Re: [PATCH 15/39] mtd: nand: denali: improve readability of handle_ecc()

[Boris Brezillon]

On Fri, 2 Dec 2016 13:26:27 +0900
Masahiro Yamada  wrote:

> Hi Boris,
> 
> 
> 2016-11-28 0:42 GMT+09:00 Boris Brezillon 
> :
> >> + if (err_byte < ECC_SECTOR_SIZE) {
> >> + struct mtd_info *mtd =
> >> + nand_to_mtd(>nand);
> >> + int offset;
> >> +
> >> + offset = (err_sector * ECC_SECTOR_SIZE + 
> >> err_byte) *
> >> + denali->devnum + err_device;
> >> + /* correct the ECC error */
> >> + buf[offset] ^= err_correction_value;
> >> + mtd->ecc_stats.corrected++;
> >> + bitflips++;  
> >
> > Hm, bitflips is what is set in max_bitflips, and apparently the
> > implementation (which is not yours) is not doing what the core expects.
> >
> > You should first count bitflips per sector with something like that:
> >
> > bitflips[err_sector]++;
> >
> >
> > And then once you've iterated over all errors do:
> >
> > for (i = 0; i < nsectors; i++)
> > max_bitflips = max(bitflips[err_sector], max_bitflips);  
> 
> 
> I see.
> 
> For soft ECC fixup, we can calculate bitflips
> for each ECC sector, so I can fix the max_bitflips
> as the core framework expects.
> 
> For hard ECC fixup, the register only reports
> the number of corrected bit-flips
> in the whole page (sum from all ECC sectors).
> We cannot calculate max_bitflips, I think.
> 

That's unfortunate. This means you'll return -EUCLEAN more quickly
(which will trigger UBI eraseblock move), since the NAND framework is
basing its 'too many bitflips' detection logic on the max_bitflips per
ECC chunk and the bitflips threshold (by default 3/4 of the ECC
strength).

That doesn't mean it won't work, you'll just wear your NAND more
quickly :-(.

ITOH, doing max_bitflips = nbitflips / nsteps is not good either,
because the bitflips might be all concentrated in the same ECC chunk,
and in this case you really want to return -EUCLEAN.

> 
> 
> BTW, I noticed another problem of the current code.
> 
>   buf[offset] ^= err_correction_value;
>   mtd->ecc_stats.corrected++;
>   bitflips++;
> 
> This code is counting the number of corrected bytes,
> not the number of corrected bits.
> 
> 
> I think multiple bit-flips within one byte can happen.

Yes.

> 
> 
> Perhaps, we should add
> 
>   hweight8(buf[offset] ^ err_correction_value)
> 
> to ecc_stats.corrected and bitflips.
> 

Looks good.

Re: [PATCH 15/39] mtd: nand: denali: improve readability of handle_ecc()

[Boris Brezillon]

On Fri, 2 Dec 2016 13:26:27 +0900
Masahiro Yamada  wrote:

> Hi Boris,
> 
> 
> 2016-11-28 0:42 GMT+09:00 Boris Brezillon 
> :
> >> + if (err_byte < ECC_SECTOR_SIZE) {
> >> + struct mtd_info *mtd =
> >> + nand_to_mtd(>nand);
> >> + int offset;
> >> +
> >> + offset = (err_sector * ECC_SECTOR_SIZE + 
> >> err_byte) *
> >> + denali->devnum + err_device;
> >> + /* correct the ECC error */
> >> + buf[offset] ^= err_correction_value;
> >> + mtd->ecc_stats.corrected++;
> >> + bitflips++;  
> >
> > Hm, bitflips is what is set in max_bitflips, and apparently the
> > implementation (which is not yours) is not doing what the core expects.
> >
> > You should first count bitflips per sector with something like that:
> >
> > bitflips[err_sector]++;
> >
> >
> > And then once you've iterated over all errors do:
> >
> > for (i = 0; i < nsectors; i++)
> > max_bitflips = max(bitflips[err_sector], max_bitflips);  
> 
> 
> I see.
> 
> For soft ECC fixup, we can calculate bitflips
> for each ECC sector, so I can fix the max_bitflips
> as the core framework expects.
> 
> For hard ECC fixup, the register only reports
> the number of corrected bit-flips
> in the whole page (sum from all ECC sectors).
> We cannot calculate max_bitflips, I think.
> 

That's unfortunate. This means you'll return -EUCLEAN more quickly
(which will trigger UBI eraseblock move), since the NAND framework is
basing its 'too many bitflips' detection logic on the max_bitflips per
ECC chunk and the bitflips threshold (by default 3/4 of the ECC
strength).

That doesn't mean it won't work, you'll just wear your NAND more
quickly :-(.

ITOH, doing max_bitflips = nbitflips / nsteps is not good either,
because the bitflips might be all concentrated in the same ECC chunk,
and in this case you really want to return -EUCLEAN.

> 
> 
> BTW, I noticed another problem of the current code.
> 
>   buf[offset] ^= err_correction_value;
>   mtd->ecc_stats.corrected++;
>   bitflips++;
> 
> This code is counting the number of corrected bytes,
> not the number of corrected bits.
> 
> 
> I think multiple bit-flips within one byte can happen.

Yes.

> 
> 
> Perhaps, we should add
> 
>   hweight8(buf[offset] ^ err_correction_value)
> 
> to ecc_stats.corrected and bitflips.
> 

Looks good.

Re: [PATCH 15/39] mtd: nand: denali: improve readability of handle_ecc()

[Masahiro Yamada]

Hi Boris,


2016-11-28 0:42 GMT+09:00 Boris Brezillon :
>> + if (err_byte < ECC_SECTOR_SIZE) {
>> + struct mtd_info *mtd =
>> + nand_to_mtd(>nand);
>> + int offset;
>> +
>> + offset = (err_sector * ECC_SECTOR_SIZE + 
>> err_byte) *
>> + denali->devnum + err_device;
>> + /* correct the ECC error */
>> + buf[offset] ^= err_correction_value;
>> + mtd->ecc_stats.corrected++;
>> + bitflips++;
>
> Hm, bitflips is what is set in max_bitflips, and apparently the
> implementation (which is not yours) is not doing what the core expects.
>
> You should first count bitflips per sector with something like that:
>
> bitflips[err_sector]++;
>
>
> And then once you've iterated over all errors do:
>
> for (i = 0; i < nsectors; i++)
> max_bitflips = max(bitflips[err_sector], max_bitflips);


I see.

For soft ECC fixup, we can calculate bitflips
for each ECC sector, so I can fix the max_bitflips
as the core framework expects.

For hard ECC fixup, the register only reports
the number of corrected bit-flips
in the whole page (sum from all ECC sectors).
We cannot calculate max_bitflips, I think.



BTW, I noticed another problem of the current code.

  buf[offset] ^= err_correction_value;
  mtd->ecc_stats.corrected++;
  bitflips++;

This code is counting the number of corrected bytes,
not the number of corrected bits.


I think multiple bit-flips within one byte can happen.


Perhaps, we should add

  hweight8(buf[offset] ^ err_correction_value)

to ecc_stats.corrected and bitflips.




-- 
Best Regards
Masahiro Yamada

Re: [PATCH 15/39] mtd: nand: denali: improve readability of handle_ecc()

[Masahiro Yamada]

Hi Boris,


2016-11-28 0:42 GMT+09:00 Boris Brezillon :
>> + if (err_byte < ECC_SECTOR_SIZE) {
>> + struct mtd_info *mtd =
>> + nand_to_mtd(>nand);
>> + int offset;
>> +
>> + offset = (err_sector * ECC_SECTOR_SIZE + 
>> err_byte) *
>> + denali->devnum + err_device;
>> + /* correct the ECC error */
>> + buf[offset] ^= err_correction_value;
>> + mtd->ecc_stats.corrected++;
>> + bitflips++;
>
> Hm, bitflips is what is set in max_bitflips, and apparently the
> implementation (which is not yours) is not doing what the core expects.
>
> You should first count bitflips per sector with something like that:
>
> bitflips[err_sector]++;
>
>
> And then once you've iterated over all errors do:
>
> for (i = 0; i < nsectors; i++)
> max_bitflips = max(bitflips[err_sector], max_bitflips);


I see.

For soft ECC fixup, we can calculate bitflips
for each ECC sector, so I can fix the max_bitflips
as the core framework expects.

For hard ECC fixup, the register only reports
the number of corrected bit-flips
in the whole page (sum from all ECC sectors).
We cannot calculate max_bitflips, I think.



BTW, I noticed another problem of the current code.

  buf[offset] ^= err_correction_value;
  mtd->ecc_stats.corrected++;
  bitflips++;

This code is counting the number of corrected bytes,
not the number of corrected bits.


I think multiple bit-flips within one byte can happen.


Perhaps, we should add

  hweight8(buf[offset] ^ err_correction_value)

to ecc_stats.corrected and bitflips.




-- 
Best Regards
Masahiro Yamada

Re: [PATCH 15/39] mtd: nand: denali: improve readability of handle_ecc()

[Boris Brezillon]

On Sun, 27 Nov 2016 03:06:01 +0900
Masahiro Yamada  wrote:

> This function is unreadable due to the deep nesting.  Note this
> function does a job only when INTR_STATUS__ECC_ERR is set.
> So, if the flag is not set, let it bail-out.
> 
> Signed-off-by: Masahiro Yamada 
> ---
> 
>  drivers/mtd/nand/denali.c | 119 
> +++---
>  1 file changed, 59 insertions(+), 60 deletions(-)
> 
> diff --git a/drivers/mtd/nand/denali.c b/drivers/mtd/nand/denali.c
> index a7dc692..b577560 100644
> --- a/drivers/mtd/nand/denali.c
> +++ b/drivers/mtd/nand/denali.c
> @@ -908,69 +908,68 @@ static bool handle_ecc(struct denali_nand_info *denali, 
> u8 *buf,
>  {
>   bool check_erased_page = false;
>   unsigned int bitflips = 0;
> + u32 err_address, err_correction_info, err_byte, err_sector, err_device,
> + err_correction_value;
>  
> - if (irq_status & INTR_STATUS__ECC_ERR) {
> - /* read the ECC errors. we'll ignore them for now */
> - u32 err_address, err_correction_info, err_byte,
> - err_sector, err_device, err_correction_value;
> - denali_set_intr_modes(denali, false);
> -
> - do {
> - err_address = ioread32(denali->flash_reg +
> - ECC_ERROR_ADDRESS);
> - err_sector = ECC_SECTOR(err_address);
> - err_byte = ECC_BYTE(err_address);
> -
> - err_correction_info = ioread32(denali->flash_reg +
> - ERR_CORRECTION_INFO);
> - err_correction_value =
> + if (!(irq_status & INTR_STATUS__ECC_ERR))
> + goto out;
> +
> + /* read the ECC errors. we'll ignore them for now */
> + denali_set_intr_modes(denali, false);
> +
> + do {
> + err_address = ioread32(denali->flash_reg + ECC_ERROR_ADDRESS);
> + err_sector = ECC_SECTOR(err_address);
> + err_byte = ECC_BYTE(err_address);
> +
> + err_correction_info = ioread32(denali->flash_reg +
> +ERR_CORRECTION_INFO);
> + err_correction_value =
>   ECC_CORRECTION_VALUE(err_correction_info);
> - err_device = ECC_ERR_DEVICE(err_correction_info);
> -
> - if (ECC_ERROR_CORRECTABLE(err_correction_info)) {
> - /*
> -  * If err_byte is larger than ECC_SECTOR_SIZE,
> -  * means error happened in OOB, so we ignore
> -  * it. It's no need for us to correct it
> -  * err_device is represented the NAND error
> -  * bits are happened in if there are more
> -  * than one NAND connected.
> -  */
> - if (err_byte < ECC_SECTOR_SIZE) {
> - struct mtd_info *mtd =
> - nand_to_mtd(>nand);
> - int offset;
> -
> - offset = (err_sector *
> - ECC_SECTOR_SIZE +
> - err_byte) *
> - denali->devnum +
> - err_device;
> - /* correct the ECC error */
> - buf[offset] ^= err_correction_value;
> - mtd->ecc_stats.corrected++;
> - bitflips++;
> - }
> - } else {
> - /*
> -  * if the error is not correctable, need to
> -  * look at the page to see if it is an erased
> -  * page. if so, then it's not a real ECC error
> -  */
> - check_erased_page = true;
> + err_device = ECC_ERR_DEVICE(err_correction_info);
> +
> + if (ECC_ERROR_CORRECTABLE(err_correction_info)) {
> + /*
> +  * If err_byte is larger than ECC_SECTOR_SIZE, means 
> error
> +  * happened in OOB, so we ignore it. It's no need for
> +  * us to correct it err_device is represented the NAND
> +  * error bits are happened in if there are more than
> +  * one NAND connected.
> +  */
> + if (err_byte < ECC_SECTOR_SIZE) {
> + struct mtd_info *mtd =
> + 

Re: [PATCH 15/39] mtd: nand: denali: improve readability of handle_ecc()

[Boris Brezillon]

On Sun, 27 Nov 2016 03:06:01 +0900
Masahiro Yamada  wrote:

> This function is unreadable due to the deep nesting.  Note this
> function does a job only when INTR_STATUS__ECC_ERR is set.
> So, if the flag is not set, let it bail-out.
> 
> Signed-off-by: Masahiro Yamada 
> ---
> 
>  drivers/mtd/nand/denali.c | 119 
> +++---
>  1 file changed, 59 insertions(+), 60 deletions(-)
> 
> diff --git a/drivers/mtd/nand/denali.c b/drivers/mtd/nand/denali.c
> index a7dc692..b577560 100644
> --- a/drivers/mtd/nand/denali.c
> +++ b/drivers/mtd/nand/denali.c
> @@ -908,69 +908,68 @@ static bool handle_ecc(struct denali_nand_info *denali, 
> u8 *buf,
>  {
>   bool check_erased_page = false;
>   unsigned int bitflips = 0;
> + u32 err_address, err_correction_info, err_byte, err_sector, err_device,
> + err_correction_value;
>  
> - if (irq_status & INTR_STATUS__ECC_ERR) {
> - /* read the ECC errors. we'll ignore them for now */
> - u32 err_address, err_correction_info, err_byte,
> - err_sector, err_device, err_correction_value;
> - denali_set_intr_modes(denali, false);
> -
> - do {
> - err_address = ioread32(denali->flash_reg +
> - ECC_ERROR_ADDRESS);
> - err_sector = ECC_SECTOR(err_address);
> - err_byte = ECC_BYTE(err_address);
> -
> - err_correction_info = ioread32(denali->flash_reg +
> - ERR_CORRECTION_INFO);
> - err_correction_value =
> + if (!(irq_status & INTR_STATUS__ECC_ERR))
> + goto out;
> +
> + /* read the ECC errors. we'll ignore them for now */
> + denali_set_intr_modes(denali, false);
> +
> + do {
> + err_address = ioread32(denali->flash_reg + ECC_ERROR_ADDRESS);
> + err_sector = ECC_SECTOR(err_address);
> + err_byte = ECC_BYTE(err_address);
> +
> + err_correction_info = ioread32(denali->flash_reg +
> +ERR_CORRECTION_INFO);
> + err_correction_value =
>   ECC_CORRECTION_VALUE(err_correction_info);
> - err_device = ECC_ERR_DEVICE(err_correction_info);
> -
> - if (ECC_ERROR_CORRECTABLE(err_correction_info)) {
> - /*
> -  * If err_byte is larger than ECC_SECTOR_SIZE,
> -  * means error happened in OOB, so we ignore
> -  * it. It's no need for us to correct it
> -  * err_device is represented the NAND error
> -  * bits are happened in if there are more
> -  * than one NAND connected.
> -  */
> - if (err_byte < ECC_SECTOR_SIZE) {
> - struct mtd_info *mtd =
> - nand_to_mtd(>nand);
> - int offset;
> -
> - offset = (err_sector *
> - ECC_SECTOR_SIZE +
> - err_byte) *
> - denali->devnum +
> - err_device;
> - /* correct the ECC error */
> - buf[offset] ^= err_correction_value;
> - mtd->ecc_stats.corrected++;
> - bitflips++;
> - }
> - } else {
> - /*
> -  * if the error is not correctable, need to
> -  * look at the page to see if it is an erased
> -  * page. if so, then it's not a real ECC error
> -  */
> - check_erased_page = true;
> + err_device = ECC_ERR_DEVICE(err_correction_info);
> +
> + if (ECC_ERROR_CORRECTABLE(err_correction_info)) {
> + /*
> +  * If err_byte is larger than ECC_SECTOR_SIZE, means 
> error
> +  * happened in OOB, so we ignore it. It's no need for
> +  * us to correct it err_device is represented the NAND
> +  * error bits are happened in if there are more than
> +  * one NAND connected.
> +  */
> + if (err_byte < ECC_SECTOR_SIZE) {
> + struct mtd_info *mtd =
> + nand_to_mtd(>nand);
> +   

Re: [PATCH 15/39] mtd: nand: denali: improve readability of handle_ecc()

[Boris Brezillon]

On Sun, 27 Nov 2016 03:06:01 +0900
Masahiro Yamada  wrote:

> This function is unreadable due to the deep nesting.  Note this
> function does a job only when INTR_STATUS__ECC_ERR is set.
> So, if the flag is not set, let it bail-out.
> 
> Signed-off-by: Masahiro Yamada 
> ---
> 
>  drivers/mtd/nand/denali.c | 119 
> +++---
>  1 file changed, 59 insertions(+), 60 deletions(-)
> 
> diff --git a/drivers/mtd/nand/denali.c b/drivers/mtd/nand/denali.c
> index a7dc692..b577560 100644
> --- a/drivers/mtd/nand/denali.c
> +++ b/drivers/mtd/nand/denali.c
> @@ -908,69 +908,68 @@ static bool handle_ecc(struct denali_nand_info *denali, 
> u8 *buf,
>  {
>   bool check_erased_page = false;
>   unsigned int bitflips = 0;
> + u32 err_address, err_correction_info, err_byte, err_sector, err_device,
> + err_correction_value;

Please use single line definitions for local variables:

u32 err_address, err_correction_info, err_byte, err_sector;
u32 err_device, err_correction_value;

Also, maybe you should use shorter names to avoid 80 chars wrapping as
much as possible.

>  
> - if (irq_status & INTR_STATUS__ECC_ERR) {
> - /* read the ECC errors. we'll ignore them for now */
> - u32 err_address, err_correction_info, err_byte,
> - err_sector, err_device, err_correction_value;
> - denali_set_intr_modes(denali, false);
> -
> - do {
> - err_address = ioread32(denali->flash_reg +
> - ECC_ERROR_ADDRESS);
> - err_sector = ECC_SECTOR(err_address);
> - err_byte = ECC_BYTE(err_address);
> -
> - err_correction_info = ioread32(denali->flash_reg +
> - ERR_CORRECTION_INFO);
> - err_correction_value =
> + if (!(irq_status & INTR_STATUS__ECC_ERR))
> + goto out;
> +
> + /* read the ECC errors. we'll ignore them for now */
> + denali_set_intr_modes(denali, false);
> +
> + do {
> + err_address = ioread32(denali->flash_reg + ECC_ERROR_ADDRESS);
> + err_sector = ECC_SECTOR(err_address);
> + err_byte = ECC_BYTE(err_address);
> +
> + err_correction_info = ioread32(denali->flash_reg +
> +ERR_CORRECTION_INFO);
> + err_correction_value =
>   ECC_CORRECTION_VALUE(err_correction_info);
> - err_device = ECC_ERR_DEVICE(err_correction_info);
> -
> - if (ECC_ERROR_CORRECTABLE(err_correction_info)) {
> - /*
> -  * If err_byte is larger than ECC_SECTOR_SIZE,
> -  * means error happened in OOB, so we ignore
> -  * it. It's no need for us to correct it
> -  * err_device is represented the NAND error
> -  * bits are happened in if there are more
> -  * than one NAND connected.
> -  */
> - if (err_byte < ECC_SECTOR_SIZE) {
> - struct mtd_info *mtd =
> - nand_to_mtd(>nand);
> - int offset;
> -
> - offset = (err_sector *
> - ECC_SECTOR_SIZE +
> - err_byte) *
> - denali->devnum +
> - err_device;
> - /* correct the ECC error */
> - buf[offset] ^= err_correction_value;
> - mtd->ecc_stats.corrected++;
> - bitflips++;
> - }
> - } else {
> - /*
> -  * if the error is not correctable, need to
> -  * look at the page to see if it is an erased
> -  * page. if so, then it's not a real ECC error
> -  */
> - check_erased_page = true;
> + err_device = ECC_ERR_DEVICE(err_correction_info);
> +
> + if (ECC_ERROR_CORRECTABLE(err_correction_info)) {
> + /*
> +  * If err_byte is larger than ECC_SECTOR_SIZE, means 
> error
> +  * happened in OOB, so we ignore it. It's no need for
> +  * us to correct it err_device is represented the NAND
> +   

Re: [PATCH 15/39] mtd: nand: denali: improve readability of handle_ecc()

[Boris Brezillon]

On Sun, 27 Nov 2016 03:06:01 +0900
Masahiro Yamada  wrote:

> This function is unreadable due to the deep nesting.  Note this
> function does a job only when INTR_STATUS__ECC_ERR is set.
> So, if the flag is not set, let it bail-out.
> 
> Signed-off-by: Masahiro Yamada 
> ---
> 
>  drivers/mtd/nand/denali.c | 119 
> +++---
>  1 file changed, 59 insertions(+), 60 deletions(-)
> 
> diff --git a/drivers/mtd/nand/denali.c b/drivers/mtd/nand/denali.c
> index a7dc692..b577560 100644
> --- a/drivers/mtd/nand/denali.c
> +++ b/drivers/mtd/nand/denali.c
> @@ -908,69 +908,68 @@ static bool handle_ecc(struct denali_nand_info *denali, 
> u8 *buf,
>  {
>   bool check_erased_page = false;
>   unsigned int bitflips = 0;
> + u32 err_address, err_correction_info, err_byte, err_sector, err_device,
> + err_correction_value;

Please use single line definitions for local variables:

u32 err_address, err_correction_info, err_byte, err_sector;
u32 err_device, err_correction_value;

Also, maybe you should use shorter names to avoid 80 chars wrapping as
much as possible.

>  
> - if (irq_status & INTR_STATUS__ECC_ERR) {
> - /* read the ECC errors. we'll ignore them for now */
> - u32 err_address, err_correction_info, err_byte,
> - err_sector, err_device, err_correction_value;
> - denali_set_intr_modes(denali, false);
> -
> - do {
> - err_address = ioread32(denali->flash_reg +
> - ECC_ERROR_ADDRESS);
> - err_sector = ECC_SECTOR(err_address);
> - err_byte = ECC_BYTE(err_address);
> -
> - err_correction_info = ioread32(denali->flash_reg +
> - ERR_CORRECTION_INFO);
> - err_correction_value =
> + if (!(irq_status & INTR_STATUS__ECC_ERR))
> + goto out;
> +
> + /* read the ECC errors. we'll ignore them for now */
> + denali_set_intr_modes(denali, false);
> +
> + do {
> + err_address = ioread32(denali->flash_reg + ECC_ERROR_ADDRESS);
> + err_sector = ECC_SECTOR(err_address);
> + err_byte = ECC_BYTE(err_address);
> +
> + err_correction_info = ioread32(denali->flash_reg +
> +ERR_CORRECTION_INFO);
> + err_correction_value =
>   ECC_CORRECTION_VALUE(err_correction_info);
> - err_device = ECC_ERR_DEVICE(err_correction_info);
> -
> - if (ECC_ERROR_CORRECTABLE(err_correction_info)) {
> - /*
> -  * If err_byte is larger than ECC_SECTOR_SIZE,
> -  * means error happened in OOB, so we ignore
> -  * it. It's no need for us to correct it
> -  * err_device is represented the NAND error
> -  * bits are happened in if there are more
> -  * than one NAND connected.
> -  */
> - if (err_byte < ECC_SECTOR_SIZE) {
> - struct mtd_info *mtd =
> - nand_to_mtd(>nand);
> - int offset;
> -
> - offset = (err_sector *
> - ECC_SECTOR_SIZE +
> - err_byte) *
> - denali->devnum +
> - err_device;
> - /* correct the ECC error */
> - buf[offset] ^= err_correction_value;
> - mtd->ecc_stats.corrected++;
> - bitflips++;
> - }
> - } else {
> - /*
> -  * if the error is not correctable, need to
> -  * look at the page to see if it is an erased
> -  * page. if so, then it's not a real ECC error
> -  */
> - check_erased_page = true;
> + err_device = ECC_ERR_DEVICE(err_correction_info);
> +
> + if (ECC_ERROR_CORRECTABLE(err_correction_info)) {
> + /*
> +  * If err_byte is larger than ECC_SECTOR_SIZE, means 
> error
> +  * happened in OOB, so we ignore it. It's no need for
> +  * us to correct it err_device is represented the NAND
> +  * error bits are happened in if there are more