*/
-/* Standard CRC8/16/32 algorithms. */
-// CRC-8 x8+x2+x1+1 0x07
-// CRC16-CCITT x16+x12+x5+1 1021 ISO HDLC, ITU X.25, V.34/V.41/V.42, PPP-FCS
-// CRC32:
-//G(x) = x32 +x26 + x23 + x22 + x16 + x12 + x11 + x10 + x8 + x7 + x5 + x4 + x2 + x1 + 1
-//If your buf is not continuous, you can use the first result to be the second parameter.
+/* Notes about CRC APIs usage
+ * The ESP32 ROM include some CRC tables and CRC APIs to speed up CRC calculation.
+ * The CRC APIs include CRC8, CRC16, CRC32 algorithms for both little endian and big endian modes.
+ * Here are the polynomials for the algorithms:
+ * CRC-8 x8+x2+x1+1 0x07
+ * CRC16-CCITT x16+x12+x5+1 0x1021
+ * CRC32 x32+x26+x23+x22+x16+x12+x11+x10+x8+x7+x5+x4+x2+x1+1 0x04c11db7
+ *
+ * These group of CRC APIs are designed to calculate the data in buffers either continuous or not.
+ * To make it easy, we had added a `~` at the beginning and the end of the functions.
+ * To calculate non-continuous buffers, we can write the code like this:
+ * init = ~init;
+ * crc = crc32_le(init, buf0, length0);
+ * crc = crc32_le(crc, buf1, length1);
+ * crc = ~crc;
+ *
+ * However, it is not easy to select which API to use and give the correct parameters.
+ * A specific CRC algorithm will include this parameters: width, polynomials, init, refin, refout, xorout
+ * refin and refout show the endian of the algorithm:
+ * if both of them are true, please use the little endian API.
+ * if both of them are false, please use the big endian API.
+ * xorout is the value which you need to be xored to the raw result.
+ * However, these group of APIs need one '~' before and after the APIs.
+ *
+ * Here are some examples for CRC16:
+ * CRC-16/CCITT, poly = 0x1021, init = 0x0000, refin = true, refout = true, xorout = 0x0000
+ * crc = ~crc16_le((uint16_t)~0x0000, buf, length);
+ *
+ * CRC-16/CCITT-FALSE, poly = 0x1021, init = 0xffff, refin = false, refout = false, xorout = 0x0000
+ * crc = ~crc16_be((uint16_t)~0xffff, buf, length);
+ *
+ * CRC-16/X25, poly = 0x1021, init = 0xffff, refin = true, refout = true, xorout = 0xffff
+ * crc = (~crc16_le((uint16_t)~(0xffff), buf, length))^0xffff;
+ *
+ * CRC-16/XMODEM, poly= 0x1021, init = 0x0000, refin = false, refout = false, xorout = 0x0000
+ * crc = ~crc16_be((uint16_t)~0x0000, buf, length);
+ *
+ *
+ */
/**
- * @brief Crc32 value that is in little endian.
+ * @brief CRC32 value that is in little endian.
*
* @param uint32_t crc : init crc value, use 0 at the first use.
*
uint32_t crc32_le(uint32_t crc, uint8_t const *buf, uint32_t len);
/**
- * @brief Crc32 value that is in big endian.
+ * @brief CRC32 value that is in big endian.
*
* @param uint32_t crc : init crc value, use 0 at the first use.
*
uint32_t crc32_be(uint32_t crc, uint8_t const *buf, uint32_t len);
/**
- * @brief Crc16 value that is in little endian.
+ * @brief CRC16 value that is in little endian.
*
* @param uint16_t crc : init crc value, use 0 at the first use.
*
uint16_t crc16_le(uint16_t crc, uint8_t const *buf, uint32_t len);
/**
- * @brief Crc16 value that is in big endian.
+ * @brief CRC16 value that is in big endian.
*
* @param uint16_t crc : init crc value, use 0 at the first use.
*
uint16_t crc16_be(uint16_t crc, uint8_t const *buf, uint32_t len);
/**
- * @brief Crc8 value that is in little endian.
+ * @brief CRC8 value that is in little endian.
*
* @param uint8_t crc : init crc value, use 0 at the first use.
*
uint8_t crc8_le(uint8_t crc, uint8_t const *buf, uint32_t len);
/**
- * @brief Crc8 value that is in big endian.
+ * @brief CRC8 value that is in big endian.
*
* @param uint32_t crc : init crc value, use 0 at the first use.
*