crc32.c

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 * A CRC is a long-division remainder.  You add the CRC to the message,
 * and the whole thing (message+CRC) is a multiple of the given
 * CRC polynomial.  To check the CRC, you can either check that the
 * CRC matches the recomputed value, *or* you can check that the
 * remainder computed on the message+CRC is 0.  This latter approach
 * is used by a lot of hardware implementations, and is why so many
 * protocols put the end-of-frame flag after the CRC.
 *
 * It's actually the same long division you learned in school, except that
 * - We're working in binary, so the digits are only 0 and 1, and
 * - When dividing polynomials, there are no carries.  Rather than add and
 *   subtract, we just xor.  Thus, we tend to get a bit sloppy about
 *   the difference between adding and subtracting.
 *
 * A 32-bit CRC polynomial is actually 33 bits long.  But since it's
 * 33 bits long, bit 32 is always going to be set, so usually the CRC
 * is written in hex with the most significant bit omitted.  (If you're
 * familiar with the IEEE 754 floating-point format, it's the same idea.)
 *
 * Note that a CRC is computed over a string of *bits*, so you have
 * to decide on the endianness of the bits within each byte.  To get
 * the best error-detecting properties, this should correspond to the
 * order they're actually sent.  For example, standard RS-232 serial is
 * little-endian; the most significant bit (sometimes used for parity)
 * is sent last.  And when appending a CRC word to a message, you should
 * do it in the right order, matching the endianness.
 *
 * Just like with ordinary division, the remainder is always smaller than
 * the divisor (the CRC polynomial) you're dividing by.  Each step of the
 * division, you take one more digit (bit) of the dividend and append it
 * to the current remainder.  Then you figure out the appropriate multiple
 * of the divisor to subtract to being the remainder back into range.
 * In binary, it's easy - it has to be either 0 or 1, and to make the
 * XOR cancel, it's just a copy of bit 32 of the remainder.
 *
 * When computing a CRC, we don't care about the quotient, so we can
 * throw the quotient bit away, but subtract the appropriate multiple of
 * the polynomial from the remainder and we're back to where we started,
 * ready to process the next bit.
 *
 * A big-endian CRC written this way would be coded like:
 * for (i = 0; i < input_bits; i++) {
 * 	multiple = remainder & 0x80000000 ? CRCPOLY : 0;
 * 	remainder = (remainder << 1 | next_input_bit()) ^ multiple;
 * }
 * Notice how, to get at bit 32 of the shifted remainder, we look
 * at bit 31 of the remainder *before* shifting it.
 *
 * But also notice how the next_input_bit() bits we're shifting into
 * the remainder don't actually affect any decision-making until
 * 32 bits later.  Thus, the first 32 cycles of this are pretty boring.
 * Also, to add the CRC to a message, we need a 32-bit-long hole for it at
 * the end, so we have to add 32 extra cycles shifting in zeros at the
 * end of every message,
 *
 * So the standard trick is to rearrage merging in the next_input_bit()
 * until the moment it's needed.  Then the first 32 cycles can be precomputed,
 * and merging in the final 32 zero bits to make room for the CRC can be
 * skipped entirely.
 * This changes the code to:
 * for (i = 0; i < input_bits; i++) {
 *      remainder ^= next_input_bit() << 31;
 * 	multiple = (remainder & 0x80000000) ? CRCPOLY : 0;
 * 	remainder = (remainder << 1) ^ multiple;
 * }
 * With this optimization, the little-endian code is simpler:
 * for (i = 0; i < input_bits; i++) {
 *      remainder ^= next_input_bit();
 * 	multiple = (remainder & 1) ? CRCPOLY : 0;
 * 	remainder = (remainder >> 1) ^ multiple;
 * }
 *
 * Note that the other details of endianness have been hidden in CRCPOLY
 * (which must be bit-reversed) and next_input_bit().
 *
 * However, as long as next_input_bit is returning the bits in a sensible
 * order, we can actually do the merging 8 or more bits at a time rather
 * than one bit at a time:
 * for (i = 0; i < input_bytes; i++) {
 * 	remainder ^= next_input_byte() << 24;
 * 	for (j = 0; j < 8; j++) {
 * 		multiple = (remainder & 0x80000000) ? CRCPOLY : 0;
 * 		remainder = (remainder << 1) ^ multiple;
 * 	}
 * }
 * Or in little-endian:
 * for (i = 0; i < input_bytes; i++) {
 * 	remainder ^= next_input_byte();
 * 	for (j = 0; j < 8; j++) {
 * 		multiple = (remainder & 1) ? CRCPOLY : 0;
 * 		remainder = (remainder << 1) ^ multiple;
 * 	}
 * }
 * If the input is a multiple of 32 bits, you can even XOR in a 32-bit
 * word at a time and increase the inner loop count to 32.
 *
 * You can also mix and match the two loop styles, for example doing the
 * bulk of a message byte-at-a-time and adding bit-at-a-time processing
 * for any fractional bytes at the end.
 *
 * The only remaining optimization is to the byte-at-a-time table method.
 * Here, rather than just shifting one bit of the remainder to decide
 * in the correct multiple to subtract, we can shift a byte at a time.
 * This produces a 40-bit (rather than a 33-bit) intermediate remainder,
 * but again the multiple of the polynomial to subtract depends only on
 * the high bits, the high 8 bits in this case.
 *
 * The multile we need in that case is the low 32 bits of a 40-bit
 * value whose high 8 bits are given, and which is a multiple of the
 * generator polynomial.  This is simply the CRC-32 of the given
 * one-byte message.
 *
 * Two more details: normally, appending zero bits to a message which
 * is already a multiple of a polynomial produces a larger multiple of that
 * polynomial.  To enable a CRC to detect this condition, it's common to
 * invert the CRC before appending it.  This makes the remainder of the
 * message+crc come out not as zero, but some fixed non-zero value.
 *
 * The same problem applies to zero bits prepended to the message, and
 * a similar solution is used.  Instead of starting with a remainder of
 * 0, an initial remainder of all ones is used.  As long as you start
 * the same way on decoding, it doesn't make a difference.
 */

#ifdef UNITTEST

#include <stdlib.h>
#include <stdio.h>

#ifdef UBI_LINUX				/*Not used at present */
static void
buf_dump(char const *prefix, unsigned char const *buf, size_t len)
{
	fputs(prefix, stdout);
	while (len--)
		printf(" %02x", *buf++);
	putchar('\n');

}
#endif

static void bytereverse(unsigned char *buf, size_t len)
{
	while (len--) {
		unsigned char x = bitrev8(*buf);
		*buf++ = x;
	}
}

static void random_garbage(unsigned char *buf, size_t len)
{
	while (len--)
		*buf++ = (unsigned char) random();
}

#ifdef UBI_LINUX				/* Not used at present */
static void store_le(u32 x, unsigned char *buf)
{
	buf[0] = (unsigned char) x;
	buf[1] = (unsigned char) (x >> 8);
	buf[2] = (unsigned char) (x >> 16);
	buf[3] = (unsigned char) (x >> 24);
}
#endif

static void store_be(u32 x, unsigned char *buf)
{
	buf[0] = (unsigned char) (x >> 24);
	buf[1] = (unsigned char) (x >> 16);
	buf[2] = (unsigned char) (x >> 8);
	buf[3] = (unsigned char) x;
}

/*
 * This checks that CRC(buf + CRC(buf)) = 0, and that
 * CRC commutes with bit-reversal.  This has the side effect
 * of bytewise bit-reversing the input buffer, and returns
 * the CRC of the reversed buffer.
 */
static u32 test_step(u32 init, unsigned char *buf, size_t len)
{
	u32 crc1, crc2;
	size_t i;

	crc1 = crc32_be(init, buf, len);
	store_be(crc1, buf + len);
	crc2 = crc32_be(init, buf, len + 4);
	if (crc2)
		printf("\nCRC cancellation fail: 0x%08x should be 0\n",
		       crc2);

	for (i = 0; i <= len + 4; i++) {
		crc2 = crc32_be(init, buf, i);
		crc2 = crc32_be(crc2, buf + i, len + 4 - i);
		if (crc2)
			printf("\nCRC split fail: 0x%08x\n", crc2);
	}

	/* Now swap it around for the other test */

	bytereverse(buf, len + 4);
	init = bitrev32(init);
	crc2 = bitrev32(crc1);
	if (crc1 != bitrev32(crc2))
		printf("\nBit reversal fail: 0x%08x -> 0x%08x -> 0x%08x\n",
		       crc1, crc2, bitrev32(crc2));
	crc1 = crc32_le(init, buf, len);
	if (crc1 != crc2)
		printf("\nCRC endianness fail: 0x%08x != 0x%08x\n", crc1,
		       crc2);
	crc2 = crc32_le(init, buf, len + 4);
	if (crc2)
		printf("\nCRC cancellation fail: 0x%08x should be 0\n",
		       crc2);

	for (i = 0; i <= len + 4; i++) {
		crc2 = crc32_le(init, buf, i);
		crc2 = crc32_le(crc2, buf + i, len + 4 - i);
		if (crc2)
			printf("\nCRC split fail: 0x%08x\n", crc2);
	}

	return crc1;
}

#define SIZE 64
#define INIT1 0
#define INIT2 0

int main(void)
{
	unsigned char buf1[SIZE + 4];
	unsigned char buf2[SIZE + 4];
	unsigned char buf3[SIZE + 4];
	int i, j;
	u32 crc1, crc2, crc3;

	for (i = 0; i <= SIZE; i++) {
		printf("\rTesting length %d...", i);
		fflush(stdout);
		random_garbage(buf1, i);
		random_garbage(buf2, i);
		for (j = 0; j < i; j++)
			buf3[j] = buf1[j] ^ buf2[j];

		crc1 = test_step(INIT1, buf1, i);
		crc2 = test_step(INIT2, buf2, i);
		/* Now check that CRC(buf1 ^ buf2) = CRC(buf1) ^ CRC(buf2) */
		crc3 = test_step(INIT1 ^ INIT2, buf3, i);
		if (crc3 != (crc1 ^ crc2))
			printf("CRC XOR fail: 0x%08x != 0x%08x ^ 0x%08x\n",
			       crc3, crc1, crc2);
	}
	printf("\nAll test complete.  No failures expected.\n");
	return 0;
}

#endif				/* UNITTEST */