Messages in this thread | | | From | Matt_Domsch@Dell ... | Subject | RE: crc32 cleanups | Date | Fri, 12 Oct 2001 22:46:11 -0500 |
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And, just when I thought I understood the crc32 stuff, here's an even better explanation/code/etc. With thanks. -Matt
-----Original Message----- From: linux@horizon.com [mailto:linux@horizon.com] Sent: Friday, October 12, 2001 10:06 PM Subject: Here's table-optimized crc32 code for both ways...
I think just having these in the kernel unconditionally is best. This version allows various space/time tradeoffs.
For a RAM kernel, the initialization code is smaller than the tables, and can be made initcode. For a ROM kernel, it would make sense to precompute the tables and compile them in.
#include <stddef.h> /* For size_t */ typedef unsigned _u32;
/* * 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 /* Half the speed, 960 bytes less space */
/* * 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 crc32_le(_u32 crc, unsigned char const *p, size_t len) { int i; while (len--) { crc ^= *p++; for (i = 0; i < i; 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 ; i < 1<<CRC_LE_BITS; i <<= 1) { crc = (crc >> 1) ^ (crc & 1 ? CRCPOLY_LE : 0); for (j = 0; j < i; j++) crc32table_le[i+j] = crc ^ crc32table_le[j]; } }
_u32 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 crc32_be(_u32 crc, unsigned char const *p, size_t len) { int i; while (len--) { crc ^= *p++ << 24; for (i = 0; i < i; 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_le[0] = 0;
for (i = 1<<(CRC_BE_BITS-1); i; i >>= 1) { crc = (crc << 1) ^ (crc & 0x80000000 ? CRCPOLY_BE : 0); for (j = 0; j < 1<<CRC_BE_BITS; j += 2*i) crc32table_le[i+j] = crc ^ crc32table_le[j]; } }
_u32 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. */ - To unsubscribe from this list: send the line "unsubscribe linux-kernel" in the body of a message to majordomo@vger.kernel.org More majordomo info at http://vger.kernel.org/majordomo-info.html Please read the FAQ at http://www.tux.org/lkml/
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