[metapost] A modest proposal

[Toby Thurston]

Now that the higher precision number systems are maturing, and being used more, it might be a good time to update "plain.mp" to remove the hard coded 5-figure decimals.  In all cases it's fairly easy to find an equivalent definition which would work accurately at full numeric precision regardless of which engine is being used.

The values I can see are 

> eps := .00049;    % this is a pretty small positive number
> infinity := 4095.99998;    % and this is the largest
> 
> .
> .
> .
> 
> %% units of measure
> 
> mm=2.83464;      pt=0.99626;        dd=1.06601;      bp:=1;
> cm=28.34645;     pc=11.95517;       cc=12.79213;     in:=72;
> 
> vardef magstep primary m = mexp(46.67432m) enddef;


The definition of epsilon shows us a better way

> epsilon := 1/256/256;   % but this is the smallest


Adopting that strategy we can write the following which work well regardless of number system

eps := 1/2048;
infinity := 64*64-epsilon;

The units require a little bit more thought (and a quick reference to the Texbook for "dd"), but nevertheless here are some exact definitions that would also work with all number systems

1 = 1 bp;
72 = 1 in;
800 = 803 pt;
360  = 127 mm;
3600 = 127 cm;
1 pc = 12 pt;
1 cc = 12 dd;
1157 dd = 1238 pt;

Finally for magstep we could have 

vardef magstep primary m = mexp(mlog(1.2)*m) enddef;

Any thoughts?  Could these be changes in the next version of plain.mp?

Toby T.