diff --git a/Doc/c-api/exceptions.rst b/Doc/c-api/exceptions.rst
index 9c75f66f683195..f525ee7a0461fe 100644
--- a/Doc/c-api/exceptions.rst
+++ b/Doc/c-api/exceptions.rst
@@ -394,6 +394,15 @@ an error value).
    .. versionadded:: 3.2
 
 
+.. c:function:: int PyErr_WarnExplicitFormat(PyObject *category, const char *filename, int lineno, const char *module, PyObject *registry, const char *format, ...)
+
+   Similar to :c:func:`PyErr_WarnExplicit`, but uses
+   :c:func:`PyUnicode_FromFormat` to format the warning message. *format* is
+   an ASCII-encoded string.
+
+   .. versionadded:: 3.2
+
+
 .. c:function:: int PyErr_ResourceWarning(PyObject *source, Py_ssize_t stack_level, const char *format, ...)
 
    Function similar to :c:func:`PyErr_WarnFormat`, but *category* is
@@ -1228,3 +1237,37 @@ Warning types
 
 .. versionadded:: 3.10
    :c:data:`PyExc_EncodingWarning`.
+
+
+Tracebacks
+==========
+
+.. c:var:: PyTypeObject PyTraceBack_Type
+
+   Type object for traceback objects. This is available as
+   :class:`types.TracebackType` in the Python layer.
+
+
+.. c:function:: int PyTraceBack_Check(PyObject *op)
+
+   Return true if *op* is a traceback object, false otherwise. This function
+   does not account for subtypes.
+
+
+.. c:function:: int PyTraceBack_Here(PyFrameObject *f)
+
+   Replace the :attr:`~BaseException.__traceback__` attribute on the current
+   exception with a new traceback prepending *f* to the existing chain.
+
+   Calling this function without an exception set is undefined behavior.
+
+   This function returns ``0`` on success, and returns ``-1`` with an
+   exception set on failure.
+
+
+.. c:function:: int PyTraceBack_Print(PyObject *tb, PyObject *f)
+
+   Write the traceback *tb* into the file *f*.
+
+   This function returns ``0`` on success, and returns ``-1`` with an
+   exception set on failure.
diff --git a/Doc/c-api/hash.rst b/Doc/c-api/hash.rst
index b5fe93573a1456..e74f5b4d18ebe1 100644
--- a/Doc/c-api/hash.rst
+++ b/Doc/c-api/hash.rst
@@ -11,42 +11,94 @@ See also the :c:member:`PyTypeObject.tp_hash` member and :ref:`numeric-hash`.
 
    .. versionadded:: 3.2
 
+
 .. c:type:: Py_uhash_t
 
    Hash value type: unsigned integer.
 
    .. versionadded:: 3.2
 
+
+.. c:macro:: Py_HASH_ALGORITHM
+
+   A numerical value indicating the algorithm for hashing of :class:`str`,
+   :class:`bytes`, and :class:`memoryview`.
+
+   The algorithm name is exposed by :data:`sys.hash_info.algorithm`.
+
+   .. versionadded:: 3.4
+
+
+.. c:macro:: Py_HASH_FNV
+             Py_HASH_SIPHASH24
+             Py_HASH_SIPHASH13
+
+   Numerical values to compare to :c:macro:`Py_HASH_ALGORITHM` to determine
+   which algorithm is used for hashing. The hash algorithm can be configured
+   via the configure :option:`--with-hash-algorithm` option.
+
+   .. versionadded:: 3.4
+      Add :c:macro:`!Py_HASH_FNV` and :c:macro:`!Py_HASH_SIPHASH24`.
+
+   .. versionadded:: 3.13
+      Add :c:macro:`!Py_HASH_SIPHASH13`.
+
+
+.. c:macro:: Py_HASH_CUTOFF
+
+   Buffers of length in range ``[1, Py_HASH_CUTOFF)`` are hashed using DJBX33A
+   instead of the algorithm described by :c:macro:`Py_HASH_ALGORITHM`.
+
+   - A :c:macro:`!Py_HASH_CUTOFF` of 0 disables the optimization.
+   - :c:macro:`!Py_HASH_CUTOFF` must be non-negative and less or equal than 7.
+
+   32-bit platforms should use a cutoff smaller than 64-bit platforms because
+   it is easier to create colliding strings. A cutoff of 7 on 64-bit platforms
+   and 5 on 32-bit platforms should provide a decent safety margin.
+
+   .. versionadded:: 3.4
+
+
 .. c:macro:: PyHASH_MODULUS
 
-   The `Mersenne prime <https://en.wikipedia.org/wiki/Mersenne_prime>`_ ``P = 2**n -1``, used for numeric hash scheme.
+   The `Mersenne prime <https://en.wikipedia.org/wiki/Mersenne_prime>`_ ``P = 2**n -1``,
+   used for numeric hash scheme.
+   This corresponds to the :data:`sys.hash_info.modulus` constant.
 
    .. versionadded:: 3.13
 
+
 .. c:macro:: PyHASH_BITS
 
    The exponent ``n`` of ``P`` in :c:macro:`PyHASH_MODULUS`.
+   This corresponds to the :data:`sys.hash_info.hash_bits` constant.
 
    .. versionadded:: 3.13
 
+
 .. c:macro:: PyHASH_MULTIPLIER
 
    Prime multiplier used in string and various other hashes.
 
    .. versionadded:: 3.13
 
+
 .. c:macro:: PyHASH_INF
 
    The hash value returned for a positive infinity.
+   This corresponds to the :data:`sys.hash_info.inf` constant.
 
    .. versionadded:: 3.13
 
+
 .. c:macro:: PyHASH_IMAG
 
    The multiplier used for the imaginary part of a complex number.
+   This corresponds to the :data:`sys.hash_info.imag` constant.
 
    .. versionadded:: 3.13
 
+
 .. c:type:: PyHash_FuncDef
 
    Hash function definition used by :c:func:`PyHash_GetFuncDef`.