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;;; calc-frac.el --- fraction functions for Calc
;; Copyright (C) 1990-1993, 2001-2015 Free Software Foundation, Inc.
;; Author: David Gillespie <>
;; Maintainer: Jay Belanger <>
;; This file is part of GNU Emacs.
;; GNU Emacs is free software: you can redistribute it and/or modify
;; it under the terms of the GNU General Public License as published by
;; the Free Software Foundation, either version 3 of the License, or
;; (at your option) any later version.
;; GNU Emacs is distributed in the hope that it will be useful,
;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;; GNU General Public License for more details.
;; You should have received a copy of the GNU General Public License
;; along with GNU Emacs. If not, see <>.
;;; Commentary:
;;; Code:
;; This file is autoloaded from calc-ext.el.
(require 'calc-ext)
(require 'calc-macs)
(defun calc-fdiv (arg)
(interactive "P")
(calc-binary-op ":" 'calcFunc-fdiv arg 1)))
(defun calc-fraction (arg)
(interactive "P")
(let ((func (if (calc-is-hyperbolic) 'calcFunc-frac 'calcFunc-pfrac)))
(if (eq arg 0)
(calc-enter-result 2 "frac" (list func
(calc-top-n 2)
(calc-top-n 1)))
(calc-enter-result 1 "frac" (list func
(calc-top-n 1)
(prefix-numeric-value (or arg 0))))))))
(defun calc-over-notation (fmt)
(interactive "sFraction separator: ")
(if (string-match "\\`\\([^ 0-9][^ 0-9]?\\)[0-9]*\\'" fmt)
(let ((n nil))
(if (/= (match-end 0) (match-end 1))
(setq n (string-to-number (substring fmt (match-end 1)))
fmt (math-match-substring fmt 1)))
(if (eq n 0) (error "Bad denominator"))
(calc-change-mode 'calc-frac-format (list fmt n) t))
(error "Bad fraction separator format"))))
(defun calc-slash-notation (n)
(interactive "P")
(calc-change-mode 'calc-frac-format (if n '("//" nil) '("/" nil)) t)))
(defun calc-frac-mode (n)
(interactive "P")
(calc-change-mode 'calc-prefer-frac n nil t)
(message (if calc-prefer-frac
"Integer division will now generate fractions"
"Integer division will now generate floating-point results"))))
;;;; Fractions.
;;; Build a normalized fraction. [R I I]
;;; (This could probably be implemented more efficiently than using
;;; the plain gcd algorithm.)
(defun math-make-frac (num den)
(if (Math-integer-negp den)
(setq num (math-neg num)
den (math-neg den)))
(let ((gcd (math-gcd num den)))
(if (eq gcd 1)
(if (eq den 1)
(list 'frac num den))
(if (equal gcd den)
(math-quotient num gcd)
(list 'frac (math-quotient num gcd) (math-quotient den gcd))))))
(defun calc-add-fractions (a b)
(if (eq (car-safe a) 'frac)
(if (eq (car-safe b) 'frac)
(math-make-frac (math-add (math-mul (nth 1 a) (nth 2 b))
(math-mul (nth 2 a) (nth 1 b)))
(math-mul (nth 2 a) (nth 2 b)))
(math-make-frac (math-add (nth 1 a)
(math-mul (nth 2 a) b))
(nth 2 a)))
(math-make-frac (math-add (math-mul a (nth 2 b))
(nth 1 b))
(nth 2 b))))
(defun calc-mul-fractions (a b)
(if (eq (car-safe a) 'frac)
(if (eq (car-safe b) 'frac)
(math-make-frac (math-mul (nth 1 a) (nth 1 b))
(math-mul (nth 2 a) (nth 2 b)))
(math-make-frac (math-mul (nth 1 a) b)
(nth 2 a)))
(math-make-frac (math-mul a (nth 1 b))
(nth 2 b))))
(defun calc-div-fractions (a b)
(if (eq (car-safe a) 'frac)
(if (eq (car-safe b) 'frac)
(math-make-frac (math-mul (nth 1 a) (nth 2 b))
(math-mul (nth 2 a) (nth 1 b)))
(math-make-frac (nth 1 a)
(math-mul (nth 2 a) b)))
(math-make-frac (math-mul a (nth 2 b))
(nth 1 b))))
;;; Convert a real value to fractional form. [T R I; T R F] [Public]
(defun calcFunc-frac (a &optional tol)
(or tol (setq tol 0))
(cond ((Math-ratp a)
((memq (car a) '(cplx polar vec hms date sdev intv mod))
(cons (car a) (mapcar (function
(lambda (x)
(calcFunc-frac x tol)))
(cdr a))))
((Math-messy-integerp a)
(math-trunc a))
((Math-negp a)
(math-neg (calcFunc-frac (math-neg a) tol)))
((not (eq (car a) 'float))
(if (math-infinitep a)
(if (math-provably-integerp a)
(math-reject-arg a 'numberp))))
((integerp tol)
(if (<= tol 0)
(setq tol (+ tol calc-internal-prec)))
(calcFunc-frac a (list 'float 5
(- (+ (math-numdigs (nth 1 a))
(nth 2 a))
(1+ tol)))))
((not (eq (car tol) 'float))
(if (Math-realp tol)
(calcFunc-frac a (math-float tol))
(math-reject-arg tol 'realp)))
((Math-negp tol)
(calcFunc-frac a (math-neg tol)))
((Math-zerop tol)
(calcFunc-frac a 0))
((not (math-lessp-float tol '(float 1 0)))
(math-trunc a))
((Math-zerop a)
(let ((cfrac (math-continued-fraction a tol))
(calc-prefer-frac t))
(math-eval-continued-fraction cfrac)))))
(defun math-continued-fraction (a tol)
(let ((calc-internal-prec (+ calc-internal-prec 2)))
(let ((cfrac nil)
(aa a)
(calc-prefer-frac nil)
(while (or (null cfrac)
(and (not (Math-zerop aa))
(not (math-lessp-float
(math-sub a
(let ((f (math-eval-continued-fraction
(math-working "Fractionalize" f)
(setq int (math-trunc aa)
aa (math-sub aa int)
cfrac (cons int cfrac))
(or (Math-zerop aa)
(setq aa (math-div 1 aa))))
(defun math-eval-continued-fraction (cf)
(let ((n (car cf))
(d 1)
(while (setq cf (cdr cf))
(setq temp (math-add (math-mul (car cf) n) d)
d n
n temp))
(math-div n d)))
(defun calcFunc-fdiv (a b) ; [R I I] [Public]
((Math-num-integerp a)
((Math-num-integerp b)
(if (Math-zerop b)
(math-reject-arg a "*Division by zero")
(math-make-frac (math-trunc a) (math-trunc b))))
((eq (car-safe b) 'frac)
(if (Math-zerop (nth 1 b))
(math-reject-arg a "*Division by zero")
(math-make-frac (math-mul (math-trunc a) (nth 2 b)) (nth 1 b))))
(t (math-reject-arg b 'integerp))))
((eq (car-safe a) 'frac)
((Math-num-integerp b)
(if (Math-zerop b)
(math-reject-arg a "*Division by zero")
(math-make-frac (cadr a) (math-mul (nth 2 a) (math-trunc b)))))
((eq (car-safe b) 'frac)
(if (Math-zerop (nth 1 b))
(math-reject-arg a "*Division by zero")
(math-make-frac (math-mul (nth 1 a) (nth 2 b)) (math-mul (nth 2 a) (nth 1 b)))))
(t (math-reject-arg b 'integerp))))
(math-reject-arg a 'integerp))))
(provide 'calc-frac)
;;; calc-frac.el ends here
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