mirror of
https://github.com/AuxXxilium/linux_dsm_epyc7002.git
synced 2025-03-04 21:59:33 +07:00
crc32.txt: standardize document format
Each text file under Documentation follows a different format. Some doesn't even have titles! Change its representation to follow the adopted standard, using ReST markups for it to be parseable by Sphinx: - Add a title for the document; - Mark literal blocks. While here, replace a comma by a dot at the end of a paragraph. Signed-off-by: Mauro Carvalho Chehab <mchehab@s-opensource.com> Signed-off-by: Jonathan Corbet <corbet@lwn.net>
This commit is contained in:
parent
e8cb6f1edc
commit
2e4e6f30f7
@ -1,4 +1,6 @@
|
|||||||
A brief CRC tutorial.
|
=================================
|
||||||
|
brief tutorial on CRC computation
|
||||||
|
=================================
|
||||||
|
|
||||||
A CRC is a long-division remainder. You add the CRC to the message,
|
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
|
and the whole thing (message+CRC) is a multiple of the given
|
||||||
@ -8,7 +10,8 @@ remainder computed on the message+CRC is 0. This latter approach
|
|||||||
is used by a lot of hardware implementations, and is why so many
|
is used by a lot of hardware implementations, and is why so many
|
||||||
protocols put the end-of-frame flag after the CRC.
|
protocols put the end-of-frame flag after the CRC.
|
||||||
|
|
||||||
It's actually the same long division you learned in school, except that
|
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
|
- 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
|
- When dividing polynomials, there are no carries. Rather than add and
|
||||||
subtract, we just xor. Thus, we tend to get a bit sloppy about
|
subtract, we just xor. Thus, we tend to get a bit sloppy about
|
||||||
@ -40,11 +43,12 @@ throw the quotient bit away, but subtract the appropriate multiple of
|
|||||||
the polynomial from the remainder and we're back to where we started,
|
the polynomial from the remainder and we're back to where we started,
|
||||||
ready to process the next bit.
|
ready to process the next bit.
|
||||||
|
|
||||||
A big-endian CRC written this way would be coded like:
|
A big-endian CRC written this way would be coded like::
|
||||||
for (i = 0; i < input_bits; i++) {
|
|
||||||
multiple = remainder & 0x80000000 ? CRCPOLY : 0;
|
for (i = 0; i < input_bits; i++) {
|
||||||
remainder = (remainder << 1 | next_input_bit()) ^ multiple;
|
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
|
Notice how, to get at bit 32 of the shifted remainder, we look
|
||||||
at bit 31 of the remainder *before* shifting it.
|
at bit 31 of the remainder *before* shifting it.
|
||||||
@ -54,25 +58,26 @@ the remainder don't actually affect any decision-making until
|
|||||||
32 bits later. Thus, the first 32 cycles of this are pretty boring.
|
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
|
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
|
the end, so we have to add 32 extra cycles shifting in zeros at the
|
||||||
end of every message,
|
end of every message.
|
||||||
|
|
||||||
These details lead to a standard trick: rearrange merging in the
|
These details lead to a standard trick: rearrange merging in the
|
||||||
next_input_bit() until the moment it's needed. Then the first 32 cycles
|
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
|
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 the CRC can be skipped entirely. This changes the code to::
|
||||||
|
|
||||||
for (i = 0; i < input_bits; i++) {
|
for (i = 0; i < input_bits; i++) {
|
||||||
remainder ^= next_input_bit() << 31;
|
remainder ^= next_input_bit() << 31;
|
||||||
multiple = (remainder & 0x80000000) ? CRCPOLY : 0;
|
multiple = (remainder & 0x80000000) ? CRCPOLY : 0;
|
||||||
remainder = (remainder << 1) ^ multiple;
|
remainder = (remainder << 1) ^ multiple;
|
||||||
}
|
}
|
||||||
|
|
||||||
With this optimization, the little-endian code is particularly simple:
|
With this optimization, the little-endian code is particularly simple::
|
||||||
for (i = 0; i < input_bits; i++) {
|
|
||||||
remainder ^= next_input_bit();
|
for (i = 0; i < input_bits; i++) {
|
||||||
multiple = (remainder & 1) ? CRCPOLY : 0;
|
remainder ^= next_input_bit();
|
||||||
remainder = (remainder >> 1) ^ multiple;
|
multiple = (remainder & 1) ? CRCPOLY : 0;
|
||||||
}
|
remainder = (remainder >> 1) ^ multiple;
|
||||||
|
}
|
||||||
|
|
||||||
The most significant coefficient of the remainder polynomial is stored
|
The most significant coefficient of the remainder polynomial is stored
|
||||||
in the least significant bit of the binary "remainder" variable.
|
in the least significant bit of the binary "remainder" variable.
|
||||||
@ -81,23 +86,25 @@ be bit-reversed) and next_input_bit().
|
|||||||
|
|
||||||
As long as next_input_bit is returning the bits in a sensible order, we don't
|
As long as next_input_bit is returning the bits in a sensible order, we don't
|
||||||
*have* to wait until the last possible moment to merge in additional bits.
|
*have* to wait until the last possible moment to merge in additional bits.
|
||||||
We can do it 8 bits at a time rather than 1 bit at a time:
|
We can do it 8 bits at a time rather than 1 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++) {
|
||||||
for (i = 0; i < input_bytes; i++) {
|
remainder ^= next_input_byte() << 24;
|
||||||
remainder ^= next_input_byte();
|
for (j = 0; j < 8; j++) {
|
||||||
for (j = 0; j < 8; j++) {
|
multiple = (remainder & 0x80000000) ? CRCPOLY : 0;
|
||||||
multiple = (remainder & 1) ? CRCPOLY : 0;
|
remainder = (remainder << 1) ^ multiple;
|
||||||
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
|
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.
|
word at a time and increase the inner loop count to 32.
|
||||||
|
Loading…
Reference in New Issue
Block a user