Let's say we use twips. Then a piece of paper 100 inches on a side would be
1440000 twips. This is well within one cell. If we need to increase the
resolution to accommodate units that aren't multiples of a twip, we can do it.
One millimeter is 5/127 inch. If our unit is 1/127 twip, then a millimeter is
also an integral number of units. The huge piece of paper is now 182880000
units, which is still a single-precision number, though it is an order of
magnitude short of overflow. It might not be safe to do this.
A millimeter is 56+88/127 twips. If we use 1/3 twip as our unit, the error is
10/127 units. Over a meter of paper, that is 10000/127 units, or 26 twips. This
is about half a millimeter. Is anyone going to notice?
Scaling is done in Forth with the operator */ , which multiplies the first two
numbers, giving a double-length (8 bytes, in our case) result, which is then
divided by the third number. When calculating distances, I use double-length
numbers to hold the squares.
4-byte floats do not have the precision of 4-byte integers. Only three bytes
are mantissa. If we use floats (for instance to take a square root - I convert
a double to float, take its square root, and convert to integer), they should
be eight bytes.
phma