[R] Why does the print method fail for very small numbers?

[Jeff Newmiller]

Go to https://cs.lmu.edu/~ray/demos/ieee754.html

and enter

2.48e-324

into the encoder box. You get

0000000000000001

which means you are well beyond normalized representation and are approximating this value with a total of 1 bit of precision.

Do you really want to fault the print method for having difficulty returning your value to you after this much rounding?

On February 17, 2022 2:40:09 PM PST, Marius Hofert <marius.hofert using uwaterloo.ca> wrote:
>Dear expeRts,
>
>I'm familiar with IEEE 754. Is there an easy way to explain why even
>just printing of small numbers fails?
>
>1e-317 # 1e-317 => fine
>1e-318 # 9.999987e-319 => gets tricky; seems to call print() => as.character() => format() => paste()
>1e-318 == 9.999987e-319 # TRUE
>2.48e-324 # prints 4.940656e-324 for me
>2.48e-324 == 4.940656e-324 # TRUE
>## Relative error as a plot
>rel_error <- function(x)
>    plot(abs((as.numeric(as.character(x)) - x) / x), type = "l",
>         ylab = "Relative error between x and as.numeric(as.character(x))")
>rel_error(seq(0.001, 0.001 + .Machine$double.xmin, length.out = 1001)) # fine
>rel_error(seq(0, .Machine$double.xmin, length.out = 1001)) # printing breaks down
>
>Of course, [0,.Machine$double.xmin] is somewhat of a strange set of numbers to consider,
>and I expect things like "==" to be easily fooled there, but already the print method (?)
>
>Thanks & cheers,
>Marius
>
>sessionInfo()
>R version 4.1.2 (2021-11-01)
>Platform: x86_64-apple-darwin21.2.0 (64-bit)
>Running under: macOS Monterey 12.1
>...
>
>
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-- 
Sent from my phone. Please excuse my brevity.