include/AD/numeric/z.h

   1 //////////////////////////////////////////////////////////////////////////////
   2 // NOTICE:
   3 //
   4 // ADLib, Prop and their related set of tools and documentation are in the
   5 // public domain.   The author(s) of this software reserve no copyrights on
   6 // the source code and any code generated using the tools.  You are encouraged
   7 // to use ADLib and Prop to develop software, in both academic and commercial
   8 // settings, and are free to incorporate any part of ADLib and Prop into
   9 // your programs.
  10 //
  11 // Although you are under no obligation to do so, we strongly recommend that
  12 // you give away all software developed using our tools.
  13 //
  14 // We also ask that credit be given to us when ADLib and/or Prop are used in
  15 // your programs, and that this notice be preserved intact in all the source
  16 // code.
  17 //
  18 // This software is still under development and we welcome any suggestions
  19 // and help from the users.
  20 //
  21 // Allen Leung
  22 // 1994
  23 //////////////////////////////////////////////////////////////////////////////
  24
  25 #ifndef small_finite_cyclic_group_h
  26 #define small_finite_cyclic_group_h
  27
  28 //
  29 // Class Z<n> is used to simulate module arithmetic
  30 // of a small finite cyclic group.
  31 //
  32
  33 #include <AD/generic/generic.h>  // Generic definitions
  34
  35 template<unsigned int n>
  36    class Z {
  37       unsigned long x;
  38    public:
  39       Z() {}
  40       Z(unsigned long y) : x(y) {}
  41
  42       operator unsigned long () const { return x; }
  43
  44       //
  45       // Operations
  46       //
  47
  48       friend Z operator - (Z a) { return Z<n>(n - a); }
  49       friend Z operator + (Z a, Z b)
  50          {  unsigned long sum = a.x + b.x;
  51             if (sum >= n) sum -= n;
  52             return Z<n>(sum);
  53          }
  54       friend Z operator * (Z a, Z b) { return Z<n>((a.x * b.x) % n); }
  55       friend Z operator - (Z a, Z b) { return Z<n>(a + (-b)); }
  56
  57       void operator += (Z a) { *this = *this + a; }
  58       void operator -= (Z a) { *this = *this - a; }
  59       void operator *= (Z a) { *this = *this * a; }
  60
  61       //
  62       // Of course, division cannot be defined
  63       //
  64
  65       //
  66       // Comparisons
  67       //
  68       friend Bool operator == (const Z a, const Z b) { return a.x == b.x; }
  69       friend Bool operator != (const Z a, const Z b) { return a.x != b.x; }
  70       friend Bool operator >  (const Z a, const Z b) { return a.x > b.x; }
  71       friend Bool operator <  (const Z a, const Z b) { return a.x < b.x; }
  72       friend Bool operator >= (const Z a, const Z b) { return a.x >= b.x; }
  73       friend Bool operator <= (const Z a, const Z b) { return a.x <= b.x; }
  74    };
  75
  76 #endif