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-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 abbreviation 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/) 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 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.