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#ifndef __FIXED_H__
#define __FIXED_H__
#include <stdlib.h>
#include <iostream>
#define _GCC_TEMPLATE_BUG_ 1
template <unsigned int SH> class fixed {
public:
inline fixed ( int i = 0 ) : m_f ( i2f( i ) ) { }
inline fixed ( double d ) : m_f ( d2f( d )) { }
inline fixed ( const fixed &f ) : m_f ( f. m_f ) { }
inline operator bool ( ) const { return m_f != 0; }
inline operator double ( ) const { return f2d( m_f ); }
inline operator float ( ) const { return (float) f2d( m_f ); }
inline operator int ( ) const { return (int) f2i( m_f ); }
inline fixed &operator = ( const fixed &f ) { m_f = f. m_f; return *this; }
inline fixed &operator = ( double d ) { m_f = d2f( d ); return *this; }
inline fixed &operator = ( float f ) { m_f = d2f( f ); return *this; }
inline fixed &operator = ( int i ) { m_f = i2f( i ); return *this; }
inline fixed &operator += ( const fixed &f ) { m_f += f. m_f; return *this; }
inline fixed &operator -= ( const fixed &f ) { m_f -= f. m_f; return *this; }
inline fixed &operator *= ( const fixed &f ) { m_f = mul ( m_f, f. m_f ); return *this; }
inline fixed &operator /= ( const fixed &f ) { m_f = div ( m_f, f. m_f ); return *this; }
inline fixed &operator += ( int i ) { m_f += i2f( i ); return *this; }
inline fixed &operator -= ( int i ) { m_f -= i2f( i ); return *this; }
inline fixed &operator *= ( int i ) { m_f *= i; return *this; }
inline fixed &operator /= ( int i ) { m_f /= i; return *this; }
inline fixed &operator += ( double d ) { m_f += d2f( d ); return *this; }
inline fixed &operator -= ( double d ) { m_f -= d2f( d ); return *this; }
inline fixed &operator *= ( double d ) { m_f = mul ( m_f, d2f( d )); return *this; }
inline fixed &operator /= ( double d ) { m_f = div ( m_f, d2f( d )); return *this; }
inline fixed operator - ( ) const { return fixed ( -m_f, true ); }
inline fixed operator + ( const fixed &f ) const { return fixed ( m_f + f. m_f, true ); }
inline fixed operator - ( const fixed &f ) const { return fixed ( m_f - f. m_f, true ); }
inline fixed operator * ( const fixed &f ) const { return fixed ( mul ( m_f, f. m_f ), true ); }
inline fixed operator / ( const fixed &f ) const { return fixed ( div ( m_f, f. m_f ), true ); }
inline fixed operator + ( double d ) const { return fixed ( m_f + d2f( d ), true ); }
inline fixed operator - ( double d ) const { return fixed ( m_f - d2f( d ), true ); }
inline fixed operator * ( double d ) const { return fixed ( mul ( m_f, d2f( d )), true ); }
inline fixed operator / ( double d ) const { return fixed ( div ( m_f, d2f( d )), true ); }
inline fixed operator + ( int i ) const { return fixed ( m_f + i2f( i ), true ); }
inline fixed operator - ( int i ) const { return fixed ( m_f - i2f( i ), true ); }
inline fixed operator * ( int i ) const { return fixed ( m_f * i, true ); }
inline fixed operator / ( int i ) const { return fixed ( m_f / i, true ); }
inline bool operator < ( const fixed &f ) const { return m_f < f. m_f; }
inline bool operator > ( const fixed &f ) const { return m_f > f. m_f; }
inline bool operator <= ( const fixed &f ) const { return m_f <= f. m_f; }
inline bool operator >= ( const fixed &f ) const { return m_f >= f. m_f; }
inline bool operator == ( const fixed &f ) const { return m_f == f. m_f; }
inline bool operator != ( const fixed &f ) const { return m_f != f. m_f; }
inline bool operator < ( double d ) const { return m_f < d2f( d ); }
inline bool operator > ( double d ) const { return m_f > d2f( d ); }
inline bool operator <= ( double d ) const { return m_f <= d2f( d ); }
inline bool operator >= ( double d ) const { return m_f >= d2f( d ); }
inline bool operator == ( double d ) const { return m_f == d2f( d ); }
inline bool operator != ( double d ) const { return m_f != d2f( d ); }
inline bool operator < ( int i ) const { return m_f < i2f( i ); }
inline bool operator > ( int i ) const { return m_f > i2f( i ); }
inline bool operator <= ( int i ) const { return m_f <= i2f( i ); }
inline bool operator >= ( int i ) const { return m_f >= i2f( i ); }
inline bool operator == ( int i ) const { return m_f == i2f( i ); }
inline bool operator != ( int i ) const { return m_f != i2f( i ); }
#if _GCC_TEMPLATE_BUG_
public:
#else
private:
#endif
typedef int fix_t;
inline static double f2d ( fix_t f ) { return ((double) f ) / ((double) ( 1 << SH )); }
inline static fix_t d2f ( double d ) { return (fix_t) ( d * ((double) ( 1 << SH ))); }
inline static int f2i ( fix_t f ) { return (int) ( f >> SH ); }
inline static fix_t i2f ( int i ) { return (fix_t) ( i << SH ); }
inline static fix_t mul ( fix_t m1, fix_t m2 ) { return (fix_t) ((((long long int) m1 ) * m2 ) >> SH ); }
inline static fix_t div ( fix_t d1, fix_t d2 ) { return (fix_t) ((((long long int) d1 ) << SH ) / d2 ); }
fixed ( fix_t f, bool /*dummy*/ ) : m_f ( f ) { }
//data
fix_t m_f;
// friends:
#if !_GCC_TEMPLATE_BUG_
friend fixed operator + <> ( int i, const fixed &f );
friend fixed operator - <> ( int i, const fixed &f );
friend fixed operator * <> ( int i, const fixed &f );
friend fixed operator / <> ( int i, const fixed &f );
friend fixed operator + <> ( double d, const fixed &f );
friend fixed operator - <> ( double d, const fixed &f );
friend fixed operator * <> ( double d, const fixed &f );
friend fixed &operator / <> ( double d, const fixed<SH> &f );
friend bool operator < <> ( double d, const fixed &f );
friend bool operator > <> ( double d, const fixed &f );
friend bool operator <= <> ( double d, const fixed &f );
friend bool operator >= <> ( double d, const fixed &f );
friend bool operator == <> ( double d, const fixed &f );
friend bool operator != <> ( double d, const fixed &f );
friend bool operator < <> ( int i, const fixed &f );
friend bool operator > <> ( int i, const fixed &f );
friend bool operator <= <> ( int i, const fixed &f );
friend bool operator >= <> ( int i, const fixed &f );
friend bool operator == <> ( int i, const fixed &f );
friend bool operator != <> ( int i, const fixed &f );
friend long int lrint ( const fixed &f );
friend fixed sqrt ( const fixed &f );
friend fixed fabs ( const fixed &f );
#endif
};
template <unsigned int SH> inline fixed<SH> operator + ( int i, const fixed<SH> &f ) { return fixed<SH> ( fixed<SH>::i2f( i ) + f. m_f, true ); }
template <unsigned int SH> inline fixed<SH> operator - ( int i, const fixed<SH> &f ) { return fixed<SH> ( fixed<SH>::i2f( i ) - f. m_f, true ); }
template <unsigned int SH> inline fixed<SH> operator * ( int i, const fixed<SH> &f ) { return fixed<SH> ( i * f. m_f, true ); }
template <unsigned int SH> inline fixed<SH> operator / ( int i, const fixed<SH> &f ) { return fixed<SH> ( fixed<SH>::div ( fixed<SH>::i2f( i ), f. m_f ), true ); }
//template <unsigned int SH> inline fixed<SH> operator / ( int i, const fixed<SH> &f ) { return fixed<SH> ( fixed<SH>::i2f ( i / fixed<SH>::f2i ( f. m_f )), true ); }
template <unsigned int SH> inline fixed<SH> operator + ( double d, const fixed<SH> &f ) { return fixed<SH> ( fixed<SH>::d2f( d ) + f. m_f, true ); }
template <unsigned int SH> inline fixed<SH> operator - ( double d, const fixed<SH> &f ) { return fixed<SH> ( fixed<SH>::d2f( d ) - f. m_f, true ); }
template <unsigned int SH> inline fixed<SH> operator * ( double d, const fixed<SH> &f ) { return fixed<SH> ( fixed<SH>::mul ( fixed<SH>::d2f( d ), f. m_f ), true ); }
template <unsigned int SH> inline fixed<SH> operator / ( double d, const fixed<SH> &f ) { return fixed<SH> ( fixed<SH>::mul ( fixed<SH>::d2f( d ), f. m_f ), true ); }
template <unsigned int SH> inline bool operator < ( double d, const fixed<SH> &f ) { return fixed<SH>::d2f( d ) < f. m_f; }
template <unsigned int SH> inline bool operator > ( double d, const fixed<SH> &f ) { return fixed<SH>::d2f( d ) > f. m_f; }
template <unsigned int SH> inline bool operator <= ( double d, const fixed<SH> &f ) { return fixed<SH>::d2f( d ) <= f. m_f; }
template <unsigned int SH> inline bool operator >= ( double d, const fixed<SH> &f ) { return fixed<SH>::d2f( d ) >= f. m_f; }
template <unsigned int SH> inline bool operator == ( double d, const fixed<SH> &f ) { return fixed<SH>::d2f( d ) == f. m_f; }
template <unsigned int SH> inline bool operator != ( double d, const fixed<SH> &f ) { return fixed<SH>::d2f( d ) != f. m_f; }
template <unsigned int SH> inline bool operator < ( int i, const fixed<SH> &f ) { return fixed<SH>::i2f( i ) < f. m_f; }
template <unsigned int SH> inline bool operator > ( int i, const fixed<SH> &f ) { return fixed<SH>::i2f( i ) > f. m_f; }
template <unsigned int SH> inline bool operator <= ( int i, const fixed<SH> &f ) { return fixed<SH>::i2f( i ) <= f. m_f; }
template <unsigned int SH> inline bool operator >= ( int i, const fixed<SH> &f ) { return fixed<SH>::i2f( i ) >= f. m_f; }
template <unsigned int SH> inline bool operator == ( int i, const fixed<SH> &f ) { return fixed<SH>::i2f( i ) == f. m_f; }
template <unsigned int SH> inline bool operator != ( int i, const fixed<SH> &f ) { return fixed<SH>::i2f( i ) != f. m_f; }
template <unsigned int SH> inline long int lrint ( const fixed<SH> &f )
{
return fixed<SH>::f2i (( f. m_f < 0 ) ? f. m_f - ( 1 << ( SH - 1 )) : f. m_f + ( 1 << ( SH - 1 )));
}
template <unsigned int SH> inline fixed<SH> fabs ( const fixed<SH> &f )
{
return ( f. m_f < 0 ) ? fixed<SH> ( -f. m_f, true ) : f;
}
// roughly from QPE / qmath.h
template <unsigned int SH> inline fixed<SH> sqrt ( const fixed<SH> &f )
{
if ( f. m_f <= 0 )
return fixed<SH> ( 0, true );
typename fixed<SH>::fix_t a0 = 0;
typename fixed<SH>::fix_t a1 = f. m_f; // take value as first approximation
do {
a0 = a1;
a1 = ( a0 + fixed<SH>::div ( f. m_f, a0 )) >> 1;
} while ( abs ( fixed<SH>::div ( a1 - a0, a1 )) > 1 );
return fixed<SH> ( a1, true );
}
#if 0 // no std::ostream needed in OPIE
template <unsigned int SH> inline std::ostream &operator << ( std::ostream &o, const fixed<SH> &f )
{
o << double( f );
return o;
}
#endif
#endif
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