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237 lines
6.7 KiB
EmacsLisp
237 lines
6.7 KiB
EmacsLisp
;;; calc-frac.el --- fraction functions for Calc
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;; Copyright (C) 1990-1993, 2001-2012 Free Software Foundation, Inc.
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;; Author: David Gillespie <daveg@synaptics.com>
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;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
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;; This file is part of GNU Emacs.
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;; GNU Emacs is free software: you can redistribute it and/or modify
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;; it under the terms of the GNU General Public License as published by
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;; the Free Software Foundation, either version 3 of the License, or
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;; (at your option) any later version.
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;; GNU Emacs is distributed in the hope that it will be useful,
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;; but WITHOUT ANY WARRANTY; without even the implied warranty of
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;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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;; GNU General Public License for more details.
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;; You should have received a copy of the GNU General Public License
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;; along with GNU Emacs. If not, see <http://www.gnu.org/licenses/>.
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;;; Commentary:
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;;; Code:
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;; This file is autoloaded from calc-ext.el.
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(require 'calc-ext)
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(require 'calc-macs)
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(defun calc-fdiv (arg)
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(interactive "P")
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(calc-slow-wrapper
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(calc-binary-op ":" 'calcFunc-fdiv arg 1)))
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(defun calc-fraction (arg)
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(interactive "P")
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(calc-slow-wrapper
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(let ((func (if (calc-is-hyperbolic) 'calcFunc-frac 'calcFunc-pfrac)))
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(if (eq arg 0)
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(calc-enter-result 2 "frac" (list func
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(calc-top-n 2)
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(calc-top-n 1)))
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(calc-enter-result 1 "frac" (list func
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(calc-top-n 1)
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(prefix-numeric-value (or arg 0))))))))
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(defun calc-over-notation (fmt)
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(interactive "sFraction separator: ")
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(calc-wrapper
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(if (string-match "\\`\\([^ 0-9][^ 0-9]?\\)[0-9]*\\'" fmt)
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(let ((n nil))
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(if (/= (match-end 0) (match-end 1))
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(setq n (string-to-number (substring fmt (match-end 1)))
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fmt (math-match-substring fmt 1)))
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(if (eq n 0) (error "Bad denominator"))
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(calc-change-mode 'calc-frac-format (list fmt n) t))
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(error "Bad fraction separator format"))))
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(defun calc-slash-notation (n)
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(interactive "P")
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(calc-wrapper
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(calc-change-mode 'calc-frac-format (if n '("//" nil) '("/" nil)) t)))
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(defun calc-frac-mode (n)
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(interactive "P")
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(calc-wrapper
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(calc-change-mode 'calc-prefer-frac n nil t)
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(message (if calc-prefer-frac
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"Integer division will now generate fractions"
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"Integer division will now generate floating-point results"))))
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;;;; Fractions.
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;;; Build a normalized fraction. [R I I]
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;;; (This could probably be implemented more efficiently than using
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;;; the plain gcd algorithm.)
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(defun math-make-frac (num den)
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(if (Math-integer-negp den)
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(setq num (math-neg num)
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den (math-neg den)))
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(let ((gcd (math-gcd num den)))
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(if (eq gcd 1)
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(if (eq den 1)
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num
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(list 'frac num den))
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(if (equal gcd den)
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(math-quotient num gcd)
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(list 'frac (math-quotient num gcd) (math-quotient den gcd))))))
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(defun calc-add-fractions (a b)
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(if (eq (car-safe a) 'frac)
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(if (eq (car-safe b) 'frac)
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(math-make-frac (math-add (math-mul (nth 1 a) (nth 2 b))
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(math-mul (nth 2 a) (nth 1 b)))
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(math-mul (nth 2 a) (nth 2 b)))
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(math-make-frac (math-add (nth 1 a)
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(math-mul (nth 2 a) b))
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(nth 2 a)))
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(math-make-frac (math-add (math-mul a (nth 2 b))
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(nth 1 b))
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(nth 2 b))))
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(defun calc-mul-fractions (a b)
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(if (eq (car-safe a) 'frac)
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(if (eq (car-safe b) 'frac)
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(math-make-frac (math-mul (nth 1 a) (nth 1 b))
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(math-mul (nth 2 a) (nth 2 b)))
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(math-make-frac (math-mul (nth 1 a) b)
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(nth 2 a)))
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(math-make-frac (math-mul a (nth 1 b))
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(nth 2 b))))
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(defun calc-div-fractions (a b)
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(if (eq (car-safe a) 'frac)
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(if (eq (car-safe b) 'frac)
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(math-make-frac (math-mul (nth 1 a) (nth 2 b))
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(math-mul (nth 2 a) (nth 1 b)))
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(math-make-frac (nth 1 a)
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(math-mul (nth 2 a) b)))
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(math-make-frac (math-mul a (nth 2 b))
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(nth 1 b))))
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;;; Convert a real value to fractional form. [T R I; T R F] [Public]
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(defun calcFunc-frac (a &optional tol)
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(or tol (setq tol 0))
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(cond ((Math-ratp a)
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a)
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((memq (car a) '(cplx polar vec hms date sdev intv mod))
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(cons (car a) (mapcar (function
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(lambda (x)
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(calcFunc-frac x tol)))
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(cdr a))))
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((Math-messy-integerp a)
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(math-trunc a))
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((Math-negp a)
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(math-neg (calcFunc-frac (math-neg a) tol)))
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((not (eq (car a) 'float))
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(if (math-infinitep a)
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a
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(if (math-provably-integerp a)
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a
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(math-reject-arg a 'numberp))))
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((integerp tol)
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(if (<= tol 0)
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(setq tol (+ tol calc-internal-prec)))
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(calcFunc-frac a (list 'float 5
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(- (+ (math-numdigs (nth 1 a))
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(nth 2 a))
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(1+ tol)))))
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((not (eq (car tol) 'float))
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(if (Math-realp tol)
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(calcFunc-frac a (math-float tol))
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(math-reject-arg tol 'realp)))
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((Math-negp tol)
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(calcFunc-frac a (math-neg tol)))
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((Math-zerop tol)
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(calcFunc-frac a 0))
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((not (math-lessp-float tol '(float 1 0)))
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(math-trunc a))
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((Math-zerop a)
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0)
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(t
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(let ((cfrac (math-continued-fraction a tol))
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(calc-prefer-frac t))
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(math-eval-continued-fraction cfrac)))))
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(defun math-continued-fraction (a tol)
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(let ((calc-internal-prec (+ calc-internal-prec 2)))
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(let ((cfrac nil)
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(aa a)
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(calc-prefer-frac nil)
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int)
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(while (or (null cfrac)
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(and (not (Math-zerop aa))
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(not (math-lessp-float
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(math-abs
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(math-sub a
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(let ((f (math-eval-continued-fraction
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cfrac)))
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(math-working "Fractionalize" f)
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f)))
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tol))))
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(setq int (math-trunc aa)
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aa (math-sub aa int)
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cfrac (cons int cfrac))
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(or (Math-zerop aa)
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(setq aa (math-div 1 aa))))
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cfrac)))
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(defun math-eval-continued-fraction (cf)
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(let ((n (car cf))
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(d 1)
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temp)
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(while (setq cf (cdr cf))
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(setq temp (math-add (math-mul (car cf) n) d)
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d n
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n temp))
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(math-div n d)))
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(defun calcFunc-fdiv (a b) ; [R I I] [Public]
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(cond
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((Math-num-integerp a)
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(cond
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((Math-num-integerp b)
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(if (Math-zerop b)
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(math-reject-arg a "*Division by zero")
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(math-make-frac (math-trunc a) (math-trunc b))))
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((eq (car-safe b) 'frac)
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(if (Math-zerop (nth 1 b))
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(math-reject-arg a "*Division by zero")
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(math-make-frac (math-mul (math-trunc a) (nth 2 b)) (nth 1 b))))
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(t (math-reject-arg b 'integerp))))
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((eq (car-safe a) 'frac)
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(cond
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((Math-num-integerp b)
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(if (Math-zerop b)
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(math-reject-arg a "*Division by zero")
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(math-make-frac (cadr a) (math-mul (nth 2 a) (math-trunc b)))))
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((eq (car-safe b) 'frac)
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(if (Math-zerop (nth 1 b))
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(math-reject-arg a "*Division by zero")
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(math-make-frac (math-mul (nth 1 a) (nth 2 b)) (math-mul (nth 2 a) (nth 1 b)))))
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(t (math-reject-arg b 'integerp))))
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(t
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(math-reject-arg a 'integerp))))
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(provide 'calc-frac)
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;;; calc-frac.el ends here
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