[Rd] Floating point issue

Olivier Benz o||v|er@benz @end|ng |rom b-d@t@@ch
Tue Jul 19 13:04:50 CEST 2022 

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

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