[clang] [CLANG] Full support of complex multiplication and division. (PR #81514)

[Joshua Cranmer via cfe-commits]

================
@@ -1847,19 +1847,50 @@ floating point semantic models: precise (the default), strict, and fast.
    * ``16`` - Forces ``_Float16`` operations to be emitted without using excess
      precision arithmetic.
 
+.. option:: -fcomplex-arithmetic=<value>:
+
+   This option specifies the implementation for complex multiplication and division.
+
+   Valid values are: ``basic``, ``improved``, ``full`` and ``promoted``.
+
+   * ``basic`` Implementation of complex division and multiplication using
+     algebraic formulas at source precision. No special handling to avoid
+     overflow. NaN and infinite values are not handled.
+   * ``improved`` Implementation of complex division using the Smith algorithm
+     at source precision. Smith's algorithm for complex division.
+     See SMITH, R. L. Algorithm 116: Complex division. Commun. ACM 5, 8 (1962).
+     This value offers improved handling for overflow in intermediate
+     calculations, but overflow may occur. NaN and infinite values are not
+     handled in some cases.
+   * ``full`` Implementation of complex division and multiplication using a
+     call to runtime library functions (generally the case, but the BE might
+     sometimes replace the library call if it knows enough about the potential
+     range of the inputs). Overflow and non-finite values are handled by the
+     library implementation. For the case of multiplication overflow will occur in
+     accordance with normal floating-point rules. This is the default value.
+   * ``promoted`` Implementation of complex division using algebraic formulas at
+     higher precision. Overflow is handled. Non-finite values are handled in some
+     cases. If the target does not have native support for a higher precision
+     data type, an implementation for the complex operation will be used to provide
+     improved guards against intermediate overflow, but overflow and underflow may
+     still occur in some cases. NaN and infinite values are not handled.
----------------
jcranmer-intel wrote:

This documentation doesn't make it clear what happens if there is no higher-precision datatype available and you use `promoted` format. And I'm somewhat uncomfortable with the idea that using `promoted` keeps you from being able to choose what happens in that case.

(In general, `promoted` is scary to me for anything larger than a `float` because `long double` is just such a cursed type and I'm not sure it's a good idea to convert `double` computations to `long double`).

https://github.com/llvm/llvm-project/pull/81514