TikZ fpu seems to be inaccurate

Question

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

\end{document}

Gives:

4.414001000000000
3.483002000000000
3.652002000000000
2.221002000000000
0.990002
0.159003
-0.571997
-1.302997000000000
-1.033997000000000
-0.064996
1.304004000000000

When I do the same, let say, with 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

Than I get following:

4.261621e+00.
3.290914e+00.
3.388431e+00.
2.098301e+00.
9.151911e-01.
5.300458e-02.
-7.017887e-01.
-1.456052e+00.
-1.139024e+00.
-2.840543e-01.
1.217927e+00.

The difference is huge.

Why is it so? Any suggestions how to solve it with fpu, if at least possible?

Thank you for your help and effort in advance!

The PGF FPU uses TeX \dimen registers for calculations, so it has the same accuracy restrictions. The smallest representable difference in a TeX \dimen is 1sp, which is 0.00002pt (try \the\dimexpr1sp\relax). If you need more accuracy, try the LaTeX3 FPU (loaded by the xfp package). — Phelype Oleinik, Dec 26 '19 at 12:32
@PhelypeOleinik fp gives good results ... but I agree with you xfp seems to be the good way. Perhaps lua is the better way ? — Alain Matthes, Dec 26 '19 at 13:15
@AlainMatthes Yes, fp has a higher accuracy than the LaTeX3 FPU. (The latter conforms to the IEEE-754 standard, accurate to 16 significant digits or so). But xfp (and Lua, for that matter) is fully expandable, while fp is not. I'm not sure about Lua's accuracy. But my job description is to advertise expl3, so I had to suggest that ;-) — Phelype Oleinik, Dec 26 '19 at 13:19
@PhelypeOleinik I agree with you xfp is fully expandable. I use fp because it was the only solution several years ago.I think you have wit lua IEEE 754 double precision floating point — Alain Matthes, Dec 26 '19 at 14:42

score 20 · Accepted Answer · answered Dec 26 '19 at 14:24

The PGF floating point module is inaccurate, as it uses TeX arithmetic, so it doesn't go beyond five decimal digits. It is not meant as an all-purpose floating point arithmetic tool, but just to do typesetting.

Use 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}

This is the first I've heard of the xfp package. Are there any known side effects (for instance, speed)? — Matthew Leingang, Dec 27 '19 at 19:57

Alain Matthes · Answer 2 · 2019-12-26T15:17:07.693

13

You can try fp, xfp (see egreg's answer) or lua

1) update : version with 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) old version with 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}

edited Dec 26 '19 at 15:17

answered Dec 26 '19 at 13:13

Alain Matthes

95,075

What is the drawback of doing so per default? I mean, pgfmath could be patched like this. – Oleg Lobachev Dec 26 '19 at 14:04
3

@OlegLobachev maintenance. The maintainers of TikZ don't want to use expl3 and have their reasons for doing so. – Skillmon Dec 26 '19 at 14:20
@OlegLobachev Balance between speed and precision. pgfmath is used usefully by some libraries and precision is not always as important – Alain Matthes Dec 26 '19 at 14:25
I don't know how to use more digits with lua – Alain Matthes Dec 26 '19 at 15:37
4

@OlegLobachev One of the reasons is performance. It would essentially double the load time. See here for a discussion. – Dec 26 '19 at 15:50

cis · Answer 3 · 2019-12-26T16:16:51.657

An implementation with the CAS Sage(math) and SageTeX:

I use arara: sagetex for compiling.

% 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}

TikZ fpu seems to be inaccurate

3 Answers3

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