Add tests for signaling NaNs, and fix function behavior for handling
signaling NaN input.

Fixes https://github.com/llvm/llvm-project/issues/124812

This is a part of #97655.

Reverts llvm/llvm-project#98075

bots are broken

This is a part of #97655.

The inexact exception flag was raised for the exact cases of signed
zeros. This was reported by Paul Zimmermann using the CORE-MATH test
suites.

Another patch is needed to cover `DyadicFloat` and `NormalFloat`
constructors.

This one might be a bit controversial since the terminology has been
introduced from the start but I think `FRACTION_LEN` is a better name
here. AFAICT it really is "the number of bits after the decimal dot when
the number is in normal form."

`MANTISSA_WIDTH` is less precise as it's unclear whether we take the
leading bit into account.
This patch also renames most of the properties to use the `_LEN` suffix
and fixes useless casts or variables.

Also make type naming consistent by using `UIntType` instead of
`intU_t`.
This patch is a reland of #75196 but does not include the "use `FPBits`
instead of `FPBits_t`, `FPB`" part. This needs more work.

Reverts llvm/llvm-project#75196

GCC complains about change of meaning for `FPBits`
```
/home/llvm-libc-buildbot/buildbot-worker/libc-x86_64-debian-fullbuild/libc-x86_64-debian-gcc-fullbuild-dbg/llvm-project/libc/src/__support/FPUtil/generic/FMod.h:188:9: error: declaration of ‘using FPBits = struct __llvm_libc_18_0_0_git::fputil::FPBits<T>’ changes meaning of ‘FPBits’ [-fpermissive]
  188 |   using FPBits = FPBits<T>;
      |         ^~~~~~
```

I'll reland with a different name.