Documentation: add CRC implementation details

Add a new section under Implementation Details explaining the CRC32
variants available in NuttX, including the difference between the
native crc32() and the new Linux/zlib-compatible crc32_ieee().

Signed-off-by: hanzhijian <hanzhijian@zepp.com>

Documentation/implementation/crc.rst

@@ -0,0 +1,90 @@
+===
+CRC
+===
+
+Overview
+========
+
+NuttX provides CRC (Cyclic Redundancy Check) implementations for CRC8, CRC16,
+and CRC32 in ``libs/libc/misc/``. Each family offers multiple polynomial
+variants, following a consistent naming convention.
+
+CRC32 Variants
+==============
+
+NuttX ships several CRC32 variants that differ in polynomial, init value,
+and final XOR. The two most commonly used are ``crc32()`` and ``crc32_ieee()``.
+
+crc32() — NuttX Native
+-----------------------
+
+The original NuttX CRC32 implementation using the standard ISO 3309 / ITU-T
+V.42 polynomial (0xEDB88320 reflected). It uses **init value 0** with
+**no final XOR**:
+
+.. code-block:: c
+
+   uint32_t crc32(FAR const uint8_t *src, size_t len);
+   uint32_t crc32part(FAR const uint8_t *src, size_t len, uint32_t crc32val);
+
+This is the default CRC32 used by internal NuttX subsystems (bbsram, sbram,
+etc.) and is maintained for backward compatibility.
+
+crc32_ieee() — Linux/zlib Compatible
+-------------------------------------
+
+An IEEE-standard CRC32 compatible with Linux ``crc32()`` (from zlib). It uses
+the same polynomial but with **init value 0xFFFFFFFF** and **final XOR
+0xFFFFFFFF**:
+
+.. code-block:: c
+
+   uint32_t crc32_ieee(FAR const uint8_t *src, size_t len);
+   uint32_t crc32_ieeepart(FAR const uint8_t *src, size_t len, uint32_t crc32val);
+
+Use this variant when interoperating with Linux systems, e.g., for CRC
+checksums in network protocols, file transfers, or UART communication layers.
+
+Comparison
+----------
+
+==============  ============  ==========  ==========
+Function        Init Value    Final XOR   Polynomial
+==============  ============  ==========  ==========
+crc32()         0x00000000    None        0xEDB88320
+crc32_ieee()    0xFFFFFFFF    0xFFFFFFFF  0xEDB88320
+==============  ============  ==========  ==========
+
+Example: computing CRC32 of the string ``"123456789"``:
+
+- ``crc32("123456789", 9)``      returns ``0x2DFD2D88``
+- ``crc32_ieee("123456789", 9)`` returns ``0xCBF43926`` (matches Linux/zlib)
+
+Incremental Calculation
+-----------------------
+
+Both variants support incremental (chunked) CRC calculation via the ``_part``
+functions. For ``crc32_ieee``, the first call should pass ``0`` as the initial
+value:
+
+.. code-block:: c
+
+   uint32_t crc = 0;
+   crc = crc32_ieeepart(chunk1, len1, crc);
+   crc = crc32_ieeepart(chunk2, len2, crc);
+   /* crc now contains the final CRC of chunk1+chunk2 */
+
+Other CRC32 Variants
+--------------------
+
+NuttX also provides CRC32 variants using different polynomials:
+
+- ``crc32h04c11db7()`` / ``crc32h04c11db7_part()`` — Castagnoli (CRC-32C)
+- ``crc32hf4acfb13()`` / ``crc32hf4acfb13_part()`` — CRC-32Q
+
+CRC16 and CRC8
+==============
+
+CRC16 and CRC8 follow the same naming pattern with multiple variant functions.
+See ``include/nuttx/crc16.h`` and ``include/nuttx/crc8.h`` for available
+variants.

Documentation/implementation/index.rst

@@ -10,6 +10,7 @@ Implementation Details
    cancellation_points.rst
    chip_h.rst
    context_switches.rst
+   crc.rst
    critical_sections.rst
    device_drivers.rst
    device_nodes.rst