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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
+