source: libcfa/src/rational.cfa @ f00b2c2c

//
// 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 : Sat Feb  8 17:56:36 2020
// Update Count     : 187
//

#include "rational.hfa"
#include "fstream.hfa"
#include "stdlib.hfa"

forall( otype RationalImpl | arithmetic( RationalImpl ) ) {
        // 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
        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

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

        // constructors

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

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

        void ?{}( Rational(RationalImpl) & r, RationalImpl n, RationalImpl d ) {
                RationalImpl t = simplify( n, d );                              // simplify
                r.[numerator, denominator] = [n / t, d / t];
        } // rational

        void ?{}( Rational(RationalImpl) & r, zero_t ) {
                r{ (RationalImpl){0}, (RationalImpl){1} };
        } // rational

        void ?{}( Rational(RationalImpl) & r, one_t ) {
                r{ (RationalImpl){1}, (RationalImpl){1} };
        } // rational

        // getter for numerator/denominator

        RationalImpl numerator( Rational(RationalImpl) r ) {
                return r.numerator;
        } // numerator

        RationalImpl denominator( Rational(RationalImpl) r ) {
                return r.denominator;
        } // denominator

        [ RationalImpl, RationalImpl ] ?=?( & [ RationalImpl, RationalImpl ] dest, Rational(RationalImpl) src ) {
                return dest = src.[ numerator, denominator ];
        } // ?=?

        // setter for numerator/denominator

        RationalImpl numerator( Rational(RationalImpl) r, RationalImpl n ) {
                RationalImpl prev = r.numerator;
                RationalImpl t = gcd( abs( n ), r.denominator ); // simplify
                r.[numerator, denominator] = [n / t, r.denominator / t];
                return prev;
        } // numerator

        RationalImpl denominator( Rational(RationalImpl) r, RationalImpl d ) {
                RationalImpl prev = r.denominator;
                RationalImpl t = simplify( r.numerator, d );    // simplify
                r.[numerator, denominator] = [r.numerator / t, d / t];
                return prev;
        } // denominator

        // comparison

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

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

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

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

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

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

        // arithmetic

        Rational(RationalImpl) +?( Rational(RationalImpl) r ) {
                return (Rational(RationalImpl)){ r.numerator, r.denominator };
        } // +?

        Rational(RationalImpl) -?( Rational(RationalImpl) r ) {
                return (Rational(RationalImpl)){ -r.numerator, r.denominator };
        } // -?

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

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

        Rational(RationalImpl) ?*?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
                return (Rational(RationalImpl)){ l.numerator * r.numerator, l.denominator * r.denominator };
        } // ?*?

        Rational(RationalImpl) ?/?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
                if ( r.numerator < (RationalImpl){0} ) {
                        r.[numerator, denominator] = [-r.numerator, -r.denominator];
                } // if
                return (Rational(RationalImpl)){ l.numerator * r.denominator, l.denominator * r.numerator };
        } // ?/?

        // I/O

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

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

                void ?|?( ostype & os, Rational(RationalImpl) r ) {
                        (ostype &)(os | r); ends( os );
                } // ?|?
        } // distribution
} // distribution

forall( otype RationalImpl | arithmetic( RationalImpl ) | { RationalImpl ?\?( RationalImpl, unsigned long ); } )
Rational(RationalImpl) ?\?( Rational(RationalImpl) x, long int y ) {
        if ( y < 0 ) {
                return (Rational(RationalImpl)){ x.denominator \ -y, x.numerator \ -y };
        } else {
                return (Rational(RationalImpl)){ x.numerator \ y, x.denominator \ y };
        } // if
}

// conversion

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

forall( otype RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); RationalImpl convert( double ); } )
Rational(RationalImpl) narrow( double f, RationalImpl md ) {
        // http://www.ics.uci.edu/~eppstein/numth/frap.c
        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

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