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

[Ralf Jung via llvm-commits]

================
@@ -3394,17 +3394,80 @@ 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
----------------
RalfJung wrote:

Yes, that is the intention. The choice of sign and (quiet + payload) is independent. (But quiet and payload are correlated.)

I'm open to suggestions for how to word this more clearly.

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