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

[Jeff Newmiller]

Indeed, if the value that is printed starts out as the character string you typed, then none of this would apply. But if you type in a numeric literal in R source code (even interactively) then R will first turn that literal into a numeric value when evaluating the print expression, which is why format()/as.character is needed to retrieve something printable.

On February 17, 2022 3:36:09 PM PST, Marius Hofert <marius.hofert using uwaterloo.ca> wrote:
>Thanks, Jeff.
>
>... all clear (as I wrote, I'm familiar with IEEE 754). I'm just wondering why this happens since the print method seems to call print() => as.character()... so shouldn't this *not* be a problem then (?). I guess at some point it is indeed handled as a number and then (as you wrote) the problem appears (for which one shouldn't blame anybody of course :-) ).
>
>Thanks & cheers,
>M
>
>________________________________________
>From: Jeff Newmiller <jdnewmil using dcn.davis.ca.us>
>Sent: Thursday, February 17, 2022 18:20
>To: r-help using r-project.org; Marius Hofert; r-help using r-project.org
>Subject: Re: [R] Why does the print method fail for very small numbers?
>
>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.

-- 
Sent from my phone. Please excuse my brevity.