[llvm] specify NaN behavior more precisely (PR #66579)

[Nuno Lopes via llvm-commits]

================
@@ -3394,17 +3394,76 @@ Floating-Point Environment
 The default LLVM floating-point environment assumes that traps are disabled and
 status flags are not observable. Therefore, floating-point math operations do
 not have side effects and may be speculated freely. Results assume the
-round-to-nearest rounding mode.
+round-to-nearest rounding mode, and subnormals are assumed to be preserved.
+
+Running LLVM code in an environment where these assumptions are not met can lead
+to undefined behavior. The ``strictfp`` and ``denormal-fp-math`` attributes as
+well as :ref:`Constrained Floating-Point Intrinsics <constrainedfp>` can be used
+to weaken LLVM's assumptions and ensure defined behavior in non-default
+floating-point environments; see their respective documentation for details.
+
+.. _floatnan:
+
+Behavior of Floating-Point NaN values
+-------------------------------------
+
+A floating-point NaN value consists of a sign bit, a quiet/signaling bit, and a
+payload (which makes up the rest of the mantissa except for the quiet/signaling
+bit). LLVM assumes that the quiet/signaling bit being set to ``1`` indicates a
+quiet NaN (QNaN), and a value of ``0`` indicates a signaling NaN (SNaN). In the
+following we will hence just call it the "quiet bit"
+
+The representation bits of a floating-point value do not mutate arbitrarily; in
+particular, if there is no floating-point operation being performed, NaN signs,
+quiet bits, and payloads are preserved.
+
+For the purpose of this section, ``bitcast`` as well as the following operations
+are not "floating-point math operations": ``fneg``, ``llvm.fabs``, and
+``llvm.copysign``. These operations act directly on the underlying bit
+representation and never change anything except possibly for the sign bit.
+
+For floating-point math operations, unless specified otherwise, the following
+rules apply when a NaN value is returned: the result has a non-deterministic
+sign; the quiet bit and payload are non-deterministically chosen from the
+following set of options:
+
+- The quiet bit is set and the payload is all-zero. ("Preferred NaN" case)
+- The quiet bit is set and the payload is copied from any input operand that is
+  a NaN. ("Quieting NaN propagation" case)
+- The quiet bit and payload are copied from any input operand that is a NaN.
+  ("Unchanged NaN propagation" case)
+- The quiet bit is set and the payload is picked from a target-specific set of
----------------
nunoplopes wrote:

Given that optimizations must be correct for all targets, this rule is equal to saying that any qnan may be returned. Can we simplify the rule to say just that?

https://github.com/llvm/llvm-project/pull/66579