mirror of
https://github.com/RobTillaart/Arduino.git
synced 2024-09-20 00:55:58 -04:00
490 lines
9.7 KiB
C++
490 lines
9.7 KiB
C++
//
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// FILE: fraction.h
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// AUTHOR: Rob Tillaart
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// VERSION: 0.1.07
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// PURPOSE: library for fractions for Arduino
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// URL:
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//
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// Released to the public domain
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//
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// TODO
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// - divide by zero errors
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// - test extensively
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//
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// 0.1.07 - major refactoring by Chris-A
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// 0.1.06 - added proper(), mediant(), angle();
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// 0.1.05 - tested negative Fractions math, added constructors,
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// minor refactoring,
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// 0.1.04 - stabilizing code, add simplify() for some code paths.
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// 0.1.03 - added toDouble(), tested several fractionize() codes, bug fixes.
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// 0.1.02 - faster fractionize code
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// 0.1.01 - some fixes
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// 0.1.00 - initial version
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#include "fraction.h"
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// CONSTRUCTORS
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Fraction::Fraction(double f)
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{
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// handle special cases?
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// PI = 355/113; // 2.7e-7
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// PI*2 = 710/113;
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// PI/2 = 335/226;
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// EULER = 2721/1001; // 1.1e-7
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// EULER = 1264/465; // 2.2e-6
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// get robust for small values.
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if (abs(f) < 0.00001)
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{
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n = 0;
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d = 1;
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return;
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}
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// Normalize to 0.0 ... 1.0
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bool neg = f < 0;
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if (neg) f = -f;
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bool rec = f > 1;
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if (rec) f = 1/f;
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fractionize(f);
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simplify();
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// denormalize
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if (rec)
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{
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int32_t t = n;
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n = d;
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d = t;
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}
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if (neg)
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{
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n = -n;
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}
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}
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Fraction::Fraction(int32_t p, int32_t q) : n(p), d(q)
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{
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simplify();
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}
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// PRINTING
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size_t Fraction::printTo(Print& p) const
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{
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size_t s = 0;
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// vs 22/7 => 3_1/7
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// if (n >= d)
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// {
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// s += p.print(n/d, DEC);
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// s += p.print("_");
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// }
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// s += p.print(n%d, DEC);
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s += p.print(n, DEC);
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s += p.print('/');
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s += p.print(d, DEC);
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return s;
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};
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// EQUALITIES
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bool Fraction::operator == (const Fraction &c)
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{
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return (n * c.d) == (d * c.n);
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}
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bool Fraction::operator != (const Fraction &c)
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{
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return (n * c.d) != (d * c.n);
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}
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bool Fraction::operator > (const Fraction &c)
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{
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return (n * c.d) > (d * c.n);
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}
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bool Fraction::operator >= (const Fraction &c)
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{
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return (n * c.d) >= (d * c.n);
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}
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bool Fraction::operator < (const Fraction &c)
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{
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return (n * c.d) < (d * c.n);
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}
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bool Fraction::operator <= (const Fraction &c)
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{
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return (n * c.d) <= (d * c.n);
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}
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// NEGATE
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Fraction Fraction::operator - ()
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{
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return Fraction(-n, d);
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}
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// BASIC MATH
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Fraction Fraction::operator + (const Fraction &c)
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{
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if (d == c.d)
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{
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return Fraction(n + c.n, d);
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}
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return Fraction(n*c.d + c.n*d, d * c.d);
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}
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Fraction Fraction::operator - (const Fraction &c)
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{
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if (d == c.d)
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{
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return Fraction(n - c.n, d);
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}
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return Fraction(n*c.d - c.n*d, d * c.d);
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}
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Fraction Fraction::operator * (const Fraction &c)
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{
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return Fraction(n * c.n, d * c.d);
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}
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Fraction Fraction::operator / (const Fraction &c)
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{
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// division by zero returns 0
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return Fraction(n * c.d, d * c.n);
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}
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Fraction& Fraction::operator += (const Fraction &c)
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{
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if (d == c.d)
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{
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n += c.n;
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}
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else
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{
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n = n * c.d + c.n * d;
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d *= c.d;
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}
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simplify();
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return *this;
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}
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Fraction& Fraction::operator -= (const Fraction &c)
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{
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if (d == c.d)
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{
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n -= c.n;
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}
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else
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{
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n = n * c.d - c.n * d;
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d *= c.d;
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}
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simplify();
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return *this;
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}
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Fraction& Fraction::operator *= (const Fraction &c)
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{
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n *= c.n;
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d *= c.d;
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simplify();
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return *this;
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}
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Fraction& Fraction::operator /= (const Fraction &c)
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{
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// division by zero returns 0
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n *= c.d;
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d *= c.n;
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simplify();
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return *this;
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}
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double Fraction::toDouble()
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{
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return (1.0 * n) / d;
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}
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// wikipedia
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// fraction is proper if abs(fraction) < 1
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bool Fraction::isProper()
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{
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return abs(n) < abs(d);
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}
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// visualize fraction as an angle in degrees
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double Fraction::toAngle()
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{
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return atan2(n, d) * 180.0 / PI;
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}
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////////////////////////////////////////////////////////////
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// STATIC
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// Mediant - http://www.cut-the-knot.org/Curriculum/Arithmetic/FCExercise.shtml
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// void Fraction::mediant(Fraction c)
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// {
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// n += c.n;
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// d += c.d;
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// simplify();
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// }
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// the mediant is a fraction that is always between 2 fractions
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// at least if within precission.
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Fraction Fraction::mediant(const Fraction &a, const Fraction &b)
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{
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return Fraction(a.n + b.n, a.d + b.d);
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}
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// approximate a fraction with defined denominator
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// sort of setDenominator(uint16_t den);
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Fraction Fraction::setDenominator(const Fraction &a, uint16_t b)
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{
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int32_t n = round((a.n * b * 1.0) / a.d);
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int32_t d = b;
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return Fraction(n, d);
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}
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////////////////////////////////////////////////////////////////
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// PRIVATE
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// http://en.wikipedia.org/wiki/Binary_GCD_algorithm
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int32_t Fraction::gcd(int32_t a , int32_t b)
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{
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long c;
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while ( a != 0 )
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{
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c = a;
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a = b % a;
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b = c;
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}
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return b;
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}
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// not that simple ...
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void Fraction::simplify()
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{
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if (n == 0)
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{
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d = 1;
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return;
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}
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bool neg = (n < 0) != (d < 0);
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int32_t p = abs(n);
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int32_t q = abs(d);
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int32_t x = gcd(p,q);
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p = p/x;
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q = q/x;
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// denominator max 4 digits keeps mul and div simple
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// in preventing overflow
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while (q > 10000)
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{
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// rounding might need improvement
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p = (p + 5)/10;
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q = (q + 5)/10;
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x = gcd(p, q);
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p = p/x;
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q = q/x;
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}
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n = (neg)?-p:p;
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d = q;
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}
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//////////////////////////////////////////////////////////////////////////////
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// fractionize() - finds the fraction representation of a double
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// PRE: 0 <= f < 1.0
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//
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// minimalistic is fast and small
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//
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// check for a discussion found later
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// - http://mathforum.org/library/drmath/view/51886.html
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// - http://www.gamedev.net/topic/354209-how-do-i-convert-a-decimal-to-a-fraction-in-c/
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//
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// MINIMALISTIC
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// (100x) micros()=51484
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/*
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double Fraction::fractionize(double f) // simple, small, 2nd fastest
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{
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n = round(f * 10000); // why not 1000000 ?
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d = 10000;
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simplify();
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return 0; // abs(f - this.toDouble());
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}
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*/
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// LINEAR SEARCH
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// (100x) micros()=18873064
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// slow not stable
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/*
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double Fraction::fractionize(double f)
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{
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long nn = 1, dd = 1;
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float r = 1 / f;
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float delta = f * dd - nn;
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while (abs(delta) > 0.00001 && (dd < 10000))
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{
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dd++;
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if (delta < 0)
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{
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nn++;
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dd = nn * r;
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}
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delta = f * dd - nn;
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}
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n = nn;
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d = dd;
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return delta;
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}
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*/
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/*
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// LINEAR SEARCH (mirror optimized)
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// (100x) micros()=
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// slow but stable version
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/*
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double Fraction::fractionize(double f)
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{
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long nn = 1, dd = 1;
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bool inverse = false;
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if (f > 0.5)
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{
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f = 1-f;
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inverse = true;
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}
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float r = 1 / f;
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float delta = f * dd - nn;
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while (abs(delta) > 0.00001 && (dd < 10000))
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{
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dd++;
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if (delta < 0)
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{
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nn++;
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dd = nn * r;
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}
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delta = f * dd - nn;
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}
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n = inverse?(dd - nn):nn;
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d = dd;
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return delta;
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}
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*/
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// ADD BY DIGIT
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// - does not find "magic fractions" e.g. pi = 355/113
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// (100x) micros()=392620
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/*
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double Fraction::fractionize(double f) // divide and conquer, simple, small, 2nd fastest
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{
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Fraction t((long)0);
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for (long dd = 10; dd < 1000001; dd *= 10)
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{
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f *= 10;
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int ff = f;
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t += Fraction(ff, dd);
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f -= ff;
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}
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n = t.n;
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d = t.d;
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return f;
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}
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*/
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// Dr. Peterson
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// - http://mathforum.org/library/drmath/view/51886.html
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// (100x) micros()=96048
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// showed errors for very small values around 0
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double Fraction::fractionize(double val)
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{ // find nearest fraction
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double Precision = 0.000001;
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Fraction low(0, 1); // "A" = 0/1
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Fraction high(1, 1); // "B" = 1/1
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for (int i = 0; i < 100; ++i)
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{
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double testLow = low.d * val - low.n;
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double testHigh = high.n - high.d * val;
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if (testHigh < Precision * high.d)
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break; // high is answer
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if (testLow < Precision * low.d)
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{ // low is answer
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high = low;
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break;
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}
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if (i & 1)
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{ // odd step: add multiple of low to high
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double test = testHigh / testLow;
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int32_t count = (int32_t)test; // "N"
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int32_t n = (count + 1) * low.n + high.n;
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int32_t d = (count + 1) * low.d + high.d;
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if ((n > 0x8000) || (d > 0x10000))
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break;
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high.n = n - low.n; // new "A"
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high.d = d - low.d;
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low.n = n; // new "B"
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low.d = d;
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}
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else
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{ // even step: add multiple of high to low
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double test = testLow / testHigh;
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int32_t count = (int32_t)test; // "N"
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int32_t n = low.n + (count + 1) * high.n;
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int32_t d = low.d + (count + 1) * high.d;
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if ((n > 0x10000) || (d > 0x10000))
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break;
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low.n = n - high.n; // new "A"
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low.d = d - high.d;
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high.n = n; // new "B"
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high.d = d;
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}
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}
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n = high.n;
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d = high.d;
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}
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// BINARY SEARCH
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// - http://www.gamedev.net/topic/354209-how-do-i-convert-a-decimal-to-a-fraction-in-c/
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// (100x) micros()=1292452
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// slower
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/*
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double Fraction::fractionize(double value) // size ok, too slow.
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{
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int max_denominator = 10000;
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int low_n = 0;
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int low_d = 1;
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int high_n = 1;
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int high_d = 1;
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int mid_n;
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int mid_d;
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do
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{
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mid_n = low_n + high_n;
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mid_d = low_d + high_d;
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if ( mid_n < value * mid_d )
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{
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low_n = mid_n;
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low_d = mid_d;
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n = high_n;
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d = high_d;
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}
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else
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{
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high_n = mid_n;
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high_d = mid_d;
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n = low_n;
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d = low_d;
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}
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} while ( mid_d <= max_denominator );
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return 0;
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}
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*/
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//
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// END OF FILE
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//
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