🚀 go-pugleaf

I propose to store the positions in cm (instead of km) :
- The world is 100 000 cm x 100 000 cm x 100 000 cm big,
- Each coordinate neads 17 bits (17 bits means up to 131 072),
- A position is stored in 3 long integers : {long x,y,z}.

The operations, now.
No problem for adding and substracting (no overflow).
The multiplication produces 34 bits numbers (2 x 17) ; you have to convert
temporarly to double. For example, let's compute the distance between 2
points :

long dist;
dist=sqrt((double)(x1-x2)*(x1-x2)
   +(double)(y1-y2)*(y1-y2)
   +(double)(z1-z2)*(z1-z2))+.5;

Because a double has a 52 bits mantissa, you can compute 2 multiplications
at the same time (a x b x c), without loss : 3 x 17 = 51 bits number.
For more complexes formulas (that is, formulas that has more than 52 bits
intermediates numbers) :
- You accept a loss of precision, or
- You cut the formula into steps, so that numbers over 52 bits are
avoided.

Yves