08. Modular-arithmetic {VeryLargeIntegers} | R Documentation |
Basic modular-arithmetic operators for vli (Very Large Integers) objects.
summod(x, y, mod) ## Default S3 method: summod(x, y, mod) ## S3 method for class 'numeric' summod(x, y, mod) ## S3 method for class 'vli' summod(x, y, mod) submod(x, y, mod) ## Default S3 method: submod(x, y, mod) ## S3 method for class 'numeric' submod(x, y, mod) ## S3 method for class 'vli' submod(x, y, mod) mulmod(x, y, mod) ## Default S3 method: mulmod(x, y, mod) ## S3 method for class 'numeric' mulmod(x, y, mod) ## S3 method for class 'vli' mulmod(x, y, mod) powmod(x, n, mod) ## Default S3 method: powmod(x, n, mod) ## S3 method for class 'numeric' powmod(x, n, mod) ## S3 method for class 'vli' powmod(x, n, mod) invmod(x, n) ## Default S3 method: invmod(x, n) ## S3 method for class 'numeric' invmod(x, n) ## S3 method for class 'vli' invmod(x, n) divmod(x, y, mod) ## Default S3 method: divmod(x, y, mod) ## S3 method for class 'numeric' divmod(x, y, mod) ## S3 method for class 'vli' divmod(x, y, mod)
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 |
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)
.
object of class vli
Javier Leiva Cuadrado
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