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diff --git a/Documentation/mtd/nand_ecc.txt b/Documentation/mtd/nand_ecc.txt new file mode 100644 index 0000000..bdf93b7 --- /dev/null +++ b/Documentation/mtd/nand_ecc.txt @@ -0,0 +1,714 @@ +Introduction +============ + +Having looked at the linux mtd/nand driver and more specific at nand_ecc.c +I felt there was room for optimisation. I bashed the code for a few hours +performing tricks like table lookup removing superfluous code etc. +After that the speed was increased by 35-40%. +Still I was not too happy as I felt there was additional room for improvement. + +Bad! I was hooked. +I decided to annotate my steps in this file. Perhaps it is useful to someone +or someone learns something from it. + + +The problem +=========== + +NAND flash (at least SLC one) typically has sectors of 256 bytes. +However NAND flash is not extremely reliable so some error detection +(and sometimes correction) is needed. + +This is done by means of a Hamming code. I'll try to explain it in +laymans terms (and apologies to all the pro's in the field in case I do +not use the right terminology, my coding theory class was almost 30 +years ago, and I must admit it was not one of my favourites). + +As I said before the ecc calculation is performed on sectors of 256 +bytes. This is done by calculating several parity bits over the rows and +columns. The parity used is even parity which means that the parity bit = 1 +if the data over which the parity is calculated is 1 and the parity bit = 0 +if the data over which the parity is calculated is 0. So the total +number of bits over the data over which the parity is calculated + the +parity bit is even. (see wikipedia if you can't follow this). +Parity is often calculated by means of an exclusive or operation, +sometimes also referred to as xor. In C the operator for xor is ^ + +Back to ecc. +Let's give a small figure: + +byte 0: bit7 bit6 bit5 bit4 bit3 bit2 bit1 bit0 rp0 rp2 rp4 ... rp14 +byte 1: bit7 bit6 bit5 bit4 bit3 bit2 bit1 bit0 rp1 rp2 rp4 ... rp14 +byte 2: bit7 bit6 bit5 bit4 bit3 bit2 bit1 bit0 rp0 rp3 rp4 ... rp14 +byte 3: bit7 bit6 bit5 bit4 bit3 bit2 bit1 bit0 rp1 rp3 rp4 ... rp14 +byte 4: bit7 bit6 bit5 bit4 bit3 bit2 bit1 bit0 rp0 rp2 rp5 ... rp14 +.... +byte 254: bit7 bit6 bit5 bit4 bit3 bit2 bit1 bit0 rp0 rp3 rp5 ... rp15 +byte 255: bit7 bit6 bit5 bit4 bit3 bit2 bit1 bit0 rp1 rp3 rp5 ... rp15 + cp1 cp0 cp1 cp0 cp1 cp0 cp1 cp0 + cp3 cp3 cp2 cp2 cp3 cp3 cp2 cp2 + cp5 cp5 cp5 cp5 cp4 cp4 cp4 cp4 + +This figure represents a sector of 256 bytes. +cp is my abbreviaton for column parity, rp for row parity. + +Let's start to explain column parity. +cp0 is the parity that belongs to all bit0, bit2, bit4, bit6. +so the sum of all bit0, bit2, bit4 and bit6 values + cp0 itself is even. +Similarly cp1 is the sum of all bit1, bit3, bit5 and bit7. +cp2 is the parity over bit0, bit1, bit4 and bit5 +cp3 is the parity over bit2, bit3, bit6 and bit7. +cp4 is the parity over bit0, bit1, bit2 and bit3. +cp5 is the parity over bit4, bit5, bit6 and bit7. +Note that each of cp0 .. cp5 is exactly one bit. + +Row parity actually works almost the same. +rp0 is the parity of all even bytes (0, 2, 4, 6, ... 252, 254) +rp1 is the parity of all odd bytes (1, 3, 5, 7, ..., 253, 255) +rp2 is the parity of all bytes 0, 1, 4, 5, 8, 9, ... +(so handle two bytes, then skip 2 bytes). +rp3 is covers the half rp2 does not cover (bytes 2, 3, 6, 7, 10, 11, ...) +for rp4 the rule is cover 4 bytes, skip 4 bytes, cover 4 bytes, skip 4 etc. +so rp4 calculates parity over bytes 0, 1, 2, 3, 8, 9, 10, 11, 16, ...) +and rp5 covers the other half, so bytes 4, 5, 6, 7, 12, 13, 14, 15, 20, .. +The story now becomes quite boring. I guess you get the idea. +rp6 covers 8 bytes then skips 8 etc +rp7 skips 8 bytes then covers 8 etc +rp8 covers 16 bytes then skips 16 etc +rp9 skips 16 bytes then covers 16 etc +rp10 covers 32 bytes then skips 32 etc +rp11 skips 32 bytes then covers 32 etc +rp12 covers 64 bytes then skips 64 etc +rp13 skips 64 bytes then covers 64 etc +rp14 covers 128 bytes then skips 128 +rp15 skips 128 bytes then covers 128 + +In the end the parity bits are grouped together in three bytes as +follows: +ECC Bit 7 Bit 6 Bit 5 Bit 4 Bit 3 Bit 2 Bit 1 Bit 0 +ECC 0 rp07 rp06 rp05 rp04 rp03 rp02 rp01 rp00 +ECC 1 rp15 rp14 rp13 rp12 rp11 rp10 rp09 rp08 +ECC 2 cp5 cp4 cp3 cp2 cp1 cp0 1 1 + +I detected after writing this that ST application note AN1823 +(http://www.st.com/stonline/books/pdf/docs/10123.pdf) gives a much +nicer picture.(but they use line parity as term where I use row parity) +Oh well, I'm graphically challenged, so suffer with me for a moment :-) +And I could not reuse the ST picture anyway for copyright reasons. + + +Attempt 0 +========= + +Implementing the parity calculation is pretty simple. +In C pseudocode: +for (i = 0; i < 256; i++) +{ + if (i & 0x01) + rp1 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp1; + else + rp0 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp1; + if (i & 0x02) + rp3 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp3; + else + rp2 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp2; + if (i & 0x04) + rp5 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp5; + else + rp4 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp4; + if (i & 0x08) + rp7 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp7; + else + rp6 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp6; + if (i & 0x10) + rp9 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp9; + else + rp8 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp8; + if (i & 0x20) + rp11 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp11; + else + rp10 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp10; + if (i & 0x40) + rp13 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp13; + else + rp12 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp12; + if (i & 0x80) + rp15 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp15; + else + rp14 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ bit3 ^ bit2 ^ bit1 ^ bit0 ^ rp14; + cp0 = bit6 ^ bit4 ^ bit2 ^ bit0 ^ cp0; + cp1 = bit7 ^ bit5 ^ bit3 ^ bit1 ^ cp1; + cp2 = bit5 ^ bit4 ^ bit1 ^ bit0 ^ cp2; + cp3 = bit7 ^ bit6 ^ bit3 ^ bit2 ^ cp3 + cp4 = bit3 ^ bit2 ^ bit1 ^ bit0 ^ cp4 + cp5 = bit7 ^ bit6 ^ bit5 ^ bit4 ^ cp5 +} + + +Analysis 0 +========== + +C does have bitwise operators but not really operators to do the above +efficiently (and most hardware has no such instructions either). +Therefore without implementing this it was clear that the code above was +not going to bring me a Nobel prize :-) + +Fortunately the exclusive or operation is commutative, so we can combine +the values in any order. So instead of calculating all the bits +individually, let us try to rearrange things. +For the column parity this is easy. We can just xor the bytes and in the +end filter out the relevant bits. This is pretty nice as it will bring +all cp calculation out of the if loop. + +Similarly we can first xor the bytes for the various rows. +This leads to: + + +Attempt 1 +========= + +const char parity[256] = { + 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, + 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, + 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, + 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, + 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, + 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, + 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, + 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, + 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, + 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, + 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, + 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, + 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, + 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, + 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, + 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0 +}; + +void ecc1(const unsigned char *buf, unsigned char *code) +{ + int i; + const unsigned char *bp = buf; + unsigned char cur; + unsigned char rp0, rp1, rp2, rp3, rp4, rp5, rp6, rp7; + unsigned char rp8, rp9, rp10, rp11, rp12, rp13, rp14, rp15; + unsigned char par; + + par = 0; + rp0 = 0; rp1 = 0; rp2 = 0; rp3 = 0; + rp4 = 0; rp5 = 0; rp6 = 0; rp7 = 0; + rp8 = 0; rp9 = 0; rp10 = 0; rp11 = 0; + rp12 = 0; rp13 = 0; rp14 = 0; rp15 = 0; + + for (i = 0; i < 256; i++) + { + cur = *bp++; + par ^= cur; + if (i & 0x01) rp1 ^= cur; else rp0 ^= cur; + if (i & 0x02) rp3 ^= cur; else rp2 ^= cur; + if (i & 0x04) rp5 ^= cur; else rp4 ^= cur; + if (i & 0x08) rp7 ^= cur; else rp6 ^= cur; + if (i & 0x10) rp9 ^= cur; else rp8 ^= cur; + if (i & 0x20) rp11 ^= cur; else rp10 ^= cur; + if (i & 0x40) rp13 ^= cur; else rp12 ^= cur; + if (i & 0x80) rp15 ^= cur; else rp14 ^= cur; + } + code[0] = + (parity[rp7] << 7) | + (parity[rp6] << 6) | + (parity[rp5] << 5) | + (parity[rp4] << 4) | + (parity[rp3] << 3) | + (parity[rp2] << 2) | + (parity[rp1] << 1) | + (parity[rp0]); + code[1] = + (parity[rp15] << 7) | + (parity[rp14] << 6) | + (parity[rp13] << 5) | + (parity[rp12] << 4) | + (parity[rp11] << 3) | + (parity[rp10] << 2) | + (parity[rp9] << 1) | + (parity[rp8]); + code[2] = + (parity[par & 0xf0] << 7) | + (parity[par & 0x0f] << 6) | + (parity[par & 0xcc] << 5) | + (parity[par & 0x33] << 4) | + (parity[par & 0xaa] << 3) | + (parity[par & 0x55] << 2); + code[0] = ~code[0]; + code[1] = ~code[1]; + code[2] = ~code[2]; +} + +Still pretty straightforward. The last three invert statements are there to +give a checksum of 0xff 0xff 0xff for an empty flash. In an empty flash +all data is 0xff, so the checksum then matches. + +I also introduced the parity lookup. I expected this to be the fastest +way to calculate the parity, but I will investigate alternatives later +on. + + +Analysis 1 +========== + +The code works, but is not terribly efficient. On my system it took +almost 4 times as much time as the linux driver code. But hey, if it was +*that* easy this would have been done long before. +No pain. no gain. + +Fortunately there is plenty of room for improvement. + +In step 1 we moved from bit-wise calculation to byte-wise calculation. +However in C we can also use the unsigned long data type and virtually +every modern microprocessor supports 32 bit operations, so why not try +to write our code in such a way that we process data in 32 bit chunks. + +Of course this means some modification as the row parity is byte by +byte. A quick analysis: +for the column parity we use the par variable. When extending to 32 bits +we can in the end easily calculate p0 and p1 from it. +(because par now consists of 4 bytes, contributing to rp1, rp0, rp1, rp0 +respectively) +also rp2 and rp3 can be easily retrieved from par as rp3 covers the +first two bytes and rp2 the last two bytes. + +Note that of course now the loop is executed only 64 times (256/4). +And note that care must taken wrt byte ordering. The way bytes are +ordered in a long is machine dependent, and might affect us. +Anyway, if there is an issue: this code is developed on x86 (to be +precise: a DELL PC with a D920 Intel CPU) + +And of course the performance might depend on alignment, but I expect +that the I/O buffers in the nand driver are aligned properly (and +otherwise that should be fixed to get maximum performance). + +Let's give it a try... + + +Attempt 2 +========= + +extern const char parity[256]; + +void ecc2(const unsigned char *buf, unsigned char *code) +{ + int i; + const unsigned long *bp = (unsigned long *)buf; + unsigned long cur; + unsigned long rp0, rp1, rp2, rp3, rp4, rp5, rp6, rp7; + unsigned long rp8, rp9, rp10, rp11, rp12, rp13, rp14, rp15; + unsigned long par; + + par = 0; + rp0 = 0; rp1 = 0; rp2 = 0; rp3 = 0; + rp4 = 0; rp5 = 0; rp6 = 0; rp7 = 0; + rp8 = 0; rp9 = 0; rp10 = 0; rp11 = 0; + rp12 = 0; rp13 = 0; rp14 = 0; rp15 = 0; + + for (i = 0; i < 64; i++) + { + cur = *bp++; + par ^= cur; + 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; + } + /* + we need to adapt the code generation for the fact that rp vars are now + long; also the column parity calculation needs to be changed. + we'll bring rp4 to 15 back to single byte entities by shifting and + xoring + */ + rp4 ^= (rp4 >> 16); rp4 ^= (rp4 >> 8); rp4 &= 0xff; + rp5 ^= (rp5 >> 16); rp5 ^= (rp5 >> 8); rp5 &= 0xff; + rp6 ^= (rp6 >> 16); rp6 ^= (rp6 >> 8); rp6 &= 0xff; + rp7 ^= (rp7 >> 16); rp7 ^= (rp7 >> 8); rp7 &= 0xff; + rp8 ^= (rp8 >> 16); rp8 ^= (rp8 >> 8); rp8 &= 0xff; + rp9 ^= (rp9 >> 16); rp9 ^= (rp9 >> 8); rp9 &= 0xff; + rp10 ^= (rp10 >> 16); rp10 ^= (rp10 >> 8); rp10 &= 0xff; + rp11 ^= (rp11 >> 16); rp11 ^= (rp11 >> 8); rp11 &= 0xff; + rp12 ^= (rp12 >> 16); rp12 ^= (rp12 >> 8); rp12 &= 0xff; + rp13 ^= (rp13 >> 16); rp13 ^= (rp13 >> 8); rp13 &= 0xff; + rp14 ^= (rp14 >> 16); rp14 ^= (rp14 >> 8); rp14 &= 0xff; + rp15 ^= (rp15 >> 16); rp15 ^= (rp15 >> 8); rp15 &= 0xff; + rp3 = (par >> 16); rp3 ^= (rp3 >> 8); rp3 &= 0xff; + rp2 = par & 0xffff; rp2 ^= (rp2 >> 8); rp2 &= 0xff; + par ^= (par >> 16); + rp1 = (par >> 8); rp1 &= 0xff; + rp0 = (par & 0xff); + par ^= (par >> 8); par &= 0xff; + + code[0] = + (parity[rp7] << 7) | + (parity[rp6] << 6) | + (parity[rp5] << 5) | + (parity[rp4] << 4) | + (parity[rp3] << 3) | + (parity[rp2] << 2) | + (parity[rp1] << 1) | + (parity[rp0]); + code[1] = + (parity[rp15] << 7) | + (parity[rp14] << 6) | + (parity[rp13] << 5) | + (parity[rp12] << 4) | + (parity[rp11] << 3) | + (parity[rp10] << 2) | + (parity[rp9] << 1) | + (parity[rp8]); + code[2] = + (parity[par & 0xf0] << 7) | + (parity[par & 0x0f] << 6) | + (parity[par & 0xcc] << 5) | + (parity[par & 0x33] << 4) | + (parity[par & 0xaa] << 3) | + (parity[par & 0x55] << 2); + code[0] = ~code[0]; + code[1] = ~code[1]; + code[2] = ~code[2]; +} + +The parity array is not shown any more. Note also that for these +examples I kinda deviated from my regular programming style by allowing +multiple statements on a line, not using { } in then and else blocks +with only a single statement and by using operators like ^= + + +Analysis 2 +========== + +The code (of course) works, and hurray: we are a little bit faster than +the linux driver code (about 15%). But wait, don't cheer too quickly. +THere is more to be gained. +If we look at e.g. rp14 and rp15 we see that we either xor our data with +rp14 or with rp15. However we also have par which goes over all data. +This means there is no need to calculate rp14 as it can be calculated from +rp15 through rp14 = par ^ 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 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 interations in order not to loose 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 assingments to rp8. This can be +encoded slightly more efficient 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 +========== + +Acutally 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 calcualate 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. |
