Version 5.0 The LEDA User Manual

interval
x(const bigfloat& a);
creates an instance x of type interval and initializes it with the
smallest possible interval containing a
interval
x(const real& a);
creates an instance x of type interval and initializes it with the
smallest possible interval containing a
interval
x(const rational& a);
creates an instance x of type interval and initializes it with the
smallest possible interval containing a
2. Operations
The arithmetic operations +, −, ∗, /, sqrt, +=, −=, ∗=, /= and the stream operators are
all available. Important: If the advanced implementation interval round outside is
used, the user has to guarantee that for each interval operation the IEEE754 rounding
mode ”towards +∞” is active. This can be achieved by calling the function
fpu :: round up( ). To avoid side effects with library functions that require the default
IEEE754 rounding mode to nearest, the function fpu :: round nearest( ) can be used to
reset the rounding mode.
double x.to double( ) returns the midpoint of the interval x as an approximation
for the exact real number represented by x.
double x.get double error( ) returns the diameter of the interval x which is the
maximal error of the approximation x.to double( )
of the exact real number represented by x.
bool x.is a point( ) returns true if and only if the interval x consists of
a single point.
bool x.is finite( ) returns true if and only if the interval x is a finite
interval.
bool x.contains(double x) returns true if and only if the interval x contains the
number x
double x.upper bound( ) returns the upper bound of the interval x.
double x.lower bound( ) returns the lower bound of the interval x.
void x.set range(VOLATILE I double x, VOLATILE I double y)
sets the current interval to [x, y].