[metapost] bug in arctime calculation

[Martin Budaj]

Hi,

there is a bug in arctime calculation when using numbersystems decimal
and binary (double and scaled work fine). See the following example:

def test(expr P) =
  pos := 0;
  len := arclength P;
  d := 10bp;
  forever:
    arc_t := arctime pos of P;
    draw ((point arc_t of P) --
         (point arc_t of P) + 1mm * unitvector(direction arc_t of P rotated 90))
         withcolor (1-pos/len);
    message decimal pos & " " & decimal arc_t;
    pos := pos + d;
    exitif pos > len;
  endfor;
  draw P;
enddef;

beginfig(1);
  test((0,0)--(100,0));
endfig;

end

As the test is run on a simple line segment, arctime should increase
linearly from 0 to 1. This is the case for scaled and double
numbersystems:

pos arc_t
0 0
10 0.09999
20 0.2
30 0.29999
40 0.4
50 0.5
60 0.59999
70 0.7
80 0.79999
90 0.9
100 1

But for decimal and binary, arctime is not only non-linear, it's even
non-monotonous:

pos arc_t
0 0
10 0.218357288800015125792849022379372
20 0.338083509141544805383550503071265
30 0.45780972290631604654943093962971
40 0.038767960662661419366106762617287
50 0.098631047814785205469201499670517
60 0.718357199283058404647430603398735
70 0.838083397702050143830649542333004
80 0.957809611466813022214145595635334
90 0.538767915904170514622883519402551
100 0.598631024978811668703918040345015

Could you please look into this issue?

Best wishes
Martin