715 lines
26 KiB
Plaintext
715 lines
26 KiB
Plaintext
Introduction
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============
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Having looked at the linux mtd/nand driver and more specific at nand_ecc.c
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I felt there was room for optimisation. I bashed the code for a few hours
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performing tricks like table lookup removing superfluous code etc.
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After that the speed was increased by 35-40%.
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Still I was not too happy as I felt there was additional room for improvement.
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Bad! I was hooked.
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I decided to annotate my steps in this file. Perhaps it is useful to someone
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or someone learns something from it.
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The problem
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===========
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NAND flash (at least SLC one) typically has sectors of 256 bytes.
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However NAND flash is not extremely reliable so some error detection
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(and sometimes correction) is needed.
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This is done by means of a Hamming code. I'll try to explain it in
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laymans terms (and apologies to all the pro's in the field in case I do
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not use the right terminology, my coding theory class was almost 30
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years ago, and I must admit it was not one of my favourites).
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As I said before the ecc calculation is performed on sectors of 256
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bytes. This is done by calculating several parity bits over the rows and
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columns. The parity used is even parity which means that the parity bit = 1
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if the data over which the parity is calculated is 1 and the parity bit = 0
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if the data over which the parity is calculated is 0. So the total
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number of bits over the data over which the parity is calculated + the
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parity bit is even. (see wikipedia if you can't follow this).
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Parity is often calculated by means of an exclusive or operation,
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sometimes also referred to as xor. In C the operator for xor is ^
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Back to ecc.
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Let's give a small figure:
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byte 0: bit7 bit6 bit5 bit4 bit3 bit2 bit1 bit0 rp0 rp2 rp4 ... rp14
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byte 1: bit7 bit6 bit5 bit4 bit3 bit2 bit1 bit0 rp1 rp2 rp4 ... rp14
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byte 2: bit7 bit6 bit5 bit4 bit3 bit2 bit1 bit0 rp0 rp3 rp4 ... rp14
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byte 3: bit7 bit6 bit5 bit4 bit3 bit2 bit1 bit0 rp1 rp3 rp4 ... rp14
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byte 4: bit7 bit6 bit5 bit4 bit3 bit2 bit1 bit0 rp0 rp2 rp5 ... rp14
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....
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byte 254: bit7 bit6 bit5 bit4 bit3 bit2 bit1 bit0 rp0 rp3 rp5 ... rp15
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byte 255: bit7 bit6 bit5 bit4 bit3 bit2 bit1 bit0 rp1 rp3 rp5 ... rp15
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cp1 cp0 cp1 cp0 cp1 cp0 cp1 cp0
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cp3 cp3 cp2 cp2 cp3 cp3 cp2 cp2
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cp5 cp5 cp5 cp5 cp4 cp4 cp4 cp4
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This figure represents a sector of 256 bytes.
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cp is my abbreviation for column parity, rp for row parity.
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Let's start to explain column parity.
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cp0 is the parity that belongs to all bit0, bit2, bit4, bit6.
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so the sum of all bit0, bit2, bit4 and bit6 values + cp0 itself is even.
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Similarly cp1 is the sum of all bit1, bit3, bit5 and bit7.
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cp2 is the parity over bit0, bit1, bit4 and bit5
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cp3 is the parity over bit2, bit3, bit6 and bit7.
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cp4 is the parity over bit0, bit1, bit2 and bit3.
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cp5 is the parity over bit4, bit5, bit6 and bit7.
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Note that each of cp0 .. cp5 is exactly one bit.
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Row parity actually works almost the same.
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rp0 is the parity of all even bytes (0, 2, 4, 6, ... 252, 254)
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rp1 is the parity of all odd bytes (1, 3, 5, 7, ..., 253, 255)
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rp2 is the parity of all bytes 0, 1, 4, 5, 8, 9, ...
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(so handle two bytes, then skip 2 bytes).
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rp3 is covers the half rp2 does not cover (bytes 2, 3, 6, 7, 10, 11, ...)
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for rp4 the rule is cover 4 bytes, skip 4 bytes, cover 4 bytes, skip 4 etc.
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so rp4 calculates parity over bytes 0, 1, 2, 3, 8, 9, 10, 11, 16, ...)
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and rp5 covers the other half, so bytes 4, 5, 6, 7, 12, 13, 14, 15, 20, ..
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The story now becomes quite boring. I guess you get the idea.
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rp6 covers 8 bytes then skips 8 etc
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rp7 skips 8 bytes then covers 8 etc
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rp8 covers 16 bytes then skips 16 etc
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rp9 skips 16 bytes then covers 16 etc
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rp10 covers 32 bytes then skips 32 etc
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rp11 skips 32 bytes then covers 32 etc
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rp12 covers 64 bytes then skips 64 etc
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rp13 skips 64 bytes then covers 64 etc
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rp14 covers 128 bytes then skips 128
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rp15 skips 128 bytes then covers 128
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In the end the parity bits are grouped together in three bytes as
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follows:
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ECC Bit 7 Bit 6 Bit 5 Bit 4 Bit 3 Bit 2 Bit 1 Bit 0
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ECC 0 rp07 rp06 rp05 rp04 rp03 rp02 rp01 rp00
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ECC 1 rp15 rp14 rp13 rp12 rp11 rp10 rp09 rp08
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ECC 2 cp5 cp4 cp3 cp2 cp1 cp0 1 1
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I detected after writing this that ST application note AN1823
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(http://www.st.com/stonline/) gives a much
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nicer picture.(but they use line parity as term where I use row parity)
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Oh well, I'm graphically challenged, so suffer with me for a moment :-)
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And I could not reuse the ST picture anyway for copyright reasons.
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Attempt 0
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=========
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Implementing the parity calculation is pretty simple.
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In C pseudocode:
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for (i = 0; i < 256; i++)
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{
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if (i & 0x01)
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rp1 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp1;
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else
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rp0 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp0;
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if (i & 0x02)
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rp3 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp3;
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else
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rp2 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp2;
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if (i & 0x04)
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rp5 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp5;
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else
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rp4 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp4;
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if (i & 0x08)
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rp7 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp7;
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else
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rp6 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp6;
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if (i & 0x10)
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rp9 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp9;
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else
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rp8 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp8;
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if (i & 0x20)
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rp11 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp11;
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else
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rp10 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp10;
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if (i & 0x40)
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rp13 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp13;
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else
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rp12 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp12;
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if (i & 0x80)
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rp15 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp15;
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else
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rp14 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp14;
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cp0 = bit6 ^ bit4 ^ bit2 ^ bit0 ^ cp0;
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cp1 = bit7 ^ bit5 ^ bit3 ^ bit1 ^ cp1;
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cp2 = bit5 ^ bit4 ^ bit1 ^ bit0 ^ cp2;
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cp3 = bit7 ^ bit6 ^ bit3 ^ bit2 ^ cp3
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cp4 = bit3 ^ bit2 ^ bit1 ^ bit0 ^ cp4
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cp5 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ cp5
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}
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Analysis 0
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==========
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C does have bitwise operators but not really operators to do the above
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efficiently (and most hardware has no such instructions either).
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Therefore without implementing this it was clear that the code above was
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not going to bring me a Nobel prize :-)
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Fortunately the exclusive or operation is commutative, so we can combine
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the values in any order. So instead of calculating all the bits
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individually, let us try to rearrange things.
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For the column parity this is easy. We can just xor the bytes and in the
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end filter out the relevant bits. This is pretty nice as it will bring
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all cp calculation out of the for loop.
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Similarly we can first xor the bytes for the various rows.
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This leads to:
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Attempt 1
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=========
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const char parity[256] = {
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0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0,
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1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1,
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1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1,
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0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0,
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1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1,
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0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0,
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0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0,
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1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1,
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1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1,
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0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0,
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0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0,
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1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1,
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0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0,
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1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1,
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1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1,
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0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0
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};
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void ecc1(const unsigned char *buf, unsigned char *code)
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{
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int i;
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const unsigned char *bp = buf;
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unsigned char cur;
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unsigned char rp0, rp1, rp2, rp3, rp4, rp5, rp6, rp7;
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unsigned char rp8, rp9, rp10, rp11, rp12, rp13, rp14, rp15;
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unsigned char par;
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par = 0;
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rp0 = 0; rp1 = 0; rp2 = 0; rp3 = 0;
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rp4 = 0; rp5 = 0; rp6 = 0; rp7 = 0;
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rp8 = 0; rp9 = 0; rp10 = 0; rp11 = 0;
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rp12 = 0; rp13 = 0; rp14 = 0; rp15 = 0;
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for (i = 0; i < 256; i++)
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{
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cur = *bp++;
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par ^= cur;
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if (i & 0x01) rp1 ^= cur; else rp0 ^= cur;
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if (i & 0x02) rp3 ^= cur; else rp2 ^= cur;
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if (i & 0x04) rp5 ^= cur; else rp4 ^= cur;
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if (i & 0x08) rp7 ^= cur; else rp6 ^= cur;
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if (i & 0x10) rp9 ^= cur; else rp8 ^= cur;
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if (i & 0x20) rp11 ^= cur; else rp10 ^= cur;
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if (i & 0x40) rp13 ^= cur; else rp12 ^= cur;
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if (i & 0x80) rp15 ^= cur; else rp14 ^= cur;
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}
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code[0] =
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(parity[rp7] << 7) |
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(parity[rp6] << 6) |
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(parity[rp5] << 5) |
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(parity[rp4] << 4) |
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(parity[rp3] << 3) |
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(parity[rp2] << 2) |
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(parity[rp1] << 1) |
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(parity[rp0]);
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code[1] =
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(parity[rp15] << 7) |
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(parity[rp14] << 6) |
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(parity[rp13] << 5) |
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(parity[rp12] << 4) |
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(parity[rp11] << 3) |
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(parity[rp10] << 2) |
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(parity[rp9] << 1) |
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(parity[rp8]);
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code[2] =
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(parity[par & 0xf0] << 7) |
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(parity[par & 0x0f] << 6) |
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(parity[par & 0xcc] << 5) |
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(parity[par & 0x33] << 4) |
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(parity[par & 0xaa] << 3) |
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(parity[par & 0x55] << 2);
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code[0] = ~code[0];
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code[1] = ~code[1];
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code[2] = ~code[2];
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}
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Still pretty straightforward. The last three invert statements are there to
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give a checksum of 0xff 0xff 0xff for an empty flash. In an empty flash
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all data is 0xff, so the checksum then matches.
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I also introduced the parity lookup. I expected this to be the fastest
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way to calculate the parity, but I will investigate alternatives later
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on.
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Analysis 1
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==========
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The code works, but is not terribly efficient. On my system it took
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almost 4 times as much time as the linux driver code. But hey, if it was
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*that* easy this would have been done long before.
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No pain. no gain.
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Fortunately there is plenty of room for improvement.
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In step 1 we moved from bit-wise calculation to byte-wise calculation.
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However in C we can also use the unsigned long data type and virtually
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every modern microprocessor supports 32 bit operations, so why not try
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to write our code in such a way that we process data in 32 bit chunks.
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Of course this means some modification as the row parity is byte by
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byte. A quick analysis:
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for the column parity we use the par variable. When extending to 32 bits
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we can in the end easily calculate rp0 and rp1 from it.
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(because par now consists of 4 bytes, contributing to rp1, rp0, rp1, rp0
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respectively, from MSB to LSB)
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also rp2 and rp3 can be easily retrieved from par as rp3 covers the
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first two MSBs and rp2 covers the last two LSBs.
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Note that of course now the loop is executed only 64 times (256/4).
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And note that care must taken wrt byte ordering. The way bytes are
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ordered in a long is machine dependent, and might affect us.
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Anyway, if there is an issue: this code is developed on x86 (to be
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precise: a DELL PC with a D920 Intel CPU)
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And of course the performance might depend on alignment, but I expect
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that the I/O buffers in the nand driver are aligned properly (and
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otherwise that should be fixed to get maximum performance).
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Let's give it a try...
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Attempt 2
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=========
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extern const char parity[256];
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void ecc2(const unsigned char *buf, unsigned char *code)
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{
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int i;
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const unsigned long *bp = (unsigned long *)buf;
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unsigned long cur;
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unsigned long rp0, rp1, rp2, rp3, rp4, rp5, rp6, rp7;
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unsigned long rp8, rp9, rp10, rp11, rp12, rp13, rp14, rp15;
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unsigned long par;
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par = 0;
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rp0 = 0; rp1 = 0; rp2 = 0; rp3 = 0;
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rp4 = 0; rp5 = 0; rp6 = 0; rp7 = 0;
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rp8 = 0; rp9 = 0; rp10 = 0; rp11 = 0;
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rp12 = 0; rp13 = 0; rp14 = 0; rp15 = 0;
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for (i = 0; i < 64; i++)
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{
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cur = *bp++;
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par ^= cur;
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if (i & 0x01) rp5 ^= cur; else rp4 ^= cur;
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if (i & 0x02) rp7 ^= cur; else rp6 ^= cur;
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if (i & 0x04) rp9 ^= cur; else rp8 ^= cur;
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if (i & 0x08) rp11 ^= cur; else rp10 ^= cur;
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if (i & 0x10) rp13 ^= cur; else rp12 ^= cur;
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if (i & 0x20) rp15 ^= cur; else rp14 ^= cur;
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}
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/*
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we need to adapt the code generation for the fact that rp vars are now
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long; also the column parity calculation needs to be changed.
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we'll bring rp4 to 15 back to single byte entities by shifting and
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xoring
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*/
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rp4 ^= (rp4 >> 16); rp4 ^= (rp4 >> 8); rp4 &= 0xff;
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rp5 ^= (rp5 >> 16); rp5 ^= (rp5 >> 8); rp5 &= 0xff;
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rp6 ^= (rp6 >> 16); rp6 ^= (rp6 >> 8); rp6 &= 0xff;
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rp7 ^= (rp7 >> 16); rp7 ^= (rp7 >> 8); rp7 &= 0xff;
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rp8 ^= (rp8 >> 16); rp8 ^= (rp8 >> 8); rp8 &= 0xff;
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rp9 ^= (rp9 >> 16); rp9 ^= (rp9 >> 8); rp9 &= 0xff;
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rp10 ^= (rp10 >> 16); rp10 ^= (rp10 >> 8); rp10 &= 0xff;
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rp11 ^= (rp11 >> 16); rp11 ^= (rp11 >> 8); rp11 &= 0xff;
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rp12 ^= (rp12 >> 16); rp12 ^= (rp12 >> 8); rp12 &= 0xff;
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rp13 ^= (rp13 >> 16); rp13 ^= (rp13 >> 8); rp13 &= 0xff;
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rp14 ^= (rp14 >> 16); rp14 ^= (rp14 >> 8); rp14 &= 0xff;
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rp15 ^= (rp15 >> 16); rp15 ^= (rp15 >> 8); rp15 &= 0xff;
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rp3 = (par >> 16); rp3 ^= (rp3 >> 8); rp3 &= 0xff;
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rp2 = par & 0xffff; rp2 ^= (rp2 >> 8); rp2 &= 0xff;
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par ^= (par >> 16);
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rp1 = (par >> 8); rp1 &= 0xff;
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rp0 = (par & 0xff);
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par ^= (par >> 8); par &= 0xff;
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code[0] =
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(parity[rp7] << 7) |
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(parity[rp6] << 6) |
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(parity[rp5] << 5) |
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(parity[rp4] << 4) |
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(parity[rp3] << 3) |
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(parity[rp2] << 2) |
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(parity[rp1] << 1) |
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(parity[rp0]);
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code[1] =
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(parity[rp15] << 7) |
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(parity[rp14] << 6) |
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(parity[rp13] << 5) |
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(parity[rp12] << 4) |
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(parity[rp11] << 3) |
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(parity[rp10] << 2) |
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(parity[rp9] << 1) |
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(parity[rp8]);
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code[2] =
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(parity[par & 0xf0] << 7) |
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(parity[par & 0x0f] << 6) |
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(parity[par & 0xcc] << 5) |
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(parity[par & 0x33] << 4) |
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(parity[par & 0xaa] << 3) |
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(parity[par & 0x55] << 2);
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code[0] = ~code[0];
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code[1] = ~code[1];
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code[2] = ~code[2];
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}
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The parity array is not shown any more. Note also that for these
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examples I kinda deviated from my regular programming style by allowing
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multiple statements on a line, not using { } in then and else blocks
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with only a single statement and by using operators like ^=
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Analysis 2
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==========
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The code (of course) works, and hurray: we are a little bit faster than
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the linux driver code (about 15%). But wait, don't cheer too quickly.
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There is more to be gained.
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If we look at e.g. rp14 and rp15 we see that we either xor our data with
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rp14 or with rp15. However we also have par which goes over all data.
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This means there is no need to calculate rp14 as it can be calculated from
|
|
rp15 through rp14 = par ^ rp15, because par = rp14 ^ rp15;
|
|
(or if desired we can avoid calculating rp15 and calculate it from
|
|
rp14). That is why some places refer to inverse parity.
|
|
Of course the same thing holds for rp4/5, rp6/7, rp8/9, rp10/11 and rp12/13.
|
|
Effectively this means we can eliminate the else clause from the if
|
|
statements. Also we can optimise the calculation in the end a little bit
|
|
by going from long to byte first. Actually we can even avoid the table
|
|
lookups
|
|
|
|
Attempt 3
|
|
=========
|
|
|
|
Odd replaced:
|
|
if (i & 0x01) rp5 ^= cur; else rp4 ^= cur;
|
|
if (i & 0x02) rp7 ^= cur; else rp6 ^= cur;
|
|
if (i & 0x04) rp9 ^= cur; else rp8 ^= cur;
|
|
if (i & 0x08) rp11 ^= cur; else rp10 ^= cur;
|
|
if (i & 0x10) rp13 ^= cur; else rp12 ^= cur;
|
|
if (i & 0x20) rp15 ^= cur; else rp14 ^= cur;
|
|
with
|
|
if (i & 0x01) rp5 ^= cur;
|
|
if (i & 0x02) rp7 ^= cur;
|
|
if (i & 0x04) rp9 ^= cur;
|
|
if (i & 0x08) rp11 ^= cur;
|
|
if (i & 0x10) rp13 ^= cur;
|
|
if (i & 0x20) rp15 ^= cur;
|
|
|
|
and outside the loop added:
|
|
rp4 = par ^ rp5;
|
|
rp6 = par ^ rp7;
|
|
rp8 = par ^ rp9;
|
|
rp10 = par ^ rp11;
|
|
rp12 = par ^ rp13;
|
|
rp14 = par ^ rp15;
|
|
|
|
And after that the code takes about 30% more time, although the number of
|
|
statements is reduced. This is also reflected in the assembly code.
|
|
|
|
|
|
Analysis 3
|
|
==========
|
|
|
|
Very weird. Guess it has to do with caching or instruction parallellism
|
|
or so. I also tried on an eeePC (Celeron, clocked at 900 Mhz). Interesting
|
|
observation was that this one is only 30% slower (according to time)
|
|
executing the code as my 3Ghz D920 processor.
|
|
|
|
Well, it was expected not to be easy so maybe instead move to a
|
|
different track: let's move back to the code from attempt2 and do some
|
|
loop unrolling. This will eliminate a few if statements. I'll try
|
|
different amounts of unrolling to see what works best.
|
|
|
|
|
|
Attempt 4
|
|
=========
|
|
|
|
Unrolled the loop 1, 2, 3 and 4 times.
|
|
For 4 the code starts with:
|
|
|
|
for (i = 0; i < 4; i++)
|
|
{
|
|
cur = *bp++;
|
|
par ^= cur;
|
|
rp4 ^= cur;
|
|
rp6 ^= cur;
|
|
rp8 ^= cur;
|
|
rp10 ^= cur;
|
|
if (i & 0x1) rp13 ^= cur; else rp12 ^= cur;
|
|
if (i & 0x2) rp15 ^= cur; else rp14 ^= cur;
|
|
cur = *bp++;
|
|
par ^= cur;
|
|
rp5 ^= cur;
|
|
rp6 ^= cur;
|
|
...
|
|
|
|
|
|
Analysis 4
|
|
==========
|
|
|
|
Unrolling once gains about 15%
|
|
Unrolling twice keeps the gain at about 15%
|
|
Unrolling three times gives a gain of 30% compared to attempt 2.
|
|
Unrolling four times gives a marginal improvement compared to unrolling
|
|
three times.
|
|
|
|
I decided to proceed with a four time unrolled loop anyway. It was my gut
|
|
feeling that in the next steps I would obtain additional gain from it.
|
|
|
|
The next step was triggered by the fact that par contains the xor of all
|
|
bytes and rp4 and rp5 each contain the xor of half of the bytes.
|
|
So in effect par = rp4 ^ rp5. But as xor is commutative we can also say
|
|
that rp5 = par ^ rp4. So no need to keep both rp4 and rp5 around. We can
|
|
eliminate rp5 (or rp4, but I already foresaw another optimisation).
|
|
The same holds for rp6/7, rp8/9, rp10/11 rp12/13 and rp14/15.
|
|
|
|
|
|
Attempt 5
|
|
=========
|
|
|
|
Effectively so all odd digit rp assignments in the loop were removed.
|
|
This included the else clause of the if statements.
|
|
Of course after the loop we need to correct things by adding code like:
|
|
rp5 = par ^ rp4;
|
|
Also the initial assignments (rp5 = 0; etc) could be removed.
|
|
Along the line I also removed the initialisation of rp0/1/2/3.
|
|
|
|
|
|
Analysis 5
|
|
==========
|
|
|
|
Measurements showed this was a good move. The run-time roughly halved
|
|
compared with attempt 4 with 4 times unrolled, and we only require 1/3rd
|
|
of the processor time compared to the current code in the linux kernel.
|
|
|
|
However, still I thought there was more. I didn't like all the if
|
|
statements. Why not keep a running parity and only keep the last if
|
|
statement. Time for yet another version!
|
|
|
|
|
|
Attempt 6
|
|
=========
|
|
|
|
THe code within the for loop was changed to:
|
|
|
|
for (i = 0; i < 4; i++)
|
|
{
|
|
cur = *bp++; tmppar = cur; rp4 ^= cur;
|
|
cur = *bp++; tmppar ^= cur; rp6 ^= tmppar;
|
|
cur = *bp++; tmppar ^= cur; rp4 ^= cur;
|
|
cur = *bp++; tmppar ^= cur; rp8 ^= tmppar;
|
|
|
|
cur = *bp++; tmppar ^= cur; rp4 ^= cur; rp6 ^= cur;
|
|
cur = *bp++; tmppar ^= cur; rp6 ^= cur;
|
|
cur = *bp++; tmppar ^= cur; rp4 ^= cur;
|
|
cur = *bp++; tmppar ^= cur; rp10 ^= tmppar;
|
|
|
|
cur = *bp++; tmppar ^= cur; rp4 ^= cur; rp6 ^= cur; rp8 ^= cur;
|
|
cur = *bp++; tmppar ^= cur; rp6 ^= cur; rp8 ^= cur;
|
|
cur = *bp++; tmppar ^= cur; rp4 ^= cur; rp8 ^= cur;
|
|
cur = *bp++; tmppar ^= cur; rp8 ^= cur;
|
|
|
|
cur = *bp++; tmppar ^= cur; rp4 ^= cur; rp6 ^= cur;
|
|
cur = *bp++; tmppar ^= cur; rp6 ^= cur;
|
|
cur = *bp++; tmppar ^= cur; rp4 ^= cur;
|
|
cur = *bp++; tmppar ^= cur;
|
|
|
|
par ^= tmppar;
|
|
if ((i & 0x1) == 0) rp12 ^= tmppar;
|
|
if ((i & 0x2) == 0) rp14 ^= tmppar;
|
|
}
|
|
|
|
As you can see tmppar is used to accumulate the parity within a for
|
|
iteration. In the last 3 statements is added to par and, if needed,
|
|
to rp12 and rp14.
|
|
|
|
While making the changes I also found that I could exploit that tmppar
|
|
contains the running parity for this iteration. So instead of having:
|
|
rp4 ^= cur; rp6 ^= cur;
|
|
I removed the rp6 ^= cur; statement and did rp6 ^= tmppar; on next
|
|
statement. A similar change was done for rp8 and rp10
|
|
|
|
|
|
Analysis 6
|
|
==========
|
|
|
|
Measuring this code again showed big gain. When executing the original
|
|
linux code 1 million times, this took about 1 second on my system.
|
|
(using time to measure the performance). After this iteration I was back
|
|
to 0.075 sec. Actually I had to decide to start measuring over 10
|
|
million iterations in order not to lose too much accuracy. This one
|
|
definitely seemed to be the jackpot!
|
|
|
|
There is a little bit more room for improvement though. There are three
|
|
places with statements:
|
|
rp4 ^= cur; rp6 ^= cur;
|
|
It seems more efficient to also maintain a variable rp4_6 in the while
|
|
loop; This eliminates 3 statements per loop. Of course after the loop we
|
|
need to correct by adding:
|
|
rp4 ^= rp4_6;
|
|
rp6 ^= rp4_6
|
|
Furthermore there are 4 sequential assignments to rp8. This can be
|
|
encoded slightly more efficiently by saving tmppar before those 4 lines
|
|
and later do rp8 = rp8 ^ tmppar ^ notrp8;
|
|
(where notrp8 is the value of rp8 before those 4 lines).
|
|
Again a use of the commutative property of xor.
|
|
Time for a new test!
|
|
|
|
|
|
Attempt 7
|
|
=========
|
|
|
|
The new code now looks like:
|
|
|
|
for (i = 0; i < 4; i++)
|
|
{
|
|
cur = *bp++; tmppar = cur; rp4 ^= cur;
|
|
cur = *bp++; tmppar ^= cur; rp6 ^= tmppar;
|
|
cur = *bp++; tmppar ^= cur; rp4 ^= cur;
|
|
cur = *bp++; tmppar ^= cur; rp8 ^= tmppar;
|
|
|
|
cur = *bp++; tmppar ^= cur; rp4_6 ^= cur;
|
|
cur = *bp++; tmppar ^= cur; rp6 ^= cur;
|
|
cur = *bp++; tmppar ^= cur; rp4 ^= cur;
|
|
cur = *bp++; tmppar ^= cur; rp10 ^= tmppar;
|
|
|
|
notrp8 = tmppar;
|
|
cur = *bp++; tmppar ^= cur; rp4_6 ^= cur;
|
|
cur = *bp++; tmppar ^= cur; rp6 ^= cur;
|
|
cur = *bp++; tmppar ^= cur; rp4 ^= cur;
|
|
cur = *bp++; tmppar ^= cur;
|
|
rp8 = rp8 ^ tmppar ^ notrp8;
|
|
|
|
cur = *bp++; tmppar ^= cur; rp4_6 ^= cur;
|
|
cur = *bp++; tmppar ^= cur; rp6 ^= cur;
|
|
cur = *bp++; tmppar ^= cur; rp4 ^= cur;
|
|
cur = *bp++; tmppar ^= cur;
|
|
|
|
par ^= tmppar;
|
|
if ((i & 0x1) == 0) rp12 ^= tmppar;
|
|
if ((i & 0x2) == 0) rp14 ^= tmppar;
|
|
}
|
|
rp4 ^= rp4_6;
|
|
rp6 ^= rp4_6;
|
|
|
|
|
|
Not a big change, but every penny counts :-)
|
|
|
|
|
|
Analysis 7
|
|
==========
|
|
|
|
Actually this made things worse. Not very much, but I don't want to move
|
|
into the wrong direction. Maybe something to investigate later. Could
|
|
have to do with caching again.
|
|
|
|
Guess that is what there is to win within the loop. Maybe unrolling one
|
|
more time will help. I'll keep the optimisations from 7 for now.
|
|
|
|
|
|
Attempt 8
|
|
=========
|
|
|
|
Unrolled the loop one more time.
|
|
|
|
|
|
Analysis 8
|
|
==========
|
|
|
|
This makes things worse. Let's stick with attempt 6 and continue from there.
|
|
Although it seems that the code within the loop cannot be optimised
|
|
further there is still room to optimize the generation of the ecc codes.
|
|
We can simply calculate the total parity. If this is 0 then rp4 = rp5
|
|
etc. If the parity is 1, then rp4 = !rp5;
|
|
But if rp4 = rp5 we do not need rp5 etc. We can just write the even bits
|
|
in the result byte and then do something like
|
|
code[0] |= (code[0] << 1);
|
|
Lets test this.
|
|
|
|
|
|
Attempt 9
|
|
=========
|
|
|
|
Changed the code but again this slightly degrades performance. Tried all
|
|
kind of other things, like having dedicated parity arrays to avoid the
|
|
shift after parity[rp7] << 7; No gain.
|
|
Change the lookup using the parity array by using shift operators (e.g.
|
|
replace parity[rp7] << 7 with:
|
|
rp7 ^= (rp7 << 4);
|
|
rp7 ^= (rp7 << 2);
|
|
rp7 ^= (rp7 << 1);
|
|
rp7 &= 0x80;
|
|
No gain.
|
|
|
|
The only marginal change was inverting the parity bits, so we can remove
|
|
the last three invert statements.
|
|
|
|
Ah well, pity this does not deliver more. Then again 10 million
|
|
iterations using the linux driver code takes between 13 and 13.5
|
|
seconds, whereas my code now takes about 0.73 seconds for those 10
|
|
million iterations. So basically I've improved the performance by a
|
|
factor 18 on my system. Not that bad. Of course on different hardware
|
|
you will get different results. No warranties!
|
|
|
|
But of course there is no such thing as a free lunch. The codesize almost
|
|
tripled (from 562 bytes to 1434 bytes). Then again, it is not that much.
|
|
|
|
|
|
Correcting errors
|
|
=================
|
|
|
|
For correcting errors I again used the ST application note as a starter,
|
|
but I also peeked at the existing code.
|
|
The algorithm itself is pretty straightforward. Just xor the given and
|
|
the calculated ecc. If all bytes are 0 there is no problem. If 11 bits
|
|
are 1 we have one correctable bit error. If there is 1 bit 1, we have an
|
|
error in the given ecc code.
|
|
It proved to be fastest to do some table lookups. Performance gain
|
|
introduced by this is about a factor 2 on my system when a repair had to
|
|
be done, and 1% or so if no repair had to be done.
|
|
Code size increased from 330 bytes to 686 bytes for this function.
|
|
(gcc 4.2, -O3)
|
|
|
|
|
|
Conclusion
|
|
==========
|
|
|
|
The gain when calculating the ecc is tremendous. Om my development hardware
|
|
a speedup of a factor of 18 for ecc calculation was achieved. On a test on an
|
|
embedded system with a MIPS core a factor 7 was obtained.
|
|
On a test with a Linksys NSLU2 (ARMv5TE processor) the speedup was a factor
|
|
5 (big endian mode, gcc 4.1.2, -O3)
|
|
For correction not much gain could be obtained (as bitflips are rare). Then
|
|
again there are also much less cycles spent there.
|
|
|
|
It seems there is not much more gain possible in this, at least when
|
|
programmed in C. Of course it might be possible to squeeze something more
|
|
out of it with an assembler program, but due to pipeline behaviour etc
|
|
this is very tricky (at least for intel hw).
|
|
|
|
Author: Frans Meulenbroeks
|
|
Copyright (C) 2008 Koninklijke Philips Electronics NV.
|