CRC32

CRC32 is a checksum/hashing algorithm that can be used in kernels and for Internet checksums. It is similar to the MD5 checksum algorithm.

The Algorithm

CRC32 begins with a 32bit checksum with all bits set (0xffffffff). This helps to give an output value other than 0 for an input string of "0" bytes.

In a loop: Look up a 32-bit value from a table, called a "polynomial", based on the next piece of input data (usually a byte) and the low n bits of the previous CRC value (where n is the size of the data you are operating on, usually bytes that are 8 bits wide).

Shift the previous 32-bit CRC value down by N bits.

Perform an exclusive-OR (XOR) operation between the polynomial and the shifted CRC value to produce a new value.

After the end of the loop, perform a XOR operation between the calculated CRC value and the value 0xffffffff to receive the final CRC32 result. (this step is identical to doing a binary NOT operation on the CRC value).

Building the Lookup Table

This is a bit more complex of a process than actually calculating the checksum itself.

A first method: To build a 256-entry (-byte) lookup table, take the 8-bit index and bit-reflect all the bits in that byte. Shift it to the upper 8 bits of a 32-bit variable. Loop over those 8 bits. If the top (sign) bit is set, then shift the uint32_t up one bit and exclusive-OR it with the magic value 0x04C11DB7. Otherwise just shift the uint32_t up one bit. Then repeat. When the loop is complete, bit-reflect the entire uint32_t. This is the value in the table.

A second method: Instead, you can simply avoid bit reflections this way: take the 8-bit index and cast it to a 32-bit variable. Loop over the lower byte. If the least significant bit (0x00000001) is set, then shift the uint32_t down one bit and exclusive-OR it with the value 0xEDB88320 (which is 0x04C11DB7 bit-reflected). Otherwise just shift it down one bit. Then repeat. When the loop is complete, the uint32_t is the value in the table.

Example Code

// calculate a checksum on a buffer -- start address = p, length = bytelength
uint32_t crc32_byte(uint8_t *p, uint32_t bytelength)
{
	uint32_t crc = 0xffffffff;
	while (bytelength-- !=0) crc = poly8_lookup[((uint8_t) crc ^ *(p++))] ^ (crc >> 8);
	// return (~crc); also works
	return (crc ^ 0xffffffff);
}

//Fill the lookup table -- table = the lookup table base address
void crc32_fill(uint32_t *table){
        uint8_t index=0,z;
        do{
                table[index]=index;
                for(z=8;z;z--) table[index]=(table[index]&1)?(table[index]>>1)^0xEDB88320:table[index]>>1;
        }while(++index);
}

uint32_t poly8_lookup[256] =
{
 0, 0x77073096, 0xEE0E612C, 0x990951BA,
 0x076DC419, 0x706AF48F, 0xE963A535, 0x9E6495A3,
 0x0EDB8832, 0x79DCB8A4, 0xE0D5E91E, 0x97D2D988,
 0x09B64C2B, 0x7EB17CBD, 0xE7B82D07, 0x90BF1D91,
 0x1DB71064, 0x6AB020F2, 0xF3B97148, 0x84BE41DE,
 0x1ADAD47D, 0x6DDDE4EB, 0xF4D4B551, 0x83D385C7,
 0x136C9856, 0x646BA8C0, 0xFD62F97A, 0x8A65C9EC,
 0x14015C4F, 0x63066CD9, 0xFA0F3D63, 0x8D080DF5,
 0x3B6E20C8, 0x4C69105E, 0xD56041E4, 0xA2677172,
 0x3C03E4D1, 0x4B04D447, 0xD20D85FD, 0xA50AB56B,
 0x35B5A8FA, 0x42B2986C, 0xDBBBC9D6, 0xACBCF940,
 0x32D86CE3, 0x45DF5C75, 0xDCD60DCF, 0xABD13D59,
 0x26D930AC, 0x51DE003A, 0xC8D75180, 0xBFD06116,
 0x21B4F4B5, 0x56B3C423, 0xCFBA9599, 0xB8BDA50F,
 0x2802B89E, 0x5F058808, 0xC60CD9B2, 0xB10BE924,
 0x2F6F7C87, 0x58684C11, 0xC1611DAB, 0xB6662D3D,
 0x76DC4190, 0x01DB7106, 0x98D220BC, 0xEFD5102A,
 0x71B18589, 0x06B6B51F, 0x9FBFE4A5, 0xE8B8D433,
 0x7807C9A2, 0x0F00F934, 0x9609A88E, 0xE10E9818,
 0x7F6A0DBB, 0x086D3D2D, 0x91646C97, 0xE6635C01,
 0x6B6B51F4, 0x1C6C6162, 0x856530D8, 0xF262004E,
 0x6C0695ED, 0x1B01A57B, 0x8208F4C1, 0xF50FC457,
 0x65B0D9C6, 0x12B7E950, 0x8BBEB8EA, 0xFCB9887C,
 0x62DD1DDF, 0x15DA2D49, 0x8CD37CF3, 0xFBD44C65,
 0x4DB26158, 0x3AB551CE, 0xA3BC0074, 0xD4BB30E2,
 0x4ADFA541, 0x3DD895D7, 0xA4D1C46D, 0xD3D6F4FB,
 0x4369E96A, 0x346ED9FC, 0xAD678846, 0xDA60B8D0,
 0x44042D73, 0x33031DE5, 0xAA0A4C5F, 0xDD0D7CC9,
 0x5005713C, 0x270241AA, 0xBE0B1010, 0xC90C2086,
 0x5768B525, 0x206F85B3, 0xB966D409, 0xCE61E49F,
 0x5EDEF90E, 0x29D9C998, 0xB0D09822, 0xC7D7A8B4,
 0x59B33D17, 0x2EB40D81, 0xB7BD5C3B, 0xC0BA6CAD,
 0xEDB88320, 0x9ABFB3B6, 0x03B6E20C, 0x74B1D29A,
 0xEAD54739, 0x9DD277AF, 0x04DB2615, 0x73DC1683,
 0xE3630B12, 0x94643B84, 0x0D6D6A3E, 0x7A6A5AA8,
 0xE40ECF0B, 0x9309FF9D, 0x0A00AE27, 0x7D079EB1,
 0xF00F9344, 0x8708A3D2, 0x1E01F268, 0x6906C2FE,
 0xF762575D, 0x806567CB, 0x196C3671, 0x6E6B06E7,
 0xFED41B76, 0x89D32BE0, 0x10DA7A5A, 0x67DD4ACC,
 0xF9B9DF6F, 0x8EBEEFF9, 0x17B7BE43, 0x60B08ED5,
 0xD6D6A3E8, 0xA1D1937E, 0x38D8C2C4, 0x4FDFF252,
 0xD1BB67F1, 0xA6BC5767, 0x3FB506DD, 0x48B2364B,
 0xD80D2BDA, 0xAF0A1B4C, 0x36034AF6, 0x41047A60,
 0xDF60EFC3, 0xA867DF55, 0x316E8EEF, 0x4669BE79,
 0xCB61B38C, 0xBC66831A, 0x256FD2A0, 0x5268E236,
 0xCC0C7795, 0xBB0B4703, 0x220216B9, 0x5505262F,
 0xC5BA3BBE, 0xB2BD0B28, 0x2BB45A92, 0x5CB36A04,
 0xC2D7FFA7, 0xB5D0CF31, 0x2CD99E8B, 0x5BDEAE1D,
 0x9B64C2B0, 0xEC63F226, 0x756AA39C, 0x026D930A,
 0x9C0906A9, 0xEB0E363F, 0x72076785, 0x05005713,
 0x95BF4A82, 0xE2B87A14, 0x7BB12BAE, 0x0CB61B38,
 0x92D28E9B, 0xE5D5BE0D, 0x7CDCEFB7, 0x0BDBDF21,
 0x86D3D2D4, 0xF1D4E242, 0x68DDB3F8, 0x1FDA836E,
 0x81BE16CD, 0xF6B9265B, 0x6FB077E1, 0x18B74777,
 0x88085AE6, 0xFF0F6A70, 0x66063BCA, 0x11010B5C,
 0x8F659EFF, 0xF862AE69, 0x616BFFD3, 0x166CCF45,
 0xA00AE278, 0xD70DD2EE, 0x4E048354, 0x3903B3C2,
 0xA7672661, 0xD06016F7, 0x4969474D, 0x3E6E77DB,
 0xAED16A4A, 0xD9D65ADC, 0x40DF0B66, 0x37D83BF0,
 0xA9BCAE53, 0xDEBB9EC5, 0x47B2CF7F, 0x30B5FFE9,
 0xBDBDF21C, 0xCABAC28A, 0x53B39330, 0x24B4A3A6,
 0xBAD03605, 0xCDD70693, 0x54DE5729, 0x23D967BF,
 0xB3667A2E, 0xC4614AB8, 0x5D681B02, 0x2A6F2B94,
 0xB40BBE37, 0xC30C8EA1, 0x5A05DF1B, 0x2D02EF8D
};

; Note: _poly8_lookup is the symbolic address of the same table from the above example
; Note2: to append to a precalculated crc, NOT the crc, then call asm_partial_crc32_byte

asm_crc32_byte:
	mov eax, 0xffffffff		; eax is running crc value
asm_partial_crc32_byte:			; entrypoint if modifying a precalculated crc
	push esi
	push ecx
	push ebx
	push edx
	mov ebx, _poly8_lookup		; addy of crc table
	xor edx, edx
	jecxz crcb_don
crc_bl1:
	mov dl, al			; dx is the low byte of crc
	xor dl, [esi]			; xor it with "*p"
	inc esi				; ++
	shr eax, 8			; high 3 bytes of crc for xor
	xor eax, [ebx+edx*4]		; xor it with the polytable
	loop crc_bl1			; decrement ecx and loop

crcb_don:
	not eax				; finally, flip all the crc bits
	pop edx
	pop ebx
	pop ecx
	pop esi
	ret

; function input values: esi points to a 256 entry bit reflection table, aligned on a 256 byte boundary
build_16b_crc_tbl:
	mov cx, 0xffff
	mov edi, Tbl_End		; store going down from Tbl_End
.crc_tbll:
	mov ebx, esi
	xor eax, eax
	mov bl, cl
	mov al, [ebx]			; bit-reflect the two input bytes
	mov bl, ch
	mov ah, [ebx]
	bswap eax			; and then put them at upper end of register

	mov dl, 16			; loop over all 16 bits in upper eax
.crc_bitl:
	shl eax, 1
	jnc .crc_nply
	xor eax, 0x04C11DB7		; if sign bit was set, xor eax with the "poly"
.crc_nply:
	dec dl
	jg short .crc_bitl

	mov ebx, esi
	mov bl, ah
	mov ah, [ebx]		; lastly, bit-reflect the value in eax
	mov bl, al
	mov al, [ebx]		; start with ax
	bswap eax
	mov bl, ah		; bswap to put the bytes in the right place, and do ax again
	mov ah, [ebx]
	mov bl, al
	mov al, [ebx]
	lea edi, [edi - 4]
	mov [edi], eax		; store next crc in the CRC32 lookup table
	dec ecx
	jge short .crc_tbll	; loop until ecx goes negative
	ret

See Also

External Links

• A detailed theoretical explanation of CRC algorithms

• The mathematics behind the CRC32 algorithm

References

• This page uses text from OSDev.org: https://wiki.osdev.org/CRC32