Alain schrieb:
>>   I assume 1e7 was chose as half of that.
>>
> Probably. It looks like a reasonable cut point when you concider that, 
> during the calculations, you need to get square roots as well as squares 
> and cubes.
> Just a multiplication of two floats can double the number of digits.

Although this is the case, multiplications do not affect the precision 
of floating-point computations too much. The same goes for square roots.

Note that even though a double-precision floating-point number can hold 
numbers with only 15 /significant/ digits, it can still hold values much 
larger than 1e+15 (albeit at lower precision).

The most troublesome operations in the realm of floating-point numbers 
are actually subtractions (or additions of values with different sign, 
for that matter): For instance, 1.000 - 0.999 will give 0.001 at a 
precision of only 12 significant digits.

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