WL#9727: Additional aggregate window functions

Affects: Server-8.0   —   Status: Complete

This is a followup of the work done in WL#9236 Add SQL window functions.
Please refer to that WL for a general background and specifications.

Under this work log we will add the aggregate window functions missing from
that WL:

  - MIN
  - MAX
  - STD, STDDEV, STDDEV_POP (same function)
  - VARIANCE, VAR_POP (same function)

These will be postponed till a later worklog:

  - BIT_OR
The evaluation of MIN/MAX is not possible using inversion, unless
we know something about the ordering of the argument. We should evaluate
using first/last value logic if there is an ORDER BY for the window which
has as its first argument (in the list of ordering expressions), the expression
which we seek MIN/MAX of. Otherwise, we need to visit all rows in a window's
frame to determine MIN/MAX in a moving window, which gives a non-linear

NOTE: If a MIN/MAX is used on a window for which other window functions
are also evaluated, the performance characteristics of those other window
functions will also be non-linear, due to the presence of the MIN/MAX function.

The evaluation of the statistics functions

STD, STDDEV_SAMP, VARIANCE and VAR_SAMP (and their synonyms)

can be evaluated in two modes: an optimized mode and a default mode, cf.
the evaluation if SUM of floating point types in WL#9236.

Ideally, we would always use optimized mode, but it we do not due to the following

For optimized mode we need to use an incremental algorithm to compute the 
aggregate functions.
When the window frame moves, old values may move out of the frame and new values
may move into the frame. In optimized mode, the function is evaluated by inverting 
the contribution to the function result from the row values that move out of the 
frame and by adding the contribution of those row values that move into the frame.

There exists an incremental algorithm for computing variance in this way, but it 
produces slightly different results in the last significant digits than the 
algorithm MySQL uses for Grouped aggregates of the same functions.

In practice the results are probably just fine, but in the interest of giving
expected results, we do not use this incremental algorithm unless instructed by
the user to do so.

The same variable that is used for controlling optimized evaluation for floating
values for SUM is used:

  windowing_use_high_precision [false / true (default) ]

For large result sets the default algorithm may be too slow; so turning this 
variable to true should be considered.