Numerics Namespace Reference

Functions
double	AbsoluteValue (double a)
	Returns the absolute value of the value a. More...
double	___safe_fpt_division (const double f1, const double f2)
	Performs a safe floating point division f1/f2. More...
bool	fpointequals (const double a, const double b, double TOL=1e-9)
	Checks if two floating numbers are "nearly" equal. More...

Function Documentation

double Numerics::___safe_fpt_division ( const double  f1, const double  f2  )

inline

Performs a safe floating point division f1/f2.

Parameters

f1	numerator
f2	denominator

Returns

f1/f2

Precondition

f1 >= 0

f2 >= 0

Postcondition

0 <= f1/f2 <= std::numeric_limits<double>::max( )

Definition at line 37 of file FloatingPointComparisson.hpp.

References max(), and min().

Referenced by fpointequals().

                                 {
                                        #ifdef ASSERT_ON
                                         assert( f1 >= static_cast< double >( 0 ) );
                                         assert( f2 >= static_cast< double >( 0 ) );
                                        #endif

                                         /* Avoid overflow */
                                         if( f2 < static_cast< double >( 1 ) && f1 > f2*std::numeric_limits< double >::max( ) )
                                                 return std::numeric_limits<double>::max( );


                                         /* Avoid underflow */
                                         if( f1 == static_cast< double >( 0 ) ||
                                         f2 > static_cast< double >( 1 ) && f1 < f2*std::numeric_limits< double >::min( ) )
                                                 return static_cast< double >( 0 );

                                         return( f1/f2 );
                                 }

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double Numerics::AbsoluteValue ( double  a )

inline

Returns the absolute value of the value a.

Parameters

a	the value whose absolute value is queried

Returns

abs the absolute value of a abs( a ).

Postcondition

abs > 0

Definition at line 23 of file FloatingPointComparisson.hpp.

Referenced by fpointequals().

                         {
                                 return( ( ( a < static_cast< double >( 0 ) )? -a : a ) );
                         }

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bool Numerics::fpointequals ( const double  a, const double  b, double  TOL = 1e-9  )

inline

Checks if two floating numbers are "nearly" equal.

Parameters

a	first floating number to check
b	second floating number to check

Returns

s true if a =~ b, else false.

Note

This implementation is based on Knuth, The Art of Computer Programming (vol II).

Definition at line 64 of file FloatingPointComparisson.hpp.

References ___safe_fpt_division(), AbsoluteValue(), and GeoPrim::TOL.

Referenced by BoundingBox::hasPoint().

                                 {
                                         double diff      = a-b;
                                         double adiff     = AbsoluteValue( diff );
                                         double d1                = ___safe_fpt_division( adiff, AbsoluteValue( a ) );
                                         double d2                = ___safe_fpt_division( adiff, AbsoluteValue( b ) );
                                         bool predicate1  = (d1 <= TOL);
                                         bool predicate2  = (d2 <= TOL);

                                         if( (predicate1 || predicate2) )
                                                 return true;
                                         return false;
                                 }

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