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