Index: src/libcfa/rational
===================================================================
--- src/libcfa/rational	(revision 4c8f86b379d36b8c8ac77b52c65369e65169bb3e)
+++ src/libcfa/rational	(revision 561f7308676f4263e3d2c5d41e9c1cf1d336fd5f)
@@ -12,6 +12,6 @@
 // Created On       : Wed Apr  6 17:56:25 2016
 // Last Modified By : Peter A. Buhr
-// Last Modified On : Mon May  1 08:25:06 2017
-// Update Count     : 33
+// Last Modified On : Sun May 14 16:49:13 2017
+// Update Count     : 78
 //
 
@@ -21,49 +21,124 @@
 #include "iostream"
 
+trait scalar( otype T ) {
+};
+
+trait arithmetic( otype T | scalar( T ) ) {
+	int !?( T );
+	int ?==?( T, T );
+	int ?!=?( T, T );
+	int ?<?( T, T );
+	int ?<=?( T, T );
+	int ?>?( T, T );
+	int ?>=?( T, T );
+	void ?{}( T *, zero_t );
+	void ?{}( T *, one_t );
+	T +?( T );
+	T -?( T );
+	T ?+?( T, T );
+	T ?-?( T, T );
+	T ?*?( T, T );
+	T ?/?( T, T );
+	T ?%?( T, T );
+	T ?/=?( T *, T );
+	T abs( T );
+};
+
 // implementation
-typedef long int RationalImpl;
+
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
 struct Rational {
-	RationalImpl numerator, denominator;					// invariant: denominator > 0
+	RationalImpl numerator, denominator;				// invariant: denominator > 0
 }; // Rational
 
-// constants
-extern struct Rational 0;
-extern struct Rational 1;
+// constructors
 
-// constructors
-void ?{}( Rational * r );
-void ?{}( Rational * r, RationalImpl n );
-void ?{}( Rational * r, RationalImpl n, RationalImpl d );
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+void ?{}( Rational(RationalImpl) * r );
+
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+void ?{}( Rational(RationalImpl) * r, RationalImpl n );
+
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+void ?{}( Rational(RationalImpl) * r, RationalImpl n, RationalImpl d );
+
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+void ?{}( Rational(RationalImpl) * r, zero_t );
+
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+void ?{}( Rational(RationalImpl) * r, one_t );
 
 // getter for numerator/denominator
-RationalImpl numerator( Rational r );
-RationalImpl denominator( Rational r );
-[ RationalImpl, RationalImpl ] ?=?( * [ RationalImpl, RationalImpl ] dest, Rational src );
+
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+RationalImpl numerator( Rational(RationalImpl) r );
+
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+RationalImpl denominator( Rational(RationalImpl) r );
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+[ RationalImpl, RationalImpl ] ?=?( * [ RationalImpl, RationalImpl ] dest, Rational(RationalImpl) src );
+
 // setter for numerator/denominator
-RationalImpl numerator( Rational r, RationalImpl n );
-RationalImpl denominator( Rational r, RationalImpl d );
+
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+RationalImpl numerator( Rational(RationalImpl) r, RationalImpl n );
+
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+RationalImpl denominator( Rational(RationalImpl) r, RationalImpl d );
 
 // comparison
-int ?==?( Rational l, Rational r );
-int ?!=?( Rational l, Rational r );
-int ?<?( Rational l, Rational r );
-int ?<=?( Rational l, Rational r );
-int ?>?( Rational l, Rational r );
-int ?>=?( Rational l, Rational r );
+
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+int ?==?( Rational(RationalImpl) l, Rational(RationalImpl) r );
+
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+int ?!=?( Rational(RationalImpl) l, Rational(RationalImpl) r );
+
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+int ?<?( Rational(RationalImpl) l, Rational(RationalImpl) r );
+
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+int ?<=?( Rational(RationalImpl) l, Rational(RationalImpl) r );
+
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+int ?>?( Rational(RationalImpl) l, Rational(RationalImpl) r );
+
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+int ?>=?( Rational(RationalImpl) l, Rational(RationalImpl) r );
 
 // arithmetic
-Rational -?( Rational r );
-Rational ?+?( Rational l, Rational r );
-Rational ?-?( Rational l, Rational r );
-Rational ?*?( Rational l, Rational r );
-Rational ?/?( Rational l, Rational r );
+
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+Rational(RationalImpl) +?( Rational(RationalImpl) r );
+
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+Rational(RationalImpl) -?( Rational(RationalImpl) r );
+
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+Rational(RationalImpl) ?+?( Rational(RationalImpl) l, Rational(RationalImpl) r );
+
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+Rational(RationalImpl) ?-?( Rational(RationalImpl) l, Rational(RationalImpl) r );
+
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+Rational(RationalImpl) ?*?( Rational(RationalImpl) l, Rational(RationalImpl) r );
+
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+Rational(RationalImpl) ?/?( Rational(RationalImpl) l, Rational(RationalImpl) r );
 
 // conversion
-double widen( Rational r );
-Rational narrow( double f, RationalImpl md );
+// forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+// double widen( Rational(RationalImpl) r );
+// forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+// Rational(RationalImpl) narrow( double f, RationalImpl md );
 
 // I/O
-forall( dtype istype | istream( istype ) ) istype * ?|?( istype *, Rational * );
-forall( dtype ostype | ostream( ostype ) ) ostype * ?|?( ostype *, Rational );
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+forall( dtype istype | istream( istype ) | { istype * ?|?( istype *, RationalImpl * ); } )
+istype * ?|?( istype *, Rational(RationalImpl) * );
+
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+forall( dtype ostype | ostream( ostype ) | { ostype * ?|?( ostype *, RationalImpl ); } )
+ostype * ?|?( ostype *, Rational(RationalImpl ) );
 
 #endif // RATIONAL_H
Index: src/libcfa/rational.c
===================================================================
--- src/libcfa/rational.c	(revision 4c8f86b379d36b8c8ac77b52c65369e65169bb3e)
+++ src/libcfa/rational.c	(revision 561f7308676f4263e3d2c5d41e9c1cf1d336fd5f)
@@ -10,6 +10,6 @@
 // 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
+// Last Modified On : Sun May 14 17:25:19 2017
+// Update Count     : 131
 // 
 
@@ -17,12 +17,4 @@
 #include "fstream"
 #include "stdlib"
-#include "math"											// floor
-
-
-// constants
-
-struct Rational 0 = {0, 1};
-struct Rational 1 = {1, 1};
-
 
 // helper routines
@@ -30,8 +22,9 @@
 // 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 == 0 ) break;
+	  if ( r == (RationalImpl){0} ) break;
 		a = b;
 		b = r;
@@ -40,10 +33,11 @@
 } // gcd
 
-static RationalImpl simplify( RationalImpl *n, RationalImpl *d ) {
-	if ( *d == 0 ) {
+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 < 0 ) { *d = -*d; *n = -*n; }				// move sign to numerator
+	if ( *d < (RationalImpl){0} ) { *d = -*d; *n = -*n; } // move sign to numerator
 	return gcd( abs( *n ), *d );						// simplify
 } // Rationalnumber::simplify
@@ -52,13 +46,16 @@
 // constructors
 
-void ?{}( Rational * r ) {
-	r{ 0, 1 };
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+void ?{}( Rational(RationalImpl) * r ) {
+	r{ (RationalImpl){0}, (RationalImpl){1} };
 } // rational
 
-void ?{}( Rational * r, RationalImpl n ) {
-	r{ n, 1 };
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+void ?{}( Rational(RationalImpl) * r, RationalImpl n ) {
+	r{ n, (RationalImpl){1} };
 } // rational
 
-void ?{}( Rational * r, RationalImpl n, RationalImpl d ) {
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+void ?{}( Rational(RationalImpl) * r, RationalImpl n, RationalImpl d ) {
 	RationalImpl t = simplify( &n, &d );				// simplify
 	r->numerator = n / t;
@@ -69,13 +66,16 @@
 // getter for numerator/denominator
 
-RationalImpl numerator( Rational r ) {
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+RationalImpl numerator( Rational(RationalImpl) r ) {
 	return r.numerator;
 } // numerator
 
-RationalImpl denominator( Rational r ) {
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+RationalImpl denominator( Rational(RationalImpl) r ) {
 	return r.denominator;
 } // denominator
 
-[ RationalImpl, RationalImpl ] ?=?( * [ RationalImpl, RationalImpl ] dest, Rational src ) {
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+[ RationalImpl, RationalImpl ] ?=?( * [ RationalImpl, RationalImpl ] dest, Rational(RationalImpl) src ) {
 	return *dest = src.[ numerator, denominator ];
 }
@@ -83,5 +83,6 @@
 // setter for numerator/denominator
 
-RationalImpl numerator( Rational r, RationalImpl n ) {
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+RationalImpl numerator( Rational(RationalImpl) r, RationalImpl n ) {
 	RationalImpl prev = r.numerator;
 	RationalImpl t = gcd( abs( n ), r.denominator );		// simplify
@@ -91,5 +92,6 @@
 } // numerator
 
-RationalImpl denominator( Rational r, RationalImpl d ) {
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+RationalImpl denominator( Rational(RationalImpl) r, RationalImpl d ) {
 	RationalImpl prev = r.denominator;
 	RationalImpl t = simplify( &r.numerator, &d );			// simplify
@@ -102,25 +104,31 @@
 // comparison
 
-int ?==?( Rational l, Rational r ) {
+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 ) {
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+int ?!=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
 	return ! ( l == r );
 } // ?!=?
 
-int ?<?( Rational l, Rational r ) {
+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 ) {
+	return l.numerator * r.denominator <= l.denominator * r.numerator;
 } // ?<=?
 
-int ?>?( Rational l, Rational r ) {
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+int ?>?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
 	return ! ( l <= r );
 } // ?>?
 
-int ?>=?( Rational l, Rational r ) {
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+int ?>=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
 	return ! ( l < r );
 } // ?>=?
@@ -129,40 +137,51 @@
 // arithmetic
 
-Rational -?( Rational r ) {
-	Rational t = { -r.numerator, r.denominator };
+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;
 } // -?
 
-Rational ?+?( Rational l, Rational r ) {
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+Rational(RationalImpl) ?+?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
 	if ( l.denominator == r.denominator ) {				// special case
-		Rational t = { l.numerator + r.numerator, l.denominator };
+		Rational(RationalImpl) t = { l.numerator + r.numerator, l.denominator };
 		return t;
 	} else {
-		Rational t = { l.numerator * r.denominator + l.denominator * r.numerator, l.denominator * r.denominator };
+		Rational(RationalImpl) t = { l.numerator * r.denominator + l.denominator * r.numerator, l.denominator * r.denominator };
 		return t;
 	} // if
 } // ?+?
 
-Rational ?-?( Rational l, Rational r ) {
+forall ( otype RationalImpl | arithmetic( RationalImpl ) )
+Rational(RationalImpl) ?-?( Rational(RationalImpl) l, Rational(RationalImpl) r ) {
 	if ( l.denominator == r.denominator ) {				// special case
-		Rational t = { l.numerator - r.numerator, l.denominator };
+		Rational(RationalImpl) t = { l.numerator - r.numerator, l.denominator };
 		return t;
 	} else {
-		Rational t = { l.numerator * r.denominator - l.denominator * r.numerator, l.denominator * r.denominator };
+		Rational(RationalImpl) 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 };
+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;
 } // ?*?
 
-Rational ?/?( Rational l, Rational r ) {
-	if ( r.numerator < 0 ) {
+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 t = { l.numerator * r.denominator, l.denominator * r.numerator };
+	Rational(RationalImpl) t = { l.numerator * r.denominator, l.denominator * r.numerator };
 	return t;
 } // ?/?
@@ -171,41 +190,44 @@
 // 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
+// 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
 
 
 // I/O
 
-forall( dtype istype | istream( istype ) )
-istype * ?|?( istype *is, Rational *r ) {
+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);
@@ -216,6 +238,7 @@
 } // ?|?
 
-forall( dtype ostype | ostream( ostype ) )
-ostype * ?|?( ostype *os, Rational r ) {
+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;
 } // ?|?