quite faster rand(::MersenneTwister, ::Type{Int}) ... (#37914)
... when the quest for superficial beauty leads to performance ...
The recent implementation of `show` for `MersenneTwister` was not
ideal, as a number of book-keeping variables had to be introduced as
fields of MT; in particular, as generating the cache for ints (using
the generic `rand!` for integer arrays) was consuming random `Float64`
numbers, 4 integers had to be shown in `show` only to reproduce the
state of the ints cache. In total 8 integers were shown.
But it is not so difficult to improve a bit, thanks to two features of
the internal cache:
1) it's 16-byte aligned, so the dSFMT low-level routine can be called
directly on it (whereas the generic `rand!` for integers has to
take care that the same stream is produced whatever the alignment)
2) it can be resized: dSFMT randomizing only 52 out of 64 bits,
i.e. a bit more than 80% of the bits, the trick is to count
the total number of needed bits, grow the array to a size
such that dSFMT produces these needed bits, and then condense
these bits back into a 100% randomized array of the original size
As a net result, two variables could be deleted which `show` doesn't
needs to display anymore.
Purely as a side effect, scalar generation of `Int64`/`UInt64` has
a speedup of about 1.8x, and about 1.6x for `Int128`/`UInt128`,
and about 1.3x or 1.5x for generation in a range of integers of size
with less than 64 bits, e.g. `rand(1:9)` (at least on this machine...)
