lisp/calc/calc-frac.el

   1 ;;; calc-frac.el --- fraction functions for Calc
   2
   3 ;; Copyright (C) 1990-1993, 2001-2014 Free Software Foundation, Inc.
   4
   5 ;; Author: David Gillespie <daveg@synaptics.com>
   6 ;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
   7
   8 ;; This file is part of GNU Emacs.
   9
  10 ;; GNU Emacs is free software: you can redistribute it and/or modify
  11 ;; it under the terms of the GNU General Public License as published by
  12 ;; the Free Software Foundation, either version 3 of the License, or
  13 ;; (at your option) any later version.
  14
  15 ;; GNU Emacs is distributed in the hope that it will be useful,
  16 ;; but WITHOUT ANY WARRANTY; without even the implied warranty of
  17 ;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  18 ;; GNU General Public License for more details.
  19
  20 ;; You should have received a copy of the GNU General Public License
  21 ;; along with GNU Emacs.  If not, see <http://www.gnu.org/licenses/>.
  22
  23 ;;; Commentary:
  24
  25 ;;; Code:
  26
  27 ;; This file is autoloaded from calc-ext.el.
  28
  29 (require 'calc-ext)
  30 (require 'calc-macs)
  31
  32 (defun calc-fdiv (arg)
  33   (interactive "P")
  34   (calc-slow-wrapper
  35    (calc-binary-op ":" 'calcFunc-fdiv arg 1)))
  36
  37
  38 (defun calc-fraction (arg)
  39   (interactive "P")
  40   (calc-slow-wrapper
  41    (let ((func (if (calc-is-hyperbolic) 'calcFunc-frac 'calcFunc-pfrac)))
  42      (if (eq arg 0)
  43          (calc-enter-result 2 "frac" (list func
  44                                            (calc-top-n 2)
  45                                            (calc-top-n 1)))
  46        (calc-enter-result 1 "frac" (list func
  47                                          (calc-top-n 1)
  48                                          (prefix-numeric-value (or arg 0))))))))
  49
  50
  51 (defun calc-over-notation (fmt)
  52   (interactive "sFraction separator: ")
  53   (calc-wrapper
  54    (if (string-match "\\`\\([^ 0-9][^ 0-9]?\\)[0-9]*\\'" fmt)
  55        (let ((n nil))
  56          (if (/= (match-end 0) (match-end 1))
  57              (setq n (string-to-number (substring fmt (match-end 1)))
  58                    fmt (math-match-substring fmt 1)))
  59          (if (eq n 0) (error "Bad denominator"))
  60          (calc-change-mode 'calc-frac-format (list fmt n) t))
  61      (error "Bad fraction separator format"))))
  62
  63 (defun calc-slash-notation (n)
  64   (interactive "P")
  65   (calc-wrapper
  66    (calc-change-mode 'calc-frac-format (if n '("//" nil) '("/" nil)) t)))
  67
  68
  69 (defun calc-frac-mode (n)
  70   (interactive "P")
  71   (calc-wrapper
  72    (calc-change-mode 'calc-prefer-frac n nil t)
  73    (message (if calc-prefer-frac
  74                 "Integer division will now generate fractions"
  75               "Integer division will now generate floating-point results"))))
  76
  77
  78 ;;;; Fractions.
  79
  80 ;;; Build a normalized fraction.  [R I I]
  81 ;;; (This could probably be implemented more efficiently than using
  82 ;;;  the plain gcd algorithm.)
  83 (defun math-make-frac (num den)
  84   (if (Math-integer-negp den)
  85       (setq num (math-neg num)
  86             den (math-neg den)))
  87   (let ((gcd (math-gcd num den)))
  88     (if (eq gcd 1)
  89         (if (eq den 1)
  90             num
  91           (list 'frac num den))
  92       (if (equal gcd den)
  93           (math-quotient num gcd)
  94         (list 'frac (math-quotient num gcd) (math-quotient den gcd))))))
  95
  96 (defun calc-add-fractions (a b)
  97   (if (eq (car-safe a) 'frac)
  98       (if (eq (car-safe b) 'frac)
  99           (math-make-frac (math-add (math-mul (nth 1 a) (nth 2 b))
 100                                     (math-mul (nth 2 a) (nth 1 b)))
 101                           (math-mul (nth 2 a) (nth 2 b)))
 102         (math-make-frac (math-add (nth 1 a)
 103                                   (math-mul (nth 2 a) b))
 104                         (nth 2 a)))
 105     (math-make-frac (math-add (math-mul a (nth 2 b))
 106                               (nth 1 b))
 107                     (nth 2 b))))
 108
 109 (defun calc-mul-fractions (a b)
 110   (if (eq (car-safe a) 'frac)
 111       (if (eq (car-safe b) 'frac)
 112           (math-make-frac (math-mul (nth 1 a) (nth 1 b))
 113                           (math-mul (nth 2 a) (nth 2 b)))
 114         (math-make-frac (math-mul (nth 1 a) b)
 115                         (nth 2 a)))
 116     (math-make-frac (math-mul a (nth 1 b))
 117                     (nth 2 b))))
 118
 119 (defun calc-div-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 2 b))
 123                           (math-mul (nth 2 a) (nth 1 b)))
 124         (math-make-frac (nth 1 a)
 125                         (math-mul (nth 2 a) b)))
 126     (math-make-frac (math-mul a (nth 2 b))
 127                     (nth 1 b))))
 128
 129
 130 ;;; Convert a real value to fractional form.  [T R I; T R F] [Public]
 131 (defun calcFunc-frac (a &optional tol)
 132   (or tol (setq tol 0))
 133   (cond ((Math-ratp a)
 134          a)
 135         ((memq (car a) '(cplx polar vec hms date sdev intv mod))
 136          (cons (car a) (mapcar (function
 137                                 (lambda (x)
 138                                   (calcFunc-frac x tol)))
 139                                (cdr a))))
 140         ((Math-messy-integerp a)
 141          (math-trunc a))
 142         ((Math-negp a)
 143          (math-neg (calcFunc-frac (math-neg a) tol)))
 144         ((not (eq (car a) 'float))
 145          (if (math-infinitep a)
 146              a
 147            (if (math-provably-integerp a)
 148                a
 149              (math-reject-arg a 'numberp))))
 150         ((integerp tol)
 151          (if (<= tol 0)
 152              (setq tol (+ tol calc-internal-prec)))
 153          (calcFunc-frac a (list 'float 5
 154                                 (- (+ (math-numdigs (nth 1 a))
 155                                       (nth 2 a))
 156                                    (1+ tol)))))
 157         ((not (eq (car tol) 'float))
 158          (if (Math-realp tol)
 159              (calcFunc-frac a (math-float tol))
 160            (math-reject-arg tol 'realp)))
 161         ((Math-negp tol)
 162          (calcFunc-frac a (math-neg tol)))
 163         ((Math-zerop tol)
 164          (calcFunc-frac a 0))
 165         ((not (math-lessp-float tol '(float 1 0)))
 166          (math-trunc a))
 167         ((Math-zerop a)
 168          0)
 169         (t
 170          (let ((cfrac (math-continued-fraction a tol))
 171                (calc-prefer-frac t))
 172            (math-eval-continued-fraction cfrac)))))
 173
 174 (defun math-continued-fraction (a tol)
 175   (let ((calc-internal-prec (+ calc-internal-prec 2)))
 176     (let ((cfrac nil)
 177           (aa a)
 178           (calc-prefer-frac nil)
 179           int)
 180       (while (or (null cfrac)
 181                  (and (not (Math-zerop aa))
 182                       (not (math-lessp-float
 183                             (math-abs
 184                              (math-sub a
 185                                        (let ((f (math-eval-continued-fraction
 186                                                  cfrac)))
 187                                          (math-working "Fractionalize" f)
 188                                          f)))
 189                             tol))))
 190         (setq int (math-trunc aa)
 191               aa (math-sub aa int)
 192               cfrac (cons int cfrac))
 193         (or (Math-zerop aa)
 194             (setq aa (math-div 1 aa))))
 195       cfrac)))
 196
 197 (defun math-eval-continued-fraction (cf)
 198   (let ((n (car cf))
 199         (d 1)
 200         temp)
 201     (while (setq cf (cdr cf))
 202       (setq temp (math-add (math-mul (car cf) n) d)
 203             d n
 204             n temp))
 205     (math-div n d)))
 206
 207 (defun calcFunc-fdiv (a b)   ; [R I I] [Public]
 208   (cond
 209    ((Math-num-integerp a)
 210     (cond
 211      ((Math-num-integerp b)
 212       (if (Math-zerop b)
 213           (math-reject-arg a "*Division by zero")
 214         (math-make-frac (math-trunc a) (math-trunc b))))
 215      ((eq (car-safe b) 'frac)
 216       (if (Math-zerop (nth 1 b))
 217           (math-reject-arg a "*Division by zero")
 218         (math-make-frac (math-mul (math-trunc a) (nth 2 b)) (nth 1 b))))
 219      (t (math-reject-arg b 'integerp))))
 220    ((eq (car-safe a) 'frac)
 221     (cond
 222      ((Math-num-integerp b)
 223       (if (Math-zerop b)
 224           (math-reject-arg a "*Division by zero")
 225         (math-make-frac (cadr a) (math-mul (nth 2 a) (math-trunc b)))))
 226      ((eq (car-safe b) 'frac)
 227       (if (Math-zerop (nth 1 b))
 228           (math-reject-arg a "*Division by zero")
 229         (math-make-frac (math-mul (nth 1 a) (nth 2 b)) (math-mul (nth 2 a) (nth 1 b)))))
 230      (t (math-reject-arg b 'integerp))))
 231    (t
 232     (math-reject-arg a 'integerp))))
 233
 234 (provide 'calc-frac)
 235
 236 ;;; calc-frac.el ends here