================
@@ -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
----------------
andykaylor wrote:

I'm not sure we should document this as being implemented using the Smith 
algorithm. That may be left as an implementation detail, particularly if we 
start generating intrinsics which are handled in the backend or by an offload 
target. I would prefer to just describe the characteristics this option is 
intended to provide -- improved handling for overflow, but no special handling 
for the "NaN + NaNi" cases. 

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