[Rd] qt() returns Inf with certain negative ncp values

[Stephen Berman]

I asked about the following observations on r-help and it was suggested
that they may indicate an algorithmic problem with qt(), so I thought I
should report them here.


The Inf results below seem surprising:

> sapply(-1:-10, \(ncp) qt(1-1*(10^(-4+ncp)), 35, ncp))
 [1]  3.6527153  3.0627759  2.4158355  1.7380812  1.0506904  0.3700821
 [7]        Inf -0.9279783 -1.5341759 -2.1085213

> sapply(seq(-6.9, -7.9, -0.1), \(ncp) qt(1-1*(10^(-4+ncp)), 35, ncp))
 [1] -0.2268386        Inf        Inf        Inf -0.4857400 -0.5497784
 [7] -0.6135402 -0.6770143 -0.7401974 -0.8030853 -0.8656810

These inputs also yield many repetitions of the following warning
message:

In qt(1 - 1 * (10^(-4 + ncp)), 35, ncp) :
  full precision may not have been achieved in 'pnt{final}'

In particular, in the range -1:-10 I don't get this warning with ncp =
-1 through -4, but I do get it once with each of -5 and -8 through -10,
32 times with -6, and 50 times with -7.  In the range -6.9:-7.9 I get
the warning twice with each of -6.9 and -7.3 through -7.7, once with
-7.8 and -7.9, and 50 times with each of -7.0 through -7.2.


In case it matters:

> sessionInfo()
R Under development (unstable) (2022-06-05 r82452)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Linux From Scratch r11.0-165

Matrix products: default
BLAS:   /usr/lib/R/lib/libRblas.so
LAPACK: /usr/lib/R/lib/libRlapack.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C
 [9] LC_ADDRESS=C               LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base

loaded via a namespace (and not attached):
[1] compiler_4.3.0 tools_4.3.0


Thanks.
Steve Berman