[metapost] arclength() tolerances

[Taco Hoekwater]

Hi Hartmut,

On 02 Apr 2014, at 21:10, Hartmut Henkel <hartmut_henkel at gmx.de> wrote:

> Hi,
> 
> in metapost there seem to be absolute tolerance values for iterative
> algorithms like arclength() even in the double numbersystem:

Yes, the arc_test() routine (the core or arclength/arctime) uses a predefined 
tolerance of unity/4096. While it is clear to me why it needs a tolerance
setting, it is not clear why that precise value, nor does lowering it actually
help, it just makes mp run slower:

With tolerance=1E-8:

0.031477030364784685, 31415.995269569834
real	0m1.606s
user	0m1.601s
sys	0m0.003s

With tolerance=1E-9:

0.031477030364784685, 31415.995269569834

real	1m40.888s
user	1m40.820s
sys	0m0.034s

Maybe there is some intrinsic error in the approximation code? One of the
more important reasons why I will quit developing metapost is that I do not 
really understand any of this computational stuff, nor can I easily grasp the
theory behind it when attempting to educate myself.

Best wishes,
Taco