[Rd] Floating point issue

Brodie Gaslam
2022-07-11T01:10:29Z

The results are not exactly the same.  Notice that on Bill's system the
bit pattern of 10^25 and 10000000000000000905969664 are the same, but
not so on yours.  So there is a mismatch happening on parsing between
your M1 mac and other's systems.

This is the main thing I wanted to point out.  But since I'm here I'm
going to add some additional lazily researched speculation.

As Dirk points out, M1 does not have long double, and if you look at
what I think is responsible for parsing of numbers like the ones we're
discussing here, we see[1]:

     double R_strtod5(const char *str, char **endptr, char dec,
     		 Rboolean NA, int exact)
     {
         LDOUBLE ans = 0.0;

IIRC long double on systems that implement it as 80 bits (most that have
x87 coprocessors) has 63-4 bits of precision, vs 53 for 64 bit long
double.  Roughly speaking, that's 19-20 digits of base 10 precision for
long double, vs 15-16 for 64 bit double.  Then:

     > substr(rep("10000000000000000905969664", 2),  c(1, 1), c(16,
20))
     [1] "1000000000000000"     "10000000000000000905"

Again, I have not carefully researched this, but it seems likely that
parsing is producing different a different outcome in this case because
the intermediate values generated can be kept at higher precision on
systems with 80 bit long doubles prior to coercing to double for the
final result.

IIRC, if you need invertible deparsing/parsing I think you can use:

     deparse(1e25, control=c('hexNumeric'))

Although I don't have an 80-bit-less system to test on (and I am too
lazy to recompile R without long double to test).

Best,

B.

[1]: https://github.com/r-devel/r-svn/blob/master/src/main/util.c#L1993



On 7/10/22 5:38 PM, Antoine Fabri wrote:
> Thanks, I get the exact same results as yours
>
> ``` r
> bitC <- function(x) noquote(vapply(as.double(x), function(x) { # split
one
> double
>    b <- substr(as.character(rev(numToBits(x))), 2L, 2L)
>        paste0(c(b[1L], " ", b[2:12], " | ", b[13:64]),
collapse = "")
>      }, ""))
> bitC(10^25)
> #> [1] 0 10001010010 |
0000100010110010101000101100001010000000001010010001
> bitC(10000000000000000905969664)
> #> [1] 0 10001010010 |
0000100010110010101000101100001010000000001010010010
> bitC(10000000000000000905969664 - 10^25)
> #> [1] 0 10000011110 |
0000000000000000000000000000000000000000000000000000
> bitC(1e25)
> #> [1] 0 10001010010 |
0000100010110010101000101100001010000000001010010001
> ```
>
> Created on 2022-07-10 by the [reprex package](
> https://reprex.tidyverse.org) (v2.0.1)
>
> Le dim. 10 juil. 2022 ? 22:23, Bill Dunlap <williamwdunlap at
gmail.com> a
> ?crit :
>
>> The following function, 'bitC' from ?numToBits, displays the
bits in a
>> double precision number, separated into the sign bit, the 11 exponent
bits,
>> and the 52 bits in the mantissa.  I've shown the results with your
numbers
>> from R-2.4.0 on my Windows 11 Lenovo laptop: what do you get?
>>
>>> bitC <- function(x) noquote(vapply(as.double(x), function(x) { #
split
>> one double
>> +     b <- substr(as.character(rev(numToBits(x))), 2L, 2L)
>> +     paste0(c(b[1L], " ", b[2:12], " | ",
b[13:64]), collapse = "")
>> +   }, ""))
>>> bitC(10^25)
>> # [1] 0 10001010010 |
0000100010110010101000101100001010000000001010010001
>>> bitC(10000000000000000905969664)
>> # [1] 0 10001010010 |
0000100010110010101000101100001010000000001010010001
>>> bitC(10000000000000000905969664 - 10^25)
>> # [1] 0 00000000000 |
0000000000000000000000000000000000000000000000000000
>>> bitC(1e25)
>> # [1] 0 10001010010 |
0000100010110010101000101100001010000000001010010001
>>
>> -Bill
>>
>> On Sun, Jul 10, 2022 at 7:00 AM Antoine Fabri <antoine.fabri at
gmail.com>
>> wrote:
>>
>>> Dear r-devel,
>>>
>>> For some numbers, the printed value is not equivalent to the input
:
>>>
>>> options(scipen = 999)
>>> ## GOOD
>>> 1e24
>>> #> [1]  999999999999999983222784
>>> 1e24 == 999999999999999983222784
>>> #> [1] TRUE
>>>
>>> ## BAD
>>> 1e25
>>> #> [1] 10000000000000000905969664
>>> 1e25 == 10000000000000000905969664
>>> #> [1] FALSE
>>>
>>> ## STILL BAD
>>> 10000000000000000905969664
>>> #> [1] 10000000000000003053453312
>>>
>>> ## GOOD AGAIN
>>> 10000000000000003053453312
>>> #> [1] 10000000000000003053453312
>>>
>>> # Additionally
>>> 10000000000000000000000000 == 1e25
>>> #> [1] FALSE
>>>
>>> Are these bugs ?
>>>
>>>          [[alternative HTML version deleted]]
>>>
>>> ______________________________________________
>>> R-devel at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-devel
>>>
>>
>
> 	[[alternative HTML version deleted]]
>
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