Fixes
https://github.com/llvm/llvm-project/pull/156344#issuecomment-3256837826

Currently, GCC can't parse `typedef _Complex __float128 cfloat128;`,
although `__typeof__` can be used as a workaround. Reported
https://gcc.gnu.org/PR121799 which was later considered as duplicate of
https://gcc.gnu.org/PR32187.

Some recent changes exposed it to GCC and then caused CI failure for
libc++. This patch adds a workaround for GCC.

It was added in dd33f9cdef9f6209aa34713e1417f4a2e24e5ca6 to describe
thread-local errno, but is no longer used in the codebase (with the
exception of a single integration test, but the llvm-libc-provided
`#define _Thread_local thread_local` is not needed there anyway, since
`_Thread_local` is a keyword from C11 onwards.

This is an implementation for template functions of localtime.

Update for this pull request: Implementation as been removed from this
pull request and will be added to a new one. This is because this pull
request is getting big. This pull request will only contain template
functions in order to implement localtime.

Update: The implementation is available in
https://github.com/zimirza/llvm-project/tree/localtime_implementation.

---------

Co-authored-by: Зишан Мирза <zmirza@tutanota.de>
Co-authored-by: Zishan Mirza <zmirza@posteo.de>

Otherwise when installing the dlfcn.h header, there is a missing
reference to Dl_info.h, which causes compilation failures in some cases,
notably libunwind.

This change fixes and closes some gaps in the YAML template for
producing the math.h header.

It adds some missing declarations (dadd/dsub function variants), correct
arguments and/or return type for other functions from this family (dsqrt
and ddiv), and add a missing fminimum_numl variant.

This PR implements `atanpif16(x)` which computes
$\frac{\arctan(x)}{\pi}$ for half-precision floating-point numbers using
polynomial approximation with domain reduction.

## Mathematical Implementation

The implementation uses a 15th-degree Taylor polynomial expansion of
$\frac{\arctan(x)}{\pi}$ that's computed using
[`python-sympy`](https://www.sympy.org/en/index.html) and it's accurate
in $|x| \in [0, 0.5)$:

$$
g(x) = \frac{\arctan(x)}{\pi} \approx 
\begin{aligned}[t]
    & 0.318309886183791x \\
    & - 0.106103295394597x^3 \\
    & + 0.0636619772367581x^5 \\
    & - 0.0454728408833987x^7 \\
    & + 0.0353677651315323x^9 \\
    & - 0.0289372623803446x^{11} \\
    & + 0.0244853758602916x^{13} \\
    & - 0.0212206590789194x^{15} + O(x^{17})
\end{aligned}
$$


--- 

To ensure accuracy across all real inputs, the domain is divided into
three cases with appropriate transformations:

**Case 1: $|x| \leq 0.5$**  
Direct polynomial evaluation: 

$$\text{atanpi}(x) = \text{sign}(x) \cdot g(|x|)$$

**Case 2: $0.5 < |x| \leq 1$**  
Double-angle reduction using:

$$\arctan(x) = 2\arctan\left(\frac{x}{1 + \sqrt{1 + x^2}}\right)$$

$$\text{atanpi}(x) = \text{sign}(x) \cdot 2g\left(\frac{|x|}{1 + \sqrt{1
+ x^2}}\right)$$

**Case 3: $|x| > 1$**  
Reciprocal transformation using 

$$\arctan(x) = \frac{\pi}{2} - \arctan\left(\frac{1}{x}\right) \
\text{for} \ x \gt 0$$

$$\text{atanpi}(x) = \text{sign}(x) \cdot \left(\frac{1}{2} -
g\left(\frac{1}{|x|}\right)\right)$$


Closes #132212