Version 5.0 The LEDA User Manual

5.8 The smod kernel of type residual ( residual )
1. Definition
Type residual ::smod is a variant of class residual ::mod that uses a signed representation.
Here numbers modulo p are represented by integral doubles in (−p/2, +p/2). All functions
have the common precondition that p is a prime between 3 and 2 26 . The functions of type
residual :: mod are also provided for class residual :: smod and have the same meaning, so
we do not list them separately here.
#include < LEDA/numbers/residual.h >
2. Operations
double residual :: frac(double a)
3. Creation
returns a + z where z is the unique integer such that
a + z ∈ [−1/2, 1/2)
residual x; creates an instance x of type residual and initializes it with zero.
residual x(long a); creates an instance x of type residual and initializes it with the
value of a.
residual x(int a); creates an instance x of type residual and initializes it with the
value of a.
residual
residual
x(double a);
x(const integer& a);
creates an instance x of type residual and initializes it with the
integral part of x.
creates an instance x of type residual and initializes it with the
value of a.
4. Operations
int
residual :: set maximal bit length(int b, bool with check = do overflow check)
sets the maximal bit size of the representable numbers
to b and returns the previous maximal bit size
int residual :: get maximal bit length( )
returns the maximal bit size of the representable
numbers