Changes in src/libcfa/rational.c [561f730:f621a148]

File:

• src/libcfa/rational.c (modified) (12 diffs)

src/libcfa/rational.c

@@ -10 +10 @@
 // Created On       : Wed Apr  6 17:54:28 2016
 // Last Modified By : Peter A. Buhr
-// Last Modified On : Sun May 14 17:25:19 2017
-// Update Count     : 131
+// Last Modified On : Thu Apr 27 17:05:06 2017
+// Update Count     : 51
 // 
 
@@ -17 +17 @@
 #include "fstream"
 #include "stdlib"
+#include "math"                                                                                 // floor
+
+
+// constants
+
+struct Rational 0 = {0, 1};
+struct Rational 1 = {1, 1};
+
 
 // helper routines
@@ -22 +30 @@
 // 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;
+          if ( r == 0 ) break;
                 a = b;
                 b = r;
@@ -33 +40 @@
 } // gcd
 
-forall ( otype RationalImpl | arithmetic( RationalImpl ) )
-static RationalImpl simplify( RationalImpl * n, RationalImpl * d ) {
-        if ( *d == (RationalImpl){0} ) {
+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 < (RationalImpl){0} ) { *d = -*d; *n = -*n; } // move sign to numerator
+        if ( *d < 0 ) { *d = -*d; *n = -*n; }                           // move sign to numerator
         return gcd( abs( *n ), *d );                                            // simplify
 } // Rationalnumber::simplify
@@ -46 +52 @@
 // constructors
 
-forall ( otype RationalImpl | arithmetic( RationalImpl ) )
-void ?{}( Rational(RationalImpl) * r ) {
-        r{ (RationalImpl){0}, (RationalImpl){1} };
+void ?{}( Rational * r ) {
+        r{ 0, 1 };
 } // rational
 
-forall ( otype RationalImpl | arithmetic( RationalImpl ) )
-void ?{}( Rational(RationalImpl) * r, RationalImpl n ) {
-        r{ n, (RationalImpl){1} };
+void ?{}( Rational * r, RationalImpl n ) {
+        r{ n, 1 };
 } // rational
 
-forall ( otype RationalImpl | arithmetic( RationalImpl ) )
-void ?{}( Rational(RationalImpl) * r, RationalImpl n, RationalImpl d ) {
+void ?{}( Rational * r, RationalImpl n, RationalImpl d ) {
         RationalImpl t = simplify( &n, &d );                            // simplify
         r->numerator = n / t;
@@ -66 +69 @@
 // getter for numerator/denominator
 
-forall ( otype RationalImpl | arithmetic( RationalImpl ) )
-RationalImpl numerator( Rational(RationalImpl) r ) {
+RationalImpl numerator( Rational r ) {
         return r.numerator;
 } // numerator
 
-forall ( otype RationalImpl | arithmetic( RationalImpl ) )
-RationalImpl denominator( Rational(RationalImpl) r ) {
+RationalImpl denominator( Rational r ) {
         return r.denominator;
 } // denominator
 
-forall ( otype RationalImpl | arithmetic( RationalImpl ) )
-[ RationalImpl, RationalImpl ] ?=?( * [ RationalImpl, RationalImpl ] dest, Rational(RationalImpl) src ) {
+[ RationalImpl, RationalImpl ] ?=?( * [ RationalImpl, RationalImpl ] dest, Rational src ) {
         return *dest = src.[ numerator, denominator ];
 }
@@ -83 +83 @@
 // setter for numerator/denominator
 
-forall ( otype RationalImpl | arithmetic( RationalImpl ) )
-RationalImpl numerator( Rational(RationalImpl) r, RationalImpl n ) {
+RationalImpl numerator( Rational r, RationalImpl n ) {
         RationalImpl prev = r.numerator;
         RationalImpl t = gcd( abs( n ), r.denominator );                // simplify
@@ -92 +91 @@
 } // numerator
 
-forall ( otype RationalImpl | arithmetic( RationalImpl ) )
-RationalImpl denominator( Rational(RationalImpl) r, RationalImpl d ) {
+RationalImpl denominator( Rational r, RationalImpl d ) {
         RationalImpl prev = r.denominator;
         RationalImpl t = simplify( &r.numerator, &d );                  // simplify
@@ -104 +102 @@
 // comparison
 
-forall ( otype RationalImpl | arithmetic( RationalImpl ) )
-int ?==?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
+int ?==?( Rational l, Rational r ) {
         return l.numerator * r.denominator == l.denominator * r.numerator;
 } // ?==?
 
-forall ( otype RationalImpl | arithmetic( RationalImpl ) )
-int ?!=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
+int ?!=?( Rational l, Rational r ) {
         return ! ( l == r );
 } // ?!=?
 
-forall ( otype RationalImpl | arithmetic( RationalImpl ) )
-int ?<?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
+int ?<?( Rational l, Rational 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;
+int ?<=?( Rational l, Rational r ) {
+        return l < r || l == r;
 } // ?<=?
 
-forall ( otype RationalImpl | arithmetic( RationalImpl ) )
-int ?>?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
+int ?>?( Rational l, Rational r ) {
         return ! ( l <= r );
 } // ?>?
 
-forall ( otype RationalImpl | arithmetic( RationalImpl ) )
-int ?>=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
+int ?>=?( Rational l, Rational r ) {
         return ! ( l < r );
 } // ?>=?
@@ -137 +129 @@
 // 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 };
+Rational -?( Rational r ) {
+        Rational t = { -r.numerator, r.denominator };
         return t;
 } // -?
 
-forall ( otype RationalImpl | arithmetic( RationalImpl ) )
-Rational(RationalImpl) ?+?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
+Rational ?+?( Rational l, Rational r ) {
         if ( l.denominator == r.denominator ) {                         // special case
-                Rational(RationalImpl) t = { l.numerator + r.numerator, l.denominator };
+                Rational 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 };
+                Rational 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 ?-?( Rational l, Rational r ) {
         if ( l.denominator == r.denominator ) {                         // special case
-                Rational(RationalImpl) t = { l.numerator - r.numerator, l.denominator };
+                Rational 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 };
+                Rational 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 };
+Rational ?*?( Rational l, Rational r ) {
+        Rational 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} ) {
+Rational ?/?( Rational l, Rational r ) {
+        if ( r.numerator < 0 ) {
                 r.numerator = -r.numerator;
                 r.denominator = -r.denominator;
         } // if
-        Rational(RationalImpl) t = { l.numerator * r.denominator, l.denominator * r.numerator };
+        Rational t = { l.numerator * r.denominator, l.denominator * r.numerator };
         return t;
 } // ?/?
@@ -190 +171 @@
 // conversion
 
-// forall ( otype RationalImpl | arithmetic( RationalImpl ) )
-// double widen( Rational(RationalImpl) r ) {
-//      return (double)r.numerator / (double)r.denominator;
-// } // widen
-
-// // http://www.ics.uci.edu/~eppstein/numth/frap.c
-// forall ( otype RationalImpl | arithmetic( RationalImpl ) )
-// Rational(RationalImpl) narrow( double f, RationalImpl md ) {
-//      if ( md <= 1 ) {                                                                        // maximum fractional digits too small?
-//              return (Rational(RationalImpl)){ 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 - (double)t);
-//        if ( f > (double)0x7FFFFFFF ) break;                          // representation failure
-//      } 
-//      return (Rational(RationalImpl)){ m00, m10 };
-// } // narrow
+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 ( otype RationalImpl | arithmetic( RationalImpl ) )
-forall( dtype istype | istream( istype ) | { istype * ?|?( istype *, RationalImpl * ); } )
-istype * ?|?( istype * is, Rational(RationalImpl) * r ) {
+forall( dtype istype | istream( istype ) )
+istype * ?|?( istype *is, Rational *r ) {
         RationalImpl t;
         is | &(r->numerator) | &(r->denominator);
@@ -238 +216 @@
 } // ?|?
 
-forall ( otype RationalImpl | arithmetic( RationalImpl ) )
-forall( dtype ostype | ostream( ostype ) | { ostype * ?|?( ostype *, RationalImpl ); } )
-ostype * ?|?( ostype * os, Rational(RationalImpl ) r ) {
+forall( dtype ostype | ostream( ostype ) )
+ostype * ?|?( ostype *os, Rational r ) {
         return os | r.numerator | '/' | r.denominator;
 } // ?|?