[libc++][modules] Fix missing and incorrect includes (#108850)

This patch adds a large number of missing includes in the libc++ headers
and the test suite. Those were found as part of the effort to

[libc++][modules] Fix missing and incorrect includes (#108850)

This patch adds a large number of missing includes in the libc++ headers
and the test suite. Those were found as part of the effort to move
towards a mostly monolithic top-level std module.

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[libc++] Adjust some of the [rand.dist] critical values that are too strict (#88669)

Adjust some of the [rand.dist] critical values that are too strict

- Most critical values are determined empir

[libc++] Adjust some of the [rand.dist] critical values that are too strict (#88669)

Adjust some of the [rand.dist] critical values that are too strict

- Most critical values are determined empirically by running each test
51
times with a different PRNG seed and finding the smallest symmetric
interval
around the median that contains 90% of the sample means, variances, etc.

- For the Kolmogorov-Smirnov tests, the alpha=0.1 critical value for
large N
is 1.224/sqrt(N).

- For normally distributed variates, the sample kurtosis is distributed
as
Normal(0, 24/N). For N=1e5, this gives a 90% confidence interval of
0+/-0.0255. For Binomial(40, 0.25), which is approximately normal, the
kurtosis is -0.0167, so the relative 90% CI is large, on the order of
0.0255/0.0167 = 153%. In most cases the distribution of the sample
kurtosis
isn't known analytically, but similarly large relative tolerances can be
expected if the kurtosis is near zero.

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Work around GCC test failure that is caused by enabling optimizations. (#73998)

While trying to work around MSAN/TSAN build timeouts, we enabled
optimizations on some tests. This caused GCC to star

Work around GCC test failure that is caused by enabling optimizations. (#73998)

While trying to work around MSAN/TSAN build timeouts, we enabled
optimizations on some tests. This caused GCC to start complaining that
some values may be uninitialized. I believe GCC is wrong, but more
investigation is needed.

The values are initialized when the variable `__g` is either < 0 or >=
0. Which only leaves out NaN I believe, which is likely well into UB
land anyway.

However, more investigation needed.

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[libc++] Revert "Compile MSAN/TSAN failing test with -O1 (#73555)"

This reverts commit 61aef978d6ab1553c48bbd9bf807a277b22451c1, which
broke the CI on GCC.

Compile MSAN/TSAN failing test with -O1 (#73555)

This attempts to fix flakes on the bots where the modified test times
out while running under sanitizers.

Turning on the optimizer for just this

Compile MSAN/TSAN failing test with -O1 (#73555)

This attempts to fix flakes on the bots where the modified test times
out while running under sanitizers.

Turning on the optimizer for just this test appears to mostly fix the
issue.

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[libc++] Support int8_t and uint8_t in integer distributions as an extension

In D125283, we ensured that integer distributions would not compile when
used with arbitrary unsupported types. This effe

[libc++] Support int8_t and uint8_t in integer distributions as an extension

In D125283, we ensured that integer distributions would not compile when
used with arbitrary unsupported types. This effectively enforced what
the Standard mentions here: http://eel.is/c++draft/rand#req.genl-1.5.

However, this also had the effect of breaking some users that were
using integer distributions with unsupported types like int8_t. Since we
already support using __int128_t in those distributions, it is reasonable
to also support smaller types like int8_t and its unsigned variant. This
commit implements that, adds tests and documents the extension. Note that
we voluntarily don't add support for instantiating these distributions
with bool and char, since those are not integer types. However, it is
trivial to replace uses of these random distributions on char using int8_t.

It is also interesting to note that in the process of adding tests
for smaller types, I discovered that our distributions sometimes don't
provide as faithful a distribution when instantiated with smaller types,
so I had to relax a couple of tests. In particular, we do a really bad
job at implementing the negative binomial, geometric and poisson distributions
for small types. I think this all boils down to the algorithm we use in
std::poisson_distribution, however I am running out of time to investigate
that and changing the algorithm would be an ABI break (which might be
reasonable).

As part of this patch, I also added a mitigation for a very likely
integer overflow bug we were hitting in our tests in negative_binomial_distribution.
I also filed http://llvm.org/PR56656 to track fixing the problematic
distributions with int8_t and uint8_t.

Supersedes D125283.

Differential Revision: https://reviews.llvm.org/D126823

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[libc++][NFC] Rename rand.dis to rand.dist

Reviewed By: ldionne, #libc

Spies: libcxx-commits, mgrang, mstorsjo

Differential Revision: https://reviews.llvm.org/D126221