The mod kernel of type residual ( residual )

Definition

Type residual::mod provides the basic modular arithmetic modulo primes of maximal size 2²⁶. 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 2²⁶.

#include < LEDA/numbers/residual.h >

Operations

double	residual::reduce_of_positive(double a, double p)
		returns a modulo p for nonnegative integral 0 < = a < 254

double	residual::reduce(double a, double p)
		returns a modulo p for any integral a with |a|< 254
double	residual::add(double a, double b, double p)
		returns (a + b)modp where a, b are integral with |a|,|b|< 252
double	residual::sub(double a, double b, double p)
		returns (a - b)modp where a, b are integral with |a|,|b|< 252
double	residual::mul(double a, double b, double p)
		returns (a*b)modp where a, b are integral with |a*b|< 253
double	residual::div(double a, double b, double p)
		returns (a*b-1)modp where a, b are integral with |a|< 226 and b! = 0modp
double	residual::negate(double a, double p)
		returns - amodp for nonnegative a < p
double	residual::inverse(double a, double p)
		returns the inverse of a modulo p for intergal 0 < = a < p < 232