source: src/libcfa/rational.c @ babeeda

//
// Cforall Version 1.0.0 Copyright (C) 2016 University of Waterloo
//
// The contents of this file are covered under the licence agreement in the
// file "LICENCE" distributed with Cforall.
//
// rational.c --
//
// Author           : Peter A. Buhr
// Created On       : Wed Apr  6 17:54:28 2016
// Last Modified By : Peter A. Buhr
// Last Modified On : Wed Dec  6 23:13:58 2017
// Update Count     : 156
//

#include "rational"
#include "fstream"
#include "stdlib"

// helper routines

// Calculate greatest common denominator of two numbers, the first of which may be negative. Used to reduce rationals.
// alternative: https://en.wikipedia.org/wiki/Binary_GCD_algorithm
forall( otype RationalImpl | arithmetic( RationalImpl ) )
static RationalImpl gcd( RationalImpl a, RationalImpl b ) {
        for ( ;; ) {                                                                            // Euclid's algorithm
                RationalImpl r = a % b;
          if ( r == (RationalImpl){0} ) break;
                a = b;
                b = r;
        } // for
        return b;
} // gcd

forall( otype RationalImpl | arithmetic( RationalImpl ) )
static RationalImpl simplify( RationalImpl & n, RationalImpl & d ) {
        if ( d == (RationalImpl){0} ) {
                serr | "Invalid rational number construction: denominator cannot be equal to 0." | endl;
                exit( EXIT_FAILURE );
        } // exit
        if ( d < (RationalImpl){0} ) { d = -d; n = -n; }        // move sign to numerator
        return gcd( abs( n ), d );                                                      // simplify
} // Rationalnumber::simplify


// constructors

forall( otype RationalImpl | arithmetic( RationalImpl ) )
void ?{}( Rational(RationalImpl) & r ) {
        r{ (RationalImpl){0}, (RationalImpl){1} };
} // rational

forall( otype RationalImpl | arithmetic( RationalImpl ) )
void ?{}( Rational(RationalImpl) & r, RationalImpl n ) {
        r{ n, (RationalImpl){1} };
} // rational

forall( otype RationalImpl | arithmetic( RationalImpl ) )
void ?{}( Rational(RationalImpl) & r, RationalImpl n, RationalImpl d ) {
        RationalImpl t = simplify( n, d );                                      // simplify
        r.numerator = n / t;
        r.denominator = d / t;
} // rational


// getter for numerator/denominator

forall( otype RationalImpl | arithmetic( RationalImpl ) )
RationalImpl numerator( Rational(RationalImpl) r ) {
        return r.numerator;
} // numerator

forall( otype RationalImpl | arithmetic( RationalImpl ) )
RationalImpl denominator( Rational(RationalImpl) r ) {
        return r.denominator;
} // denominator

forall( otype RationalImpl | arithmetic( RationalImpl ) )
[ RationalImpl, RationalImpl ] ?=?( & [ RationalImpl, RationalImpl ] dest, Rational(RationalImpl) src ) {
        return dest = src.[ numerator, denominator ];
}

// setter for numerator/denominator

forall( otype RationalImpl | arithmetic( RationalImpl ) )
RationalImpl numerator( Rational(RationalImpl) r, RationalImpl n ) {
        RationalImpl prev = r.numerator;
        RationalImpl t = gcd( abs( n ), r.denominator );                // simplify
        r.numerator = n / t;
        r.denominator = r.denominator / t;
        return prev;
} // numerator

forall( otype RationalImpl | arithmetic( RationalImpl ) )
RationalImpl denominator( Rational(RationalImpl) r, RationalImpl d ) {
        RationalImpl prev = r.denominator;
        RationalImpl t = simplify( r.numerator, d );                    // simplify
        r.numerator = r.numerator / t;
        r.denominator = d / t;
        return prev;
} // denominator


// comparison

forall( otype RationalImpl | arithmetic( RationalImpl ) )
int ?==?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
        return l.numerator * r.denominator == l.denominator * r.numerator;
} // ?==?

forall( otype RationalImpl | arithmetic( RationalImpl ) )
int ?!=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
        return ! ( l == r );
} // ?!=?

forall( otype RationalImpl | arithmetic( RationalImpl ) )
int ?<?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
        return l.numerator * r.denominator < l.denominator * r.numerator;
} // ?<?

forall( otype RationalImpl | arithmetic( RationalImpl ) )
int ?<=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
        return l.numerator * r.denominator <= l.denominator * r.numerator;
} // ?<=?

forall( otype RationalImpl | arithmetic( RationalImpl ) )
int ?>?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
        return ! ( l <= r );
} // ?>?

forall( otype RationalImpl | arithmetic( RationalImpl ) )
int ?>=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
        return ! ( l < r );
} // ?>=?


// arithmetic

forall( otype RationalImpl | arithmetic( RationalImpl ) )
Rational(RationalImpl) +?( Rational(RationalImpl) r ) {
        Rational(RationalImpl) t = { r.numerator, r.denominator };
        return t;
} // +?

forall( otype RationalImpl | arithmetic( RationalImpl ) )
Rational(RationalImpl) -?( Rational(RationalImpl) r ) {
        Rational(RationalImpl) t = { -r.numerator, r.denominator };
        return t;
} // -?

forall( otype RationalImpl | arithmetic( RationalImpl ) )
Rational(RationalImpl) ?+?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
        if ( l.denominator == r.denominator ) {                         // special case
                Rational(RationalImpl) t = { l.numerator + r.numerator, l.denominator };
                return t;
        } else {
                Rational(RationalImpl) t = { l.numerator * r.denominator + l.denominator * r.numerator, l.denominator * r.denominator };
                return t;
        } // if
} // ?+?

forall( otype RationalImpl | arithmetic( RationalImpl ) )
Rational(RationalImpl) ?-?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
        if ( l.denominator == r.denominator ) {                         // special case
                Rational(RationalImpl) t = { l.numerator - r.numerator, l.denominator };
                return t;
        } else {
                Rational(RationalImpl) t = { l.numerator * r.denominator - l.denominator * r.numerator, l.denominator * r.denominator };
                return t;
        } // if
} // ?-?

forall( otype RationalImpl | arithmetic( RationalImpl ) )
Rational(RationalImpl) ?*?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
        Rational(RationalImpl) t = { l.numerator * r.numerator, l.denominator * r.denominator };
        return t;
} // ?*?

forall( otype RationalImpl | arithmetic( RationalImpl ) )
Rational(RationalImpl) ?/?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
        if ( r.numerator < (RationalImpl){0} ) {
                r.numerator = -r.numerator;
                r.denominator = -r.denominator;
        } // if
        Rational(RationalImpl) t = { l.numerator * r.denominator, l.denominator * r.numerator };
        return t;
} // ?/?


// conversion

forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); } )
double widen( Rational(RationalImpl) r ) {
        return convert( r.numerator ) / convert( r.denominator );
} // widen

// http://www.ics.uci.edu/~eppstein/numth/frap.c
forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); RationalImpl convert( double ); } )
Rational(RationalImpl) narrow( double f, RationalImpl md ) {
        if ( md <= (RationalImpl){1} ) {                                        // maximum fractional digits too small?
                return (Rational(RationalImpl)){ convert( f ), (RationalImpl){1}}; // truncate fraction
        } // if

        // continued fraction coefficients
        RationalImpl m00 = {1}, m11 = { 1 }, m01 = { 0 }, m10 = { 0 };
        RationalImpl ai, t;

        // find terms until denom gets too big
        for ( ;; ) {
                ai = convert( f );
          if ( ! (m10 * ai + m11 <= md) ) break;
                t = m00 * ai + m01;
                m01 = m00;
                m00 = t;
                t = m10 * ai + m11;
                m11 = m10;
                m10 = t;
                double temp = convert( ai );
          if ( f == temp ) break;                                                       // prevent division by zero
                f = 1 / (f - temp);
          if ( f > (double)0x7FFFFFFF ) break;                          // representation failure
        } // for
        return (Rational(RationalImpl)){ m00, m10 };
} // narrow


// I/O

forall( otype RationalImpl | arithmetic( RationalImpl ) )
forall( dtype istype | istream( istype ) | { istype & ?|?( istype &, RationalImpl & ); } )
istype & ?|?( istype & is, Rational(RationalImpl) & r ) {
        RationalImpl t;
        is | r.numerator | r.denominator;
        t = simplify( r.numerator, r.denominator );
        r.numerator /= t;
        r.denominator /= t;
        return is;
} // ?|?

forall( otype RationalImpl | arithmetic( RationalImpl ) )
forall( dtype ostype | ostream( ostype ) | { ostype & ?|?( ostype &, RationalImpl ); } )
ostype & ?|?( ostype & os, Rational(RationalImpl ) r ) {
        return os | r.numerator | '/' | r.denominator;
} // ?|?

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