In #94078, `write_to_stdout` had not been fully implemented. However,
now that it has been implemented, to conform with the C standard
(7.23.6.3. The printf function, specifically point 2), we use `stdout`.
This issue is tracked in #94685.

- Also prefer `static constexpr`
- Made it explicit that we are writing to `stdout`

The perror function writes an error message directly to stderr. This
patch adds an implementation, tests, and header generation details.

This is the first step in preparation for:
https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450

The GPU stdio functions were depending on indirect inclusion for some of
their dependencies. This patch should fix all of that.

Summary:
We use the storage class for `long double` in the printing
implementations. We don't fully support the PPC double double type,
which that maps to, but we can stub out just the support needed for the
print interface to works. This required using the internal interface for
storage type, but it should be good enough.

Fixes: https://github.com/llvm/llvm-project/issues/136596

There is a problem with such unsigned comparison pattern:
```
if(unsigned_a - unsigned_b > 0) { /* only NOT go here when unsigned_a==unsigned_b */ }
```
When `unsigned_a` < `unsigned_b`, the result will still be `>0` due to
underflow.
This patch fixes two of the occurrences I found.
Also remove two redundant `if` where its condition is guaranteed by
outer `if`.

Summary:
We have 'generic' implementations for some functions stdio functions.
The current logic mandates that all generic functions are implemented by
the target. This obviously isn't true and this caused the GPU builds to
fail once baremtal added some extra ones.

This patch changes the logic to always include the generic sources only
if they aren't already defined. This can probably be cleaned up and
formalized later, since this pattern is copied in many places, but for
now this fixes the failing GPU build bots.

This uses the templatized scanf Reader interface introduced in #131037.