From 8a1f540499727797b44d4ab491bdb115c93bfc71 Mon Sep 17 00:00:00 2001
From: kaz462 <kangjie.zhang@bayer.com>
Date: Mon, 24 Jul 2023 21:27:01 -0700
Subject: [PATCH 1/8] #71: rounding draft

---
 posts/2023-07-24_rounding/appendix.R   |  78 ++++++++++++++
 posts/2023-07-24_rounding/rounding.png | Bin 0 -> 45734 bytes
 posts/2023-07-24_rounding/rounding.qmd | 142 +++++++++++++++++++++++++
 3 files changed, 220 insertions(+)
 create mode 100644 posts/2023-07-24_rounding/appendix.R
 create mode 100644 posts/2023-07-24_rounding/rounding.png
 create mode 100644 posts/2023-07-24_rounding/rounding.qmd

diff --git a/posts/2023-07-24_rounding/appendix.R b/posts/2023-07-24_rounding/appendix.R
new file mode 100644
index 00000000..946a007a
--- /dev/null
+++ b/posts/2023-07-24_rounding/appendix.R
@@ -0,0 +1,78 @@
+# markdown helpers --------------------------------------------------------
+
+markdown_appendix <- function(name, content) {
+  paste(paste("##", name, "{.appendix}"), " ", content, sep = "\n")
+}
+markdown_link <- function(text, path) {
+  paste0("[", text, "](", path, ")")
+}
+
+
+
+# worker functions --------------------------------------------------------
+
+insert_source <- function(repo_spec, name,
+                          collection = "posts",
+                          branch = "main",
+                          host = "https://github.com",
+                          text = "source code") {
+  path <- paste(
+    host,
+    repo_spec,
+    "tree",
+    branch,
+    collection,
+    name,
+    "index.qmd",
+    sep = "/"
+  )
+  return(markdown_link(text, path))
+}
+
+insert_timestamp <- function(tzone = Sys.timezone()) {
+  time <- lubridate::now(tzone = tzone)
+  stamp <- as.character(time, tz = tzone, usetz = TRUE)
+  return(stamp)
+}
+
+insert_lockfile <- function(repo_spec, name,
+                            collection = "posts",
+                            branch = "main",
+                            host = "https://github.com",
+                            text = "R environment") {
+  path <- paste(
+    host,
+    repo_spec,
+    "tree",
+    branch,
+    collection,
+    name,
+    "renv.lock",
+    sep = "/"
+  )
+  return(markdown_link(text, path))
+}
+
+
+
+# top level function ------------------------------------------------------
+
+insert_appendix <- function(repo_spec, name, collection = "posts") {
+  appendices <- paste(
+    markdown_appendix(
+      name = "Last updated",
+      content = insert_timestamp()
+    ),
+    " ",
+    markdown_appendix(
+      name = "Details",
+      content = paste(
+        insert_source(repo_spec, name, collection),
+        insert_lockfile(repo_spec, name, collection),
+        sep = ", "
+      )
+    ),
+    sep = "\n"
+  )
+  knitr::asis_output(appendices)
+}
diff --git a/posts/2023-07-24_rounding/rounding.png b/posts/2023-07-24_rounding/rounding.png
new file mode 100644
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diff --git a/posts/2023-07-24_rounding/rounding.qmd b/posts/2023-07-24_rounding/rounding.qmd
new file mode 100644
index 00000000..fcc2d7d7
--- /dev/null
+++ b/posts/2023-07-24_rounding/rounding.qmd
@@ -0,0 +1,142 @@
+---
+title: "Rounding"
+author:
+  - name: Kangjie Zhang
+description: "base R `round()` and round half up in R"
+date: "2023-07-24"
+# please do not use any non-default categories.
+# You can find the default categories in the repository README.md
+categories: [rounding]
+# feel free to change the image
+image: "rounding.png"
+---
+
+<!--------------- typical setup ----------------->
+
+```{r setup, include=FALSE}
+long_slug <- "2023-07-24_rounding"
+# renv::use(lockfile = "renv.lock")
+```
+
+<!--------------- post begins here ----------------->
+
+## Rounding methods
+
+Both SAS and base R have the function `round()`, which rounds the input to the specified number of decimal places.
+However, they use different approaches when rounding off a 5:
+
+-   SAS `round()` rounds half up (the common method of rounding)
+
+-   base R `round()` [rounds to the nearest even](https://en.m.wikipedia.org/wiki/IEEE_754#Roundings_to_nearest)
+
+Although base R does not have the option for "round half up", there are functions available in other R packages (e.g., `janitor`, `tidytlg`).
+The following table lists some often-used rounding methods and their corresponding functions in SAS and R.
+
++---------------+----------------------------------------+--------------------------------------------+--------------------------------------------+--------------------------------------------+--------------------------------------------+
+|               | round half up                          | round to even                              | round up                                   | round down                                 | round towards zero                         |
++:=============:+:======================================:+:==========================================:+:==========================================:+:==========================================:+:==========================================:+
+| SAS           | `round()`                              | `rounde()`                                 | `ceil()`                                   | `floor()`                                  | `int()`                                    |
++---------------+----------------------------------------+--------------------------------------------+--------------------------------------------+--------------------------------------------+--------------------------------------------+
+| R             | ::: {style="background-color: yellow"} | ::: {style="background-color: lightgreen"} | ::: {style="background-color: lightgreen"} | ::: {style="background-color: lightgreen"} | ::: {style="background-color: lightgreen"} |
+|               | `janitor::round_half_up()`             | `round()`                                  | `ceiling()`                                | `floor()`                                  | `trunc()`                                  |
+|               |                                        |                                            |                                            |                                            |                                            |
+|               | <div>                                  | {base}                                     | {base}                                     | {base}                                     | {base}                                     |
+|               |                                        | :::                                        | :::                                        | :::                                        | :::                                        |
+|               | `tidytlg::roundSAS()`                  |                                            |                                            |                                            |                                            |
+|               |                                        |                                            |                                            |                                            |                                            |
+|               | </div>                                 |                                            |                                            |                                            |                                            |
+|               | :::                                    |                                            |                                            |                                            |                                            |
++---------------+----------------------------------------+--------------------------------------------+--------------------------------------------+--------------------------------------------+--------------------------------------------+
+| Example: 1.45 | 1.5                                    | 1.4                                        | 2                                          | 1                                          | 1                                          |
+|               |                                        |                                            |                                            |                                            |                                            |
+|               | (round to 1 decimal place)             | (round to 1 decimal place)                 |                                            |                                            |                                            |
++---------------+----------------------------------------+--------------------------------------------+--------------------------------------------+--------------------------------------------+--------------------------------------------+
+
+This table is summarized from links below, where more detailed discussions can be found -
+
+-   Two SAS blogs about [round-to-even](https://blogs.sas.com/content/iml/2019/11/11/round-to-even.html) and [rounding-up-rounding-down](https://blogs.sas.com/content/iml/2011/10/03/rounding-up-rounding-down.html)
+
+-   R documentation: Base R [Round](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/Round), [`janitor::round_half_up()`](https://sfirke.github.io/janitor/reference/round_half_up.html), [`tidytlg::roundSAS()`](https://pharmaverse.github.io/tidytlg/main/reference/roundSAS.html)
+
+-   [CAMIS](https://psiaims.github.io/CAMIS/) (Comparing Analysis Method Implementations in Software)
+
+## Round half up in R
+
+The motivation for having a 'round half up' function is clear: it's a widely used rounding method, but there are no such options available in base R.
+
+There are multiple forums that discussed this topic, and a few functions available in some R packages.
+Hope you won't need to spend much time identifying a safe option for rounding half up in R after reading the following section.
+
+### Bug fix
+
+The first time I needed to round half up in R, I chose the function from a [PHUSE paper](https://www.lexjansen.com/phuse-us/2020/ct/CT05.pdf) and applied it to my study.
+It works fine most of the time, but has issues like the following example -
+
+```{r, message = FALSE}
+# a function that rounds half up
+# exact copy from: https://www.lexjansen.com/phuse-us/2020/ct/CT05.pdf
+ut_round <- function(x, n=0)
+{
+ # x is the value to be rounded
+ # n is the precision of the rounding
+ scale <- 10^n
+ y <- trunc(x * scale + sign(x) * 0.5) / scale
+ # Return the rounded number
+ return(y)
+}
+# round half up for 2436.845, with 2 decimal places
+ut_round(2436.845, 2)
+```
+
+The expected result is 2436.85, but the output rounds it down.
+The function's logic seems fine, I was not able to find the root cause.
+Thanks to the community effort, there are already discussions and resolution available in a [StackOverflow post](https://stackoverflow.com/questions/12688717/round-up-from-5#comment110611119_12688836) -
+
+> There are numerical precision issues, e.g., `round2(2436.845, 2)` returns `2436.84.` Changing `z + 0.5 to z + 0.5 + sqrt(.Machine$double.eps)` seems to work for me. -- Gregor Thomas Jun 24, 2020 at 2:16
+
+After fixing this bug:
+
+```{r, message = FALSE}
+# revised rounds half up
+ut_round1 <- function(x, n=0)
+{
+ # x is the value to be rounded
+ # n is the precision of the rounding
+ scale <- 10^n
+ y <- trunc(x * scale + sign(x) * 0.5 + sqrt(.Machine$double.eps)) / scale
+ # Return the rounded number
+ return(y)
+}
+# round half up for 2436.845, with 2 decimal places
+ut_round1(2436.845, 2)
+```
+
+### We are not alone
+
+The same issue occurred in the following ones as well, and has been raised by users:
+
+-   `janitor::round_half_up()`: [issue](https://github.com/sfirke/janitor/issues/396) was raised and fixed in v2.1.0
+
+-   `Tplyr`: `options(tplyr.IBMRounding = TRUE)`, [issue](https://github.com/atorus-research/Tplyr/issues/124) was raised
+
+-   `scrutiny::round_up_from()/round_up()`: [issue](https://lhdjung.github.io/scrutiny/reference/index.html#rounding) was raised
+
+-   ...
+
+### Which one to use?
+
+The following two functions have the above bug fixed, they both came from the same [StackOverflow post](https://stackoverflow.com/questions/12688717/round-up-from-5).
+
+-   [`janitor::round_half_up()`](https://sfirke.github.io/janitor/reference/round_half_up.html) **version \>= 2.1.0**
+-   [`tidytlg::roundSAS()`](https://pharmaverse.github.io/tidytlg/main/reference/roundSAS.html)
+    -   this function has two more arguments that can convert the result to character and allow a character string to indicate missing values
+
+<!--------------- appendices go here ----------------->
+
+```{r, echo=FALSE}
+source("appendix.R")
+insert_appendix(
+  repo_spec = "pharmaverse/blog",
+  name = long_slug
+)
+```

From b129ca38f05b4d30c2afb95049880e9ba820a56b Mon Sep 17 00:00:00 2001
From: kaz462 <kangjie.zhang@bayer.com>
Date: Mon, 31 Jul 2023 19:11:17 -0700
Subject: [PATCH 2/8] #71: address comments

---
 inst/WORDLIST.txt                      |  37 ++++++++
 posts/2023-07-24_rounding/rounding.qmd | 118 ++++++++++++++-----------
 2 files changed, 105 insertions(+), 50 deletions(-)

diff --git a/inst/WORDLIST.txt b/inst/WORDLIST.txt
index fa9a91d8..27290cb4 100644
--- a/inst/WORDLIST.txt
+++ b/inst/WORDLIST.txt
@@ -252,3 +252,40 @@ tlg
 TLG
 TLGs
 xpt
+anderson
+atorus
+CAMIS
+ceil
+dn
+doesn
+edu
+eps
+gp
+Gregor
+htm
+IBMRounding
+iml
+ji
+lexjansen
+lhdjung
+lrcon
+phuse
+psiaims
+rdocumentation
+rounde
+Roundings
+roundSAS
+rw
+SAS's
+sfirke
+stackoverflow
+StackOverflow
+thm
+tidytlg
+tplyr
+Tplyr
+trunc
+ucla
+unv
+ut
+zMachine
diff --git a/posts/2023-07-24_rounding/rounding.qmd b/posts/2023-07-24_rounding/rounding.qmd
index fcc2d7d7..ad427ed9 100644
--- a/posts/2023-07-24_rounding/rounding.qmd
+++ b/posts/2023-07-24_rounding/rounding.qmd
@@ -2,7 +2,7 @@
 title: "Rounding"
 author:
   - name: Kangjie Zhang
-description: "base R `round()` and round half up in R"
+description: "Exploration of some commonly used rounding methods and their corresponding functions in SAS and R, with a focus on 'round half up' and reliable solutions for numerical precision challenges"
 date: "2023-07-24"
 # please do not use any non-default categories.
 # You can find the default categories in the repository README.md
@@ -25,32 +25,34 @@ long_slug <- "2023-07-24_rounding"
 Both SAS and base R have the function `round()`, which rounds the input to the specified number of decimal places.
 However, they use different approaches when rounding off a 5:
 
--   SAS `round()` rounds half up (the common method of rounding)
+-   SAS `round()` [rounds half up](https://en.wikipedia.org/wiki/Rounding#Rounding_half_up).
+    This is the most common method of rounding.
 
--   base R `round()` [rounds to the nearest even](https://en.m.wikipedia.org/wiki/IEEE_754#Roundings_to_nearest)
+-   base R `round()` [rounds to the nearest even](https://en.m.wikipedia.org/wiki/IEEE_754#Roundings_to_nearest), which matches SAS's `rounde()` function.
 
 Although base R does not have the option for "round half up", there are functions available in other R packages (e.g., `janitor`, `tidytlg`).
+
 The following table lists some often-used rounding methods and their corresponding functions in SAS and R.
 
-+---------------+----------------------------------------+--------------------------------------------+--------------------------------------------+--------------------------------------------+--------------------------------------------+
-|               | round half up                          | round to even                              | round up                                   | round down                                 | round towards zero                         |
-+:=============:+:======================================:+:==========================================:+:==========================================:+:==========================================:+:==========================================:+
-| SAS           | `round()`                              | `rounde()`                                 | `ceil()`                                   | `floor()`                                  | `int()`                                    |
-+---------------+----------------------------------------+--------------------------------------------+--------------------------------------------+--------------------------------------------+--------------------------------------------+
-| R             | ::: {style="background-color: yellow"} | ::: {style="background-color: lightgreen"} | ::: {style="background-color: lightgreen"} | ::: {style="background-color: lightgreen"} | ::: {style="background-color: lightgreen"} |
-|               | `janitor::round_half_up()`             | `round()`                                  | `ceiling()`                                | `floor()`                                  | `trunc()`                                  |
-|               |                                        |                                            |                                            |                                            |                                            |
-|               | <div>                                  | {base}                                     | {base}                                     | {base}                                     | {base}                                     |
-|               |                                        | :::                                        | :::                                        | :::                                        | :::                                        |
-|               | `tidytlg::roundSAS()`                  |                                            |                                            |                                            |                                            |
-|               |                                        |                                            |                                            |                                            |                                            |
-|               | </div>                                 |                                            |                                            |                                            |                                            |
-|               | :::                                    |                                            |                                            |                                            |                                            |
-+---------------+----------------------------------------+--------------------------------------------+--------------------------------------------+--------------------------------------------+--------------------------------------------+
-| Example: 1.45 | 1.5                                    | 1.4                                        | 2                                          | 1                                          | 1                                          |
-|               |                                        |                                            |                                            |                                            |                                            |
-|               | (round to 1 decimal place)             | (round to 1 decimal place)                 |                                            |                                            |                                            |
-+---------------+----------------------------------------+--------------------------------------------+--------------------------------------------+--------------------------------------------+--------------------------------------------+
++---------------+----------------------------------------+----------------------------+-------------------+-----------------+--------------------+
+|               | round half up                          | round to even              | round up          | round down      | round towards zero |
++:=============:+:======================================:+:==========================:+:=================:+:===============:+:==================:+
+| SAS           | `round()`                              | `rounde()`                 | `ceil()`          | `floor()`       | `int()`            |
++---------------+----------------------------------------+----------------------------+-------------------+-----------------+--------------------+
+| R             | ::: {style="background-color: yellow"} | <div>                      | <div>             | <div>           | <div>              |
+|               | `janitor::round_half_up()`             |                            |                   |                 |                    |
+|               |                                        | `base::round()`            | `base::ceiling()` | `base::floor()` | `base::trunc()`    |
+|               | <div>                                  |                            |                   |                 |                    |
+|               |                                        | </div>                     | </div>            | </div>          | </div>             |
+|               | `tidytlg::roundSAS()`                  |                            |                   |                 |                    |
+|               |                                        |                            |                   |                 |                    |
+|               | </div>                                 |                            |                   |                 |                    |
+|               | :::                                    |                            |                   |                 |                    |
++---------------+----------------------------------------+----------------------------+-------------------+-----------------+--------------------+
+| Example: 1.45 | 1.5                                    | 1.4                        | 2                 | 1               | 1                  |
+|               |                                        |                            |                   |                 |                    |
+|               | (round to 1 decimal place)             | (round to 1 decimal place) |                   |                 |                    |
++---------------+----------------------------------------+----------------------------+-------------------+-----------------+--------------------+
 
 This table is summarized from links below, where more detailed discussions can be found -
 
@@ -58,54 +60,63 @@ This table is summarized from links below, where more detailed discussions can b
 
 -   R documentation: Base R [Round](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/Round), [`janitor::round_half_up()`](https://sfirke.github.io/janitor/reference/round_half_up.html), [`tidytlg::roundSAS()`](https://pharmaverse.github.io/tidytlg/main/reference/roundSAS.html)
 
--   [CAMIS](https://psiaims.github.io/CAMIS/) (Comparing Analysis Method Implementations in Software)
+-   [CAMIS](https://psiaims.github.io/CAMIS/) (Comparing Analysis Method Implementations in Software): A cross-industry initiative to document discrepant results between software.
+    [Rounding](https://psiaims.github.io/CAMIS/Comp/r-sas_rounding.html) is one of the comparisons, and there are much more [on this page](https://psiaims.github.io/CAMIS/)!
 
 ## Round half up in R
 
 The motivation for having a 'round half up' function is clear: it's a widely used rounding method, but there are no such options available in base R.
 
-There are multiple forums that discussed this topic, and a few functions available in some R packages.
-Hope you won't need to spend much time identifying a safe option for rounding half up in R after reading the following section.
-
-### Bug fix
+There are multiple forums that have discussed this topic, and quite a few functions already available.
+But which one to choose?
 
 The first time I needed to round half up in R, I chose the function from a [PHUSE paper](https://www.lexjansen.com/phuse-us/2020/ct/CT05.pdf) and applied it to my study.
-It works fine most of the time, but has issues like the following example -
+It works fine for a while until I encountered the following precision issue when double programming in R for TLGs made in SAS.
+
+### Numerical precision issue
+
+Example of rounding half up for 2436.845, with 2 decimal places:
 
 ```{r, message = FALSE}
 # a function that rounds half up
 # exact copy from: https://www.lexjansen.com/phuse-us/2020/ct/CT05.pdf
-ut_round <- function(x, n=0)
-{
- # x is the value to be rounded
- # n is the precision of the rounding
- scale <- 10^n
- y <- trunc(x * scale + sign(x) * 0.5) / scale
- # Return the rounded number
- return(y)
+ut_round <- function(x, n = 0) {
+  # x is the value to be rounded
+  # n is the precision of the rounding
+  scale <- 10^n
+  y <- trunc(x * scale + sign(x) * 0.5) / scale
+  # Return the rounded number
+  return(y)
 }
 # round half up for 2436.845, with 2 decimal places
 ut_round(2436.845, 2)
 ```
 
 The expected result is 2436.85, but the output rounds it down.
-The function's logic seems fine, I was not able to find the root cause.
 Thanks to the community effort, there are already discussions and resolution available in a [StackOverflow post](https://stackoverflow.com/questions/12688717/round-up-from-5#comment110611119_12688836) -
 
 > There are numerical precision issues, e.g., `round2(2436.845, 2)` returns `2436.84.` Changing `z + 0.5 to z + 0.5 + sqrt(.Machine$double.eps)` seems to work for me. -- Gregor Thomas Jun 24, 2020 at 2:16
 
-After fixing this bug:
+-   `.Machine$double.eps` is a built-in constant in R that represents the smallest positive floating-point number that can be represented on the system (reference: [Machine Characteristics](https://www.math.ucla.edu/~anderson/rw1001/library/base/html/zMachine.html))
+
+-   The expression `+ sqrt(.Machine$double.eps)` is used to add a very small value to mitigate floating-point precision issues.
+
+-   For more information about computational precision and floating-point, see the following links -
+
+    -   R: [Why doesn't R think these numbers are equal?](https://cran.r-project.org/doc/FAQ/R-FAQ.html#Why-doesn_0027t-R-think-these-numbers-are-equal_003f)
+    -   SAS: [Numerical Accuracy in SAS Software](https://documentation.sas.com/doc/en/lrcon/9.4/p0ji1unv6thm0dn1gp4t01a1u0g6.htm)
+
+After the fix:
 
 ```{r, message = FALSE}
 # revised rounds half up
-ut_round1 <- function(x, n=0)
-{
- # x is the value to be rounded
- # n is the precision of the rounding
- scale <- 10^n
- y <- trunc(x * scale + sign(x) * 0.5 + sqrt(.Machine$double.eps)) / scale
- # Return the rounded number
- return(y)
+ut_round1 <- function(x, n = 0) {
+  # x is the value to be rounded
+  # n is the precision of the rounding
+  scale <- 10^n
+  y <- trunc(x * scale + sign(x) * 0.5 + sqrt(.Machine$double.eps)) / scale
+  # Return the rounded number
+  return(y)
 }
 # round half up for 2436.845, with 2 decimal places
 ut_round1(2436.845, 2)
@@ -113,23 +124,30 @@ ut_round1(2436.845, 2)
 
 ### We are not alone
 
-The same issue occurred in the following ones as well, and has been raised by users:
+The same issue occurred in the following functions/options as well, and has been raised by users:
 
 -   `janitor::round_half_up()`: [issue](https://github.com/sfirke/janitor/issues/396) was raised and fixed in v2.1.0
 
 -   `Tplyr`: `options(tplyr.IBMRounding = TRUE)`, [issue](https://github.com/atorus-research/Tplyr/issues/124) was raised
 
--   `scrutiny::round_up_from()/round_up()`: [issue](https://lhdjung.github.io/scrutiny/reference/index.html#rounding) was raised
+-   `scrutiny::round_up_from()/round_up()`: [issue](https://github.com/lhdjung/scrutiny/issues/43) was raised and fixed
 
--   ...
+-   \...
+    and many others!
 
 ### Which one to use?
 
-The following two functions have the above bug fixed, they both came from the same [StackOverflow post](https://stackoverflow.com/questions/12688717/round-up-from-5).
+After reading this post, I hope it will help you save some time identifying which functions are safe to use for rounding half up.
+
+The following functions have the precision issue mentioned above fixed, they all share the same logic from this [StackOverflow post](https://stackoverflow.com/questions/12688717/round-up-from-5).
 
 -   [`janitor::round_half_up()`](https://sfirke.github.io/janitor/reference/round_half_up.html) **version \>= 2.1.0**
 -   [`tidytlg::roundSAS()`](https://pharmaverse.github.io/tidytlg/main/reference/roundSAS.html)
     -   this function has two more arguments that can convert the result to character and allow a character string to indicate missing values
+-   [`scrutiny::round_up_from()/round_up()`](https://lhdjung.github.io/scrutiny/reference/rounding-common.html) **version \>= 0.2.5**
+    -   `round_up_from()` has a `threshold` argument for rounding up, which adds flexibility for rounding up
+
+    -   `round_up()` rounds up from 5, which is a special case of `round_up_from()`
 
 <!--------------- appendices go here ----------------->
 

From 448d19852e800094c8ae6f8e8a80887b25e63de7 Mon Sep 17 00:00:00 2001
From: kaz462 <kangjie.zhang@bayer.com>
Date: Wed, 2 Aug 2023 11:58:27 -0700
Subject: [PATCH 3/8] #71: split the summary table

---
 posts/2023-07-24_rounding/rounding.qmd | 50 +++++++++++++++-----------
 1 file changed, 29 insertions(+), 21 deletions(-)

diff --git a/posts/2023-07-24_rounding/rounding.qmd b/posts/2023-07-24_rounding/rounding.qmd
index ad427ed9..6fec7bc6 100644
--- a/posts/2023-07-24_rounding/rounding.qmd
+++ b/posts/2023-07-24_rounding/rounding.qmd
@@ -32,27 +32,35 @@ However, they use different approaches when rounding off a 5:
 
 Although base R does not have the option for "round half up", there are functions available in other R packages (e.g., `janitor`, `tidytlg`).
 
-The following table lists some often-used rounding methods and their corresponding functions in SAS and R.
-
-+---------------+----------------------------------------+----------------------------+-------------------+-----------------+--------------------+
-|               | round half up                          | round to even              | round up          | round down      | round towards zero |
-+:=============:+:======================================:+:==========================:+:=================:+:===============:+:==================:+
-| SAS           | `round()`                              | `rounde()`                 | `ceil()`          | `floor()`       | `int()`            |
-+---------------+----------------------------------------+----------------------------+-------------------+-----------------+--------------------+
-| R             | ::: {style="background-color: yellow"} | <div>                      | <div>             | <div>           | <div>              |
-|               | `janitor::round_half_up()`             |                            |                   |                 |                    |
-|               |                                        | `base::round()`            | `base::ceiling()` | `base::floor()` | `base::trunc()`    |
-|               | <div>                                  |                            |                   |                 |                    |
-|               |                                        | </div>                     | </div>            | </div>          | </div>             |
-|               | `tidytlg::roundSAS()`                  |                            |                   |                 |                    |
-|               |                                        |                            |                   |                 |                    |
-|               | </div>                                 |                            |                   |                 |                    |
-|               | :::                                    |                            |                   |                 |                    |
-+---------------+----------------------------------------+----------------------------+-------------------+-----------------+--------------------+
-| Example: 1.45 | 1.5                                    | 1.4                        | 2                 | 1               | 1                  |
-|               |                                        |                            |                   |                 |                    |
-|               | (round to 1 decimal place)             | (round to 1 decimal place) |                   |                 |                    |
-+---------------+----------------------------------------+----------------------------+-------------------+-----------------+--------------------+
+
+In general, there are many often used rounding methods. In the table below, you can find examples of them applied to the number 1.45.
+
++---------------+----------------------------+----------------------------+----------+------------+--------------------+
+|               | round half up              | round to even              | round up | round down | round towards zero |
++:=============:+:==========================:+:==========================:+:========:+:==========:+:==================:+
+| Example: 1.45 | 1.5                        | 1.4                        | 2        | 1          | 1                  |
+|               |                            |                            |          |            |                    |
+|               | (round to 1 decimal place) | (round to 1 decimal place) |          |            |                    |
++---------------+----------------------------+----------------------------+----------+------------+--------------------+
+
+Here are the corresponding ways to implement these methods in SAS and R.
+
++---------+----------------------------------------+-----------------+-------------------+-----------------+--------------------+
+|         | round half up                          | round to even   | round up          | round down      | round towards zero |
++:=======:+:======================================:+:===============:+:=================:+:===============:+:==================:+
+| SAS     | `round()`                              | `rounde()`      | `ceil()`          | `floor()`       | `int()`            |
++---------+----------------------------------------+-----------------+-------------------+-----------------+--------------------+
+| R       | ::: {style="background-color: yellow"} | <div>           | <div>             | <div>           | <div>              |
+|         | `janitor::round_half_up()`             |                 |                   |                 |                    |
+|         |                                        | `base::round()` | `base::ceiling()` | `base::floor()` | `base::trunc()`    |
+|         | <div>                                  |                 |                   |                 |                    |
+|         |                                        | </div>          | </div>            | </div>          | </div>             |
+|         | `tidytlg::roundSAS()`                  |                 |                   |                 |                    |
+|         |                                        |                 |                   |                 |                    |
+|         | </div>                                 |                 |                   |                 |                    |
+|         | :::                                    |                 |                   |                 |                    |
++---------+----------------------------------------+-----------------+-------------------+-----------------+--------------------+
+
 
 This table is summarized from links below, where more detailed discussions can be found -
 

From c973204eba88e8424d52df86e1e863b6a821496a Mon Sep 17 00:00:00 2001
From: kaz462 <kangjie.zhang@bayer.com>
Date: Wed, 2 Aug 2023 12:03:25 -0700
Subject: [PATCH 4/8] #71: update .lycheeignore

---
 .lycheeignore | 1 +
 1 file changed, 1 insertion(+)

diff --git a/.lycheeignore b/.lycheeignore
index cdb85a26..9f57b8a6 100644
--- a/.lycheeignore
+++ b/.lycheeignore
@@ -5,3 +5,4 @@ https://www.linkedin.com/*
 https://cosa.cdisc.org/events/Admiral
 ///home/runner/work/blog/blog/posts/2023-06-28_welcome/pharmaverse.slack.com
 https://pharmaverse.github.io/blog/posts/2023-06-27_hackathon_app/
+https://cran.r-project.org/doc/FAQ/R-FAQ.html#Why-doesn_0027t-R-think-these-numbers-are-equal_003f

From baae1b90ee763aeca6ac17fbbe26b249b890294d Mon Sep 17 00:00:00 2001
From: kaz462 <kangjie.zhang@bayer.com>
Date: Mon, 21 Aug 2023 18:16:24 -0700
Subject: [PATCH 5/8] #71: update the last section

---
 posts/2023-07-24_rounding/rounding.qmd | 67 ++++++++++++++++++++++----
 1 file changed, 58 insertions(+), 9 deletions(-)

diff --git a/posts/2023-07-24_rounding/rounding.qmd b/posts/2023-07-24_rounding/rounding.qmd
index 6fec7bc6..1eff46b2 100644
--- a/posts/2023-07-24_rounding/rounding.qmd
+++ b/posts/2023-07-24_rounding/rounding.qmd
@@ -32,8 +32,8 @@ However, they use different approaches when rounding off a 5:
 
 Although base R does not have the option for "round half up", there are functions available in other R packages (e.g., `janitor`, `tidytlg`).
 
-
-In general, there are many often used rounding methods. In the table below, you can find examples of them applied to the number 1.45.
+In general, there are many often used rounding methods.
+In the table below, you can find examples of them applied to the number 1.45.
 
 +---------------+----------------------------+----------------------------+----------+------------+--------------------+
 |               | round half up              | round to even              | round up | round down | round towards zero |
@@ -53,15 +53,16 @@ Here are the corresponding ways to implement these methods in SAS and R.
 | R       | ::: {style="background-color: yellow"} | <div>           | <div>             | <div>           | <div>              |
 |         | `janitor::round_half_up()`             |                 |                   |                 |                    |
 |         |                                        | `base::round()` | `base::ceiling()` | `base::floor()` | `base::trunc()`    |
-|         | <div>                                  |                 |                   |                 |                    |
-|         |                                        | </div>          | </div>            | </div>          | </div>             |
+|         | ::: {style="background-color: yellow"} |                 |                   |                 |                    |
+|         | <div>                                  | </div>          | </div>            | </div>          | </div>             |
+|         |                                        |                 |                   |                 |                    |
 |         | `tidytlg::roundSAS()`                  |                 |                   |                 |                    |
 |         |                                        |                 |                   |                 |                    |
 |         | </div>                                 |                 |                   |                 |                    |
 |         | :::                                    |                 |                   |                 |                    |
+|         | :::                                    |                 |                   |                 |                    |
 +---------+----------------------------------------+-----------------+-------------------+-----------------+--------------------+
 
-
 This table is summarized from links below, where more detailed discussions can be found -
 
 -   Two SAS blogs about [round-to-even](https://blogs.sas.com/content/iml/2019/11/11/round-to-even.html) and [rounding-up-rounding-down](https://blogs.sas.com/content/iml/2011/10/03/rounding-up-rounding-down.html)
@@ -76,7 +77,8 @@ This table is summarized from links below, where more detailed discussions can b
 The motivation for having a 'round half up' function is clear: it's a widely used rounding method, but there are no such options available in base R.
 
 There are multiple forums that have discussed this topic, and quite a few functions already available.
-But which one to choose?
+But which ones to choose?
+Are they safe options?
 
 The first time I needed to round half up in R, I chose the function from a [PHUSE paper](https://www.lexjansen.com/phuse-us/2020/ct/CT05.pdf) and applied it to my study.
 It works fine for a while until I encountered the following precision issue when double programming in R for TLGs made in SAS.
@@ -143,9 +145,7 @@ The same issue occurred in the following functions/options as well, and has been
 -   \...
     and many others!
 
-### Which one to use?
-
-After reading this post, I hope it will help you save some time identifying which functions are safe to use for rounding half up.
+### Which ones to use?
 
 The following functions have the precision issue mentioned above fixed, they all share the same logic from this [StackOverflow post](https://stackoverflow.com/questions/12688717/round-up-from-5).
 
@@ -157,6 +157,55 @@ The following functions have the precision issue mentioned above fixed, they all
 
     -   `round_up()` rounds up from 5, which is a special case of `round_up_from()`
 
+### Are they safe options?
+
+Those "round half up" functions do not offer the same level of precision and accuracy as the base R round function.
+
+For example, let's consider a value `a` that is slightly less than `1.5`.
+If we choose round half up approach to round `a` to 0 decimal places, an output of `1` is expected.
+However, those functions yield a result of `2` because `1.5 - a` is less than `sqrt(.Machine$double.eps)`.
+
+```{r, message = FALSE}
+a <- 1.5 - 0.5*sqrt(.Machine$double.eps)
+ut_round1(a, 0)
+janitor::round_half_up(a, digits = 0)
+```
+
+This behavior aligns the floating point number comparison functions `all.equal()` and `dplyr::near()` with default tolerance `.Machine$double.eps^0.5`, where 1.5 and `a` are treated as equal.
+
+```{r, message = FALSE}
+all.equal(a, 1.5)
+dplyr::near(a, 1.5)
+```
+
+We can get the expected results from base R `round` as it provides greater accuracy.
+
+```{r, message = FALSE}
+round(a)
+```
+
+Here is an example when base R `round` reaches the precision limit:
+
+```{r, message=FALSE}
+# b is slightly less than 1.5
+b <- 1.5 - 0.5*.Machine$double.eps
+# 1 is expected but the result is 2 
+round(b)
+```
+
+The precision and accuracy requirements can vary depending on the application.
+Therefore, it is essential to be aware each function's performance in your specific context before making a choice.
+
+## Conclusion
+
+> With the differences in default behaviour across languages, you could consider your QC strategy and whether an acceptable level of fuzz in the electronic comparisons could be allowed for cases such as rounding when making comparisons between 2 codes written in different languages as long as this is documented.
+> Alternatively you could document the exact rounding approach to be used in the SAP and then match this regardless of programming language used.
+> - Ross Farrugia
+
+Thanks Ross Farrugia, Ben Straub, Edoardo Mancini and Liming for reviewing this blog post and providing valuable feedback!
+
+If you spot an issue or have different opinions, please don't hesitate to raise them through [pharmaverse/blog](https://github.com/pharmaverse/blog)!
+
 <!--------------- appendices go here ----------------->
 
 ```{r, echo=FALSE}

From 3abb047a7c99f43b1badfe9c29ccdcafe6472b44 Mon Sep 17 00:00:00 2001
From: kaz462 <kangjie.zhang@bayer.com>
Date: Mon, 21 Aug 2023 18:23:05 -0700
Subject: [PATCH 6/8] #71: update wordlist

---
 inst/WORDLIST.txt | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/inst/WORDLIST.txt b/inst/WORDLIST.txt
index aefbf9c6..d2b5ee0c 100644
--- a/inst/WORDLIST.txt
+++ b/inst/WORDLIST.txt
@@ -321,3 +321,5 @@ dy
 lubridate
 TRTSDTM
 ymd
+behaviour
+Farrugia

From 53a59926f6a2da26f1cd0d312298453027a85c58 Mon Sep 17 00:00:00 2001
From: kaz462 <kangjie.zhang@bayer.com>
Date: Mon, 21 Aug 2023 18:28:43 -0700
Subject: [PATCH 7/8] #71: styler/link

---
 posts/2023-07-24_rounding/rounding.qmd | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/posts/2023-07-24_rounding/rounding.qmd b/posts/2023-07-24_rounding/rounding.qmd
index 1eff46b2..6a1ad0e6 100644
--- a/posts/2023-07-24_rounding/rounding.qmd
+++ b/posts/2023-07-24_rounding/rounding.qmd
@@ -67,7 +67,7 @@ This table is summarized from links below, where more detailed discussions can b
 
 -   Two SAS blogs about [round-to-even](https://blogs.sas.com/content/iml/2019/11/11/round-to-even.html) and [rounding-up-rounding-down](https://blogs.sas.com/content/iml/2011/10/03/rounding-up-rounding-down.html)
 
--   R documentation: Base R [Round](https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/Round), [`janitor::round_half_up()`](https://sfirke.github.io/janitor/reference/round_half_up.html), [`tidytlg::roundSAS()`](https://pharmaverse.github.io/tidytlg/main/reference/roundSAS.html)
+-   R documentation: Base R [Round](https://stat.ethz.ch/R-manual/R-devel/library/base/html/Round.html), [`janitor::round_half_up()`](https://sfirke.github.io/janitor/reference/round_half_up.html), [`tidytlg::roundSAS()`](https://pharmaverse.github.io/tidytlg/main/reference/roundSAS.html)
 
 -   [CAMIS](https://psiaims.github.io/CAMIS/) (Comparing Analysis Method Implementations in Software): A cross-industry initiative to document discrepant results between software.
     [Rounding](https://psiaims.github.io/CAMIS/Comp/r-sas_rounding.html) is one of the comparisons, and there are much more [on this page](https://psiaims.github.io/CAMIS/)!
@@ -166,7 +166,7 @@ If we choose round half up approach to round `a` to 0 decimal places, an output
 However, those functions yield a result of `2` because `1.5 - a` is less than `sqrt(.Machine$double.eps)`.
 
 ```{r, message = FALSE}
-a <- 1.5 - 0.5*sqrt(.Machine$double.eps)
+a <- 1.5 - 0.5 * sqrt(.Machine$double.eps)
 ut_round1(a, 0)
 janitor::round_half_up(a, digits = 0)
 ```
@@ -188,8 +188,8 @@ Here is an example when base R `round` reaches the precision limit:
 
 ```{r, message=FALSE}
 # b is slightly less than 1.5
-b <- 1.5 - 0.5*.Machine$double.eps
-# 1 is expected but the result is 2 
+b <- 1.5 - 0.5 * .Machine$double.eps
+# 1 is expected but the result is 2
 round(b)
 ```
 

From 1a031b6e09c4669b3c67aeb7884aa102ea21f453 Mon Sep 17 00:00:00 2001
From: kaz462 <kangjie.zhang@bayer.com>
Date: Mon, 21 Aug 2023 18:30:32 -0700
Subject: [PATCH 8/8] #71: update wordlist

---
 inst/WORDLIST.txt | 1 +
 1 file changed, 1 insertion(+)

diff --git a/inst/WORDLIST.txt b/inst/WORDLIST.txt
index d2b5ee0c..e14029fe 100644
--- a/inst/WORDLIST.txt
+++ b/inst/WORDLIST.txt
@@ -323,3 +323,4 @@ TRTSDTM
 ymd
 behaviour
 Farrugia
+ethz