How to use the TikZ fpu library?

Question

When I calculate something, sometimes become the interim results to big for the pgf system. One can use the fpu library. I read about it in the TikZ & PGF manual (see page 627), here and here but I still get this error:

Paragraph ended before `\pgfflt@readlowlevelfloat` was complete.

What is wrong?

Here is my code:

\documentclass{scrartcl}
\usepackage{tikz}
\usetikzlibrary{fpu}
\begin{document}

  %data values:
  \def\RTable{{100,100.391,100.781,101.172,101.562,101.953,102.343,102.733,103.123,103.513,103.903,104.292,104.682,105.071,105.46,105.849,106.238,106.627,107.016,107.405,107.794,108.182,108.57,108.959,109.347,109.735,110.123,110.51,110.898,111.286,111.673,112.06,112.447,112.835,113.221,113.608,113.995,114.382,114.768,115.155,115.541,115.927,116.313,116.699,117.085,117.47,117.856,118.241,118.627,119.012,119.397,119.782,120.167,120.552,120.936,121.321,121.705,122.09,122.474,122.858,123.242,123.626,124.009,124.393,124.777,125.16,125.543,125.926,126.309,126.692,127.075,127.458,127.84,128.223,128.605,128.987,129.37,129.752,130.133,130.515,130.897}}

  %prints the result to the console:
  \pgfkeys{/pgf/fpu}
  \foreach \i in {0, ..., 80}
    {
     \pgfmathparse{abs(\RTable[\i] - 100 - 3.0897 / 8 * \i)}\i, \pgfmathresult\\
    }
  \pgfkeys{/pgf/fpu=false}

\end{document}

Update:

I'am using a macro from here (thanks to Schrödinger's cat). See my MWE:

\documentclass{scrartcl}
\usepackage{tikz}
\usetikzlibrary{fpu}
\newcommand\pgfmathparseFPU[1]{
                               \begingroup
                                 \pgfkeys{
                                          /pgf/fpu,
                                          /pgf/fpu/output format = fixed
                                         }
                                 \pgfmathparse{#1}
                                 \pgfmathsmuggle
                                 \pgfmathresult
                               \endgroup}

\begin{document}

  %data values:
  \def\UABmValues{{14.9, 15.8, 17.7, 18.3, 19, 20, 21.1, 22.2, 24.3, 26.9, 30.1}}

  %prints the result to the console:
  \foreach[count = \i from 0] \k in {30, 35, ..., 80}
    {
     \pgfmathparseFPU{-25500 / (\UABmValues[\i] / 1000 - 255 / 52) - 5200 - 3.0897 / 8 * \k}\i, \pgfmathresult\\
    }

\end{document}

and get still a

Paragraph ended before `\pgfflt@readlowlevelfloat` was complete.

error. What do am I wrong?

Thank you for your help and effort in advance!

Answer 1

Sounds like a job for the LaTeX3 FPU:

\documentclass{article}
\usepackage{expl3}
\ExplSyntaxOn
\cs_new_eq:NN \fpeval \fp_eval:n
\cs_new_eq:NN \clistitem \clist_item:Nn
\cs_new_eq:NN \foreachint \int_step_inline:nnnn
\ExplSyntaxOff
\begin{document}

  %data values:

  \def\RTable{100,100.391,100.781,101.172,101.562,101.953,102.343,102.733,103.123,103.513,103.903,104.292,104.682,105.071,105.46,105.849,106.238,106.627,107.016,107.405,107.794,108.182,108.57,108.959,109.347,109.735,110.123,110.51,110.898,111.286,111.673,112.06,112.447,112.835,113.221,113.608,113.995,114.382,114.768,115.155,115.541,115.927,116.313,116.699,117.085,117.47,117.856,118.241,118.627,119.012,119.397,119.782,120.167,120.552,120.936,121.321,121.705,122.09,122.474,122.858,123.242,123.626,124.009,124.393,124.777,125.16,125.543,125.926,126.309,126.692,127.075,127.458,127.84,128.223,128.605,128.987,129.37,129.752,130.133,130.515,130.897}

  %prints the result to the console:

  \foreachint{1}{1}{81}{%
    #1,
    \fpeval{abs(\clistitem\RTable{#1} - 100 - 3.0897 / 8 * (#1 - 1))}\\
  }

\end{document}

(The convention in expl3 is to index from 1 as this aligns with the most common use case: typesetting. I've therefore indexed the list from one but corrected to index from zero for the equation itself.)