linear_congruential_engine: add using more precision to prevent overflow (#81583)
This PR is a followup to #81080.
This PR makes two major changes to how the LCG operation is computed:
The first is that I added an additional case where `ax + c` might
overflow the intermediate variable, but `ax` by itself won't. In this
case, it's much better to use `(ax mod m) + c mod m` than the previous
behavior of falling back to Schrage's algorithm. The addition modulo is
done in the same way as when using Schrage's algorithm (i.e. `x += c -
(x >= m - c)*m`), but the multiplication modulo is calculated directly,
which is faster.
The second is that I added handling for the case where the `ax`
intermediate might overflow, but Schrage's algorithm doesn't apply (i.e.
r > q). In this case, the only real option is to increase the precision
of the intermediate values. The good news is that - for `x`, `a`, and
`c` being n-bit values - `ax + c` will never overflow a 2n-bit
intermediary, meaning this promotion can only happen once, and will
always be able to use the simplest implementation. This is already the
case for 16-bit LCGs, as libcxx chooses to compute them with 32-bit
intermediate values. For 32-bit LCGs, I simply added code similar to the
16-bit case to use the existing 64-bit implementations. Lastly, for
64-bit LCGs, I wrote a case that calculates it using `unsigned __int128`
if it is available to use.
While this implementation covers a *lot* of the missing cases from
#81080, this still won't compile **every** possible
`linear_congruential_engine`. Specifically, if `a`, `c`, and `m` are
chosen such that it needs 128-bit integers, but the platform doesn't
support `__int128` (eg. 32-bit x86), then it will fail to compile.
However, this is a fairly rare case to see actually used, and libcxx
would be in good company with this, as [libstdc++ also fails to compile
under these
circumstances](https://gcc.gnu.org/bugzilla/show_bug.cgi?id=87744).
Fixing **this** gap would require even **more** work of further
complexity, so that would probably be best handled by a different PR
(I'll put more details on what that PR would entail in a comment).
GitOrigin-RevId: 41e696291c64fe19629e14887ed1ed9b9c2271f0
6 files changed
