[patch v4 1/7] crc32: move-to-documentation.diff

Bob Pearson
2011-08-09T05:59:47Z

Moved a nice but long comment from lib/crc32.c to Documentation/crc32.txt
where it will more likely get read.

Added filename and description to Documentation/00-INDEX

Signed-off-by: Bob Pearson <rpearson@systemfabricworks.com>

---
Documentation/00-INDEX | 2
Documentation/crc32.txt | 129 ++++++++++++++++++++++++++++++++++++++++++++++++
lib/crc32.c | 127 -----------------------------------------------
3 files changed, 131 insertions(+), 127 deletions(-)

Index: infiniband/lib/crc32.c
===================================================================
--- infiniband.orig/lib/crc32.c
+++ infiniband/lib/crc32.c
@@ -208,133 +208,6 @@ u32 __pure crc32_be(u32 crc, unsigned ch
EXPORT_SYMBOL(crc32_le);
EXPORT_SYMBOL(crc32_be);

-/*
- * 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 multiple 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>
Index: infiniband/Documentation/crc32.txt
===================================================================
--- /dev/null
+++ infiniband/Documentation/crc32.txt
@@ -0,0 +1,129 @@
+
+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 multiple 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.
+
Index: infiniband/Documentation/00-INDEX
===================================================================
--- infiniband.orig/Documentation/00-INDEX
+++ infiniband/Documentation/00-INDEX
@@ -104,6 +104,8 @@ cpuidle/
- info on CPU_IDLE, CPU idle state management subsystem.
cputopology.txt
- documentation on how CPU topology info is exported via sysfs.
+crc32.txt
+ - brief tutorial on CRC computation
cris/
- directory with info about Linux on CRIS architecture.
crypto/