diff --git a/llvm/docs/LangRef.rst b/llvm/docs/LangRef.rst
index b17e3c828ed3d..38f0a019cab5d 100644
--- a/llvm/docs/LangRef.rst
+++ b/llvm/docs/LangRef.rst
@@ -2405,6 +2405,8 @@ example:
     function which has an ``ssp`` or ``sspstrong`` attribute, the calling
     function's attribute will be upgraded to ``sspreq``.
 
+.. _strictfp:
+
 ``strictfp``
     This attribute indicates that the function was called from a scope that
     requires strict floating-point semantics.  LLVM will not attempt any
@@ -3582,11 +3584,12 @@ 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, 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.
+Running LLVM code in an environment where these assumptions are not met
+typically leads 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:
 
@@ -3608,10 +3611,11 @@ 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:
+Floating-point math operations that return a NaN are an exception from the
+general principle that LLVM implements IEEE-754 semantics. Unless specified
+otherwise, the following rules apply whenever the IEEE-754 semantics say that 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
@@ -3657,6 +3661,40 @@ specification on some architectures:
   LLVM does not correctly represent this. See `issue #60796
   <https://github.com/llvm/llvm-project/issues/60796>`_.
 
+.. _floatsem:
+
+Floating-Point Semantics
+------------------------
+
+This section defines the semantics for core floating-point operations on types
+that use a format specified by IEEE-745. These types are: ``half``, ``float``,
+``double``, and ``fp128``, which correspond to the binary16, binary32, binary64,
+and binary128 formats, respectively. The "core" operations are those defined in
+section 5 of IEEE-745, which all have corresponding LLVM operations.
+
+The value returned by those operations matches that of the corresponding
+IEEE-754 operation executed in the :ref:`default LLVM floating-point environment
+<floatenv>`, except that the behavior of NaN results is instead :ref:`as
+specified here <floatnan>`. In particular, such a floating-point instruction
+returning a non-NaN value is guaranteed to always return the same bit-identical
+result on all machines and optimization levels.
+
+This means that optimizations and backends may not change the observed bitwise
+result of these operations in any way (unless NaNs are returned), and frontends
+can rely on these operations providing correctly rounded results as described in
+the standard.
+
+(Note that this is only about the value returned by these operations; see the
+:ref:`floating-point environment section <floatenv>` regarding flags and
+exceptions.)
+
+Various flags, attributes, and metadata can alter the behavior of these
+operations and thus make them not bit-identical across machines and optimization
+levels any more: most notably, the :ref:`fast-math flags <fastmath>` as well as
+the :ref:`strictfp <strictfp>` and :ref:`denormal-fp-math <denormal_fp_math>`
+attributes and :ref:`!fpmath metadata <fpmath-metadata>`. See their
+corresponding documentation for details.
+
 .. _fastmath:
 
 Fast-Math Flags
@@ -3943,7 +3981,7 @@ Floating-Point Types
      - Description
 
    * - ``half``
-     - 16-bit floating-point value
+     - 16-bit floating-point value (IEEE-754 binary16)
 
    * - ``bfloat``
      - 16-bit "brain" floating-point value (7-bit significand).  Provides the
@@ -3952,13 +3990,13 @@ Floating-Point Types
        extensions and Arm's ARMv8.6-A extensions, among others.
 
    * - ``float``
-     - 32-bit floating-point value
+     - 32-bit floating-point value (IEEE-754 binary32)
 
    * - ``double``
-     - 64-bit floating-point value
+     - 64-bit floating-point value (IEEE-754 binary64)
 
    * - ``fp128``
-     - 128-bit floating-point value (113-bit significand)
+     - 128-bit floating-point value (IEEE-754 binary128)
 
    * - ``x86_fp80``
      -  80-bit floating-point value (X87)
@@ -3966,10 +4004,6 @@ Floating-Point Types
    * - ``ppc_fp128``
      - 128-bit floating-point value (two 64-bits)
 
-The binary format of half, float, double, and fp128 correspond to the
-IEEE-754-2008 specifications for binary16, binary32, binary64, and binary128
-respectively.
-
 X86_amx Type
 """"""""""""
 
@@ -6925,6 +6959,8 @@ For example,
     %2 = load float, ptr %c, align 4, !alias.scope !6
     store float %0, ptr %arrayidx.i, align 4, !noalias !7
 
+.. _fpmath-metadata:
+
 '``fpmath``' Metadata
 ^^^^^^^^^^^^^^^^^^^^^