gmp (version 0.5-4)

bigz operators: Basic Arithmetic Operators for Large Integers ("bigz")

Description

Addition, substraction, multiplication, (integer) division, remainder of division, multiplicative inverse, power and logarithm functions.

Usage

add.bigz(e1, e2)
sub.bigz(e1, e2 = NULL)
mul.bigz(e1, e2)
div.bigz(e1, e2)
divq.bigz(e1,e2) ## ==  e1 %/% e2
mod.bigz(e1, e2) ## ==  e1 %%  e2
## S3 method for class 'bigz':
abs(x)
inv.bigz(a, b,...)## == (1 / a) (modulo b)pow.bigz(e1, e2,...)## == e1 ^ e2## S3 method for class 'bigz':
log(x, base=exp(1))
## S3 method for class 'bigz':
log2(x)
## S3 method for class 'bigz':
log10(x)

Arguments

x

bigz, integer or string from an integer

e1, e2, a,b

bigz, integer or string from an integer

base

base of the logarithm; base e as default

...

Additional parameters

Value

• A bigz class representing the result of the arithmetic operation.

Details

For details about the internal modulus state, see the manpage of bigz.

div or "/" return a rational number; divq or "%/%" return the quotient of integer division.

Operators can be used directly when objects are of class bigz: a + b, log(a), etc.

References

The GNU MP Library, see http://gmplib.org

Examples

# 1+1=2
as.bigz(1) + 1
as.bigz(2)^10
as.bigz(2)^200

# if my.large.num.string is set to a number, this returns the least byte
(my.large.num.string <- paste(sample(0:9, 200, replace=TRUE), collapse=""))
mod.bigz(as.bigz(my.large.num.string), "0xff")

# power exponents can be up to MAX_INT in size, or unlimited if a
# bigz's modulus is set.
pow.bigz(10,10000)

## Modulo 11,   7 and 8 are inverses :
as.bigz(7, mod = 11) * 8 ## ==>  1  (mod 11)
inv.bigz(7, 11)## hence, 8
a <- 1:10
(i.a <- inv.bigz(a, 11))
d <- as.bigz(7)
a %/% d  # = divq(a, d)
a %%  d  # = mod.bigz (a, d)

stopifnot(inv.bigz(7, 11) == 8,
          all(as.bigz(i.a, 11) * a == 1),
          identical(a %/% d, divq.bigz(1:10, 7)),
          identical(a %%  d, mod.bigz (a, d))
 )