Rijndael S-box in C - c

I am trying to write a function which computes the Rijndael S-box according to this Wikipedia article. Rijndael S-box
#define ROTL8(x,shift) ((uint8_t) ((x) << shift | ((x) >> (8 - (shift)))))
uint8_t sbox(uint8_t b)
{
uint8_t s = b ^ ROTL8(b,1) ^ ROTL8(b,2) ^ ROTL8(b,3) ^ ROTL8(b,4) ^ 0x63;
return s;
}
Now this works when I try sbox(0x00)=0x63 and sbox(0x01)=0x7c, but it starts to go astray from sbox(0x02), which should be 0x77, but I get 0x5d instead. I suspected the issue might be the rotation not working correctly, but that now does not seem like an issue...
What is wrong here?


This is the wrong way to implement AES's S-box - most implementations are either hardcoded (they explicitly write the entire S-box as a 256-byte array), or they iteratively build the entries of the S-box, as in the Wikipedia article you linked:
void initialize_aes_sbox(uint8_t sbox[256]) {
uint8_t p = 1, q = 1;
/* loop invariant: p * q == 1 in the Galois field */
do {
/* multiply p by 3 */
p = p ^ (p << 1) ^ (p & 0x80 ? 0x1B : 0);
/* divide q by 3 (equals multiplication by 0xf6) */
q ^= q << 1;
q ^= q << 2;
q ^= q << 4;
q ^= q & 0x80 ? 0x09 : 0;
/* compute the affine transformation */
uint8_t xformed = q ^ ROTL8(q, 1) ^ ROTL8(q, 2) ^ ROTL8(q, 3) ^ ROTL8(q, 4);
sbox[p] = xformed ^ 0x63;
} while (p != 1);
/* 0 is a special case since it has no inverse */
sbox[0] = 0x63;
}
notice that xformed's value - which is the value you calculated in your own implementation - changes iteratively over the iterations (and it is not the S-box value of its q the way you implemented). In practice, every manual S-box construction has some sort of similar iterative process - look over at Code Golf for some creative implementations.

Related

Flipping Pebble Screen Issue

I'm writing a Pebble Time Watch app using Pebble SDK 3.0 on the basalt platform that requires text to be displayed upsidedown.
The logic is:-
Write to screen
Capture screen buffer
Flip screen buffer (using flipHV routine, see below)
Release buffer.
After a fair amount of experimentation I've got it working after a fashion but the (black) text has what seems to be random vertical white lines through it (see image below) which I suspect is something to do with shifting bits.
The subroutine I'm using is:-
void flipHV(GBitmap *bitMap) {
GRect fbb = gbitmap_get_bounds(bitMap);
int Width = 72; // fbb.size.w;
int Height = 84; // fbb.size.h;
uint32_t *pBase = (uint32_t *)gbitmap_get_data(bitMap);
uint32_t *pTopRemainingPixel = pBase;
uint32_t *pBottomRemainingPixel = pBase + (Height * Width);
while (pTopRemainingPixel < pBottomRemainingPixel) {
uint32_t TopPixel = *pTopRemainingPixel;
uint32_t BottomPixel = *pBottomRemainingPixel;
TopPixel = (TopPixel << 16) | (TopPixel >> 16);
*pBottomRemainingPixel = TopPixel;
BottomPixel = (BottomPixel << 16) | (BottomPixel >> 16);
*pTopRemainingPixel = BottomPixel;
pTopRemainingPixel++;
pBottomRemainingPixel--;
}
}
and its purpose is to work though the screen buffer taking the first pixel and swapping with the last one, the second one and swapping it with the second last one etc etc.
Because each 32 bit 'byte' holds 2 pixels I also need to rotate it through 16 bits.
I suspect that that is where the problem lies.
Can someone have a look at my code and see if they can see what is going wrong and put me right. I should say that I'm both a C and Pebble SDK newbie so please explain everything as if to a child!

Your assignments like
TopPixel = (TopPixel << 16) | (TopPixel >> 16)
swap pixels pair-wise
+--+--+ +--+--+
|ab|cd| => |cd|ab|
+--+--+ +--+--+
What you want instead is a full swap:
+--+--+ +--+--+
|ab|cd| => |dc|ba|
+--+--+ +--+--+
That can be done with even more bit-fiddling, e.g
TopPixel = ((TopPixel << 24) | // move d from 0..7 to 24..31
((TopPixel << 8) & 0x00ff0000) | // move c from 8..15 to 16..23
((TopPixel >> 8) & 0x0000ff00) | // move b from 16..23 to 8..15
((TopPixel >> 24) | // move a from 24..31 to 0..7
or - way more readable(!) - by using GColor8 instead of uint32_t and a loop on a per-pixel-basis:
// only loop to half of the distance to avoid swapping twice
for (int16_t y = 0; y <= max_y / 2; y++) {
for (int16_t x = 0; x <= max_x / 2; x++) {
GColor8 *value_1 = gbitmap_get_bytes_per_row(bmp) * y + x;
GColor8 *value_2 = gbitmap_get_bytes_per_row(bmp) * (max_y - y) + (max_x - x);
// swapping the two pixel values, could be simplified with a SWAP(a,b) macro
GColor8 tmp = *value_1;
*value_1 = *value_2;
*value_2 = tmp;
}
}
Disclaimer: I haven't compiled this code. It might also be necessary to cast the gbitmap_get_byes_per_row()... expressions to GColor8*. And the whole pointer arithmetic can be tuned if you see that this is a performance bottle-neck.

It turns out that I needed to replace all of the uint32_t with uint8_t and do away with the shifting.

How to check the number of set bits in an 8-bit unsigned char?

So I have to find the set bits (on 1) of an unsigned char variable in C?
A similar question is How to count the number of set bits in a 32-bit integer? But it uses an algorithm that's not easily adaptable to 8-bit unsigned chars (or its not apparent).

The algorithm suggested in the question How to count the number of set bits in a 32-bit integer? is trivially adapted to 8 bit:
int NumberOfSetBits( uint8_t b )
{
b = b - ((b >> 1) & 0x55);
b = (b & 0x33) + ((b >> 2) & 0x33);
return (((b + (b >> 4)) & 0x0F) * 0x01);
}
It is simply a case of shortening the constants the the least significant eight bits, and removing the final 24 bit right-shift. Equally it could be adapted for 16bit using an 8 bit shift. Note that in the case for 8 bit, the mechanical adaptation of the 32 bit algorithm results in a redundant * 0x01 which could be omitted.

The fastest approach for an 8-bit variable is using a lookup table.
Build an array of 256 values, one per 8-bit combination. Each value should contain the count of bits in its corresponding index:
int bit_count[] = {
// 00 01 02 03 04 05 06 07 08 09 0a, ... FE FF
0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, ..., 7, 8
};
Getting a count of a combination is the same as looking up a value from the bit_count array. The advantage of this approach is that it is very fast.
You can generate the array using a simple program that counts bits one by one in a slow way:
for (int i = 0 ; i != 256 ; i++) {
int count = 0;
for (int p = 0 ; p != 8 ; p++) {
if (i & (1 << p)) {
count++;
}
}
printf("%d, ", count);
}
(demo that generates the table).
If you would like to trade some CPU cycles for memory, you can use a 16-byte lookup table for two 4-bit lookups:
static const char split_lookup[] = {
0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4
};
int bit_count(unsigned char n) {
return split_lookup[n&0xF] + split_lookup[n>>4];
}
Demo.

I think you are looking for Hamming Weight algorithm for 8bits?
If it is true, here is the code:
unsigned char in = 22; //This is your input number
unsigned char out = 0;
in = in - ((in>>1) & 0x55);
in = (in & 0x33) + ((in>>2) & 0x33);
out = ((in + (in>>4) & 0x0F) * 0x01) ;

Counting the number of digits different than 0 is also known as a Hamming Weight. In this case, you are counting the number of 1's.
Dasblinkenlight provided you with a table driven implementation, and Olaf provided you with a software based solution. I think you have two other potential solutions. The first is to use a compiler extension, the second is to use an ASM specific instruction with inline assembly from C.
For the first alternative, see GCC's __builtin_popcount(). (Thanks to Artless Noise).
For the second alternative, you did not specify the embedded processor, but I'm going to offer this in case its ARM based.
Some ARM processors have the VCNT instruction, which performs the count for you. So you could do it from C with inline assembly:
inline
unsigned int hamming_weight(unsigned char value) {
__asm__ __volatile__ (
"VCNT.8"
: "=value"
: "value"
);
return value;
}
Also see Fastest way to count number of 1s in a register, ARM assembly.
For completeness, here is Kernighan's bit counting algorithm:
int count_bits(int n) {
int count = 0;
while(n != 0) {
n &= (n-1);
count++;
}
return count;
}
Also see Please explain the logic behind Kernighan's bit counting algorithm.

I made an optimized version. With a 32-bit processor, utilizing multiplication, bit shifting and masking can make smaller code for the same task, especially when the input domain is small (8-bit unsigned integer).
The following two code snippets are equivalent:
unsigned int bit_count_uint8(uint8_t x)
{
uint32_t n;
n = (uint32_t)(x * 0x08040201UL);
n = (uint32_t)(((n >> 3) & 0x11111111UL) * 0x11111111UL);
/* The "& 0x0F" will be optimized out but I add it for clarity. */
return (n >> 28) & 0x0F;
}
/*
unsigned int bit_count_uint8_traditional(uint8_t x)
{
x = x - ((x >> 1) & 0x55);
x = (x & 0x33) + ((x >> 2) & 0x33);
x = ((x + (x >> 4)) & 0x0F);
return x;
}
*/
This produces smallest binary code for IA-32, x86-64 and AArch32 (without NEON instruction set) as far as I can find.
For x86-64, this doesn't use the fewest number of instructions, but the bit shifts and downcasting avoid the use of 64-bit instructions and therefore save a few bytes in the compiled binary.
Interestingly, in IA-32 and x86-64, a variant of the above algorithm using a modulo ((((uint32_t)(x * 0x08040201U) >> 3) & 0x11111111U) % 0x0F) actually generates larger code, due to a requirement to move the remainder register for return value (mov eax,edx) after the div instruction. (I tested all of these in Compiler Explorer)
Explanation
I denote the eight bits of the byte x, from MSB to LSB, as a, b, c, d, e, f, g and h.
abcdefgh
* 00001000 00000100 00000010 00000001 (make 4 copies of x
--------------------------------------- with appropriate
abc defgh0ab cdefgh0a bcdefgh0 abcdefgh bit spacing)
>> 3
---------------------------------------
000defgh 0abcdefg h0abcdef gh0abcde
& 00010001 00010001 00010001 00010001
---------------------------------------
000d000h 000c000g 000b000f 000a000e
* 00010001 00010001 00010001 00010001
---------------------------------------
000d000h 000c000g 000b000f 000a000e
... 000h000c 000g000b 000f000a 000e
... 000c000g 000b000f 000a000e
... 000g000b 000f000a 000e
... 000b000f 000a000e
... 000f000a 000e
... 000a000e
... 000e
^^^^ (Bits 31-28 will contain the sum of the bits
a, b, c, d, e, f, g and h. Extract these
bits and we are done.)

Maybe not the fastest, but straightforward:
int count = 0;
for (int i = 0; i < 8; ++i) {
unsigned char c = 1 << i;
if (yourVar & c) {
//bit n°i is set
//first bit is bit n°0
count++;
}
}

For 8/16 bit MCUs, a loop will very likely be faster than the parallel-addition approach, as these MCUs cannot shift by more than one bit per instruction, so:
size_t popcount(uint8_t val)
{
size_t cnt = 0;
do {
cnt += val & 1U; // or: if ( val & 1 ) cnt++;
} while ( val >>= 1 ) ;
return cnt;
}
For the incrementation of cnt, you might profile. If still too slow, an assember implementation might be worth a try using carry flag (if available). While I am in against using assembler optimizations in general, such algorithms are one of the few good exceptions (still just after the C version fails).
If you can omit the Flash, a lookup table as proposed by #dasblinkenlight is likey the fastest approach.
Just a hint: For some architectures (notably ARM and x86/64), gcc has a builtin: __builtin_popcount(), you also might want to try if available (although it takes int at least). This might use a single CPU instruction - you cannot get faster and more compact.

Allow me to post a second answer. This one is the smallest possible for ARM processors with Advanced SIMD extension (NEON). It's even smaller than __builtin_popcount() (since __builtin_popcount() is optimized for unsigned int input, not uint8_t).
#ifdef __ARM_NEON
/* ARM C Language Extensions (ACLE) recommends us to check __ARM_NEON before
including <arm_neon.h> */
#include <arm_neon.h>
unsigned int bit_count_uint8(uint8_t x)
{
/* Set all lanes at once so that the compiler won't emit instruction to
zero-initialize other lanes. */
uint8x8_t v = vdup_n_u8(x);
/* Count the number of set bits for each lane (8-bit) in the vector. */
v = vcnt_u8(v);
/* Get lane 0 and discard other lanes. */
return vget_lane_u8(v, 0);
}
#endif

How to use table based CRC-16 code?

I was hoping someone might be able to shed some light on why my CRC-16 implementation does not seem to run correctly on Visual Studio? I got the algorithm from a manual for a specific device, and wrote the int main() myself. There are always 'type' errors when I try to pass the arguments to the function, so I suspect there is something wrong with the format? This is the info that came with the code:
CRC Name : CRC-16
Width : 16 Bits
Polynomial Used : 1189 (hex)
Seed Value : FFFF (hex)
Reflected Input/Output : No
Exclusive OR Output : No
Test CRC for string "123456789" : 5502 (hex)
#include <stdio.h>
unsigned int crctable[256] =
{
0x0000, 0x1189, 0x2312, 0x329B, 0x4624, 0x57AD, 0x6536, 0x74BF,
0x8C48, 0x9DC1, 0xAF5A, 0xBED3, 0xCA6C, 0xDBE5, 0xE97E, 0xF8F7,
0x0919, 0x1890, 0x2A0B, 0x3B82, 0x4F3D, 0x5EB4, 0x6C2F, 0x7DA6,
0x8551, 0x94D8, 0xA643, 0xB7CA, 0xC375, 0xD2FC, 0xE067, 0xF1EE,
0x1232, 0x03BB, 0x3120, 0x20A9, 0x5416, 0x459F, 0x7704, 0x668D,
0x9E7A, 0x8FF3, 0xBD68, 0xACE1, 0xD85E, 0xC9D7, 0xFB4C, 0xEAC5,
0x1B2B, 0x0AA2, 0x3839, 0x29B0, 0x5D0F, 0x4C86, 0x7E1D, 0x6F94,
0x9763, 0x86EA, 0xB471, 0xA5F8, 0xD147, 0xC0CE, 0xF255, 0xE3DC,
0x2464, 0x35ED, 0x0776, 0x16FF, 0x6240, 0x73C9, 0x4152, 0x50DB,
0xA82C, 0xB9A5, 0x8B3E, 0x9AB7, 0xEE08, 0xFF81, 0xCD1A, 0xDC93,
0x2D7D, 0x3CF4, 0x0E6F, 0x1FE6, 0x6B59, 0x7AD0, 0x484B, 0x59C2,
0xA135, 0xB0BC, 0x8227, 0x93AE, 0xE711, 0xF698, 0xC403, 0xD58A,
0x3656, 0x27DF, 0x1544, 0x04CD, 0x7072, 0x61FB, 0x5360, 0x42E9,
0xBA1E, 0xAB97, 0x990C, 0x8885, 0xFC3A, 0xEDB3, 0xDF28, 0xCEA1,
0x3F4F, 0x2EC6, 0x1C5D, 0x0DD4, 0x796B, 0x68E2, 0x5A79, 0x4BF0,
0xB307, 0xA28E, 0x9015, 0x819C, 0xF523, 0xE4AA, 0xD631, 0xC7B8,
0x48C8, 0x5941, 0x6BDA, 0x7A53, 0x0EEC, 0x1F65, 0x2DFE, 0x3C77,
0xC480, 0xD509, 0xE792, 0xF61B, 0x82A4, 0x932D, 0xA1B6, 0xB03F,
0x41D1, 0x5058, 0x62C3, 0x734A, 0x07F5, 0x167C, 0x24E7, 0x356E,
0xCD99, 0xDC10, 0xEE8B, 0xFF02, 0x8BBD, 0x9A34, 0xA8AF, 0xB926,
0x5AFA, 0x4B73, 0x79E8, 0x6861, 0x1CDE, 0x0D57, 0x3FCC, 0x2E45,
0xD6B2, 0xC73B, 0xF5A0, 0xE429, 0x9096, 0x811F, 0xB384, 0xA20D,
0x53E3, 0x426A, 0x70F1, 0x6178, 0x15C7, 0x044E, 0x36D5, 0x275C,
0xDFAB, 0xCE22, 0xFCB9, 0xED30, 0x998F, 0x8806, 0xBA9D, 0xAB14,
0x6CAC, 0x7D25, 0x4FBE, 0x5E37, 0x2A88, 0x3B01, 0x099A, 0x1813,
0xE0E4, 0xF16D, 0xC3F6, 0xD27F, 0xA6C0, 0xB749, 0x85D2, 0x945B,
0x65B5, 0x743C, 0x46A7, 0x572E, 0x2391, 0x3218, 0x0083, 0x110A,
0xE9FD, 0xF874, 0xCAEF, 0xDB66, 0xAFD9, 0xBE50, 0x8CCB, 0x9D42,
0x7E9E, 0x6F17, 0x5D8C, 0x4C05, 0x38BA, 0x2933, 0x1BA8, 0x0A21,
0xF2D6, 0xE35F, 0xD1C4, 0xC04D, 0xB4F2, 0xA57B, 0x97E0, 0x8669,
0x7787, 0x660E, 0x5495, 0x451C, 0x31A3, 0x202A, 0x12B1, 0x0338,
0xFBCF, 0xEA46, 0xD8DD, 0xC954, 0xBDEB, 0xAC62, 0x9EF9, 0x8F70
};
unsigned int // Returns Calculated CRC value
CalculateCRC16(
unsigned int crc_seed, // Seed for CRC calculation
void *c_ptr, // Pointer to byte array to perform CRC on
unsigned int len) // Number of bytes to CRC
{
unsigned char *c = c_ptr;
unsigned int crc = crc_seed;
while (len--){
crc = (crc << 8) ^ crctable[((crc >> 8) ^ *c++)];
printf("%d", crc);
}
return (crc);
}
int main(){
printf("%d", CalculateCRC16(0xFFFF, "123456789", 2));
return 0;
}

All cleaned up and ready to go:
#include <stdio.h>
#include <stdint.h>
static const uint16_t crctable[256] =
{
0x0000, 0x1189, 0x2312, 0x329B, 0x4624, 0x57AD, 0x6536, 0x74BF,
0x8C48, 0x9DC1, 0xAF5A, 0xBED3, 0xCA6C, 0xDBE5, 0xE97E, 0xF8F7,
0x0919, 0x1890, 0x2A0B, 0x3B82, 0x4F3D, 0x5EB4, 0x6C2F, 0x7DA6,
0x8551, 0x94D8, 0xA643, 0xB7CA, 0xC375, 0xD2FC, 0xE067, 0xF1EE,
0x1232, 0x03BB, 0x3120, 0x20A9, 0x5416, 0x459F, 0x7704, 0x668D,
0x9E7A, 0x8FF3, 0xBD68, 0xACE1, 0xD85E, 0xC9D7, 0xFB4C, 0xEAC5,
0x1B2B, 0x0AA2, 0x3839, 0x29B0, 0x5D0F, 0x4C86, 0x7E1D, 0x6F94,
0x9763, 0x86EA, 0xB471, 0xA5F8, 0xD147, 0xC0CE, 0xF255, 0xE3DC,
0x2464, 0x35ED, 0x0776, 0x16FF, 0x6240, 0x73C9, 0x4152, 0x50DB,
0xA82C, 0xB9A5, 0x8B3E, 0x9AB7, 0xEE08, 0xFF81, 0xCD1A, 0xDC93,
0x2D7D, 0x3CF4, 0x0E6F, 0x1FE6, 0x6B59, 0x7AD0, 0x484B, 0x59C2,
0xA135, 0xB0BC, 0x8227, 0x93AE, 0xE711, 0xF698, 0xC403, 0xD58A,
0x3656, 0x27DF, 0x1544, 0x04CD, 0x7072, 0x61FB, 0x5360, 0x42E9,
0xBA1E, 0xAB97, 0x990C, 0x8885, 0xFC3A, 0xEDB3, 0xDF28, 0xCEA1,
0x3F4F, 0x2EC6, 0x1C5D, 0x0DD4, 0x796B, 0x68E2, 0x5A79, 0x4BF0,
0xB307, 0xA28E, 0x9015, 0x819C, 0xF523, 0xE4AA, 0xD631, 0xC7B8,
0x48C8, 0x5941, 0x6BDA, 0x7A53, 0x0EEC, 0x1F65, 0x2DFE, 0x3C77,
0xC480, 0xD509, 0xE792, 0xF61B, 0x82A4, 0x932D, 0xA1B6, 0xB03F,
0x41D1, 0x5058, 0x62C3, 0x734A, 0x07F5, 0x167C, 0x24E7, 0x356E,
0xCD99, 0xDC10, 0xEE8B, 0xFF02, 0x8BBD, 0x9A34, 0xA8AF, 0xB926,
0x5AFA, 0x4B73, 0x79E8, 0x6861, 0x1CDE, 0x0D57, 0x3FCC, 0x2E45,
0xD6B2, 0xC73B, 0xF5A0, 0xE429, 0x9096, 0x811F, 0xB384, 0xA20D,
0x53E3, 0x426A, 0x70F1, 0x6178, 0x15C7, 0x044E, 0x36D5, 0x275C,
0xDFAB, 0xCE22, 0xFCB9, 0xED30, 0x998F, 0x8806, 0xBA9D, 0xAB14,
0x6CAC, 0x7D25, 0x4FBE, 0x5E37, 0x2A88, 0x3B01, 0x099A, 0x1813,
0xE0E4, 0xF16D, 0xC3F6, 0xD27F, 0xA6C0, 0xB749, 0x85D2, 0x945B,
0x65B5, 0x743C, 0x46A7, 0x572E, 0x2391, 0x3218, 0x0083, 0x110A,
0xE9FD, 0xF874, 0xCAEF, 0xDB66, 0xAFD9, 0xBE50, 0x8CCB, 0x9D42,
0x7E9E, 0x6F17, 0x5D8C, 0x4C05, 0x38BA, 0x2933, 0x1BA8, 0x0A21,
0xF2D6, 0xE35F, 0xD1C4, 0xC04D, 0xB4F2, 0xA57B, 0x97E0, 0x8669,
0x7787, 0x660E, 0x5495, 0x451C, 0x31A3, 0x202A, 0x12B1, 0x0338,
0xFBCF, 0xEA46, 0xD8DD, 0xC954, 0xBDEB, 0xAC62, 0x9EF9, 0x8F70
};
uint16_t // Returns Calculated CRC value
CalculateCRC16(
uint16_t crc, // Seed for CRC calculation
const void *c_ptr, // Pointer to byte array to perform CRC on
size_t len) // Number of bytes to CRC
{
const uint8_t *c = c_ptr;
while (len--)
crc = (crc << 8) ^ crctable[((crc >> 8) ^ *c++)];
return crc;
}
int main()
{
printf("%04x\n", CalculateCRC16(0xFFFF, "123456789", 9));
return 0;
}

there is not a computer near me now. Just a try:
crc = (crc << 8) ^ crctable[(unsigned char)(crc >> 8) ^ *c++];

On this line
crc = (crc << 8) ^ crctable[((crc >> 8) ^ *c++)];
the result of ((crc >> 8) ^ *c++) can become > 255, and cause an access violation. Just make sure the result is always 0.255 by masking the index into crctable
crc = (crc << 8) ^ crctable[((crc >> 8) ^ *c++) & 0x00FF];
// but you will need to clean up the result as its upper 16 bits
// are not guaranteed to be all 0
return crc & 0xffff;
or better, the resulting crc value as it ensures that crc will never contain a value > 0x0000ffff
crc = ( (crc << 8) ^ crctable[((crc >> 8) ^ *c++)] ) & 0xffff;
and you'll be all set. The base of the issue is that the original code seems to be 16 bits code (where int was 16 bits), and you are using a 32 bits compiler.

The table you are using appears to be incorrectly generated. The first sixteen entries are correct, but it diverges after that. I don't think you will have much luck decoding CCITT CRC-16 with it.
See CRC for cross platform applications for an example of the correctly-generated table.

I have used the same CRC checks and in your code you need to change only the following line:
crc = (crc >> 8) ^ crctable[(crc^(*c++))&0xFF];

that table lists the powers of the polynomial, to avoid errors in the table calculate the powers during the calculation, and make the polynomial an entry as well as the initial value. Use Dartpad to simulate it: https://dartpad.dev/?null_safety=true
void main() {
final int polynomial = 0x1189;
final int initialValue = 0xFFFF;
String crc16(String expression, int polynomial, int initialValue) {
int checkSum = initialValue;
for (int i = 0; i < expression.length; i++) {
checkSum ^= (expression.codeUnitAt(i) << 8);
for (int j = 0; j < 8; j++) {
if (((checkSum <<= 1) & 0x10000) == 0x10000) checkSum ^= polynomial;
checkSum &= 0xFFFF;
}
}
return checkSum.toRadixString(16).toUpperCase();
}
print(crc16('123456789', polynomial, initialValue));
}
To be compliant to CRC16 CCITT you should use polynomial=0x1021 and initial value = 0xFFFF.
https://www.gatevidyalay.com/cyclic-redundancy-check-crc-error-detection/ has a good explanation about CRC.

how to disable fast frames in ath5k wireless driver

By default, fast frames are enabled in ath5k. (http://wireless.kernel.org/en/users/Drivers/ath5k)
I have found the macro which disables it
#define AR5K_EEPROM_FF_DIS(_v) (((_v) >> 2) & 0x1
The question is what do I do with it?
Do I replace the above line with
#define AR5K_EEPROM_FF_DIS(_v) 1
?
Do I compile it passing some parameter?
The bit-shift expression confuses me. Is _v a variable?
The question is more general as to how to deal with such macros in drivers. I've seen them in other codes too and always got confused.

Ok, I try to explain with a simplified example
#include <stdio.h>
/* Just for print in binary mode */
char *chartobin(unsigned char c)
{
static char a[9];
int i;
for (i = 0; i < 8; i++)
a[7 - i] = (c & (1 << i)) == (1 << i) ? '1' : '0';
a[8] = '\0';
return a;
}
int main(void)
{
unsigned char u = 0xf;
printf("%s\n", chartobin(u));
u >>= 2; // Shift bits 2 positions (to the right)
printf("%s\n", chartobin(u));
printf("%s\n", chartobin(u & 0x1)); // Check if the last bit is on
return 0;
}
Output:
00001111
00000011
00000001
Do I replace the above line with #define AR5K_EEPROM_FF_DIS(_v) 1?
Nooooo!!
If you initialize u with 0xb instead of 0xf you get:
00001011
00000010
00000000
As you can see (((_v) >> 2) & 0x1 != 1

Fast frames are not enabled or used on ath5k. It's a feature allowing the card to send multiple frames at once (think of it as an early version of 11n frame aggregation) that's implemented on MadWiFi and their proprietary drivers and can only be used with an Access Point that also supports it. What you see there is a flag stored at the device's EEPROM that instructs the driver if fast frames can be used or not, that macro you refer to just checks if that flag is set. You can modify the header file to always return 1 but that wouldn't make any difference, the driver never uses that information.

Function to Calculate a CRC16 Checksum

I'm working on a library to provide simple reliable communication over an RS232 or RS485 connection. Part of this code involves using a CRC16 checksum on the data to detect corruption from line noise. I've created a function to calculate a CRC16 checksum, but it doesn't seem to be outputting correct values.
The relevant code I've written is below (it can also be found 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;
}
I'm checking my output against this online CRC calculator.
I've come to the conclusion that either my understanding of how to calculate a CRC16 is wrong, or the online calculator is wrong (the former seems more likely). Can someone tell me where I might be going wrong?

There are several details you need to 'match up' with for a particular CRC implementation - even using the same polynomial there can be different results because of minor differences in how data bits are handled, using a particular initial value for the CRC (sometimes it's zero, sometimes 0xffff), and/or inverting the bits of the CRC. For example, sometimes one implementation will work from the low order bits of the data bytes up, while sometimes they'll work from the high order bits down (as yours currently does).
Also, you need to 'push out' the last bits of the CRC after you've run all the data bits through.
Keep in mind that CRC algorithms were designed to be implemented in hardware, so some of how bit ordering is handled may not make so much sense from a software point of view.
If you want to match the CRC16 with polynomial 0x8005 as shown on the lammertbies.nl CRC calculator page, you need to make the following changes to your CRC function:
a) run the data bits through the CRC loop starting from the least significant bit instead of from the most significant bit
b) push the last 16 bits of the CRC out of the CRC register after you've finished with the input data
c) reverse the CRC bits (I'm guessing this bit is a carry over from hardware implementations)
So, your function might look like:
#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;
}
That function returns 0xbb3d for me when I pass in "123456789".

Here follows a working code to calculate crc16 CCITT. I tested it and the results matched with those provided by http://www.lammertbies.nl/comm/info/crc-calculation.html.
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;
}

crcany will generate efficient C code for any CRC, and includes a library of over one hundred known CRC definitions.
Efficient CRC code uses tables instead of bit-wise calculations. crcany generates both byte-wise routines and word-wise routines, the latter tuned to the architecture they are generated on. Word-wise is the fastest. Byte-wise is still much faster than bit-wise, but the implementation is more easily portable over architectures.
You do not seem to have a protocol definition with a specific CRC definition that you need to match. In this case, you can pick any 16-bit CRC in the catalog, and you will get good performance.
If you have a relatively low bit error rate, e.g. single digit number of errors per packet, and you want to maximize your error detection performance, you would need to look at the packet size you are applying the CRC to, assuming that that is constant or bounded, and look at the performance of the best polynomials in Philip Koopman's extensive research. The classic CRCs, such as the CCITT/Kermit 16-bit CRC or the X.25 16-bit CRC are not the best performers.
One of the good 16-bit performers in Koopman's tables that is also in the catalog of CRCs used in practice is CRC-16/DNP. It has very good performance detecting up to 6-bit errors in a packet. Following is the code generated by crcany for that CRC definition. This code assumes a little-endian architecture for the word-wise calculation, e.g. Intel x86 and x86-64, and it assumes that uintmax_t is 64 bits. crcany can be used to generate alternative code for big-endian and other word sizes.
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;
}

There are several different varieties of CRC-16. See wiki page.
Every of those will return different results from the same input.
So you must carefully select correct one for your program.

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;

I used the code example from:
http://www.sunshine2k.de/articles/coding/crc/understanding_crc.html#ch5
And also this utility to verify:
http://www.sunshine2k.de/coding/javascript/crc/crc_js.html

This function works for CRC-16 Modbus version. Not for CRC-16

Resources