Version 5.0 The LEDA User Manual

5.7 The mod kernel of type residual ( residual )
1. Definition
Type residual ::mod provides the basic modular arithmetic modulo primes of maximal size
2 26 . Here numbers modulo the prime p are represented by integral doubles in [0, · · · p − 1].
This type cannot be instantiated, so there are only static functions and no constructors.
The following functions have the common precondition that p is a prime between 2 and
2 26 .
#include < LEDA/numbers/residual.h >
2. Operations
double residual :: reduce of positive(double a, double p)
double residual :: reduce(double a, double p)
double residual :: add(double a, double b, double p)
double residual :: sub(double a, double b, double p)
double residual :: mul(double a, double b, double p)
double residual :: div(double a, double b, double p)
double residual :: negate(double a, double p)
double residual :: inverse(double a, double p)
returns a modulo p for nonnegative integral 0 ≤ a <
2 54
returns a modulo p for any integral a with |a| < 2 54
returns (a + b) mod p where a, b are integral with
|a|, |b| < 2 52
returns (a − b) mod p where a, b are integral with
|a|, |b| < 2 52
returns (a·b) mod p where a, b are integral with |a·b| <
2 53
returns (a · b −1 ) mod p where a, b are integral with
|a| < 2 26 and b ≠ 0 mod p
returns −a mod p for nonnegative a < p
returns the inverse of a modulo p for intergal 0 ≤ a <
p < 2 32