RE: crc32 cleanups

Matt_Domsch
2001-10-14T03:19:54Z

> I don't think this does what was intended. Should that perhaps be
>
> > for (i = 0; i < 1; i++)
>

Good catch. linux@horizon.com sent me a cleaned up version.

--
Matt Domsch
Sr. Software Engineer
Dell Linux Solutions
www.dell.com/linux
#2 Linux Server provider with 17% in the US and 14% Worldwide (IDC)!
#3 Unix provider with 18% in the US (Dataquest)!

That'll teach me to clean up code by hand and not test it afterwards.
That's supposed to be "i < 8" in that for() loop, but there are a couple
of other glitches, too. In particular, I got bits of the
table-initialization
code transposed when I generalized it for less than 8 bits.

Here's a *tested* version, with test harness (if compiled with -DUNITTEST).

#include <stddef.h> /* For size_t */
typedef unsigned _u32;

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

/*
* This code is in the public domain; copyright abandoned.
* Liability for non-performance of this code is limited to the amount
* you paid for it. Since it is distributed for free, your refund will
* be very very small. If it breaks, you get to keep both pieces.
*/

/*
* 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

/* How many bits at a time to use. Requires a table of 4<<CRC_xx_BITS
bytes. */
#define CRC_LE_BITS 8
#define CRC_BE_BITS 4 /* Less performance-sensitive */

/*
* Little-endian CRC computation. Used with serial bit streams sent
* lsbit-first. Be sure to use cpu_to_le32() to append the computed CRC.
*/
#if CRC_LE_BITS > 8 || CRC_LE_BITS < 1 || CRC_LE_BITS & CRC_LE_BITS-1
# error CRC_LE_BITS must be a power of 2 between 1 and 8
#endif

#if CRC_LE_BITS == 1
/*
* In fact, the table-based code will work in this case, but it can be
* simplified by inlining the table in ?: form.
*/
void
crc32init_le(void)
{/* no-op */;}

_u32 attribute((pure))
crc32_le(_u32 crc, unsigned char const *p, size_t len)
{
int i;
while (len--) {
crc ^= *p++;
for (i = 0; i < 8; i++)
crc = (crc >> 1) ^ ((crc & 1) ? CRCPOLY_LE : 0);
}
return crc;
}
#else /* Table-based approach */

_u32 crc32table_le[1<<CRC_LE_BITS];

/*
* crc is the crc of the byte i; other entries are filled in based on the
* fact that crctable[i^j] = crctable[i] ^ crctable[j].
*
* Note that the _init functions never write anything but the final correct
* value to each table entry, so they're safe to call repeatedly, even if
* someone else is currently using the table.
*/
void
crc32init_le(void)
{
unsigned i, j;
_u32 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];
}
}

_u32 attribute((pure))
crc32_le(_u32 crc, unsigned char const *p, size_t len)
{
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;
}
#endif

/*
* Big-endian CRC computation. Used with serial bit streams sent
* msbit-first. Be sure to use cpu_to_be32() to append the computed CRC.
*/
#if CRC_BE_BITS > 8 || CRC_BE_BITS < 1 || CRC_BE_BITS & CRC_BE_BITS-1
# error CRC_BE_BITS must be a power of 2 between 1 and 8
#endif

#if CRC_BE_BITS == 1
/*
* In fact, the table-based code will work in this case, but it can be
* simplified by inlining the table in ?: form.
*/
void
crc32init_be(void)
{/*no-op*/;}

_u32 attribute((pure))
crc32_be(_u32 crc, unsigned char const *p, size_t len)
{
int i;
while (len--) {
crc ^= *p++ << 24;
for (i = 0; i < 8; i++)
crc = (crc << 1) ^ ((crc & 0x80000000) ? CRCPOLY_BE
: 0);
}
return crc;
}

#else /* Table-based approach */
_u32 crc32table_be[256];

void
crc32init_be(void)
{
unsigned i, j;
_u32 crc = 0x80000000;

crc32table_be[0] = 0;

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];
}
}

_u32 attribute((pure))
crc32_be(_u32 crc, unsigned char const *p, size_t len)
{
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;
}
#endif

/*
* 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.
*/

#if UNITTEST

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

#if 0 /*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 _u32 attribute((const))
bitreverse(_u32 x)
{
x = (x >> 16) | (x << 16);
x = (x >> 8 & 0x00ff00ff) | (x << 8 & 0xff00ff00);
x = (x >> 4 & 0x0f0f0f0f) | (x << 4 & 0xf0f0f0f0);
x = (x >> 2 & 0x33333333) | (x << 2 & 0xcccccccc);
x = (x >> 1 & 0x55555555) | (x << 1 & 0xaaaaaaaa);
return x;
}

static void
bytereverse(unsigned char *buf, size_t len)
{
while (len--) {
unsigned char x = *buf;
x = (x >> 4) | (x << 4);
x = (x >> 2 & 0x33) | (x << 2 & 0xcc);
x = (x >> 1 & 0x55) | (x << 1 & 0xaa);
*buf++ = x;
}
}

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

#if 0 /* 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 = bitreverse(init);
crc2 = bitreverse(crc1);
if (crc1 != bitreverse(crc2))
printf("\nBit reversal fail: 0x%08x -> %0x08x -> 0x%08x\n",
crc1, crc2, bitreverse(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;

crc32init_le();
crc32init_be();

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 */