Reduce tailtol tolerance in expecatation of CRAN note regarding OpenB…

…LAS test, EVEN THOUGH THIS PLATFORM HAS BEEN USING OPENBLAS FOR > 10 YEARS AND PASSED THE TESTS!

DESCRIPTION

@@ -2,8 +2,8 @@ Package: minimaxApprox
 Type: Package
 Title: Implementation of Remez Algorithm for Polynomial and Rational Function
     Approximation
-Version: 0.2.1
-Date: 2023-09-04
+Version: 0.2.1.9000
+Date: 2023-09-05
 Authors@R: person(given="Avraham", family="Adler",role=c("aut", "cre", "cph"),
     email="[email protected]", comment = c(ORCID = "0000-0002-3039-0703"))
 Description: Implements the algorithm of Remez (1962) for polynomial minimax

R/MiniMaxApprox.R

@@ -38,7 +38,7 @@ minimaxApprox <- function(fn, lower, upper, degree, relErr = FALSE, xi = NULL,
   # Used for cases where we check polynomial degree n + 1.
   # See issue 2 https://github.com/aadler/minimaxApprox/issues/2
   if (!("tailtol" %in% names(opts))) {
-    opts$tailtol <- min(1e-10, (upper - lower) / 1e6)
+    opts$tailtol <- min(sqrt(.Machine$double.eps), (upper - lower) / 1e6)
   }
 
   if (!("ztol" %in% names(opts))) {
@@ -99,10 +99,10 @@ minimaxApprox <- function(fn, lower, upper, degree, relErr = FALSE, xi = NULL,
                           "of degree", degree, "but successfully completed",
                           "when looking for a polynomial of degree",
                           degree + 1L, "with the largest coefficient's",
-                          "contribution to the approximation <=",
-                          paste0(opts$tailtol, ":"), "the tailtol option. The",
-                          "result is a polynomial of length", degree, "as the",
-                          "uppermost coefficient is effectively 0.")
+                          "contribution to the approximation <= the tailtol",
+                          "option. The result is a polynomial of length",
+                          degree, "as the uppermost coefficient is effectively",
+                          "0.")
             mmA$a <- mmA$a[-length(mmA$a)]
             message(mess)
           } else {

README.md

@@ -19,7 +19,7 @@ If you use the package, please cite it as:
   Adler A (2023). minimaxApprox: Implementation of Remez Algorithm for
   Polynomial and Rational Function Approximation.
   [doi: 10.5281/zenodo.8158855](https://doi.org/10.5281/zenodo.8158855),
-  R package version 0.2.0, https://CRAN.R-project.org/package=minimaxApprox
+  R package version 0.2.1.9000, https://CRAN.R-project.org/package=minimaxApprox
 
 A BibTeX entry for LaTeX users is:
 
@@ -30,7 +30,7 @@ A BibTeX entry for LaTeX users is:
     year = {2023},
     url = {https://CRAN.R-project.org/package=minimaxApprox},
     doi = {10.5281/zenodo.8158855},
-    note = {R package version 0.2.0},
+    note = {R package version 0.2.1.9000},
   }
 ```
 

inst/CITATION

@@ -10,5 +10,5 @@ bibentry(bibtype     = "Manual",
          year         = "2023",
          url          = "https://CRAN.R-project.org/package=minimaxApprox",
          doi          = "10.5281/zenodo.8158855",
-         note         = "R package version 0.2.1"
+         note         = "R package version 0.2.1.9000"
 )

inst/NEWS.Rd

@@ -15,12 +15,24 @@
   }
 }
 
+\section{Version 0.2.1.9000 (2023-09-05)}{
+  \subsection{Changed}{
+    \itemize{
+      \item \strong{Breaking:} Reduced \code{tailtol} tolerance to
+      \code{sqrt(.Machine$double.eps)} as one of the myriad \acronym{CRAN}
+      testbeds also had issues with convergence. Different \acronym{BLAS}
+      implementations seem to display different levels of precision.
+    }
+  }
+}
+
 \section{Version 0.2.1 (2023-09-04)}{
   \subsection{Changed}{
     \itemize{
       \item Test for calculating polynomial of degree \code{n + 1} when one of
-      degree \code{n} fails, while passing both R Mac Builder and Github's Mac
-      platform, failed on CRAN's testbed. So test is not run for Mac.
+      degree \code{n} fails, while passing both R \acronym{Mac} Builder and
+      Github's \acronym{Mac} platform, failed on \acronym{CRAN}'s testbed.
+      So test is no longer run for \acronym{Mac} on \acronym{CRAN}.
     }
   }
 }

inst/tinytest/test_MiniMaxApprox.R

@@ -171,7 +171,7 @@ if (!("darwin" %in% tolower(Sys.info()[["sysname"]]))) {
   mess <- paste("The algorithm failed while looking for a polynomial of degree",
                 "10 but successfully completed when looking for a polynomial of",
                 "degree 11 with the largest coefficient's contribution to the",
-                "approximation <= 1e-10: the tailtol option. The result is a",
+                "approximation <= the tailtol option. The result is a",
                 "polynomial of length 10 as the uppermost coefficient is",
                 "effectively 0.")
   fn <- function(x) 1 / (1 + (5 * x) ^ 2)

man/MiniMaxApprox.Rd

@@ -57,10 +57,11 @@ minimaxApprox(fn, lower, upper, degree, relErr = FALSE, xi = NULL,
             \item \code{tailtol}: numeric; The tolerance of the coefficient of
             the largest power of \code{x} to be ignored when performing the
             polynomial approximation a second time. Defaults to the smaller of
-            \eqn{1\times 10^{-10}}{1e-10} or \eqn{\frac{\code{upper} -
-            \code{lower}}{10^6}}{(\code{upper} - \code{upper}) / 1e6}. Set to
-            \code{NULL} to skip the \code{degree + 1} check completely. See
-            \strong{Details}.
+            \eqn{\sqrt{\text{.Machine\$double.eps}} \approx 1.49\times
+            10^{-8}}{\code{sqrt(.Machine$double.eps)}} or
+            \eqn{\frac{\code{upper} - \code{lower}}{10^6}}{(\code{upper} -
+            \code{upper}) / 1e6}. Set to \code{NULL} to skip the
+            \code{degree + 1} check completely. See \strong{Details}.
             \item \code{ztol}: numeric; The tolerance for each polynomial or
             rational numerator or denominator coefficient's contribution to
             \strong{not} to be set to 0. Similar to polynomial \code{tailtol}