[Rd] Floating point issue
Taras Zakharko
t@r@@@z@kh@rko @end|ng |rom uzh@ch
Tue Jul 19 14:22:36 CEST 2022
Just a quick note of this in case someone finds Olivier's results puzzling. Standard ARM64 ABI (which Linux follows) defines long double as a 16-byte extended precision type. LLVM’s compiler-rt has a software implementation for doing operations on such types. Apple instead defines long double as identical to double in their ABIs.
References
https://developer.arm.com/documentation/ka004751/1-0
https://developer.apple.com/documentation/xcode/writing-arm64-code-for-apple-platforms
> On 19 Jul 2022, at 13:04, Olivier Benz <olivier.benz using b-data.ch> wrote:
>
> The difference between macOS 12.4 and Debian 11 (Docker, virtualization framework) running on a MacBook Pro (M1 Max).
> -> `.Machine$sizeof.longdouble` on macOS returns 8 whereas on Debian 11 it returns 16.
>
> macOS 12.4 on MacBook Pro (M1 Max):
> ``` r
> .Machine
> #> $double.eps
> #> [1] 2.220446e-16
> #>
> #> $double.neg.eps
> #> [1] 1.110223e-16
> #>
> #> $double.xmin
> #> [1] 2.225074e-308
> #>
> #> $double.xmax
> #> [1] 1.797693e+308
> #>
> #> $double.base
> #> [1] 2
> #>
> #> $double.digits
> #> [1] 53
> #>
> #> $double.rounding
> #> [1] 5
> #>
> #> $double.guard
> #> [1] 0
> #>
> #> $double.ulp.digits
> #> [1] -52
> #>
> #> $double.neg.ulp.digits
> #> [1] -53
> #>
> #> $double.exponent
> #> [1] 11
> #>
> #> $double.min.exp
> #> [1] -1022
> #>
> #> $double.max.exp
> #> [1] 1024
> #>
> #> $integer.max
> #> [1] 2147483647
> #>
> #> $sizeof.long
> #> [1] 8
> #>
> #> $sizeof.longlong
> #> [1] 8
> #>
> #> $sizeof.longdouble
> #> [1] 8
> #>
> #> $sizeof.pointer
> #> [1] 8
>
> 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
> ```
>
> <sup>Created on 2022-07-19 by the [reprex package](https://reprex.tidyverse.org) (v2.0.1)</sup>
>
> <details style="margin-bottom:10px;">
> <summary>
> Session info
> </summary>
>
> ``` r
> sessioninfo::session_info()
> #> ─ Session info ───────────────────────────────────────────────────────────────
> #> setting value
> #> version R version 4.2.1 (2022-06-23)
> #> os macOS Monterey 12.4
> #> system aarch64, darwin20
> #> ui X11
> #> language (EN)
> #> collate en_US.UTF-8
> #> ctype UTF-8
> #> tz Europe/Copenhagen
> #> date 2022-07-19
> #> pandoc 2.18 @ /opt/local/bin/ (via rmarkdown)
> #>
> #> ─ Packages ───────────────────────────────────────────────────────────────────
> #> package * version date (UTC) lib source
> #> cli 3.3.0 2022-04-25 [1] CRAN (R 4.2.0)
> #> digest 0.6.29 2021-12-01 [1] CRAN (R 4.2.0)
> #> ellipsis 0.3.2 2021-04-29 [1] CRAN (R 4.2.0)
> #> evaluate 0.15 2022-02-18 [1] CRAN (R 4.2.0)
> #> fansi 1.0.3 2022-03-24 [1] CRAN (R 4.2.0)
> #> fastmap 1.1.0 2021-01-25 [1] CRAN (R 4.2.0)
> #> fs 1.5.2 2021-12-08 [1] CRAN (R 4.2.0)
> #> glue 1.6.2 2022-02-24 [1] CRAN (R 4.2.0)
> #> highr 0.9 2021-04-16 [1] CRAN (R 4.2.0)
> #> htmltools 0.5.3 2022-07-18 [1] CRAN (R 4.2.1)
> #> knitr 1.39 2022-04-26 [1] CRAN (R 4.2.0)
> #> lifecycle 1.0.1 2021-09-24 [1] CRAN (R 4.2.0)
> #> magrittr 2.0.3 2022-03-30 [1] CRAN (R 4.2.0)
> #> pillar 1.8.0 2022-07-18 [1] CRAN (R 4.2.1)
> #> pkgconfig 2.0.3 2019-09-22 [1] CRAN (R 4.2.0)
> #> purrr 0.3.4 2020-04-17 [1] CRAN (R 4.2.0)
> #> R.cache 0.15.0 2021-04-30 [1] CRAN (R 4.2.0)
> #> R.methodsS3 1.8.2 2022-06-13 [1] CRAN (R 4.2.0)
> #> R.oo 1.25.0 2022-06-12 [1] CRAN (R 4.2.0)
> #> R.utils 2.12.0 2022-06-28 [1] CRAN (R 4.2.0)
> #> reprex 2.0.1 2021-08-05 [1] CRAN (R 4.2.0)
> #> rlang 1.0.4 2022-07-12 [1] CRAN (R 4.2.1)
> #> rmarkdown 2.14 2022-04-25 [1] CRAN (R 4.2.0)
> #> sessioninfo 1.2.2 2021-12-06 [1] CRAN (R 4.2.0)
> #> stringi 1.7.8 2022-07-11 [1] CRAN (R 4.2.1)
> #> stringr 1.4.0 2019-02-10 [1] CRAN (R 4.2.0)
> #> styler 1.7.0 2022-03-13 [1] CRAN (R 4.2.0)
> #> tibble 3.1.7 2022-05-03 [1] CRAN (R 4.2.0)
> #> utf8 1.2.2 2021-07-24 [1] CRAN (R 4.2.0)
> #> vctrs 0.4.1 2022-04-13 [1] CRAN (R 4.2.0)
> #> withr 2.5.0 2022-03-03 [1] CRAN (R 4.2.0)
> #> xfun 0.31 2022-05-10 [1] CRAN (R 4.2.0)
> #> yaml 2.3.5 2022-02-21 [1] CRAN (R 4.2.0)
> #>
> #> [1] /Users/benz0li/Library/R/arm64/4.2/library
> #> [2] /Library/Frameworks/R.framework/Versions/4.2-arm64/Resources/library
> #>
> #> ──────────────────────────────────────────────────────────────────────────────
> ```
>
> </details>
>
> Debian 11 (Docker, virtualization framework) on MacBook Pro (M1 Max)
> ``` r
> .Machine
> #> $double.eps
> #> [1] 2.220446e-16
> #>
> #> $double.neg.eps
> #> [1] 1.110223e-16
> #>
> #> $double.xmin
> #> [1] 2.225074e-308
> #>
> #> $double.xmax
> #> [1] 1.797693e+308
> #>
> #> $double.base
> #> [1] 2
> #>
> #> $double.digits
> #> [1] 53
> #>
> #> $double.rounding
> #> [1] 5
> #>
> #> $double.guard
> #> [1] 0
> #>
> #> $double.ulp.digits
> #> [1] -52
> #>
> #> $double.neg.ulp.digits
> #> [1] -53
> #>
> #> $double.exponent
> #> [1] 11
> #>
> #> $double.min.exp
> #> [1] -1022
> #>
> #> $double.max.exp
> #> [1] 1024
> #>
> #> $integer.max
> #> [1] 2147483647
> #>
> #> $sizeof.long
> #> [1] 8
> #>
> #> $sizeof.longlong
> #> [1] 8
> #>
> #> $sizeof.longdouble
> #> [1] 16
> #>
> #> $sizeof.pointer
> #> [1] 8
> #>
> #> $longdouble.eps
> #> [1] 1.92593e-34
> #>
> #> $longdouble.neg.eps
> #> [1] 9.62965e-35
> #>
> #> $longdouble.digits
> #> [1] 113
> #>
> #> $longdouble.rounding
> #> [1] 5
> #>
> #> $longdouble.guard
> #> [1] 0
> #>
> #> $longdouble.ulp.digits
> #> [1] -112
> #>
> #> $longdouble.neg.ulp.digits
> #> [1] -113
> #>
> #> $longdouble.exponent
> #> [1] 15
> #>
> #> $longdouble.min.exp
> #> [1] -16382
> #>
> #> $longdouble.max.exp
> #> [1] 16384
>
> 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
> ```
>
> <sup>Created on 2022-07-19 by the [reprex package](https://reprex.tidyverse.org) (v2.0.1)</sup>
>
> <details style="margin-bottom:10px;">
> <summary>
> Session info
> </summary>
>
> ``` r
> sessioninfo::session_info()
> #> ─ Session info ───────────────────────────────────────────────────────────────
> #> setting value
> #> version R version 4.2.1 (2022-06-23)
> #> os Debian GNU/Linux 11 (bullseye)
> #> system aarch64, linux-gnu
> #> ui X11
> #> language (EN)
> #> collate en_US.UTF-8
> #> ctype en_US.UTF-8
> #> tz Etc/UTC
> #> date 2022-07-19
> #> pandoc 2.18 @ /usr/bin/ (via rmarkdown)
> #>
> #> ─ Packages ───────────────────────────────────────────────────────────────────
> #> package * version date (UTC) lib source
> #> cli 3.3.0 2022-04-25 [2] CRAN (R 4.2.1)
> #> crayon 1.5.1 2022-03-26 [2] CRAN (R 4.2.1)
> #> digest 0.6.29 2021-12-01 [2] CRAN (R 4.2.1)
> #> ellipsis 0.3.2 2021-04-29 [2] CRAN (R 4.2.1)
> #> evaluate 0.15 2022-02-18 [2] CRAN (R 4.2.1)
> #> fansi 1.0.3 2022-03-24 [2] CRAN (R 4.2.1)
> #> fastmap 1.1.0 2021-01-25 [2] CRAN (R 4.2.1)
> #> fs 1.5.2 2021-12-08 [2] CRAN (R 4.2.1)
> #> glue 1.6.2 2022-02-24 [2] CRAN (R 4.2.1)
> #> highr 0.9 2021-04-16 [2] CRAN (R 4.2.1)
> #> htmltools 0.5.2 2021-08-25 [2] CRAN (R 4.2.1)
> #> knitr 1.39 2022-04-26 [2] CRAN (R 4.2.1)
> #> lifecycle 1.0.1 2021-09-24 [2] CRAN (R 4.2.1)
> #> magrittr 2.0.3 2022-03-30 [2] CRAN (R 4.2.1)
> #> pillar 1.7.0 2022-02-01 [2] CRAN (R 4.2.1)
> #> pkgconfig 2.0.3 2019-09-22 [2] CRAN (R 4.2.1)
> #> purrr 0.3.4 2020-04-17 [2] CRAN (R 4.2.1)
> #> R.cache 0.15.0 2021-04-30 [2] CRAN (R 4.2.1)
> #> R.methodsS3 1.8.2 2022-06-13 [2] CRAN (R 4.2.1)
> #> R.oo 1.25.0 2022-06-12 [2] CRAN (R 4.2.1)
> #> R.utils 2.12.0 2022-06-28 [2] CRAN (R 4.2.1)
> #> reprex 2.0.1 2021-08-05 [2] CRAN (R 4.2.1)
> #> rlang 1.0.4 2022-07-12 [2] CRAN (R 4.2.1)
> #> rmarkdown 2.14 2022-04-25 [2] CRAN (R 4.2.1)
> #> sessioninfo 1.2.2 2021-12-06 [2] CRAN (R 4.2.1)
> #> stringi 1.7.8 2022-07-11 [2] CRAN (R 4.2.1)
> #> stringr 1.4.0 2019-02-10 [2] CRAN (R 4.2.1)
> #> styler 1.7.0 2022-03-13 [2] CRAN (R 4.2.1)
> #> tibble 3.1.7 2022-05-03 [2] CRAN (R 4.2.1)
> #> utf8 1.2.2 2021-07-24 [2] CRAN (R 4.2.1)
> #> vctrs 0.4.1 2022-04-13 [2] CRAN (R 4.2.1)
> #> withr 2.5.0 2022-03-03 [2] CRAN (R 4.2.1)
> #> xfun 0.31 2022-05-10 [2] CRAN (R 4.2.1)
> #> yaml 2.3.5 2022-02-21 [2] CRAN (R 4.2.1)
> #>
> #> [1] /home/benz0li/R/aarch64-unknown-linux-gnu-library/4.2
> #> [2] /usr/local/lib/R/site-library
> #> [3] /usr/local/lib/R/library
> #>
> #> ──────────────────────────────────────────────────────────────────────────────
> ```
>
> </details>
>
>> On 10 Jul 2022, at 22:23, Bill Dunlap <williamwdunlap using gmail.com> wrote:
>>
>> 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 using 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 using r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-devel
>>>
>>
>> [[alternative HTML version deleted]]
>>
>> ______________________________________________
>> R-devel using r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-devel
>
> --
> benz0li.b-data.io | @benz0li | olivier.benz using b-data.ch
>
> ______________________________________________
> R-devel using r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-devel
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