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-/*
- * frac.cc -- ePiX rational number class
- *
- * This file is part of ePiX, a C++ library for creating high-quality
- * figures in LaTeX
- *
- * Version 1.2.0-2
- * Last Change: September 26, 2007
- */
-
-/*
- * Copyright (C) 2001, 2002, 2003, 2004, 2005, 2006, 2007
- * Andrew D. Hwang <rot 13 nujnat at zngupf dot ubylpebff dot rqh>
- * Department of Mathematics and Computer Science
- * College of the Holy Cross
- * Worcester, MA, 01610-2395, USA
- */
-
-/*
- * ePiX 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 2 of the License, or
- * (at your option) any later version.
- *
- * ePiX is distributed in the hope that it will be useful, but WITHOUT
- * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
- * or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
- * License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with ePiX; if not, write to the Free Software Foundation, Inc.,
- * 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
- */
-#include <cmath>
-
-#include "frac.h"
-
-namespace ePiX {
-
- const int MAX_DENOM(10000);
- const double EPS(1.0/MAX_DENOM);
-
- unsigned int __epix_gcd (int i, unsigned int j);
-
- frac::frac(const int n, const unsigned int d)
- : m_num(n), m_denom(d) { }
-
- // express arg as a fraction with denominator no larger than MAX_DENOM
- frac::frac(double arg)
- {
- unsigned int denom(1);
- if (fabs(arg) < EPS)
- {
- m_num = 0;
- m_denom = 1;
- }
-
- else
- {
- int sgn(arg < 0 ? -1 : 1);
- double abs_arg(sgn*arg);
-
- // store best approximation
- int best_num(0);
- double running_error(0.5);
-
- while (denom <= 1+MAX_DENOM)
- {
- const double tmp(abs_arg*denom);
-
- int tmp_lo((int) floor(tmp));
-
- if (tmp - tmp_lo < EPS) // good approx
- {
- best_num = tmp_lo;
- break;
- }
-
- else if (tmp - tmp_lo < running_error) // improved approx
- {
- best_num = tmp_lo;
- running_error = tmp - best_num;
- }
-
- int tmp_hi((int) ceil(tmp));
- if (tmp_hi - tmp < EPS)
- {
- best_num = tmp_hi;
- break;
- }
-
- else if (tmp_hi - tmp < running_error)
- {
- best_num = tmp_hi;
- running_error = best_num - tmp;
- }
-
- ++denom;
- }
-
- m_num = sgn*best_num;
- m_denom = denom;
- }
- } // end of frac::frac(double arg)
-
-
- // increment operators
- frac& frac::operator += (const frac& arg)
- {
- m_num *= arg.m_denom;
- m_num += m_denom*arg.m_num;
- m_denom *= arg.m_denom;
-
- return *this;
- }
-
- frac& frac::operator -= (const frac& arg)
- {
- m_num *= arg.m_denom;
- m_num -= m_denom*arg.m_num;
- m_denom *= arg.m_denom;
-
- return *this;
- }
-
- frac& frac::operator *= (const frac& arg)
- {
- m_num *= arg.m_num;
- m_denom *= arg.m_denom;
-
- return *this;
- }
-
- frac& frac::operator /= (const frac& arg)
- {
- unsigned int arg_num(arg.m_num < 0 ? -arg.m_num : arg.m_num);
-
- m_num *= arg.m_denom;
- m_denom *= arg_num;
-
- if (arg.m_num < 0)
- m_num = -1;
-
- return *this;
- }
-
- frac& frac::reduce()
- {
- unsigned int factor(__epix_gcd(m_num, m_denom));
- m_num /= factor;
- m_denom /= factor;
-
- return *this;
- }
-
- double frac::eval() const
- {
- double temp(m_num);
- return temp /= m_denom;
- }
-
- int frac::num() const
- {
- return m_num;
- }
-
- unsigned int frac::denom() const
- {
- return m_denom;
- }
-
- bool frac::is_int() const
- {
- return __epix_gcd(m_num, m_denom) == m_denom;
- }
-
-
- frac operator+ (frac arg1, const frac& arg2)
- {
- return arg1 += arg2;
- }
-
- frac operator- (frac arg1)
- {
- return arg1 *= -1;
- }
-
- frac operator- (frac arg1, const frac& arg2)
- {
- return arg1 -= arg2;
- }
-
- frac operator* (frac arg1, const frac& arg2)
- {
- return arg1 *= arg2;
- }
-
- frac operator/ (frac arg1, const frac& arg2)
- {
- return arg1 /= arg2;
- }
-
- // (in)equality
- bool operator == (const frac& u, const frac& v)
- {
- return u.num()*v.denom() == v.num()*u.denom();
- }
-
- bool operator != (const frac& u, const frac& v)
- {
- return !(u == v);
- }
-
- // denoms are unsigned
- bool operator < (const frac& u, const frac& v)
- {
- return u.num()*v.denom() < v.num()*u.denom();
- }
-
- bool operator > (const frac& u, const frac& v)
- {
- return u.num()*v.denom() > v.num()*u.denom();
- }
-
- bool operator <= (const frac& u, const frac& v)
- {
- return u.num()*v.denom() <= v.num()*u.denom();
- }
-
- bool operator >= (const frac& u, const frac& v)
- {
- return u.num()*v.denom() >= v.num()*u.denom();
- }
-
- // N.B.: gcd(0,i) = |i|
- unsigned int __epix_gcd (int i, unsigned int j)
- {
- unsigned int new_i(i<0 ? -i : i);
- unsigned int temp;
-
- if (new_i==0 || j==0) // (1,0) and (0,1) coprime, others not
- return new_i + j;
-
- else {
- if (j < new_i) // swap them
- {
- temp = j;
- j = new_i;
- new_i = temp;
- }
- // Euclidean algorithm
- while ((temp = j%new_i)) // i does not evenly divide j
- {
- j = new_i;
- new_i = temp;
- }
-
- return new_i;
- }
- }
-} // end of namespace
-