gmp-conversions: Conversion Utilities gmp <-> Rmpfr

In Rmpfr: Interface R to MPFR - Multiple Precision Floating-Point Reliable

Conversion Utilities gmp <-> Rmpfr

Description

Coerce from and to big integers (bigz) and mpfr numbers.

Further, coerce from big rationals (bigq) to mpfr numbers.

Usage

.bigz2mpfr(x, precB = NULL, rnd.mode = c('N','D','U','Z','A'))
.bigq2mpfr(x, precB = NULL, rnd.mode = c('N','D','U','Z','A'))
.mpfr2bigz(x, mod = NA)
.mpfr2bigq(x)

Arguments

x	an R object of class bigz, bigq or mpfr respectively.
precB	precision in bits for the result. The default, NULL, means to use the minimal precision necessary for correct representation.
rnd.mode	a 1-letter string specifying how rounding should happen at C-level conversion to MPFR, see details of mpfr.
mod	a possible modulus, see as.bigz in package gmp.

Details

Note that we also provide the natural (S4) coercions, as(x, "mpfr") for x inheriting from class "bigz" or "bigq".

Value

a numeric vector of the same length as x, of the desired class.

See Also

mpfr(), as.bigz and as.bigq in package gmp.

Examples

 S <- gmp::Stirling2(50,10)
 show(S)
 SS <- S * as.bigz(1:3)^128
 stopifnot(all.equal(log2(SS[2]) - log2(S), 128, tolerance=1e-15),
           identical(SS, .mpfr2bigz(.bigz2mpfr(SS))))

 .bigz2mpfr(S)            # 148 bit precision
 .bigz2mpfr(S, precB=256) # 256 bit

 ## rational --> mpfr:
 sq <- SS / as.bigz(2)^100
 MP <- as(sq, "mpfr")
 stopifnot(identical(MP, .bigq2mpfr(sq)),
           SS == MP * as(2, "mpfr")^100)

 ## New since 2024-01-20:   mpfr --> big rational "bigq"
 Pi <- Const("pi", 128)
 m <- Pi* 2^(-5:5)
 (m <- c(m, mpfr(2, 128)^(-5:5)))

 ## 1 x large num/denom, then 2^(-5:5) as frac
 tail( Q <- .mpfr2bigq(m) , 12)
 getDenom <- Rmpfr:::getDenom
 stopifnot(is.whole(m * (d.m <- getDenom(m))))
 stopifnot(all.equal(m, mpfr(Q, 130), tolerance = 2^-130)) # I see even
           all.equal(m, mpfr(Q, 130), tolerance = 0) # TRUE

 m <- m * mpfr(2, 128)^200 # quite a bit larger
 tail( Q. <- .mpfr2bigq(m) , 12) # large integers ..
 stopifnot(is.whole(m * (d.m <- getDenom(m))))
 stopifnot(all.equal(m, mpfr(Q., 130), tolerance = 2^-130)) # I see even
           all.equal(m, mpfr(Q., 130), tolerance = 0) # TRUE

 m2 <- m * mpfr(2, 128)^20000 ## really huge
 stopifnot(is.whole(m2 * (d.m2 <- getDenom(m2))))
 denominator(Q2 <- .mpfr2bigq(m2)) ## all 1 ! (all m2 ~~ 2^20200 )
 stopifnot(all.equal(m2, mpfr(Q2, 130), tolerance = 2^-130)) # I see even
           all.equal(m2, mpfr(Q2, 130), tolerance = 0) # TRUE

Rmpfr documentation built on Nov. 18, 2024, 3:01 p.m.