mpr_complex.h

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#ifndef MPR_COMPLEX_H
#define MPR_COMPLEX_H
/****************************************
*  Computer Algebra System SINGULAR     *
****************************************/
 
/*
* ABSTRACT - multipolynomial resultants - real floating-point numbers using gmp
*            and complex numbers based on pairs of real floating-point numbers
*
*/
 
//-> include & define stuff
// must have gmp version >= 2
#include "coeffs/si_gmp.h"
#include "coeffs/mpr_global.h"
 
#define ZTOF 1
#define QTOF 2
#define RTOF 3
#define CTOF 4
 
void setGMPFloatDigits( size_t digits, size_t rest );
 
//-> class gmp_float
/**
 * @short wrapper class for GNU Multi Precision Floats
 */
class gmp_float;
char *floatToStr( const gmp_float & r, const unsigned int oprec );
class gmp_float
{
public:
  gmp_float( const int v = 0 )
  {
    mpf_init_set_si( t, (long)v );
  }
  gmp_float( const long v )
  {
    mpf_init_set_si( t, v );
  }
  gmp_float( const mprfloat v ) // double
  {
    mpf_init_set_d( t, v );
  }
  gmp_float( const mpf_t v )
  {
    mpf_init_set( t, v );
  }
  gmp_float( const mpz_t v ) // gnu mp Z
  {
    mpf_init( t );
    mpf_set_z( t, v );
  }
  gmp_float( const gmp_float & v ) // copy constructor
  {
    mpf_init_set( t, v.t );
  }
 
  ~gmp_float()
  {
    mpf_clear( t );
  }
 
  inline gmp_float & operator = ( const gmp_float & a )
  {
    mpf_set( t, a.t );
    return *this;
  };
  inline gmp_float & operator = ( const mpz_t & a )
  {
    mpf_set_z( t, a );
    return *this;
  };
  inline gmp_float & operator = ( const mprfloat a )
  {
    mpf_set_d( t, (double) a );
    return *this;
  };
  inline gmp_float & operator = ( const long a )
  {
    mpf_set_d( t, (double) a );
    return *this;
  };
 
  gmp_float & operator += ( const gmp_float & a );
  gmp_float & operator -= ( const gmp_float & a );
  inline gmp_float & operator *= ( const gmp_float & a )
  {
    mpf_mul( t, t, a.t );
    return *this;
  };
 
  inline gmp_float & operator /= ( const gmp_float & a )
  {
    mpf_div( t, t, a.t );
    return *this;
  };
 
  inline gmp_float & neg ( ) { mpf_neg(t,t); return *this; };
 
  friend gmp_float operator + ( const gmp_float & a, const gmp_float & b );
  friend gmp_float operator - ( const gmp_float & a, const gmp_float & b );
  friend gmp_float operator * ( const gmp_float & a, const gmp_float & b );
  friend gmp_float operator / ( const gmp_float & a, const gmp_float & b );
 
  inline gmp_float operator ^ ( const int exp ) const
  {
    mpf_t b;
    mpf_init(b);
    mpf_pow_ui( b, this->t, (unsigned long)exp );
    return gmp_float(b);
  };
 
  friend bool operator == ( const gmp_float & a, const gmp_float & b );
  friend bool operator  > ( const gmp_float & a, const gmp_float & b );
  friend bool operator  < ( const gmp_float & a, const gmp_float & b );
  friend bool operator >= ( const gmp_float & a, const gmp_float & b );
  friend bool operator <= ( const gmp_float & a, const gmp_float & b );
 
  friend gmp_float operator - ( const gmp_float & a );
 
  inline int sign()    // t>0:+1, t==0:0, t<0:-1
  { return mpf_sgn( t ); };
 
  bool isZero() const;  // t == 0 ?
  bool isOne() const;   // t == 1 ?
  bool isMOne() const;  // t == -1 ?
 
  void setFromStr(const char * in );
 
  // access
  inline const mpf_t *mpfp() const { return &t; };
  inline mpf_t *_mpfp() { return &t; };
 
  inline operator double() { return mpf_get_d( t ); };
  inline operator double() const { return mpf_get_d( t ); };
 
#if 0
  inline operator int() { return (int)mpf_get_d( t ); };
  inline operator int() const { return (int)mpf_get_d( t ); };
//#else
  inline operator int() const
  { if (mpf_fits_sint_p(t))
    { return (int)mpf_get_si( t ); }
    return 0;
  };
#endif
 
public:
  mpf_t t;
};
 
 
// built-in functions of GMP
gmp_float abs( const gmp_float & );
gmp_float sqrt( const gmp_float & );
gmp_float hypot( const gmp_float &, const gmp_float & );
//gmp_float pow( const gmp_float &, int & );
 
// simulated functions using double functions
gmp_float sin( const gmp_float & );
gmp_float cos( const gmp_float & );
gmp_float log( const gmp_float & );
gmp_float exp( const gmp_float & );
 
gmp_float max( const gmp_float &, const gmp_float & );
 
gmp_float numberToFloat( number num, const coeffs src );
gmp_float numberFieldToFloat( number num, int src );
//char *floatToStr( const gmp_float & r, const unsigned int oprec );
//<-
 
//-> class gmp_complex
/**
 * @short gmp_complex numbers based on
 */
class gmp_complex
{
private:
  gmp_float r, i;
 
public:
  gmp_complex( const gmp_float re= 0.0, const gmp_float im= 0.0 )
  {
    r= re;
    i= im;
  }
  gmp_complex( const mprfloat re, const mprfloat im = 0.0 )
  {
    r= re;
    i= im;
  }
  gmp_complex( const long re, const long im )
  {
    r= re;
    i= im;
  }
  gmp_complex( const gmp_complex & v )
  {
    r= v.r;
    i= v.i;
  }
  ~gmp_complex() {}
 
  gmp_complex & neg ( );
 
  friend gmp_complex operator + ( const gmp_complex & a, const gmp_complex & b );
  friend gmp_complex operator - ( const gmp_complex & a, const gmp_complex & b );
  friend gmp_complex operator * ( const gmp_complex & a, const gmp_complex & b );
  friend gmp_complex operator / ( const gmp_complex & a, const gmp_complex & b );
 
  // gmp_complex <operator> real
  inline friend gmp_complex operator + ( const gmp_complex & a, const gmp_float b_d );
  inline friend gmp_complex operator - ( const gmp_complex & a, const gmp_float b_d );
  inline friend gmp_complex operator * ( const gmp_complex & a, const gmp_float b_d );
  inline friend gmp_complex operator / ( const gmp_complex & a, const gmp_float b_d );
 
  gmp_complex & operator += ( const gmp_complex & a );
  gmp_complex & operator -= ( const gmp_complex & a );
  gmp_complex & operator *= ( const gmp_complex & a );
  gmp_complex & operator /= ( const gmp_complex & a );
 
  inline friend bool operator == ( const gmp_complex & a, const gmp_complex & b );
  inline friend bool operator  > ( const gmp_complex & a, const gmp_complex & b );
  inline friend bool operator  < ( const gmp_complex & a, const gmp_complex & b );
  inline friend bool operator >= ( const gmp_complex & a, const gmp_complex & b );
  inline friend bool operator <= ( const gmp_complex & a, const gmp_complex & b );
 
  inline gmp_complex & operator = ( const gmp_complex & a );
  inline gmp_complex & operator = ( const gmp_float & f );
 
  // access to real and imaginary part
  inline gmp_float real() const { return r; }
  inline gmp_float imag() const { return i; }
 
  inline void real( gmp_float val ) { r = val; }
  inline void imag( gmp_float val ) { i = val; }
 
 
  inline bool isZero() { return (r.isZero() && i.isZero()); }
  void SmallToZero();
};
 
// <gmp_complex> = <gmp_complex> operator <gmp_float>
//
inline gmp_complex operator + ( const gmp_complex & a, const gmp_float b_d )
{
  return gmp_complex( a.r + b_d, a.i );
}
inline gmp_complex operator - ( const gmp_complex & a, const gmp_float b_d )
{
  return gmp_complex( a.r - b_d, a.i );
}
inline gmp_complex operator * ( const gmp_complex & a, const gmp_float b_d )
{
  return gmp_complex( a.r * b_d, a.i * b_d );
}
inline gmp_complex operator / ( const gmp_complex & a, const gmp_float b_d )
{
  return gmp_complex( a.r / b_d, a.i / b_d );
}
 
// <gmp_complex> == <gmp_complex> ?
inline bool operator == ( const gmp_complex & a, const gmp_complex & b )
{
  return ( b.real() == a.real() ) && ( b.imag() == a.imag() );
}
inline bool operator  > ( const gmp_complex & a, const gmp_complex & b )
{
  return ( a.real() > b.real() );
}
inline bool operator  < ( const gmp_complex & a, const gmp_complex & b )
{
  return ( a.real() < b.real() );
}
inline bool operator >= ( const gmp_complex & a, const gmp_complex & b )
{
  return ( a.real() >= b.real() );
}
inline bool operator <= ( const gmp_complex & a, const gmp_complex & b )
{
  return ( a.real() <= b.real() );
}
 
 
// <gmp_complex> = <gmp_complex>
inline gmp_complex & gmp_complex::operator = ( const gmp_complex & a )
{
  r= a.r;
  i= a.i;
  return *this;
}
 
// <gmp_complex> = <gmp_complex>
inline gmp_complex & gmp_complex::operator = ( const gmp_float & f )
{
  r= f;
  i= (long int)0;
  return *this;
}
 
// Returns absolute value of a gmp_complex number
//
inline gmp_float abs( const gmp_complex & c )
{
  return hypot(c.real(),c.imag());
}
 
gmp_complex sqrt( const gmp_complex & x );
 
inline gmp_complex numberToComplex( number num, const coeffs r )
{
  if (nCoeff_is_long_C(r))
  {
    return *(gmp_complex*)num;
  }
  else
  {
    return gmp_complex( numberToFloat(num, r) );
  }
}
 
char *complexToStr( gmp_complex & c, const  unsigned int oprec, const coeffs src );
//<-
 
bool complexNearZero( gmp_complex * c, int digits );
 
#endif /* MPR_COMPLEX_H */
 
// local Variables: ***
// folded-file: t ***
// compile-command-1: "make installg" ***
// compile-command-2: "make install" ***
// End: ***