Version 5.0 The LEDA User Manual

void
x.set midpoint(VOLATILE I double num, VOLATILE I double error)
sets the current interval to a superset of [num −
error, num + error], i.e., to an interval with midpoint
num and radius error.
bool x.sign is known( ) returns true if and only if all numbers in the interval
x have the same sign
int x.sign( ) returns the sign of all numbers in the interval x if
this sign is unique; aborts with an error message if
x.sign is known( ) gives false
3. Implementation
The types interval round inside and interval round outside represent intervals directly
by (the negative of) its lower bound and its upper bound as doubles. Here all
arithmetic operations require that the IEEE754 rounding mode ”towards +∞” is active.
For type interval round inside this is done inside each operation, and for type
interval round outside the user has to do this manually ”from outside the operations” by
an explicit call of fpu :: round up( ).
The types interval bound absolute and interval bound relative represent intervals by their
double midpoint NUM and diameter ERROR. The interpretation is that NUM is the
numerical approximation of a real number and ERROR is a bound for the absolute,
respectively relative error of NUM .