I like the ability to specify the number of bits either side of the decimal point, but this does get in the way for doing the math functions --- you need a table with magic numbers in at the appropriate precision for exp and sin/cos.
Presumably the tables could be computed at run time once per type.
Yes, but that would add to the app startup cost, or make the first math function call *very* expensive. The arctan table (for sin and cos) has 30 entries, and the log tables used for exp total 91 entries. 30 calls to atan and 91 calls to log can take a while.
If you were doing this in a loop, yes, but as a single, one time, startup cost? Even if each call to atan/log takes a microsecond, and you use all 64 different precisions, that's *still* only a few milliseconds on the startup - who is going to care? Um. If you are doing this in an embedded 16-bit processor (which is just the sort of place that fixed point often /is/ useful), that microsecond might be a bit optimistic - and you would really want the constants in ROM not RAM.
If you increase the precision, then you need more entries than that.
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