[RFC]: Add C implementation for @stdlib/math/base/special/betaincinv

### Description

**Description**
The JavaScript implementation of `@stdlib/stats/base/dists/beta/quantile` depends on `@stdlib/math/base/special/betaincinv`.
However, there is no C implementation of betaincinv, making it impossible to implement quantile in C.
We need to add a C implementation of betaincinv, which can be used for quantile.

**Potential approaches:**
Use an existing numerical method (e.g., Newton-Raphson, Bisection).
Wrap an existing GSL or Cephes library function.

**Why This Matters**
This is a blocking issue for the C implementation of `@stdlib/stats/base/dists/beta/quantile`
The lack of betaincinv in C prevents further progress.

**Checklist**
✅ I have checked that betaincinv does not have a C implementation.
✅ This issue is required for completing @stdlib/stats/base/dists/beta/quantile.
✅ I am open to suggestions on how to implement it.

### Related Issues

Related issues #3433

### Questions

No.

### Other

No.

### Checklist

- [x] I have read and understood the [Code of Conduct](https://github.com/stdlib-js/stdlib/blob/develop/CODE_OF_CONDUCT.md).
- [x] Searched for existing issues and pull requests.
- [x] The issue name begins with `RFC:`.

Review the JavaScript implementation of @stdlib/math/base/special/betaincinv and its consumer, @stdlib/stats/base/dists/beta/quantile; then inspect related issue #3433. Compare the proposed numerical approaches or supported external libraries before defining the C implementation. Done means C beta quantile can use betaincinv.

由索引模型根据 Issue 内容生成。