include/AD/numeric/gaussint.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 Gaussian_integers_h
  26 #define Gaussian_integers_h
  27
  28 #include <math.h>
  29 #include <iostream.h>
  30 #include <AD/generic/generic.h>  // Generic definitions
  31
  32 struct GaussInt {
  33    int real, imag;
  34
  35    /////////////////////////////////////////////////////////////////////
  36    // Constructor and initializer
  37    /////////////////////////////////////////////////////////////////////
  38    GaussInt(int x = 0, int y = 0) : real(x), imag(y) {}
  39    GaussInt(GaussInt& c) : real(c.real), imag(c.imag) {}
  40
  41    /////////////////////////////////////////////////////////////////////
  42    // In place arithmetic
  43    /////////////////////////////////////////////////////////////////////
  44    void operator += (const GaussInt& c) { real += c.real; imag += c.imag; }
  45    void operator -= (const GaussInt& c) { real -= c.real; imag -= c.imag; }
  46    void operator *= (const GaussInt& c) { *this = *this * c; }
  47    void operator /= (const GaussInt& c) { *this = *this / c; }
  48    void operator += (int r)             { real += r; }
  49    void operator -= (int r)             { real -= r; }
  50    void operator *= (int r)             { real *= r; imag *= r; }
  51    void operator /= (int r)             { real /= r; imag /= r; }
  52
  53    //
  54    // GaussInt arithmetic
  55    //
  56    friend GaussInt operator - (const GaussInt& c)
  57       { return GaussInt(-c.real,-c.imag); }
  58
  59    friend GaussInt operator + (const GaussInt& a, const GaussInt& b)
  60       { return GaussInt(a.real + b.real, a.imag + b.imag); }
  61    friend GaussInt operator + (const GaussInt& a, int b)
  62       { return GaussInt(a.real + b, a.imag); }
  63    friend GaussInt operator + (int a, const GaussInt& b)
  64       { return GaussInt(a + b.real, b.imag); }
  65
  66    friend GaussInt operator - (const GaussInt& a, const GaussInt& b)
  67       { return GaussInt(a.real - b.real, a.imag - b.imag); }
  68    friend GaussInt operator - (const GaussInt& a, int b)
  69       { return GaussInt(a.real - b, a.imag); }
  70    friend GaussInt operator - (int a, const GaussInt& b)
  71       { return GaussInt(a - b.real, -b.imag); }
  72
  73    friend GaussInt operator * (const GaussInt& a, const GaussInt& b)
  74       { return GaussInt(a.real * b.real - a.imag * b.imag,
  75                        a.imag * b.real + a.real * b.imag);
  76       }
  77    friend GaussInt operator * (const GaussInt& a, int b)
  78       { return GaussInt(a.real * b, a.imag * b); }
  79    friend GaussInt operator * (int a, const GaussInt& b)
  80       { return GaussInt(a * b.real, a * b.imag); }
  81
  82    friend GaussInt operator / (const GaussInt& a, const GaussInt& b);
  83    friend GaussInt operator / (const GaussInt& a, int b)
  84       { return GaussInt(a.real / b, a.imag / b); }
  85    friend GaussInt operator / (int a, const GaussInt& b);
  86
  87    //////////////////////////////////////////////////////////////////////
  88    // Comparisons between Gaussian integers and int
  89    //////////////////////////////////////////////////////////////////////
  90    friend Bool operator == (const GaussInt& a, const GaussInt& b)
  91       { return a.real == b.real && a.imag == b.imag; }
  92    friend Bool operator == (const GaussInt& a, int b)
  93       { return a.real == b && a.imag == 0.0; }
  94    friend Bool operator == (int a, const GaussInt& b)
  95       { return a == b.real && b.imag == 0.0; }
  96
  97    friend Bool operator != (const GaussInt& a, const GaussInt& b)
  98       { return a.real != b.real || a.imag != b.imag; }
  99    friend Bool operator != (const GaussInt& a, int b)
 100       { return a.real != b || a.imag != 0.0; }
 101    friend Bool operator != (int a, const GaussInt& b)
 102       { return a != b.real || b.imag != 0.0; }
 103
 104    //////////////////////////////////////////////////////////////////////
 105    // Operations on complex numbers: conjugate, polar, norm and abs.
 106    //////////////////////////////////////////////////////////////////////
 107    GaussInt operator ! () const { return GaussInt(real,-imag); }
 108    friend int norm(const GaussInt& c)
 109       { return c.real * c.real + c.imag * c.imag; }
 110    friend double abs(const GaussInt& c) { return sqrt(norm(c)); }
 111
 112    ////////////////////////////////////////////////////////////////
 113    // Input and output
 114    ////////////////////////////////////////////////////////////////
 115    friend ostream& operator << (ostream&, const GaussInt&);
 116    friend istream& operator >> (istream&, GaussInt&);
 117 };
 118
 119 #endif