bigrational: Large sized rationals

In gmp: Multiple Precision Arithmetic

Large sized rationals

Description

Class "bigq" encodes rationals encoded as ratios of arbitrary large integers (via GMP). A simple S3 class (internally a raw vector), it has been registered as formal (S4) class (via setOldClass), too.

Usage

as.bigq(n, d = 1)
## S3 method for class 'bigq'
as.character(x, b=10,...)
## S3 method for class 'bigq'
as.double(x,...)
as.bigz.bigq(a, mod=NA)
is.bigq(x)
## S3 method for class 'bigq'
is.na(x)
## S3 method for class 'bigq'
print(x, quote=FALSE, initLine = TRUE, ...)
denominator(x)
numerator(x)
NA_bigq_
c_bigq(L)

Arguments

n,d	either integer, numeric or string value (String value: either starting with 0x for hexadecimal, 0b for binary or without prefix for decimal values. Any format error results in 0). n stands for numerator, d for denominator.
a	an element of class "bigq"
mod	optional modulus to convert into biginteger
x	a “rational number” (vector), of class "bigq".
b	base: from 2 to 36
...	additional arguments passed to methods
quote	(for printing:) logical indicating if the numbers should be quoted (as characters are); the default used to be TRUE (implicitly) till 2011.
initLine	(for printing:) logical indicating if an initial line (with the class and length or dimension) should be printed.
L	a list where each element contains "bigq" numbers, for c_bigq(), this allows something like an sapply() for "bigq" vectors, see sapplyQ() in the examples below.

Details

as.bigq(x) when x is numeric (aka double precision) calls the ‘GMP’ function mpq_set_d() which is documented to be exact (every finite double precision number is a rational number).

as.bigz.bigq() returns the smallest integers not less than the corresponding rationals bigq.

NA_bigq_ is computed on package load time as as.bigq(NA).

Value

An R object of (S3) class "bigq" representing the parameter value.

Author(s)

Antoine Lucas

Examples

x <- as.bigq(21,6)
x
# 7 / 2
# Wow ! result is simplified.

y <- as.bigq(5,3)

# addition works !
x + y

# You can even try multiplication, division...
x * y / 13

# and, since May 2012,
x ^ 20
stopifnot(is.bigq(x), is.bigq(x + y),
	  x ^ 20 == as.bigz(7)^20 / 2^20)

# convert to string, double
as.character(x)
as.double(x)

stopifnot( is.na(NA_bigq_) )

# Depict the "S4-class" bigq, i.e., the formal (S4) methods:
if(require("Rmpfr")) # mostly interesting there
  showMethods(class="bigq")

# an  sapply() version that works for big rationals "bigq":
sapplyQ <- function(X, FUN, ...) c_bigq(lapply(X, FUN, ...))

# dummy example showing it works (here):
qq <- as.bigq(1, 1:999)
q1 <- sapplyQ(qq, function(q) q^2)
stopifnot( identical(q1, qq^2) )

gmp documentation built on July 9, 2023, 7 p.m.