doc: kernel: timeutil: add documentation for timespec apis

Add documentation in the timeutil group for recently added functions
for validating, comparing, and manipulating `struct timespec`
objects as well as functions for converting between representation
of time durations as either `struct timespec` or `k_timeout_t`.

Signed-off-by: Chris Friedt <cfriedt@tenstorrent.com>

doc/kernel/timeutil.rst

@@ -28,6 +28,7 @@ The time utilities API supports:
 
 * :ref:`converting between time representations <timeutil_repr>`
 * :ref:`synchronizing and aligning time scales <timeutil_sync>`
+* :ref:`comparing, adding, and subtracting representations <timeutil_manip>`
 
 For terminology and concepts that support these functions see
 :ref:`timeutil_concepts`.
@@ -65,6 +66,20 @@ The inverse transformation is not standardized: APIs like ``mktime()`` expect
 information about time zones.  Zephyr provides this transformation with
 :c:func:`timeutil_timegm` and :c:func:`timeutil_timegm64`.
 
+To convert between ``struct timespec`` and ``k_timeout_t`` durations,
+use :c:func:`timespec_to_timeout` and :c:func:`timespec_from_timeout`.
+
+.. code-block:: c
+
+    k_timeout_t to;
+    struct timespec ts;
+
+    timespec_from_timeout(K_FOREVER, &ts);
+    to = timespec_to_timeout(&ts); /* to == K_FOREVER */
+
+    timespec_from_timeout(K_MSEC(100), &ts);
+    to = timespec_to_timeout(&ts); /* to == K_MSEC(100) */
+
 .. doxygengroup:: timeutil_repr_apis
 
 .. _timeutil_sync:
@@ -106,6 +121,90 @@ process:
 
 .. doxygengroup:: timeutil_sync_apis
 
+.. _timeutil_manip:
+
+``timespec`` Manipulation
+=========================
+
+Checking the validity of a ``timespec`` can be done with :c:func:`timespec_is_valid`.
+
+.. code-block:: c
+
+    struct timespec ts = {
+        .tv_sec = 0,
+        .tv_nsec = -1, /* out of range! */
+    };
+
+    if (!timespec_is_valid(&ts)) {
+        /* error-handing code */
+    }
+
+In some cases, invalid ``timespec`` objects may be re-normalized using
+:c:func:`timespec_normalize`.
+
+.. code-block:: c
+
+    if (!timespec_normalize(&ts)) {
+        /* error-handling code */
+    }
+
+    /* ts should be normalized */
+    __ASSERT(timespec_is_valid(&ts) == true, "expected normalized timespec");
+
+It is possible to compare two ``timespec`` objects for equality using :c:func:`timespec_equal`.
+
+.. code-block:: c
+
+    if (timespec_equal(then, now)) {
+        /* time is up! */
+    }
+
+It is possible to compare and fully order (valid) ``timespec`` objects using
+:c:func:`timespec_compare`.
+
+.. code-block:: c
+
+    int cmp = timespec_compare(a, b);
+
+    switch (cmp) {
+    case 0:
+        /* a == b */
+        break;
+    case -1:
+        /* a < b */
+        break;
+    case +1:
+        /* a > b */
+        break;
+    }
+
+It is possible to add, subtract, and negate ``timespec`` objects using
+:c:func:`timespec_add`, :c:func:`timespec_sub`, and :c:func:`timespec_negate`,
+respectively. Like :c:func:`timespec_normalize`, these functions will output
+a normalized ``timespec`` when doing so would not result in overflow.
+On success, these functions return ``true``. If overflow would occur, the
+functions return ``false``.
+
+.. code-block:: c
+
+    /* a += b */
+    if (!timespec_add(&a, &b)) {
+        /* overflow */
+    }
+
+    /* a -= b */
+    if (!timespec_sub(&a, &b)) {
+        /* overflow */
+    }
+
+    /* a = -a */
+    if (!timespec_negate(&a)) {
+        /* overflow */
+    }
+
+.. doxygengroup:: timeutil_timespec_apis
+
+
 .. _timeutil_concepts:
 
 Concepts Underlying Time Support in Zephyr
@@ -236,3 +335,29 @@ The mechanism used to populate synchronization points is not relevant: it may
 involve reading from a local high-precision RTC peripheral, exchanging packets
 over a network using a protocol like NTP or PTP, or processing NMEA messages
 received a GPS with or without a 1pps signal.
+
+``timespec`` Concepts
+=====================
+
+Originally from POSIX, ``struct timespec`` has been a part of the C standard
+since C11. The definition of ``struct timespec`` is as shown below.
+
+.. code-block:: c
+
+   struct timespec {
+       time_t tv_sec;  /* seconds */
+       long   tv_nsec; /* nanoseconds */
+   };
+
+.. _note:
+
+    The C standard does not define the size of ``time_t``. However, Zephyr
+    uses 64-bits for ``time_t``. The ``long`` type is required to be at least
+    32-bits, but usually matches the word size of the architecture. Both
+    elements of ``struct timespec`` are signed integers. ``time_t`` is defined
+    to be 64-bits both for historical reasons and to be robust enough to
+    represent times in the future.
+
+The ``tv_nsec`` field is only valid with values in the range ``[0, 999999999]``. The
+``tv_sec`` field is the number of seconds since the epoch. If ``struct timespec`` is
+used to express a difference, the ``tv_sec`` field may fall into a negative range.