end 1)))
  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))
  64      (error "Bad fraction separator format"))))
  65
  66 (defun calc-slash-notation (n)
  67   (interactive "P")
  68   (calc-wrapper
  69    (calc-change-mode 'calc-frac-format (if n '("//" nil) '("/" nil)) t)))
  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
  77                 "Integer division will now generate fractions"
  78               "Integer division will now generate floating-point results"))))
  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)
  97         (list 'frac (math-quotient num gcd) (math-quotient den gcd))))))
  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))
 110                     (nth 2 b))))
 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))
 120                     (nth 2 b))))
 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))
 130                     (nth 1 b))))
 131
 132
 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))
 175            (math-eval-continued-fraction cfrac)))))
 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))))
 198       cfrac)))
 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))
 208     (math-div n d)))
 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))
 219     (math-reject-arg a 'integerp)))
 220
 221 (provide 'calc-frac)
 222
 223 ;;; arch-tag: 89d65274-0b3b-42d8-aacd-eaf86da5b4ea
 224 ;;; calc-frac.el ends here