rufus/src/bled/crc32.c

/*
 * GPLv2+ CRC32 implementation for busybox
 *
 * Based on crc32.c from util-linux v2.17's partx v2.17 - Public Domain
 * Adjusted for busybox' by Pete Batard <pete@akeo.ie>
 *
 * Licensed under GPLv2 or later, see file LICENSE in this source tree.
 */

#include "libbb.h"

#if __GNUC__ >= 3	/* 2.x has "attribute", but only 3.0 has "pure */
#define attribute(x) __attribute__(x)
#else
#define attribute(x)
#endif

/* Do NOT alter these */
#define CRC_LE_BITS 8
#define CRC_BE_BITS 8

/*
 * There are multiple 16-bit CRC polynomials in common use, but this is
 * *the* standard CRC-32 polynomial, first popularized by Ethernet.
 * x^32+x^26+x^23+x^22+x^16+x^12+x^11+x^10+x^8+x^7+x^5+x^4+x^2+x^1+x^0
 */
#define CRCPOLY_LE 0xedb88320
#define CRCPOLY_BE 0x04c11db7

/* This needs to be defined somewhere */
uint32_t *global_crc32_table;

static void crc32init_le(uint32_t *crc32table_le)
{
	unsigned i, j;
	uint32_t crc = 1;

	crc32table_le[0] = 0;

	for (i = 1 << (CRC_LE_BITS - 1); i; i >>= 1) {
		crc = (crc >> 1) ^ ((crc & 1) ? CRCPOLY_LE : 0);
		for (j = 0; j < 1 << CRC_LE_BITS; j += 2 * i)
			crc32table_le[i + j] = crc ^ crc32table_le[j];
	}
}

/**
 * crc32_le() - Calculate bitwise little-endian Ethernet AUTODIN II CRC32
 * @crc - seed value for computation.  ~0 for Ethernet, sometimes 0 for
 *        other uses, or the previous crc32 value if computing incrementally.
 * @p   - pointer to buffer over which CRC is run
 * @len - length of buffer @p
 * 
 */
uint32_t attribute((pure)) crc32_le(uint32_t crc, unsigned char const *p, size_t len, uint32_t *crc32table_le)
{
	while (len--) {
# if CRC_LE_BITS == 8
		crc = (crc >> 8) ^ crc32table_le[(crc ^ *p++) & 255];
# elif CRC_LE_BITS == 4
		crc ^= *p++;
		crc = (crc >> 4) ^ crc32table_le[crc & 15];
		crc = (crc >> 4) ^ crc32table_le[crc & 15];
# elif CRC_LE_BITS == 2
		crc ^= *p++;
		crc = (crc >> 2) ^ crc32table_le[crc & 3];
		crc = (crc >> 2) ^ crc32table_le[crc & 3];
		crc = (crc >> 2) ^ crc32table_le[crc & 3];
		crc = (crc >> 2) ^ crc32table_le[crc & 3];
# endif
	}
	return crc;
}

/**
 * crc32init_be() - allocate and initialize BE table data
 */
static void crc32init_be(uint32_t *crc32table_be)
{
	unsigned i, j;
	uint32_t crc = 0x80000000;

	for (i = 1; i < 1 << CRC_BE_BITS; i <<= 1) {
		crc = (crc << 1) ^ ((crc & 0x80000000) ? CRCPOLY_BE : 0);
		for (j = 0; j < i; j++)
			crc32table_be[i + j] = crc ^ crc32table_be[j];
	}
}

/**
 * crc32_be() - Calculate bitwise big-endian Ethernet AUTODIN II CRC32
 * @crc - seed value for computation.  ~0 for Ethernet, sometimes 0 for
 *        other uses, or the previous crc32 value if computing incrementally.
 * @p   - pointer to buffer over which CRC is run
 * @len - length of buffer @p
 * 
 */
uint32_t attribute((pure)) crc32_be(uint32_t crc, unsigned char const *p, size_t len, uint32_t *crc32table_be)
{
	while (len--) {
# if CRC_BE_BITS == 8
		crc = (crc << 8) ^ crc32table_be[(crc >> 24) ^ *p++];
# elif CRC_BE_BITS == 4
		crc ^= *p++ << 24;
		crc = (crc << 4) ^ crc32table_be[crc >> 28];
		crc = (crc << 4) ^ crc32table_be[crc >> 28];
# elif CRC_BE_BITS == 2
		crc ^= *p++ << 24;
		crc = (crc << 2) ^ crc32table_be[crc >> 30];
		crc = (crc << 2) ^ crc32table_be[crc >> 30];
		crc = (crc << 2) ^ crc32table_be[crc >> 30];
		crc = (crc << 2) ^ crc32table_be[crc >> 30];
# endif
	}
	return crc;
}

uint32_t* crc32_filltable(uint32_t *crc_table, int endian)
{
	/* Expects the caller to do the cleanup */
	if (!crc_table)
		crc_table = malloc((1 << CRC_LE_BITS) * sizeof(uint32_t));
	if (crc_table) {
		if (endian)
			crc32init_be(crc_table);
		else
			crc32init_le(crc_table);
	}
	return crc_table;
}

/*
 * A brief CRC tutorial.
 *
 * 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.
 */