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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
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