gmp (version 0.6-8)

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 bigz
abs(x)
inv.bigz(a, b,...)## == (1 / a) (modulo b)

pow.bigz(e1, e2,...)## == e1 ^ e2

# S3 method for bigz
log(x, base=exp(1))
# S3 method for bigz
log2(x)
# S3 method for bigz
log10(x)

Value

Apart from / (or div), where rational numbers (bigq) may result, these functions return an object of class "bigz", representing the result of the arithmetic operation.

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

Author

Immanuel Scholz and Antoine Lucas

Details

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

For details about the internal modulus state, and the rules applied for arithmetic operations on big integers with a modulus, see the bigz help page.

a / b \(=\) div(a,b) returns a rational number unless the operands have a (matching) modulus where a * b^-1 results.
a %/% b (or, equivalently, divq(a,b)) returns the quotient of simple integer division (with truncation towards zero), possibly re-adding a modulus at the end (but not using a modulus like in a / b).

r <- inv.bigz(a, m), the multiplicative inverse of a modulo \(m\), corresponds to 1/a or a ^-1 from above when a has modulus m. Note that \(a\) not always has an inverse modulo \(m\), in which case r will be NA with a warning that can be turned off via

options("gmp:warnNoInv" = FALSE)

.

References

The GNU MP Library, see https://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)

(ii <- inv.bigz(1:10, 16))
## with 5 warnings (one for each NA)
op <- options("gmp:warnNoInv" = FALSE)
i2 <- inv.bigz(1:10, 16) # no warnings
(i3 <- 1 / as.bigz(1:10, 16))
i4 <- as.bigz(1:10, 16) ^ -1
stopifnot(identical(ii, i2),
	  identical(as.bigz(i2, 16), i3),
	  identical(i3, i4))
options(op)# revert previous options' settings

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))
 )