fr_ld_expMpfr: Base-2 Representation and Multiplication of Mpfr Numbers

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

Base-2 Representation and Multiplication of Mpfr Numbers

Description

MPFR - versions of the C99 (and POSIX) standard C (and C++) mathlib functions frexp() and ldexp().

frexpMpfr(x) computes base-2 exponent e and “mantissa”, or fraction r, such that x = r * 2^e, where r \in [0.5, 1) (unless when x is in c(0, -Inf, Inf, NaN) where r == x and e is 0), and e is integer valued.

ldexpMpfr(f, E) is the inverse of frexpMpfr(): Given fraction or mantissa f and integer exponent E, it returns x = f * 2^E. Viewed differently, it's the fastest way to multiply or divide MPFR numbers with 2^E.

Usage

frexpMpfr(x,    rnd.mode = c("N", "D", "U", "Z", "A"))
ldexpMpfr(f, E, rnd.mode = c("N", "D", "U", "Z", "A"))

Arguments

x	numeric (coerced to double) vector.
f	numeric fraction (vector), in [0.5, 1).
E	integer valued, exponent of 2, i.e., typically in (-1024-50):1024, otherwise the result will underflow to 0 or overflow to +/- Inf.
rnd.mode	a 1-letter string specifying how rounding should happen at C-level conversion to MPFR, see mpfr.

Value

frexpMpfr returns a list with named components r (of class mpfr) and e (integer valued, of type integer is small enough, "double" otherwise).

Author(s)

Martin Maechler

References

On unix-alikes, typically man frexp and man ldexp

See Also

Somewhat related, .mpfr2exp(). frexp() and ldexp() in package DPQ.

Examples

set.seed(47)
x <- c(0, 2^(-3:3), (-1:1)/0,
       sort(rlnorm(2^12, 10, 20) * sample(c(-1,1), 512, replace=TRUE)))
head(xM <- mpfr(x, 128), 11)
str(rFM <- frexpMpfr(xM))
d.fr <- with(rFM, data.frame(x=x, r=asNumeric(r), e=e))
head(d.fr , 16)
tail(d.fr)
ar <- abs(rFM$r)
stopifnot(0.5 <= ar[is.finite(x) & x != 0], ar[is.finite(x)] < 1,
          is.integer(rFM$e))
ldx <- with(rFM, ldexpMpfr(r, e))
(iN <- which(is.na(x))) # 10
stopifnot(exprs = {
  all.equal(xM, ldx, tol = 2^-124) # allow 4 bits loss, but apart from the NA, even:
  identical(xM[-iN], ldx[-iN])
  is.na(xM [iN])
  is.na(ldx[iN])
})

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