A strange TikZ numerical anomaly with ln function

Despite TikZ manual’s making clear that PGF’s mathematical libraries should not be expected to be extremely precise, there is a discontinuity when plotting the ln function which I find abnormally large (the discontinuity, which occurs about the argument value 0.125, is of roughly 0.03, which is quite visible on plots—even plots which are not made specifically to show the bug!). Even stranger, the bug disappears when the density of plotting values becomes high enough! See the following MWE and its result:

documentclass{minimal}
usepackage{tikz}
begin{document}
begin{tikzpicture}[x=500cm, y=50cm, thick]
foreach x in {0.120, 0.122, 0.124, 0.126, 0.128, 0.130}
 draw (x, -2.13) -- +(0, -4pt) node[below]{x};
foreach y in {-2.12, -2.10, -2.08, -2.06, -2.04, -2.02}
 draw (0.119, y) -- +(-4pt, 0) node[left]{y};
draw[green] plot[domain=0.12:0.13, samples=95] (x, {ln(x)});
draw[red] plot[domain=0.12:0.13, samples=94] (x, {ln(x)});
end{tikzpicture}
end{document}

Has anyone any explanations for what happens…?

documentclass{minimal}
usepackage{tikz}
usetikzlibrary{fpu}
begin{document}
begin{tikzpicture}[x=500cm, y=50cm, thick, /pgf/fpu/install only={ln}]
foreach x in {0.120, 0.122, 0.124, 0.126, 0.128, 0.130}
 draw (x, -2.13) -- +(0, -4pt) node[below]{x};
foreach y in {-2.12, -2.10, -2.08, -2.06, -2.04, -2.02}
 draw (0.119, y) -- +(-4pt, 0) node[left]{y};
draw[green] plot[ domain=0.12:0.13, samples=95] (x, {ln(x)});
draw[red] plot[ domain=0.12:0.13, samples=94] (x, {ln(x)});
end{tikzpicture}
end{document}