Wrong calculation in Tikz foreach

Question

I've a misunderstanding about the method Tikz compute some numbers. I draw a graph with some scale. Here is a MWE :

\documentclass{standalone}
\usepackage[french]{babel}
\usepackage{tikz}

\begin{document}
    \begin{tikzpicture}[yscale=0.1,xscale=25]
    \draw[<->] (0.5,0) node[below right]{t} -- (0,0) -- (0,100) node[above left]{x(t)};

    %%Graduation
    \foreach \t in {0, 0.08, ..., 0.48}{%
        \draw (\t,1) -- (\t,-1) node[below]{\t};}
    \end{tikzpicture}
\end{document}

I thought 0.08 x 5 = 0.40 and not 0.40001. And why the number 0.48 does not appear ?

I guess the xscale factor is not foreign by this problem but i can't address the problem by changing this factor. Otherwise i have a coefficient in all the following graphplots.

I read on this post that pgf has a uniform relative precision of about 4–5 correct digits. Is it the same for Tikz ? Is there a way to increase the precision of Tikz ?

Thx for you help !

Answer 1

The limited precision is the obstacle.

You can get much greater accuracy using expl3.

\documentclass{standalone}
\usepackage{tikz}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\fpforeach}{mmmm}
 {% #1 = start, #2 = step, #3 = end, #4 = what to do
  \fp_step_inline:nnnn { #1 } { #2 } { #3 } { #4 }
 }
\ExplSyntaxOff

\begin{document}

\begin{tikzpicture}[yscale=0.1,xscale=25]
\draw[<->] (0.5,0) node[below right]{t} -- (0,0) -- (0,100) node[above left]{x(t)};

%%Graduation
\fpforeach{0}{0.08}{0.48}
 {
  \draw (#1,1) -- (#1,-1) node[below]{#1};
 }
\end{tikzpicture}

\end{document}

Beware of divisions, though, because the problems are still there and the final step might be missing due to accuracy issues nonetheless, but this is a problem with all floating point computations.

Answer 2

The Tikz manual states that this is normal, and I quote (p 902):

Normally, when a list item ... is encountered, there should already have been two list items before it, which where numbers. Examples of numbers are 1, -10, or -0.24. Let us call these numbers x and y and let d := y − x be their difference. Next, there should also be one number following the three dots, let us call this number z.

In this situation, the part of the list reading x,y,...,z is replaced by x, x + d, x + 2d, x + 3d, ..., x + md where the last dots are semantic dots, not syntactic dots. The value m is the largest number such that x + md ≤ z if d is positive or such that x + md ≥ z if d is negative.

Perhaps it is best to explain this by some examples: The following <list> have the same effects:

\foreach \x in {1,2,...,6} {\x, } yields 1, 2, 3, 4, 5, 6

\foreach \x in {1,2,3,...,6} {\x, } yields 1, 2, 3, 4, 5, 6

\foreach \x in {1,3,...,11} {\x, } yields 1, 3, 5, 7, 9, 11

\foreach \x in {1,3,...,10} {\x, } yields 1, 3, 5, 7, 9

\foreach \x in {0,0.1,...,0.5} {\x, } yields 0, 0.1, 0.20001, 0.30002, 0.40002

\foreach \x in {a,b,9,8,...,1,2,2.125,...,2.5} {\x, } yields a, b, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 2.125, 2.25, 2.375, 2.5

Like you, I asked myself the question and @egreg answered it excellently here: Why does pgffor estimate that 0.1-0=0.100005 in a \foreach loop?

Answer 3

You can fix this by first working with integers and then reformatting the numbers to be the decimal representation you'd like to have:

First, I set the precision for the floating point

\pgfkeys{/pgf/number format/precision=2}

Then in the foreach loop I parse the integers to become the desired decimals using the following code

\pgfmathparse{\t/100}
\pgfmathroundtozerofill{\pgfmathresult}
\pgfmathsetmacro\t{\pgfmathresult}

Here's the full code:

\documentclass{standalone}
\usepackage[french]{babel}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}[yscale=0.1,xscale=25]
  \draw[<->] (0.5,0) node[below right]{t} -- (0,0) -- (0,100) node[above left]{x(t)};

  %%Graduation  
  \pgfkeys{/pgf/number format/precision=2}
  \foreach \t in {0, 8, ..., 48}
    {
      \pgfmathparse{\t/100}
      \pgfmathroundtozerofill{\pgfmathresult}
      \pgfmathsetmacro\t{\pgfmathresult}
      \draw (\t,1) -- (\t,-1) 
             node[below]
            {\t};
    }
\end{tikzpicture}

\end{document}