Index: libcfa/src/rational.cfa =================================================================== --- libcfa/src/rational.cfa (revision fd54fef231baeeb0016103bf19cc8e6d87287faf) +++ libcfa/src/rational.cfa (revision e3984a684833e16081f5dce5114618aff065a5f0) @@ -10,6 +10,6 @@ // 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 +// Last Modified On : Tue Jul 20 16:30:06 2021 +// Update Count : 193 // @@ -18,13 +18,13 @@ #include "stdlib.hfa" -forall( RationalImpl | arithmetic( RationalImpl ) ) { +forall( T | Arithmetic( T ) ) { // 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 ) { + static T gcd( T a, T b ) { for ( ;; ) { // Euclid's algorithm - RationalImpl r = a % b; - if ( r == (RationalImpl){0} ) break; + T r = a % b; + if ( r == (T){0} ) break; a = b; b = r; @@ -33,9 +33,9 @@ } // gcd - static RationalImpl simplify( RationalImpl & n, RationalImpl & d ) { - if ( d == (RationalImpl){0} ) { + static T simplify( T & n, T & d ) { + if ( d == (T){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 + if ( d < (T){0} ) { d = -d; n = -n; } // move sign to numerator return gcd( abs( n ), d ); // simplify } // Rationalnumber::simplify @@ -43,36 +43,36 @@ // 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 + void ?{}( Rational(T) & r, zero_t ) { + r{ (T){0}, (T){1} }; + } // rational + + void ?{}( Rational(T) & r, one_t ) { + r{ (T){1}, (T){1} }; + } // rational + + void ?{}( Rational(T) & r ) { + r{ (T){0}, (T){1} }; + } // rational + + void ?{}( Rational(T) & r, T n ) { + r{ n, (T){1} }; + } // rational + + void ?{}( Rational(T) & r, T n, T d ) { + T 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 ) { + T numerator( Rational(T) r ) { return r.numerator; } // numerator - RationalImpl denominator( Rational(RationalImpl) r ) { + T denominator( Rational(T) r ) { return r.denominator; } // denominator - [ RationalImpl, RationalImpl ] ?=?( & [ RationalImpl, RationalImpl ] dest, Rational(RationalImpl) src ) { + [ T, T ] ?=?( & [ T, T ] dest, Rational(T) src ) { return dest = src.[ numerator, denominator ]; } // ?=? @@ -80,14 +80,14 @@ // setter for numerator/denominator - RationalImpl numerator( Rational(RationalImpl) r, RationalImpl n ) { - RationalImpl prev = r.numerator; - RationalImpl t = gcd( abs( n ), r.denominator ); // simplify + T numerator( Rational(T) r, T n ) { + T prev = r.numerator; + T 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 + T denominator( Rational(T) r, T d ) { + T prev = r.denominator; + T t = simplify( r.numerator, d ); // simplify r.[numerator, denominator] = [r.numerator / t, d / t]; return prev; @@ -96,25 +96,29 @@ // comparison - int ?==?( Rational(RationalImpl) l, Rational(RationalImpl) r ) { + int ?==?( Rational(T) l, Rational(T) r ) { return l.numerator * r.denominator == l.denominator * r.numerator; } // ?==? - int ?!=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) { + int ?!=?( Rational(T) l, Rational(T) r ) { return ! ( l == r ); } // ?!=? - int ??( Rational(RationalImpl) l, Rational(RationalImpl) r ) { + int ?>?( Rational(T) l, Rational(T) r ) { return ! ( l <= r ); } // ?>? - int ?>=?( Rational(RationalImpl) l, Rational(RationalImpl) r ) { + int ?>=?( Rational(T) l, Rational(T) r ) { return ! ( l < r ); } // ?>=? @@ -122,45 +126,73 @@ // arithmetic - Rational(RationalImpl) +?( Rational(RationalImpl) r ) { - return (Rational(RationalImpl)){ r.numerator, r.denominator }; + Rational(T) +?( Rational(T) r ) { + return (Rational(T)){ r.numerator, r.denominator }; } // +? - Rational(RationalImpl) -?( Rational(RationalImpl) r ) { - return (Rational(RationalImpl)){ -r.numerator, r.denominator }; + Rational(T) -?( Rational(T) r ) { + return (Rational(T)){ -r.numerator, r.denominator }; } // -? - Rational(RationalImpl) ?+?( Rational(RationalImpl) l, Rational(RationalImpl) r ) { + Rational(T) ?+?( Rational(T) l, Rational(T) r ) { if ( l.denominator == r.denominator ) { // special case - return (Rational(RationalImpl)){ l.numerator + r.numerator, l.denominator }; + return (Rational(T)){ l.numerator + r.numerator, l.denominator }; } else { - return (Rational(RationalImpl)){ l.numerator * r.denominator + l.denominator * r.numerator, l.denominator * r.denominator }; + return (Rational(T)){ l.numerator * r.denominator + l.denominator * r.numerator, l.denominator * r.denominator }; } // if } // ?+? - Rational(RationalImpl) ?-?( Rational(RationalImpl) l, Rational(RationalImpl) r ) { + Rational(T) ?+=?( Rational(T) & l, Rational(T) r ) { + l = l + r; + return l; + } // ?+? + + Rational(T) ?+=?( Rational(T) & l, one_t ) { + l = l + (Rational(T)){ 1 }; + return l; + } // ?+? + + Rational(T) ?-?( Rational(T) l, Rational(T) r ) { if ( l.denominator == r.denominator ) { // special case - return (Rational(RationalImpl)){ l.numerator - r.numerator, l.denominator }; + return (Rational(T)){ l.numerator - r.numerator, l.denominator }; } else { - return (Rational(RationalImpl)){ l.numerator * r.denominator - l.denominator * r.numerator, l.denominator * r.denominator }; + return (Rational(T)){ 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(T) ?-=?( Rational(T) & l, Rational(T) r ) { + l = l - r; + return l; + } // ?-? + + Rational(T) ?-=?( Rational(T) & l, one_t ) { + l = l - (Rational(T)){ 1 }; + return l; + } // ?-? + + Rational(T) ?*?( Rational(T) l, Rational(T) r ) { + return (Rational(T)){ l.numerator * r.numerator, l.denominator * r.denominator }; } // ?*? - Rational(RationalImpl) ?/?( Rational(RationalImpl) l, Rational(RationalImpl) r ) { - if ( r.numerator < (RationalImpl){0} ) { + Rational(T) ?*=?( Rational(T) & l, Rational(T) r ) { + return l = l * r; + } // ?*? + + Rational(T) ?/?( Rational(T) l, Rational(T) r ) { + if ( r.numerator < (T){0} ) { r.[numerator, denominator] = [-r.numerator, -r.denominator]; } // if - return (Rational(RationalImpl)){ l.numerator * r.denominator, l.denominator * r.numerator }; + return (Rational(T)){ l.numerator * r.denominator, l.denominator * r.numerator }; } // ?/? + Rational(T) ?/=?( Rational(T) & l, Rational(T) r ) { + return l = l / r; + } // ?/? + // I/O - forall( istype & | istream( istype ) | { istype & ?|?( istype &, RationalImpl & ); } ) - istype & ?|?( istype & is, Rational(RationalImpl) & r ) { + forall( istype & | istream( istype ) | { istype & ?|?( istype &, T & ); } ) + istype & ?|?( istype & is, Rational(T) & r ) { is | r.numerator | r.denominator; - RationalImpl t = simplify( r.numerator, r.denominator ); + T t = simplify( r.numerator, r.denominator ); r.numerator /= t; r.denominator /= t; @@ -168,10 +200,10 @@ } // ?|? - forall( ostype & | ostream( ostype ) | { ostype & ?|?( ostype &, RationalImpl ); } ) { - ostype & ?|?( ostype & os, Rational(RationalImpl) r ) { + forall( ostype & | ostream( ostype ) | { ostype & ?|?( ostype &, T ); } ) { + ostype & ?|?( ostype & os, Rational(T) r ) { return os | r.numerator | '/' | r.denominator; } // ?|? - void ?|?( ostype & os, Rational(RationalImpl) r ) { + void ?|?( ostype & os, Rational(T) r ) { (ostype &)(os | r); ends( os ); } // ?|? @@ -179,30 +211,35 @@ } // distribution -forall( 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 -} +forall( T | Arithmetic( T ) | { T ?\?( T, unsigned long ); } ) { + Rational(T) ?\?( Rational(T) x, long int y ) { + if ( y < 0 ) { + return (Rational(T)){ x.denominator \ -y, x.numerator \ -y }; + } else { + return (Rational(T)){ x.numerator \ y, x.denominator \ y }; + } // if + } // ?\? + + Rational(T) ?\=?( Rational(T) & x, long int y ) { + return x = x \ y; + } // ?\? +} // distribution // conversion -forall( RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); } ) -double widen( Rational(RationalImpl) r ) { +forall( T | Arithmetic( T ) | { double convert( T ); } ) +double widen( Rational(T) r ) { return convert( r.numerator ) / convert( r.denominator ); } // widen -forall( RationalImpl | arithmetic( RationalImpl ) | { double convert( RationalImpl ); RationalImpl convert( double ); } ) -Rational(RationalImpl) narrow( double f, RationalImpl md ) { +forall( T | Arithmetic( T ) | { double convert( T ); T convert( double ); } ) +Rational(T) narrow( double f, T 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 ( md <= (T){1} ) { // maximum fractional digits too small? + return (Rational(T)){ convert( f ), (T){1}}; // truncate fraction } // if // continued fraction coefficients - RationalImpl m00 = {1}, m11 = { 1 }, m01 = { 0 }, m10 = { 0 }; - RationalImpl ai, t; + T m00 = {1}, m11 = { 1 }, m01 = { 0 }, m10 = { 0 }; + T ai, t; // find terms until denom gets too big @@ -221,5 +258,5 @@ if ( f > (double)0x7FFFFFFF ) break; // representation failure } // for - return (Rational(RationalImpl)){ m00, m10 }; + return (Rational(T)){ m00, m10 }; } // narrow