TikZ fpu parece ser impreciso

Question

Estou usando uma macro deaqui(graças agato de Schrodinger). Veja meu 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}
    {
     \pgfmathsetmacro{\UABmValues}{\UABmValues[\i]}
     \pgfmathparseFPU{-25500 / (\UABmValues / 1000 - 255 / 52) - 5200 - 3.0897 / 8 * \k}\i, \pgfmathresult\\
    }

\end{document}

Dá:

1. 4.414001000000000
2. 3.483002000000000
3. 3,652002000000000
4. 2.221002000000000
5. 0,990002
6. 0,159003
7. -0,571997
8. -1,302997000000000
9. -1,033997000000000
10. -0,064996
11. 1.304004000000000

Quando faço o mesmo, digamos, com MATLAB:

    UABmValues = [14.9 15.8 17.7 18.3 19 20 21.1 22.2 24.3 26.9 30.1];
    R = 30 : 5 : 80;

    %prints the result to the console:
    for j = 1 : 11

      result = -25500 / (UABmValues(j) / 1000 - 255 / 52) - 5200 - 3.0897 / 8 * R(j);
      fprintf('j=%d, ', j)
      fprintf('%d.\n', result)

    end

Do que recebo o seguinte:

1. 4.261621e+00.
2. 3.290914e+00.
3. 3.388431e+00.
4. 2.098301e+00.
5. 9.151911e-01.
6. 5.300458e-02.
7. -7.017887e-01.
8. -1,456052e+00.
9. -1.139024e+00.
10. -2.840543e-01.
11. 1.217927e+00.

A diferença é enorme.

Por que é tão? Alguma sugestão de como resolver isso fpu, se pelo menos possível?

Obrigado pela sua ajuda e esforço antecipadamente!

Answer 1

O módulo de ponto flutuante PGFéimpreciso, pois usa aritmética TeX, portanto não ultrapassa cinco dígitos decimais. Não se destina a ser uma ferramenta aritmética de ponto flutuante para todos os fins, mas apenas para fazer composição tipográfica.

Usar xfp.

\documentclass{article}
\usepackage{tikz}
\usepackage{xfp}

\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}
  {
   \pgfmathsetmacro{\UABmValues}{\UABmValues[\i]}
   \i, $\fpeval{-25500 / (\UABmValues / 1000 - 255 / 52) - 5200 - 3.0897 / 8 * \k}$\par
  }

\end{document}

Answer 2

Podes tentarFP,xfp(veja a resposta de egreg) ouLua

1)atualização: versão com lua

% !TEX TS-program = lualatex

\documentclass{scrartcl}
\usepackage{pgffor,pgfmath}
\def\luafun#1#2{
    \directlua{
        x = #1;
        y = #2;
       r=-25500/(x/1000-255/52)-5200-3.0897/8*y
       tex.print(r)}
} 

\begin{document}
\def\UABmValues{{14.9, 15.8, 17.7, 18.3, 19, 20, 21.1, 22.2, 24.3, 26.9, 30.1}}

\foreach[count = \i from 0] \k in {30, 35, ..., 80}
{
\pgfmathsetmacro{\myval}{\UABmValues[\i]}%
\luafun{\myval}{\k}\par
 }

\end{document}

2) versão antiga com fp

\documentclass{scrartcl}
\usepackage{tikz,fp}
\newcommand\pgfmathparseFP[1]{
   \begingroup
        \FPeval\pgfmathresult{(#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}
{
\pgfmathsetmacro{\myval}{\UABmValues[\i]}%
\pgfmathparseFP{-25500/(\myval/1000-255/52)-5200-3.0897/8*\k}\i, \pgfmathresult\par
 }

\end{document}

Answer 3

Uma implementação com o CASSábio (matemática)eSageTeX:

eu usoarara: sagetexpara compilar.

% arara: pdflatex
% arara: sagetex
% arara: pdflatex

\documentclass{scrartcl}
\usepackage{sagetex, amsmath}
\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}}

\section{pgfmath}
\foreach[count = \i from 0] \k in {30, 35, ..., 80}
{
\pgfmathsetmacro{\UABmValues}{\UABmValues[\i]}
\pgfmathparseFPU{-25500 / (\UABmValues / 1000 - 255 / 52) - 5200 - 3.0897 / 8 * \k}\noindent\i, \UABmValues, \pgfmathresult \\
}

\section{SageTeX}
\subsection{Sage-Output}
$\sagestr{MyOut}$

\subsection{From sageblock or sagesilent}
\begin{sageblock}
Val = ([14.9, 15.8, 17.7, 18.3, 19, 20, 21.1, 22.2, 24.3, 26.9, 30.1])
## Test:
#print Val[1]
#print len(Val)

# Function
f(x,y) = -25500/(x/1000 - 255/52) -5200 -3.0897/8 *(30+5*y)

# Short Output
#for i in range (len(Val)): print i,',',float(Val[i]),',', f(Val[i],i)

# Better Output    
data = [(i,  float(Val[i]), f(Val[i],i)) for i in range(len(Val))] 
data_str = [',   '.join(map(str, t)) for t in data] 
data_str = '\n'.join(data_str) 

MyOut = latex(data_str)
#print data_str
\end{sageblock}
\end{document}