VeryLargeIntegers (version 0.1.8)

08. Modular-arithmetic: Basic Modular-Arithmetic Operators for vli Objects

Description

Basic modular-arithmetic operators for vli (Very Large Integers) objects.

Usage

summod(x, y, mod)
# S3 method for default
summod(x, y, mod)
# S3 method for numeric
summod(x, y, mod)
# S3 method for vli
summod(x, y, mod)
submod(x, y, mod)
# S3 method for default
submod(x, y, mod)
# S3 method for numeric
submod(x, y, mod)
# S3 method for vli
submod(x, y, mod)
mulmod(x, y, mod)
# S3 method for default
mulmod(x, y, mod)
# S3 method for numeric
mulmod(x, y, mod)
# S3 method for vli
mulmod(x, y, mod)
powmod(x, n, mod)
# S3 method for default
powmod(x, n, mod)
# S3 method for numeric
powmod(x, n, mod)
# S3 method for vli
powmod(x, n, mod)
invmod(x, n)
# S3 method for default
invmod(x, n)
# S3 method for numeric
invmod(x, n)
# S3 method for vli
invmod(x, n)
divmod(x, y, mod)
# S3 method for default
divmod(x, y, mod)
# S3 method for numeric
divmod(x, y, mod)
# S3 method for vli
divmod(x, y, mod)

Value

object of class vli

Arguments

x

vli class object or 32 bits integer

y

vli class object or 32 bits integer

mod

vli class object or 32 bits integer

n

vli class object or 32 bits integer

Author

Javier Leiva Cuadrado

Details

The functions summod, submod and mulmod compute respectively the sum, the substraction and the multiplication of x and y under modulo mod.

The function powmod computes the n-th power of x under modulo mod.

The function invmod returns the modular multiplicative inverse of x in Zn; that is, y = x^(-1) such that x * y = 1 (mod n).

The function divmod returns the modular division of x over y; that is, z such that y * z (mod mod) = x (mod mod).

Examples

x <- as.vli("8925378246957826904701")
y <- as.vli("347892325634785693")
mod <- as.vli(21341)

summod(x, y, mod)

mulmod(x, invmod(x, n = 123), mod = 123) == 1

z <- divmod(x, y, mod)
mulmod(z, y, mod) == x %% mod