source: src/libcfa/rational.c@ 6e300d9

// 
// 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 : Thu Apr 27 17:05:06 2017
// Update Count     : 51
// 

#include "rational"
#include "fstream"
#include "stdlib"
#include "math"                                                                                 // floor


// constants

struct Rational 0 = {0, 1};
struct Rational 1 = {1, 1};


// 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 == 0 ) break;
                a = b;
                b = r;
        } // for
        return b;
} // gcd

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


// constructors

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

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

void ?{}( Rational * r, RationalImpl n, RationalImpl d ) {
        RationalImpl t = simplify( &n, &d );                            // simplify
        r->numerator = n / t;
        r->denominator = d / t;
} // rational


// getter for numerator/denominator

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

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

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

// setter for numerator/denominator

RationalImpl numerator( Rational 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

RationalImpl denominator( Rational 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

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

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

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

int ?<=?( Rational l, Rational r ) {
        return l < r || l == r;
} // ?<=?

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

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


// arithmetic

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

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

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

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

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


// conversion

double widen( Rational r ) {
        return (double)r.numerator / (double)r.denominator;
} // widen

// http://www.ics.uci.edu/~eppstein/numth/frap.c
Rational narrow( double f, RationalImpl md ) {
        if ( md <= 1 ) {                                                                        // maximum fractional digits too small?
                return (Rational){ f, 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 = (RationalImpl)f;
          if ( ! (m10 * ai + m11 <= md) ) break;
                t = m00 * ai + m01;
                m01 = m00;
                m00 = t;
                t = m10 * ai + m11;
                m11 = m10;
                m10 = t;
                t = (double)ai;
          if ( f == t ) break;                                                          // prevent division by zero
                f = 1 / (f - t);
          if ( f > (double)0x7FFFFFFF ) break;                          // representation failure
        } 
        return (Rational){ m00, m10 };
} // narrow


// I/O

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

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

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