我正在使用以下函数生成 CRC 和，与在线 CRC-CCITT 计算器相比，它似乎没有返回相同的校验和。
该函数专门使用 XMODEM CRC 生成，其多项式为 0x8408，初始 fcs 为 0xFFFF。
uint16_t crc16(uint8_t byte, uint16_t fcs)
{
uint8_t bit;
for(bit=0; bit<8; bit++)
{
fcs ^= (byte & 0x01);
fcs = (fcs & 0x01) ? (fcs >> 1) ^ 0x8408 : (fcs >> 1);
byte = byte >> 1;
}
return fcs;
}
我做错了什么吗？如果我发送 0xFF 或 0x00，我不会得到与 http://depa.usst.edu.cn/chenjq/www2/SDesign/JavaScript/CRCcalculation.htm
相同的校验和printf("%04X\n", crc16(0x31, 0xFFFF)); //returns 2F8D
看看Greg Cook 的优秀 CRC 目录。有一种变体经常被错误地识别为 CCITT CRC，但事实并非如此。这就是您的代码（带有
0xFFFF0xFFFF0x1021KERMIT
width=16 poly=0x1021 init=0x0000 refin=true refout=true xorout=0x0000 check=0x2189 name="KERMIT"
XMODEM
width=16 poly=0x1021 init=0x0000 refin=false refout=false xorout=0x0000 check=0x31c3 name="XMODEM"
CRC-16/CCITT-FALSE
width=16 poly=0x1021 init=0xffff refin=false refout=false xorout=0x0000 check=0x29b1 name="CRC-16/CCITT-FALSE"
我已阅读您的问题，我也遇到了和您类似的问题。
我已经解决了在XMODEM中计算CRC-CCITT的这个问题。这里我附上计算 CRC-CCITT 的示例程序。
我已经用在线转换器和这个程序尝试过数据。如果您愿意，请使用这个。
unsigned short crc16(char *ptr, int count)
{
int crc;
char i;
crc = 0;
while (--count >= 0)
{
crc = crc ^ (int) *ptr++ << 8;
i = 8;
do
{
if (crc & 0x8000)
crc = crc << 1 ^ 0x1021;
else
crc = crc << 1;
} while(--i);
}
return (crc);
}
CRC 应定义为无符号短整型，因为
crc16static const unsigned short CRC_CCITT_TABLE[256] =
{
0x0000, 0x1021, 0x2042, 0x3063, 0x4084, 0x50A5, 0x60C6, 0x70E7,
0x8108, 0x9129, 0xA14A, 0xB16B, 0xC18C, 0xD1AD, 0xE1CE, 0xF1EF,
0x1231, 0x0210, 0x3273, 0x2252, 0x52B5, 0x4294, 0x72F7, 0x62D6,
0x9339, 0x8318, 0xB37B, 0xA35A, 0xD3BD, 0xC39C, 0xF3FF, 0xE3DE,
0x2462, 0x3443, 0x0420, 0x1401, 0x64E6, 0x74C7, 0x44A4, 0x5485,
0xA56A, 0xB54B, 0x8528, 0x9509, 0xE5EE, 0xF5CF, 0xC5AC, 0xD58D,
0x3653, 0x2672, 0x1611, 0x0630, 0x76D7, 0x66F6, 0x5695, 0x46B4,
0xB75B, 0xA77A, 0x9719, 0x8738, 0xF7DF, 0xE7FE, 0xD79D, 0xC7BC,
0x48C4, 0x58E5, 0x6886, 0x78A7, 0x0840, 0x1861, 0x2802, 0x3823,
0xC9CC, 0xD9ED, 0xE98E, 0xF9AF, 0x8948, 0x9969, 0xA90A, 0xB92B,
0x5AF5, 0x4AD4, 0x7AB7, 0x6A96, 0x1A71, 0x0A50, 0x3A33, 0x2A12,
0xDBFD, 0xCBDC, 0xFBBF, 0xEB9E, 0x9B79, 0x8B58, 0xBB3B, 0xAB1A,
0x6CA6, 0x7C87, 0x4CE4, 0x5CC5, 0x2C22, 0x3C03, 0x0C60, 0x1C41,
0xEDAE, 0xFD8F, 0xCDEC, 0xDDCD, 0xAD2A, 0xBD0B, 0x8D68, 0x9D49,
0x7E97, 0x6EB6, 0x5ED5, 0x4EF4, 0x3E13, 0x2E32, 0x1E51, 0x0E70,
0xFF9F, 0xEFBE, 0xDFDD, 0xCFFC, 0xBF1B, 0xAF3A, 0x9F59, 0x8F78,
0x9188, 0x81A9, 0xB1CA, 0xA1EB, 0xD10C, 0xC12D, 0xF14E, 0xE16F,
0x1080, 0x00A1, 0x30C2, 0x20E3, 0x5004, 0x4025, 0x7046, 0x6067,
0x83B9, 0x9398, 0xA3FB, 0xB3DA, 0xC33D, 0xD31C, 0xE37F, 0xF35E,
0x02B1, 0x1290, 0x22F3, 0x32D2, 0x4235, 0x5214, 0x6277, 0x7256,
0xB5EA, 0xA5CB, 0x95A8, 0x8589, 0xF56E, 0xE54F, 0xD52C, 0xC50D,
0x34E2, 0x24C3, 0x14A0, 0x0481, 0x7466, 0x6447, 0x5424, 0x4405,
0xA7DB, 0xB7FA, 0x8799, 0x97B8, 0xE75F, 0xF77E, 0xC71D, 0xD73C,
0x26D3, 0x36F2, 0x0691, 0x16B0, 0x6657, 0x7676, 0x4615, 0x5634,
0xD94C, 0xC96D, 0xF90E, 0xE92F, 0x99C8, 0x89E9, 0xB98A, 0xA9AB,
0x5844, 0x4865, 0x7806, 0x6827, 0x18C0, 0x08E1, 0x3882, 0x28A3,
0xCB7D, 0xDB5C, 0xEB3F, 0xFB1E, 0x8BF9, 0x9BD8, 0xABBB, 0xBB9A,
0x4A75, 0x5A54, 0x6A37, 0x7A16, 0x0AF1, 0x1AD0, 0x2AB3, 0x3A92,
0xFD2E, 0xED0F, 0xDD6C, 0xCD4D, 0xBDAA, 0xAD8B, 0x9DE8, 0x8DC9,
0x7C26, 0x6C07, 0x5C64, 0x4C45, 0x3CA2, 0x2C83, 0x1CE0, 0x0CC1,
0xEF1F, 0xFF3E, 0xCF5D, 0xDF7C, 0xAF9B, 0xBFBA, 0x8FD9, 0x9FF8,
0x6E17, 0x7E36, 0x4E55, 0x5E74, 0x2E93, 0x3EB2, 0x0ED1, 0x1EF0
};
我使用以下代码来计算 CRC-CCITT (0xFFFF)：
unsigned short Calculate_CRC_CCITT(const unsigned char* buffer, int size)
{
unsigned short tmp;
unsigned short crc = 0xffff;
for (int i=0; i < size ; i++)
{
tmp = (crc >> 8) ^ buffer[i];
crc = (crc << 8) ^ CRC_CCITT_TABLE[tmp];
}
return crc;
}
正如 Mark Adler 上面所说，不同 CRC 算法的命名法相当混乱，并且并不总是正确处理。他对Greg Cook 出色的 CRC 目录的参考可能是您获得简洁命名法的最佳选择。
为了方便地实现各个算法，请参阅下面的 C++ 示例实现[仅 16 位 CRC]。
#include <climits>
#include <cstdint>
static_assert(8 == CHAR_BIT);
namespace Helpers
{
uint8_t bitSwap(uint8_t const value)
{
uint8_t workValue = value;
{
uint8_t constexpr mask = 0xf0;
workValue = ((workValue & mask) >> 4) | ((workValue & ~mask) << 4);
}
{
uint8_t constexpr mask = 0xcc;
workValue = ((workValue & mask) >> 2) | ((workValue & ~mask) << 2);
}
{
uint8_t constexpr mask = 0xaa;
workValue = ((workValue & mask) >> 1) | ((workValue & ~mask) << 1);
}
return workValue;
}
uint16_t bitSwap(uint16_t const value)
{
uint16_t workValue = value;
{
uint16_t constexpr mask = 0xff00;
workValue = ((workValue & mask) >> 8) | ((workValue & ~mask) << 8);
}
{
uint16_t constexpr mask = 0xf0f0;
workValue = ((workValue & mask) >> 4) | ((workValue & ~mask) << 4);
}
{
uint16_t constexpr mask = 0xcccc;
workValue = ((workValue & mask) >> 2) | ((workValue & ~mask) << 2);
}
{
uint16_t constexpr mask = 0xaaaa;
workValue = ((workValue & mask) >> 1) | ((workValue & ~mask) << 1);
}
return workValue;
}
} // namespace Helpers
namespace Internal_
{
template <typename T, bool reflect>
class BitSwap
{
public:
static T of(T const value);
private:
BitSwap() = delete;
};
template <typename T>
class BitSwap<T, false>
{
public:
static T of(T const value)
{
return value;
}
private:
BitSwap() = delete;
};
template <typename T>
class BitSwap<T, true>
{
public:
static T of(T const value)
{
return Helpers::bitSwap(value);
}
private:
BitSwap() = delete;
};
} // namespace Internal_
template <uint16_t polynomial,
uint16_t initialCrc,
bool reflectIn,
bool reflectOut,
uint16_t xorOut>
class Crc16
{
public:
Crc16() noexcept
: crc_(initialCrc)
{
}
void process(uint8_t const * const data, size_t const octectCount) noexcept
{
for (uint8_t const * datumPointer = data; (data + octectCount) > datumPointer; ++datumPointer)
{
// Include the new data in the CRC calculation by virtually appending it to accumulated
// and already processed data. Now make it represented in the CRC calculation by the
// XOR operation [i.e. simply pretend, this datum has always been here and is thus reflected
// in the remainder of the previous calculation already].
// Do so with the upper byte, as to conform to the notion of "appending 16 bits of 0 for the
// calculation" [8 bits shifted here, 8 bits shifted in below loop] - so as to perform the
// XOR until the last bit of data and really only retain the remainder. Which is what the CRC
// is supposed to be.
crc_ ^= (static_cast<uint16_t>(
Internal_::BitSwap<uint8_t, reflectIn>::of(*datumPointer)
) << 8);
for (int bitIndex = 0; bitIndex < CHAR_BIT; ++bitIndex)
{
// Perform XOR only if the MSb [Most Significant bit] is set [as the CRC is "[...] the
// remainder of a polynomial division, modulo two.", Jack Crenshaw's "Implementing CRCs"
// article in the January 1992 issue of Embedded Systems Programming].
bool const applyPolynomial = (0 != (0x8000 & crc_));
// In the polynomial the MSb is not encoded and instead assumed to always be 1 [otherwise
// the 16-order polynomial would have required 17-bits, which would exceed the value type].
// So:
// - If we are going to apply the polynomial, we already know that 0 == (1 ^ 1) and thus
// we disregard this bit.
// - If we are not going to apply the polynomial, the bit was 0 and is simply discarded
// as well.
// So in any case, simply shift out the MSb.
crc_ <<= 1;
if (applyPolynomial)
{
crc_ ^= polynomial;
}
}
}
}
uint16_t get() const noexcept
{
return (xorOut ^ Internal_::BitSwap<uint16_t, reflectOut>::of(crc_));
}
private:
uint16_t crc_;
};
// https://reveng.sourceforge.io/crc-catalogue/16.htm#crc.cat.crc-16-xmodem
// CRC-16/XMODEM
// width=16 poly=0x1021 init=0x0000 refin=false refout=false xorout=0x0000 check=0x31c3 residue=0x0000 name="CRC-16/XMODEM"
// Class: attested
// Alias: CRC-16/ACORN, CRC-16/LTE, CRC-16/V-41-MSB, XMODEM, ZMODEM
// The MSB-first form of the V.41 algorithm. For the LSB-first form see CRC-16/KERMIT. CRC presented high byte first.
// Used in the MultiMediaCard interface. In XMODEM and Acorn MOS the message bits are processed out of transmission order,
// compromising the guarantees on burst error detection.
// ITU-T Recommendation V.41 (November 1988)
typedef Crc16<0x1021, 0x0000, false, false, 0x0000> Crc16Xmodem;
// https://reveng.sourceforge.io/crc-catalogue/16.htm#crc.cat.crc-16-kermit
// CRC-16/KERMIT
// width=16 poly=0x1021 init=0x0000 refin=true refout=true xorout=0x0000 check=0x2189 residue=0x0000 name="CRC-16/KERMIT"
// Class: attested
// Alias: CRC-16/BLUETOOTH, CRC-16/CCITT, CRC-16/CCITT-TRUE, CRC-16/V-41-LSB, CRC-CCITT, KERMIT
// Used in Bluetooth error detection. Init=0x0000 is used in the Inquiry Response substate.
// Press et al. identify the CCITT algorithm with the one implemented in Kermit. V.41 is endianness-agnostic, referring
// only to bit sequences, but the CRC appears reflected when used with LSB-first modems. Ironically, the unreflected form
// is used in CRC-16/XMODEM.
typedef Crc16<0x1021, 0x0000, true, true, 0x0000> Crc16Kermit;
// https://reveng.sourceforge.io/crc-catalogue/16.htm#crc.cat.crc-16-ibm-3740
// CRC-16/IBM-3740
// width=16 poly=0x1021 init=0xffff refin=false refout=false xorout=0x0000 check=0x29b1 residue=0x0000 name="CRC-16/IBM-3740"
// Class: attested
// Alias: CRC-16/AUTOSAR, CRC-16/CCITT-FALSE
// An algorithm commonly misidentified as CRC-CCITT. CRC-CCITT customarily refers to the LSB-first form of the algorithm in
// ITU-T Recommendation V.41 (see CRC-16/KERMIT); its MSB-first counterpart is CRC-16/XMODEM.
// AUTOSAR (24 November 2022), AUTOSAR Classic Platform release R22-11, Specification of CRC Routines
typedef Crc16<0x1021, 0xffff, false, false, 0x0000> Crc16Ibm3740;
// https://reveng.sourceforge.io/crc-catalogue/16.htm#crc.cat.crc-16-spi-fujitsu
// CRC-16/SPI-FUJITSU
// width=16 poly=0x1021 init=0x1d0f refin=false refout=false xorout=0x0000 check=0xe5cc residue=0x0000 name="CRC-16/SPI-FUJITSU"
// Class: attested
// Alias: CRC-16/AUG-CCITT
// Init value is equivalent to an augment of 0xFFFF prepended to the message.
// Fujitsu Semiconductor (10 October 2007), FlexRay ASSP MB88121B User's Manual (courtesy of the Internet Archive)
typedef Crc16<0x1021, 0x1d0f, false, false, 0x0000> Crc16SpiFujitsu;
对于 Xmodem CRC 它将返回 0x2672，如您所料 [参见 AlphabetaPhi 2013 年 6 月 19 日 19:05 的评论]：
uint8_t const data = 0x31;
Crc16Xmodem crc;
crc.process(&data, 1);
uint16_t const crcValue = crc.get(); // 0x2672
对于Java
安装：https://mvnrepository.com/artifact/com.github.snksoft/crc/1.0.2
长 returnValue = CRC.calculateCRC(Parameters.CCITT, "yourStringValue");