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

[Andy Kaylor via cfe-commits]

================
@@ -1847,19 +1847,33 @@ floating point semantic models: precise (the default), strict, and fast.
    * ``16`` - Forces ``_Float16`` operations to be emitted without using excess
      precision arithmetic.
 
-.. option:: -fcx-limited-range:
-
-   This option enables the naive mathematical formulas for complex division and
-   multiplication with no NaN checking of results. The default is
-   ``-fno-cx-limited-range``, but this option is enabled by the ``-ffast-math``
-   option.
-
-.. option:: -fcx-fortran-rules:
-
-   This option enables the naive mathematical formulas for complex
-   multiplication and enables application of Smith's algorithm for complex
-   division. See SMITH, R. L. Algorithm 116: Complex division. Commun.
-   ACM 5, 8 (1962). The default is ``-fno-cx-fortran-rules``.
+.. 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 and  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 and  values are not handled in some
----------------
andykaylor wrote:

"but overflow may occur" -- I'm getting a little bit over my head here, but I think the academic papers for the Smith algorithm say that it underflows but doesn't overflow. Or maybe that was a description of an improvement to Smith that I came across. If we're going to be technical here, we should be sure that our wording is accurate.

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