计算 CRC16 校验和的函数
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【中文标题】计算 CRC16 校验和的函数【英文标题】：Function to Calculate a CRC16 Checksum 【发布时间】：2012-05-20 19:48:32 【问题描述】：我正在开发一个库，以通过 RS232 或 RS485 连接提供简单可靠的通信。此代码的一部分涉及对数据使用 CRC16 校验和来检测线路噪声造成的损坏。我创建了一个函数来计算 CRC16 校验和，但它似乎没有输出正确的值。
我写的相关代码如下（也可以找到here）。
#include <stdint.h>
#define CRC16 0x8005
uint16_t gen_crc16(const uint8_t *data, uint16_t size)
uint16_t out = 0;
int bits_read = 0, bit_flag;
/* Sanity check: */
if(data == NULL)
return 0;
while(size > 0)
bit_flag = out >> 15;
/* Get next bit: */
out <<= 1;
out |= (*data >> (7 - bits_read)) & 1;
/* Increment bit counter: */
bits_read++;
if(bits_read > 7)
bits_read = 0;
data++;
size--;
/* Cycle check: */
if(bit_flag)
out ^= CRC16;
return out;
我正在对照this online CRC calculator 检查我的输出。
我得出的结论要么是我对如何计算 CRC16 的理解是错误的，要么是在线计算器是错误的（前者似乎更有可能）。谁能告诉我哪里出错了？
【问题讨论】：
另请参阅我的问题***.com/questions/4455257/…，它基于同一个在线计算器，并包含一个方便的矩阵表来比较各种公式。 不要使用此处发布的任何位代码。使用表驱动算法。速度是原来的 8 倍。 【参考方案1】：CRC-16 有几种不同的变体。见wiki page。
每一个都会从相同的输入返回不同的结果。
所以你必须为你的程序仔细选择正确的一个。
【讨论】：
我正在使用与他们相同的多项式 (x^16 + x^15 + x^2 + 1) 是的，但是有几个初始值、异或等。见regregex.bbcmicro.net/crc-catalogue.htm【参考方案2】：对于特定的 CRC 实现，您需要“匹配”几个细节 - 即使使用相同的多项式，也可能会出现不同的结果，因为使用 CRC 的特定初始值处理数据位的方式存在细微差别（有时为零，有时为 0xffff），和/或反转 CRC 的位。例如，有时一种实现会从数据字节的低位向上工作，而有时它们会从高位向下工作（就像你目前所做的那样）。
此外，您需要在运行完所有数据位后“推出”CRC 的最后一位。
请记住，CRC 算法是为在硬件中实现而设计的，因此从软件的角度来看，一些位排序的处理方式可能没有太大意义。
如果您想将 CRC16 与多项式 0x8005 匹配，如 lammertbies.nl CRC 计算器页面所示，您需要对您的 CRC 函数进行以下更改：
a) 从最低有效位而不是最高有效位开始通过 CRC 循环运行数据位 b) 完成输入数据后，将 CRC 的最后 16 位从 CRC 寄存器中推出 c) 反转 CRC 位（我猜这个位是硬件实现的结转）因此，您的函数可能如下所示：
#define CRC16 0x8005
uint16_t gen_crc16(const uint8_t *data, uint16_t size)
uint16_t out = 0;
int bits_read = 0, bit_flag;
/* Sanity check: */
if(data == NULL)
return 0;
while(size > 0)
bit_flag = out >> 15;
/* Get next bit: */
out <<= 1;
out |= (*data >> bits_read) & 1; // item a) work from the least significant bits
/* Increment bit counter: */
bits_read++;
if(bits_read > 7)
bits_read = 0;
data++;
size--;
/* Cycle check: */
if(bit_flag)
out ^= CRC16;
// item b) "push out" the last 16 bits
int i;
for (i = 0; i < 16; ++i)
bit_flag = out >> 15;
out <<= 1;
if(bit_flag)
out ^= CRC16;
// item c) reverse the bits
uint16_t crc = 0;
i = 0x8000;
int j = 0x0001;
for (; i != 0; i >>=1, j <<= 1)
if (i & out) crc |= j;
return crc;
当我传入"123456789" 时，该函数会为我返回0xbb3d。
【讨论】：
我完全忘记了“推出”最后 16 位。我不敢相信我没听懂。至于位反转……我可能要花很长时间才能弄清楚。谢谢。 此文件将需要根据问题代码在此函数上方定义#define CRC16 0x8005。 gist.github.com/jlamothe/2666368 此实现仅适用于 32 或 64 位整数环境。如果 sizeof(int) == 2，则失败。将 i 的类型从 int 更改为 uint16_t。 这是一个非常糟糕的实现。完全相同的 CRC 可以更优雅、更有效地计算，即使按位计算也是如此。因此：uint16_t crc16(uint8_t const *data, size_t size) uint16_t crc = 0; while (size--) crc ^= *data++; for (unsigned k = 0; k < 8; k++) crc = crc & 1 ? (crc >> 1) ^ 0xa001 : crc >> 1; return crc;
@PipeSoto CRC 是位反转的，因此对于有效的实现，多项式是位反转的（而不是替代方案，即对所有输入和结果进行位反转）。 0xa001 是 0x8005 反转。【参考方案3】：
下面是计算 crc16 CCITT 的工作代码。我对其进行了测试，结果与http://www.lammertbies.nl/comm/info/crc-calculation.html 提供的结果相符。
unsigned short crc16(const unsigned char* data_p, unsigned char length)
unsigned char x;
unsigned short crc = 0xFFFF;
while (length--)
x = crc >> 8 ^ *data_p++;
x ^= x>>4;
crc = (crc << 8) ^ ((unsigned short)(x << 12)) ^ ((unsigned short)(x <<5)) ^ ((unsigned short)x);
return crc;
【讨论】：
CRC-16-CCITT (poly 0x1021) 是最常见的 CRC-16 并且在使用中得到了最充分的证明，所以我建议使用这个。例如，这是您可以在带有内置 CRC 计算器的微控制器中找到的 CRC。 两件事：您可能会发现一些 CRC-CCITT 实现期望初始 crc 值为0x1D0F 以匹配测试向量。其次，unsigned short 只保证至少 16 位，这是规范的，但可以 更宽。所以我建议使用最终的crc &= 0xffff;，这样一来，您就不需要在循环的最后一行使用(unsigned short) 强制转换，更宽的类型应该可以正常工作。
此例程不起作用...它确实为短字符串（例如“123456789”）给出正确答案，但不为较长字符串给出正确答案（在我的情况是一个 260 字节的二进制文件）。
@Richard: 260 太大，无法放入 unsigned char length 参数。将该参数的类型更改为unsigned short 应该可以修复它：unsigned short crc16(const unsigned char* data_p, unsigned short length)。
这个算法接近CCITT但错误。请在srecord.sourceforge.net/crc16-ccitt.html查看测试字符串【参考方案4】：
for (pos = 0; pos < len; pos++)
crc ^= (uint16_t)buf[pos]; // XOR byte into least sig. byte of crc
for (i = 8; i != 0; i--) // Loop over each bit
if ((crc & 0x0001) != 0) // If the LSB is set
crc >>= 1; // Shift right and XOR 0xA001
crc ^= CRC16;
else // Else LSB is not set
crc >>= 1; // Just shift right
return crc;
【讨论】：
【参考方案5】：我使用了以下代码示例： http://www.sunshine2k.de/articles/coding/crc/understanding_crc.html#ch5
还有这个实用程序来验证： http://www.sunshine2k.de/coding/javascript/crc/crc_js.html
【讨论】：
【参考方案6】：crcany 将为任何 CRC 生成高效的 C 代码，并包含一个包含一百多个已知 CRC 定义的库。
高效的 CRC 代码使用表格而不是按位计算。 crcany 生成逐字节例程和逐字例程，后者针对生成它们的体系结构进行了调整。 Word-wise 是最快的。 Byte-wise 仍然比 bit-wise 快得多，但实现更容易在架构上移植。
您似乎没有需要匹配的具有特定 CRC 定义的协议定义。在这种情况下，您可以在catalog 中选择任何 16 位 CRC，您将获得良好的性能。
如果您的误码率相对较低，例如每个数据包的单个数字错误数，并且您希望最大限度地提高错误检测性能，您需要查看应用 CRC 的数据包大小，假设它是恒定的或有界的，并查看最佳的性能Philip Koopman's extensive research 中的多项式。经典的 CRC，例如 CCITT/Kermit 16 位 CRC 或 X.25 16 位 CRC 并不是表现最好的。
CRC-16/DNP 是 Koopman 表中表现出色的 16 位算法之一，也是在实践中使用的 CRC 目录中。它具有非常好的性能，可以检测数据包中多达 6 位的错误。以下是 crcany 为该 CRC 定义生成的代码。此代码假定按字计算的小端架构，例如Intel x86 和 x86-64，它假定 uintmax_t 是 64 位。 crcany 可用于为 big-endian 和其他字长生成替代代码。
crc16dnp.h:
// The _bit, _byte, and _word routines return the CRC of the len bytes at mem,
// applied to the previous CRC value, crc. If mem is NULL, then the other
// arguments are ignored, and the initial CRC, i.e. the CRC of zero bytes, is
// returned. Those routines will all return the same result, differing only in
// speed and code complexity. The _rem routine returns the CRC of the remaining
// bits in the last byte, for when the number of bits in the message is not a
// multiple of eight. The low bits bits of the low byte of val are applied to
// crc. bits must be in 0..8.
#include <stddef.h>
// Compute the CRC a bit at a time.
unsigned crc16dnp_bit(unsigned crc, void const *mem, size_t len);
// Compute the CRC of the low bits bits in val.
unsigned crc16dnp_rem(unsigned crc, unsigned val, unsigned bits);
// Compute the CRC a byte at a time.
unsigned crc16dnp_byte(unsigned crc, void const *mem, size_t len);
// Compute the CRC a word at a time.
unsigned crc16dnp_word(unsigned crc, void const *mem, size_t len);
crc16dnp.c:
#include <stdint.h>
#include "crc16dnp.h"
// This code assumes that unsigned is 4 bytes.
unsigned crc16dnp_bit(unsigned crc, void const *mem, size_t len)
unsigned char const *data = mem;
if (data == NULL)
return 0xffff;
crc = ~crc;
crc &= 0xffff;
while (len--)
crc ^= *data++;
for (unsigned k = 0; k < 8; k++)
crc = crc & 1 ? (crc >> 1) ^ 0xa6bc : crc >> 1;
crc ^= 0xffff;
return crc;
unsigned crc16dnp_rem(unsigned crc, unsigned val, unsigned bits)
crc = ~crc;
crc &= 0xffff;
val &= (1U << bits) - 1;
crc ^= val;
while (bits--)
crc = crc & 1 ? (crc >> 1) ^ 0xa6bc : crc >> 1;
crc ^= 0xffff;
return crc;
#define table_byte table_word[0]
static unsigned short const table_word[][256] =
0xed35, 0xdb6b, 0x8189, 0xb7d7, 0x344d, 0x0213, 0x58f1, 0x6eaf, 0x12bc, 0x24e2,
0x7e00, 0x485e, 0xcbc4, 0xfd9a, 0xa778, 0x9126, 0x5f5e, 0x6900, 0x33e2, 0x05bc,
0x8626, 0xb078, 0xea9a, 0xdcc4, 0xa0d7, 0x9689, 0xcc6b, 0xfa35, 0x79af, 0x4ff1,
0x1513, 0x234d, 0xc49a, 0xf2c4, 0xa826, 0x9e78, 0x1de2, 0x2bbc, 0x715e, 0x4700,
0x3b13, 0x0d4d, 0x57af, 0x61f1, 0xe26b, 0xd435, 0x8ed7, 0xb889, 0x76f1, 0x40af,
0x1a4d, 0x2c13, 0xaf89, 0x99d7, 0xc335, 0xf56b, 0x8978, 0xbf26, 0xe5c4, 0xd39a,
0x5000, 0x665e, 0x3cbc, 0x0ae2, 0xbe6b, 0x8835, 0xd2d7, 0xe489, 0x6713, 0x514d,
0x0baf, 0x3df1, 0x41e2, 0x77bc, 0x2d5e, 0x1b00, 0x989a, 0xaec4, 0xf426, 0xc278,
0x0c00, 0x3a5e, 0x60bc, 0x56e2, 0xd578, 0xe326, 0xb9c4, 0x8f9a, 0xf389, 0xc5d7,
0x9f35, 0xa96b, 0x2af1, 0x1caf, 0x464d, 0x7013, 0x97c4, 0xa19a, 0xfb78, 0xcd26,
0x4ebc, 0x78e2, 0x2200, 0x145e, 0x684d, 0x5e13, 0x04f1, 0x32af, 0xb135, 0x876b,
0xdd89, 0xebd7, 0x25af, 0x13f1, 0x4913, 0x7f4d, 0xfcd7, 0xca89, 0x906b, 0xa635,
0xda26, 0xec78, 0xb69a, 0x80c4, 0x035e, 0x3500, 0x6fe2, 0x59bc, 0x4b89, 0x7dd7,
0x2735, 0x116b, 0x92f1, 0xa4af, 0xfe4d, 0xc813, 0xb400, 0x825e, 0xd8bc, 0xeee2,
0x6d78, 0x5b26, 0x01c4, 0x379a, 0xf9e2, 0xcfbc, 0x955e, 0xa300, 0x209a, 0x16c4,
0x4c26, 0x7a78, 0x066b, 0x3035, 0x6ad7, 0x5c89, 0xdf13, 0xe94d, 0xb3af, 0x85f1,
0x6226, 0x5478, 0x0e9a, 0x38c4, 0xbb5e, 0x8d00, 0xd7e2, 0xe1bc, 0x9daf, 0xabf1,
0xf113, 0xc74d, 0x44d7, 0x7289, 0x286b, 0x1e35, 0xd04d, 0xe613, 0xbcf1, 0x8aaf,
0x0935, 0x3f6b, 0x6589, 0x53d7, 0x2fc4, 0x199a, 0x4378, 0x7526, 0xf6bc, 0xc0e2,
0x9a00, 0xac5e, 0x18d7, 0x2e89, 0x746b, 0x4235, 0xc1af, 0xf7f1, 0xad13, 0x9b4d,
0xe75e, 0xd100, 0x8be2, 0xbdbc, 0x3e26, 0x0878, 0x529a, 0x64c4, 0xaabc, 0x9ce2,
0xc600, 0xf05e, 0x73c4, 0x459a, 0x1f78, 0x2926, 0x5535, 0x636b, 0x3989, 0x0fd7,
0x8c4d, 0xba13, 0xe0f1, 0xd6af, 0x3178, 0x0726, 0x5dc4, 0x6b9a, 0xe800, 0xde5e,
0x84bc, 0xb2e2, 0xcef1, 0xf8af, 0xa24d, 0x9413, 0x1789, 0x21d7, 0x7b35, 0x4d6b,
0x8313, 0xb54d, 0xefaf, 0xd9f1, 0x5a6b, 0x6c35, 0x36d7, 0x0089, 0x7c9a, 0x4ac4,
0x1026, 0x2678, 0xa5e2, 0x93bc, 0xc95e, 0xff00,
0x740f, 0xdf41, 0x6fea, 0xc4a4, 0x43c5, 0xe88b, 0x5820, 0xf36e, 0x1b9b, 0xb0d5,
0x007e, 0xab30, 0x2c51, 0x871f, 0x37b4, 0x9cfa, 0xab27, 0x0069, 0xb0c2, 0x1b8c,
0x9ced, 0x37a3, 0x8708, 0x2c46, 0xc4b3, 0x6ffd, 0xdf56, 0x7418, 0xf379, 0x5837,
0xe89c, 0x43d2, 0x8726, 0x2c68, 0x9cc3, 0x378d, 0xb0ec, 0x1ba2, 0xab09, 0x0047,
0xe8b2, 0x43fc, 0xf357, 0x5819, 0xdf78, 0x7436, 0xc49d, 0x6fd3, 0x580e, 0xf340,
0x43eb, 0xe8a5, 0x6fc4, 0xc48a, 0x7421, 0xdf6f, 0x379a, 0x9cd4, 0x2c7f, 0x8731,
0x0050, 0xab1e, 0x1bb5, 0xb0fb, 0xdf24, 0x746a, 0xc4c1, 0x6f8f, 0xe8ee, 0x43a0,
0xf30b, 0x5845, 0xb0b0, 0x1bfe, 0xab55, 0x001b, 0x877a, 0x2c34, 0x9c9f, 0x37d1,
0x000c, 0xab42, 0x1be9, 0xb0a7, 0x37c6, 0x9c88, 0x2c23, 0x876d, 0x6f98, 0xc4d6,
0x747d, 0xdf33, 0x5852, 0xf31c, 0x43b7, 0xe8f9, 0x2c0d, 0x8743, 0x37e8, 0x9ca6,
0x1bc7, 0xb089, 0x0022, 0xab6c, 0x4399, 0xe8d7, 0x587c, 0xf332, 0x7453, 0xdf1d,
0x6fb6, 0xc4f8, 0xf325, 0x586b, 0xe8c0, 0x438e, 0xc4ef, 0x6fa1, 0xdf0a, 0x7444,
0x9cb1, 0x37ff, 0x8754, 0x2c1a, 0xab7b, 0x0035, 0xb09e, 0x1bd0, 0x6f20, 0xc46e,
0x74c5, 0xdf8b, 0x58ea, 0xf3a4, 0x430f, 0xe841, 0x00b4, 0xabfa, 0x1b51, 0xb01f,
0x377e, 0x9c30, 0x2c9b, 0x87d5, 0xb008, 0x1b46, 0xabed, 0x00a3, 0x87c2, 0x2c8c,
0x9c27, 0x3769, 0xdf9c, 0x74d2, 0xc479, 0x6f37, 0xe856, 0x4318, 0xf3b3, 0x58fd,
0x9c09, 0x3747, 0x87ec, 0x2ca2, 0xabc3, 0x008d, 0xb026, 0x1b68, 0xf39d, 0x58d3,
0xe878, 0x4336, 0xc457, 0x6f19, 0xdfb2, 0x74fc, 0x4321, 0xe86f, 0x58c4, 0xf38a,
0x74eb, 0xdfa5, 0x6f0e, 0xc440, 0x2cb5, 0x87fb, 0x3750, 0x9c1e, 0x1b7f, 0xb031,
0x009a, 0xabd4, 0xc40b, 0x6f45, 0xdfee, 0x74a0, 0xf3c1, 0x588f, 0xe824, 0x436a,
0xab9f, 0x00d1, 0xb07a, 0x1b34, 0x9c55, 0x371b, 0x87b0, 0x2cfe, 0x1b23, 0xb06d,
0x00c6, 0xab88, 0x2ce9, 0x87a7, 0x370c, 0x9c42, 0x74b7, 0xdff9, 0x6f52, 0xc41c,
0x437d, 0xe833, 0x5898, 0xf3d6, 0x3722, 0x9c6c, 0x2cc7, 0x8789, 0x00e8, 0xaba6,
0x1b0d, 0xb043, 0x58b6, 0xf3f8, 0x4353, 0xe81d, 0x6f7c, 0xc432, 0x7499, 0xdfd7,
0xe80a, 0x4344, 0xf3ef, 0x58a1, 0xdfc0, 0x748e, 0xc425, 0x6f6b, 0x879e, 0x2cd0,
0x9c7b, 0x3735, 0xb054, 0x1b1a, 0xabb1, 0x00ff,
0x7c67, 0x65df, 0x4f17, 0x56af, 0x1a87, 0x033f, 0x29f7, 0x304f, 0xb1a7, 0xa81f,
0x82d7, 0x9b6f, 0xd747, 0xceff, 0xe437, 0xfd8f, 0xaa9e, 0xb326, 0x99ee, 0x8056,
0xcc7e, 0xd5c6, 0xff0e, 0xe6b6, 0x675e, 0x7ee6, 0x542e, 0x4d96, 0x01be, 0x1806,
0x32ce, 0x2b76, 0x9cec, 0x8554, 0xaf9c, 0xb624, 0xfa0c, 0xe3b4, 0xc97c, 0xd0c4,
0x512c, 0x4894, 0x625c, 0x7be4, 0x37cc, 0x2e74, 0x04bc, 0x1d04, 0x4a15, 0x53ad,
0x7965, 0x60dd, 0x2cf5, 0x354d, 0x1f85, 0x063d, 0x87d5, 0x9e6d, 0xb4a5, 0xad1d,
0xe135, 0xf88d, 0xd245, 0xcbfd, 0xf008, 0xe9b0, 0xc378, 0xdac0, 0x96e8, 0x8f50,
0xa598, 0xbc20, 0x3dc8, 0x2470, 0x0eb8, 0x1700, 0x5b28, 0x4290, 0x6858, 0x71e0,
0x26f1, 0x3f49, 0x1581, 0x0c39, 0x4011, 0x59a9, 0x7361, 0x6ad9, 0xeb31, 0xf289,
0xd841, 0xc1f9, 0x8dd1, 0x9469, 0xbea1, 0xa719, 0x1083, 0x093b, 0x23f3, 0x3a4b,
0x7663, 0x6fdb, 0x4513, 0x5cab, 0xdd43, 0xc4fb, 0xee33, 0xf78b, 0xbba3, 0xa21b,
0x88d3, 0x916b, 0xc67a, 0xdfc2, 0xf50a, 0xecb2, 0xa09a, 0xb922, 0x93ea, 0x8a52,
0x0bba, 0x1202, 0x38ca, 0x2172, 0x6d5a, 0x74e2, 0x5e2a, 0x4792, 0x29c0, 0x3078,
0x1ab0, 0x0308, 0x4f20, 0x5698, 0x7c50, 0x65e8, 0xe400, 0xfdb8, 0xd770, 0xcec8,
0x82e0, 0x9b58, 0xb190, 0xa828, 0xff39, 0xe681, 0xcc49, 0xd5f1, 0x99d9, 0x8061,
0xaaa9, 0xb311, 0x32f9, 0x2b41, 0x0189, 0x1831, 0x5419, 0x4da1, 0x6769, 0x7ed1,
0xc94b, 0xd0f3, 0xfa3b, 0xe383, 0xafab, 0xb613, 0x9cdb, 0x8563, 0x048b, 0x1d33,
0x37fb, 0x2e43, 0x626b, 0x7bd3, 0x511b, 0x48a3, 0x1fb2, 0x060a, 0x2cc2, 0x357a,
0x7952, 0x60ea, 0x4a22, 0x539a, 0xd272, 0xcbca, 0xe102, 0xf8ba, 0xb492, 0xad2a,
0x87e2, 0x9e5a, 0xa5af, 0xbc17, 0x96df, 0x8f67, 0xc34f, 0xdaf7, 0xf03f, 0xe987,
0x686f, 0x71d7, 0x5b1f, 0x42a7, 0x0e8f, 0x1737, 0x3dff, 0x2447, 0x7356, 0x6aee,
0x4026, 0x599e, 0x15b6, 0x0c0e, 0x26c6, 0x3f7e, 0xbe96, 0xa72e, 0x8de6, 0x945e,
0xd876, 0xc1ce, 0xeb06, 0xf2be, 0x4524, 0x5c9c, 0x7654, 0x6fec, 0x23c4, 0x3a7c,
0x10b4, 0x090c, 0x88e4, 0x915c, 0xbb94, 0xa22c, 0xee04, 0xf7bc, 0xdd74, 0xc4cc,
0x93dd, 0x8a65, 0xa0ad, 0xb915, 0xf53d, 0xec85, 0xc64d, 0xdff5, 0x5e1d, 0x47a5,
0x6d6d, 0x74d5, 0x38fd, 0x2145, 0x0b8d, 0x1235,
0xf917, 0x3bff, 0x31be, 0xf356, 0x253c, 0xe7d4, 0xed95, 0x2f7d, 0x0c38, 0xced0,
0xc491, 0x0679, 0xd013, 0x12fb, 0x18ba, 0xda52, 0x5e30, 0x9cd8, 0x9699, 0x5471,
0x821b, 0x40f3, 0x4ab2, 0x885a, 0xab1f, 0x69f7, 0x63b6, 0xa15e, 0x7734, 0xb5dc,
0xbf9d, 0x7d75, 0xfa20, 0x38c8, 0x3289, 0xf061, 0x260b, 0xe4e3, 0xeea2, 0x2c4a,
0x0f0f, 0xcde7, 0xc7a6, 0x054e, 0xd324, 0x11cc, 0x1b8d, 0xd965, 0x5d07, 0x9fef,
0x95ae, 0x5746, 0x812c, 0x43c4, 0x4985, 0x8b6d, 0xa828, 0x6ac0, 0x6081, 0xa269,
0x7403, 0xb6eb, 0xbcaa, 0x7e42, 0xff79, 0x3d91, 0x37d0, 0xf538, 0x2352, 0xe1ba,
0xebfb, 0x2913, 0x0a56, 0xc8be, 0xc2ff, 0x0017, 0xd67d, 0x1495, 0x1ed4, 0xdc3c,
0x585e, 0x9ab6, 0x90f7, 0x521f, 0x8475, 0x469d, 0x4cdc, 0x8e34, 0xad71, 0x6f99,
0x65d8, 0xa730, 0x715a, 0xb3b2, 0xb9f3, 0x7b1b, 0xfc4e, 0x3ea6, 0x34e7, 0xf60f,
0x2065, 0xe28d, 0xe8cc, 0x2a24, 0x0961, 0xcb89, 0xc1c8, 0x0320, 0xd54a, 0x17a2,
0x1de3, 0xdf0b, 0x5b69, 0x9981, 0x93c0, 0x5128, 0x8742, 0x45aa, 0x4feb, 0x8d03,
0xae46, 0x6cae, 0x66ef, 0xa407, 0x726d, 0xb085, 0xbac4, 0x782c, 0xf5cb, 0x3723,
0x3d62, 0xff8a, 0x29e0, 0xeb08, 0xe149, 0x23a1, 0x00e4, 0xc20c, 0xc84d, 0x0aa5,
0xdccf, 0x1e27, 0x1466, 0xd68e, 0x52ec, 0x9004, 0x9a45, 0x58ad, 0x8ec7, 0x4c2f,
0x466e, 0x8486, 0xa7c3, 0x652b, 0x6f6a, 0xad82, 0x7be8, 0xb900, 0xb341, 0x71a9,
0xf6fc, 0x3414, 0x3e55, 0xfcbd, 0x2ad7, 0xe83f, 0xe27e, 0x2096, 0x03d3, 0xc13b,
0xcb7a, 0x0992, 0xdff8, 0x1d10, 0x1751, 0xd5b9, 0x51db, 0x9333, 0x9972, 0x5b9a,
0x8df0, 0x4f18, 0x4559, 0x87b1, 0xa4f4, 0x661c, 0x6c5d, 0xaeb5, 0x78df, 0xba37,
0xb076, 0x729e, 0xf3a5, 0x314d, 0x3b0c, 0xf9e4, 0x2f8e, 0xed66, 0xe727, 0x25cf,
0x068a, 0xc462, 0xce23, 0x0ccb, 0xdaa1, 0x1849, 0x1208, 0xd0e0, 0x5482, 0x966a,
0x9c2b, 0x5ec3, 0x88a9, 0x4a41, 0x4000, 0x82e8, 0xa1ad, 0x6345, 0x6904, 0xabec,
0x7d86, 0xbf6e, 0xb52f, 0x77c7, 0xf092, 0x327a, 0x383b, 0xfad3, 0x2cb9, 0xee51,
0xe410, 0x26f8, 0x05bd, 0xc755, 0xcd14, 0x0ffc, 0xd996, 0x1b7e, 0x113f, 0xd3d7,
0x57b5, 0x955d, 0x9f1c, 0x5df4, 0x8b9e, 0x4976, 0x4337, 0x81df, 0xa29a, 0x6072,
0x6a33, 0xa8db, 0x7eb1, 0xbc59, 0xb618, 0x74f0,
0x3108, 0x120e, 0x7704, 0x5402, 0xbd10, 0x9e16, 0xfb1c, 0xd81a, 0x6441, 0x4747,
0x224d, 0x014b, 0xe859, 0xcb5f, 0xae55, 0x8d53, 0x9b9a, 0xb89c, 0xdd96, 0xfe90,
0x1782, 0x3484, 0x518e, 0x7288, 0xced3, 0xedd5, 0x88df, 0xabd9, 0x42cb, 0x61cd,
0x04c7, 0x27c1, 0x2955, 0x0a53, 0x6f59, 0x4c5f, 0xa54d, 0x864b, 0xe341, 0xc047,
0x7c1c, 0x5f1a, 0x3a10, 0x1916, 0xf004, 0xd302, 0xb608, 0x950e, 0x83c7, 0xa0c1,
0xc5cb, 0xe6cd, 0x0fdf, 0x2cd9, 0x49d3, 0x6ad5, 0xd68e, 0xf588, 0x9082, 0xb384,
0x5a96, 0x7990, 0x1c9a, 0x3f9c, 0x01b2, 0x22b4, 0x47be, 0x64b8, 0x8daa, 0xaeac,
0xcba6, 0xe8a0, 0x54fb, 0x77fd, 0x12f7, 0x31f1, 0xd8e3, 0xfbe5, 0x9eef, 0xbde9,
0xab20, 0x8826, 0xed2c, 0xce2a, 0x2738, 0x043e, 0x6134, 0x4232, 0xfe69, 0xdd6f,
0xb865, 0x9b63, 0x7271, 0x5177, 0x347d, 0x177b, 0x19ef, 0x3ae9, 0x5fe3, 0x7ce5,
0x95f7, 0xb6f1, 0xd3fb, 0xf0fd, 0x4ca6, 0x6fa0, 0x0aaa, 0x29ac, 0xc0be, 0xe3b8,
0x86b2, 0xa5b4, 0xb37d, 0x907b, 0xf571, 0xd677, 0x3f65, 0x1c63, 0x7969, 0x5a6f,
0xe634, 0xc532, 0xa038, 0x833e, 0x6a2c, 0x492a, 0x2c20, 0x0f26, 0x507c, 0x737a,
0x1670, 0x3576, 0xdc64, 0xff62, 0x9a68, 0xb96e, 0x0535, 0x2633, 0x4339, 0x603f,
0x892d, 0xaa2b, 0xcf21, 0xec27, 0xfaee, 0xd9e8, 0xbce2, 0x9fe4, 0x76f6, 0x55f0,
0x30fa, 0x13fc, 0xafa7, 0x8ca1, 0xe9ab, 0xcaad, 0x23bf, 0x00b9, 0x65b3, 0x46b5,
0x4821, 0x6b27, 0x0e2d, 0x2d2b, 0xc439, 0xe73f, 0x8235, 0xa133, 0x1d68, 0x3e6e,
0x5b64, 0x7862, 0x9170, 0xb276, 0xd77c, 0xf47a, 0xe2b3, 0xc1b5, 0xa4bf, 0x87b9,
0x6eab, 0x4dad, 0x28a7, 0x0ba1, 0xb7fa, 0x94fc, 0xf1f6, 0xd2f0, 0x3be2, 0x18e4,
0x7dee, 0x5ee8, 0x60c6, 0x43c0, 0x26ca, 0x05cc, 0xecde, 0xcfd8, 0xaad2, 0x89d4,
0x358f, 0x1689, 0x7383, 0x5085, 0xb997, 0x9a91, 0xff9b, 0xdc9d, 0xca54, 0xe952,
0x8c58, 0xaf5e, 0x464c, 0x654a, 0x0040, 0x2346, 0x9f1d, 0xbc1b, 0xd911, 0xfa17,
0x1305, 0x3003, 0x5509, 0x760f, 0x789b, 0x5b9d, 0x3e97, 0x1d91, 0xf483, 0xd785,
0xb28f, 0x9189, 0x2dd2, 0x0ed4, 0x6bde, 0x48d8, 0xa1ca, 0x82cc, 0xe7c6, 0xc4c0,
0xd209, 0xf10f, 0x9405, 0xb703, 0x5e11, 0x7d17, 0x181d, 0x3b1b, 0x8740, 0xa446,
0xc14c, 0xe24a, 0x0b58, 0x285e, 0x4d54, 0x6e52,
0xffb8, 0x4a5f, 0xd90f, 0x6ce8, 0xb2d6, 0x0731, 0x9461, 0x2186, 0x6564, 0xd083,
0x43d3, 0xf634, 0x280a, 0x9ded, 0x0ebd, 0xbb5a, 0x8779, 0x329e, 0xa1ce, 0x1429,
0xca17, 0x7ff0, 0xeca0, 0x5947, 0x1da5, 0xa842, 0x3b12, 0x8ef5, 0x50cb, 0xe52c,
0x767c, 0xc39b, 0x0e3a, 0xbbdd, 0x288d, 0x9d6a, 0x4354, 0xf6b3, 0x65e3, 0xd004,
0x94e6, 0x2101, 0xb251, 0x07b6, 0xd988, 0x6c6f, 0xff3f, 0x4ad8, 0x76fb, 0xc31c,
0x504c, 0xe5ab, 0x3b95, 0x8e72, 0x1d22, 0xa8c5, 0xec27, 0x59c0, 0xca90, 0x7f77,
0xa149, 0x14ae, 0x87fe, 0x3219, 0x51c5, 0xe422, 0x7772, 0xc295, 0x1cab, 0xa94c,
0x3a1c, 0x8ffb, 0xcb19, 0x7efe, 0xedae, 0x5849, 0x8677, 0x3390, 0xa0c0, 0x1527,
0x2904, 0x9ce3, 0x0fb3, 0xba54, 0x646a, 0xd18d, 0x42dd, 0xf73a, 0xb3d8, 0x063f,
0x956f, 0x2088, 0xfeb6, 0x4b51, 0xd801, 0x6de6, 0xa047, 0x15a0, 0x86f0, 0x3317,
0xed29, 0x58ce, 0xcb9e, 0x7e79, 0x3a9b, 0x8f7c, 0x1c2c, 0xa9cb, 0x77f5, 0xc212,
0x5142, 0xe4a5, 0xd886, 0x6d61, 0xfe31, 0x4bd6, 0x95e8, 0x200f, 0xb35f, 0x06b8,
0x425a, 0xf7bd, 0x64ed, 0xd10a, 0x0f34, 0xbad3, 0x2983, 0x9c64, 0xee3b, 0x5bdc,
0xc88c, 0x7d6b, 0xa355, 0x16b2, 0x85e2, 0x3005, 0x74e7, 0xc100, 0x5250, 0xe7b7,
0x3989, 0x8c6e, 0x1f3e, 0xaad9, 0x96fa, 0x231d, 0xb04d, 0x05aa, 0xdb94, 0x6e73,
0xfd23, 0x48c4, 0x0c26, 0xb9c1, 0x2a91, 0x9f76, 0x4148, 0xf4af, 0x67ff, 0xd218,
0x1fb9, 0xaa5e, 0x390e, 0x8ce9, 0x52d7, 0xe730, 0x7460, 0xc187, 0x8565, 0x3082,
0xa3d2, 0x1635, 0xc80b, 0x7dec, 0xeebc, 0x5b5b, 0x6778, 0xd29f, 0x41cf, 0xf428,
0x2a16, 0x9ff1, 0x0ca1, 0xb946, 0xfda4, 0x4843, 0xdb13, 0x6ef4, 0xb0ca, 0x052d,
0x967d, 0x239a, 0x4046, 0xf5a1, 0x66f1, 0xd316, 0x0d28, 0xb8cf, 0x2b9f, 0x9e78,
0xda9a, 0x6f7d, 0xfc2d, 0x49ca, 0x97f4, 0x2213, 0xb143, 0x04a4, 0x3887, 0x8d60,
0x1e30, 0xabd7, 0x75e9, 0xc00e, 0x535e, 0xe6b9, 0xa25b, 0x17bc, 0x84ec, 0x310b,
0xef35, 0x5ad2, 0xc982, 0x7c65, 0xb1c4, 0x0423, 0x9773, 0x2294, 0xfcaa, 0x494d,
0xda1d, 0x6ffa, 0x2b18, 0x9eff, 0x0daf, 0xb848, 0x6676, 0xd391, 0x40c1, 0xf526,
0xc905, 0x7ce2, 0xefb2, 0x5a55, 0x846b, 0x318c, 0xa2dc, 0x173b, 0x53d9, 0xe63e,
0x756e, 0xc089, 0x1eb7, 0xab50, 0x3800, 0x8de7,
0xc20e, 0x9d6c, 0x7cca, 0x23a8, 0xf2ff, 0xad9d, 0x4c3b, 0x1359, 0xa3ec, 0xfc8e,
0x1d28, 0x424a, 0x931d, 0xcc7f, 0x2dd9, 0x72bb, 0x01ca, 0x5ea8, 0xbf0e, 0xe06c,
0x313b, 0x6e59, 0x8fff, 0xd09d, 0x6028, 0x3f4a, 0xdeec, 0x818e, 0x50d9, 0x0fbb,
0xee1d, 0xb17f, 0x08ff, 0x579d, 0xb63b, 0xe959, 0x380e, 0x676c, 0x86ca, 0xd9a8,
0x691d, 0x367f, 0xd7d9, 0x88bb, 0x59ec, 0x068e, 0xe728, 0xb84a, 0xcb3b, 0x9459,
0x75ff, 0x2a9d, 0xfbca, 0xa4a8, 0x450e, 0x1a6c, 0xaad9, 0xf5bb, 0x141d, 0x4b7f,
0x9a28, 0xc54a, 0x24ec, 0x7b8e, 0x1a95, 0x45f7, 0xa451, 0xfb33, 0x2a64, 0x7506,
0x94a0, 0xcbc2, 0x7b77, 0x2415, 0xc5b3, 0x9ad1, 0x4b86, 0x14e4, 0xf542, 0xaa20,
0xd951, 0x8633, 0x6795, 0x38f7, 0xe9a0, 0xb6c2, 0x5764, 0x0806, 0xb8b3, 0xe7d1,
0x0677, 0x5915, 0x8842, 0xd720, 0x3686, 0x69e4, 0xd064, 0x8f06, 0x6ea0, 0x31c2,
0xe095, 0xbff7, 0x5e51, 0x0133, 0xb186, 0xeee4, 0x0f42, 0x5020, 0x8177, 0xde15,
0x3fb3, 0x60d1, 0x13a0, 0x4cc2, 0xad64, 0xf206, 0x2351, 0x7c33, 0x9d95, 0xc2f7,
0x7242, 0x2d20, 0xcc86, 0x93e4, 0x42b3, 0x1dd1, 0xfc77, 0xa315, 0x3e41, 0x6123,
0x8085, 0xdfe7, 0x0eb0, 0x51d2, 0xb074, 0xef16, 0x5fa3, 0x00c1, 0xe167, 0xbe05,
0x6f52, 0x3030, 0xd196, 0x8ef4, 0xfd85, 0xa2e7, 0x4341, 0x1c23, 0xcd74, 0x9216,
0x73b0, 0x2cd2, 0x9c67, 0xc305, 0x22a3, 0x7dc1, 0xac96, 0xf3f4, 0x1252, 0x4d30,
0xf4b0, 0xabd2, 0x4a74, 0x1516, 0xc441, 0x9b23, 0x7a85, 0x25e7, 0x9552, 0xca30,
0x2b96, 0x74f4, 0xa5a3, 0xfac1, 0x1b67, 0x4405, 0x3774, 0x6816, 0x89b0, 0xd6d2,
0x0785, 0x58e7, 0xb941, 0xe623, 0x5696, 0x09f4, 0xe852, 0xb730, 0x6667, 0x3905,
0xd8a3, 0x87c1, 0xe6da, 0xb9b8, 0x581e, 0x077c, 0xd62b, 0x8949, 0x68ef, 0x378d,
0x8738, 0xd85a, 0x39fc, 0x669e, 0xb7c9, 0xe8ab, 0x090d, 0x566f, 0x251e, 0x7a7c,
0x9bda, 0xc4b8, 0x15ef, 0x4a8d, 0xab2b, 0xf449, 0x44fc, 0x1b9e, 0xfa38, 0xa55a,
0x740d, 0x2b6f, 0xcac9, 0x95ab, 0x2c2b, 0x7349, 0x92ef, 0xcd8d, 0x1cda, 0x43b8,
0xa21e, 0xfd7c, 0x4dc9, 0x12ab, 0xf30d, 0xac6f, 0x7d38, 0x225a, 0xc3fc, 0x9c9e,
0xefef, 0xb08d, 0x512b, 0x0e49, 0xdf1e, 0x807c, 0x61da, 0x3eb8, 0x8e0d, 0xd16f,
0x30c9, 0x6fab, 0xbefc, 0xe19e, 0x0038, 0x5f5a,
0x4a8f, 0x5c9d, 0x66ab, 0x70b9, 0x12c7, 0x04d5, 0x3ee3, 0x28f1, 0xfa1f, 0xec0d,
0xd63b, 0xc029, 0xa257, 0xb445, 0x8e73, 0x9861, 0x66d6, 0x70c4, 0x4af2, 0x5ce0,
0x3e9e, 0x288c, 0x12ba, 0x04a8, 0xd646, 0xc054, 0xfa62, 0xec70, 0x8e0e, 0x981c,
0xa22a, 0xb438, 0x123d, 0x042f, 0x3e19, 0x280b, 0x4a75, 0x5c67, 0x6651, 0x7043,
0xa2ad, 0xb4bf, 0x8e89, 0x989b, 0xfae5, 0xecf7, 0xd6c1, 0xc0d3, 0x3e64, 0x2876,
0x1240, 0x0452, 0x662c, 0x703e, 0x4a08, 0x5c1a, 0x8ef4, 0x98e6, 0xa2d0, 0xb4c2,
0xd6bc, 0xc0ae, 0xfa98, 0xec8a, 0xfbeb, 0xedf9, 0xd7cf, 0xc1dd, 0xa3a3, 0xb5b1,
0x8f87, 0x9995, 0x4b7b, 0x5d69, 0x675f, 0x714d, 0x1333, 0x0521, 0x3f17, 0x2905,
0xd7b2, 0xc1a0, 0xfb96, 0xed84, 0x8ffa, 0x99e8, 0xa3de, 0xb5cc, 0x6722, 0x7130,
0x4b06, 0x5d14, 0x3f6a, 0x2978, 0x134e, 0x055c, 0xa359, 0xb54b, 0x8f7d, 0x996f,
0xfb11, 0xed03, 0xd735, 0xc127, 0x13c9, 0x05db, 0x3fed, 0x29ff, 0x4b81, 0x5d93,
0x67a5, 0x71b7, 0x8f00, 0x9912, 0xa324, 0xb536, 0xd748, 0xc15a, 0xfb6c, 0xed7e,
0x3f90, 0x2982, 0x13b4, 0x05a6, 0x67d8, 0x71ca, 0x4bfc, 0x5dee, 0x653e, 0x732c,
0x491a, 0x5f08, 0x3d76, 0x2b64, 0x1152, 0x0740, 0xd5ae, 0xc3bc, 0xf98a, 0xef98,
0x8de6, 0x9bf4, 0xa1c2, 0xb7d0, 0x4967, 0x5f75, 0x6543, 0x7351, 0x112f, 0x073d,
0x3d0b, 0x2b19, 0xf9f7, 0xefe5, 0xd5d3, 0xc3c1, 0xa1bf, 0xb7ad, 0x8d9b, 0x9b89,
0x3d8c, 0x2b9e, 0x11a8, 0x07ba, 0x65c4, 0x73d6, 0x49e0, 0x5ff2, 0x8d1c, 0x9b0e,
0xa138, 0xb72a, 0xd554, 0xc346, 0xf970, 0xef62, 0x11d5, 0x07c7, 0x3df1, 0x2be3,
0x499d, 0x5f8f, 0x65b9, 0x73ab, 0xa145, 0xb757, 0x8d61, 0x9b73, 0xf90d, 0xef1f,
0xd529, 0xc33b, 0xd45a, 0xc248, 0xf87e, 0xee6c, 0x8c12, 0x9a00, 0xa036, 0xb624,
0x64ca, 0x72d8, 0x48ee, 0x5efc, 0x3c82, 0x2a90, 0x10a6, 0x06b4, 0xf803, 0xee11,
0xd427, 0xc235, 0xa04b, 0xb659, 0x8c6f, 0x9a7d, 0x4893, 0x5e81, 0x64b7, 0x72a5,
0x10db, 0x06c9, 0x3cff, 0x2aed, 0x8ce8, 0x9afa, 0xa0cc, 0xb6de, 0xd4a0, 0xc2b2,
0xf884, 0xee96, 0x3c78, 0x2a6a, 0x105c, 0x064e, 0x6430, 0x7222, 0x4814, 0x5e06,
0xa0b1, 0xb6a3, 0x8c95, 0x9a87, 0xf8f9, 0xeeeb, 0xd4dd, 0xc2cf, 0x1021, 0x0633,
0x3c05, 0x2a17, 0x4869, 0x5e7b, 0x644d, 0x725f
;
unsigned crc16dnp_byte(unsigned crc, void const *mem, size_t len)
unsigned char const *data = mem;
if (data == NULL)
return 0xffff;
crc &= 0xffff;
while (len--)
crc = (crc >> 8) ^
table_byte[(crc ^ *data++) & 0xff];
return crc;
// This code assumes that integers are stored little-endian.
unsigned crc16dnp_word(unsigned crc, void const *mem, size_t len)
unsigned char const *data = mem;
if (data == NULL)
return 0xffff;
crc &= 0xffff;
while (len && ((ptrdiff_t)data & 0x7))
crc = (crc >> 8) ^
table_byte[(crc ^ *data++) & 0xff];
len--;
if (len >= 8)
do
uintmax_t word = crc ^ *(uintmax_t const *)data;
crc = table_word[7][word & 0xff] ^
table_word[6][(word >> 8) & 0xff] ^
table_word[5][(word >> 16) & 0xff] ^
table_word[4][(word >> 24) & 0xff] ^
table_word[3][(word >> 32) & 0xff] ^
table_word[2][(word >> 40) & 0xff] ^
table_word[1][(word >> 48) & 0xff] ^
table_word[0][word >> 56];
data += 8;
len -= 8;
while (len >= 8);
while (len--)
crc = (crc >> 8) ^
table_byte[(crc ^ *data++) & 0xff];
return crc;
【讨论】：
我对CRC的了解非常有限。我认为按位、按字节和按字实现返回相同的结果。正确的？如果是，例如逐字实现如何处理数据输入，这不是 4 字节的倍数，结果仍然与逐字节实现相同？ 是的，它们返回相同的结果。它们仅在速度上有所不同。如果逐字实现在一次处理四个字节后最后剩下 1、2 或 3 个字节，则使用逐字节算法处理这些字节。【参考方案7】：此功能适用于 CRC-16 Modbus 版本。不适用于 CRC-16
【讨论】：
你能详细说明一下吗？有什么区别以及需要改变什么？ CRC-16 和 CRC-16 Modbus 的区别在于初始值。其中一个是0xFFFF，另一个是0x0000以上是关于计算 CRC16 校验和的函数的主要内容，如果未能解决你的问题，请参考以下文章