- detailed documentation of known problematic behaviour
when working with rational fractions
- demonstrate the heuristic predicate to detect dangerous numbers
- add extensive coverage and microbenchmarks for the integer-logarithm
implementation, based on an example on Stackoverflow. Surprising result:
The std::ilog(double) function is of comparable speed, at least for
GCC-8 on Debian-Buster.
Especially rational numbers with large denominator can be insidious,
since they might cause numeric overflow on seemingly harmless operations,
like adding a small number.
A solution might be to *requantise* the number into a different,
way smaller denominator. Obviously this is a lossy operation;
yet a small and controlled numeric error is always better than
an uncontrolled numeric wrap-around.
Extensive tests with corner cases soon highlighted this problem
inherent to integer calculations with fractional numbers: it is
possible to derail the calculation by numeric overflow with values
not excessively large, but using large numbers as denominator.
This problem is typically triggered by addition and subtraction,
where you'd naively not expect any problems.
Thus changed the approach in the normalisation function, relying
on an explicitly coded test rather, and performing the adjustment
only after conversion back to simple integral micro-tick scale.
Writing this specification unveiled a limitation of our internal
time base implementation, which is a 64bit microsecond grid.
As it turns out, any grid based time representation will always
be not precise enough to handle some relevant time specifications,
which are defined by a divisor. Most notably this affects the precise
display of frame duration in the GUI, and even more relevant,
the sample accurate editing of sound in the timeline.
Thus I decided to perform the internal computation in ZoomWindow
as rational numbers, based on boost::rational
Note: implementation stubbed only, test fails
