Re: [PATCH] x86: add a crc32 checksum to the kernel image.
Ian Campbell wrote: On Tue, 2008-02-05 at 17:09 -0800, Randy Dunlap wrote: On Fri, 01 Feb 2008 09:02:48 + Ian Campbell wrote: + THE IMAGE CHECKSUM + +The CRC-32 is calculated over the entire file using an initial +remainder of 0x. The checksum is appended to the file Run-on sentences. Use period (full stop) or semi-colon at end of above sentence. If using a period, capitalize the next word. Thanks. +therefore the CRC of the file up to the limit specified in the syssize +field of the header is always 0. Thanks. I went with: +The CRC-32 is calculated over the entire file using an initial +remainder of 0x. The checksum is appended to the file; +therefore the CRC of the file up to the limit specified in the syssize +field of the header is always 0. Fine, thanks. -- ~Randy -- To unsubscribe from this list: send the line "unsubscribe linux-kernel" in the body of a message to [EMAIL PROTECTED] More majordomo info at http://vger.kernel.org/majordomo-info.html Please read the FAQ at http://www.tux.org/lkml/
Re: [PATCH] x86: add a crc32 checksum to the kernel image.
On Tue, 2008-02-05 at 17:09 -0800, Randy Dunlap wrote: > On Fri, 01 Feb 2008 09:02:48 + Ian Campbell wrote: > > > > + THE IMAGE CHECKSUM > > + > > +The CRC-32 is calculated over the entire file using an initial > > +remainder of 0x. The checksum is appended to the file > > Run-on sentences. > Use period (full stop) or semi-colon at end of above sentence. > If using a period, capitalize the next word. Thanks. > > > > +therefore the CRC of the file up to the limit specified in the syssize > > +field of the header is always 0. Thanks. I went with: +The CRC-32 is calculated over the entire file using an initial +remainder of 0x. The checksum is appended to the file; +therefore the CRC of the file up to the limit specified in the syssize +field of the header is always 0. -- Ian Campbell If the master dies and the disciple grieves, the lives of both have been wasted. -- To unsubscribe from this list: send the line "unsubscribe linux-kernel" in the body of a message to [EMAIL PROTECTED] More majordomo info at http://vger.kernel.org/majordomo-info.html Please read the FAQ at http://www.tux.org/lkml/
Re: [PATCH] x86: add a crc32 checksum to the kernel image.
On Fri, 01 Feb 2008 09:02:48 + Ian Campbell wrote: > --- > >From 1c614383dc9cb0c7791ebab386dc012db336b28c Mon Sep 17 00:00:00 2001 > From: Ian Campbell <[EMAIL PROTECTED]> > Date: Fri, 1 Feb 2008 09:01:22 +0000 > Subject: [PATCH] x86: add a crc32 checksum to the kernel image. > > Signed-off-by: Ian Campbell <[EMAIL PROTECTED]> > Cc: Thomas Gleixner <[EMAIL PROTECTED]> > Cc: Ingo Molnar <[EMAIL PROTECTED]> > Cc: H. Peter Anvin <[EMAIL PROTECTED]> > --- > Documentation/i386/boot.txt |7 +++ > arch/x86/boot/tools/build.c | 88 > ++- > 2 files changed, 94 insertions(+), 1 deletions(-) > > diff --git a/Documentation/i386/boot.txt b/Documentation/i386/boot.txt > index b5f5ba1..f853d49 100644 > --- a/Documentation/i386/boot.txt > +++ b/Documentation/i386/boot.txt > @@ -531,6 +531,13 @@ Protocol:2.08+ > >The length of the compressed payload. > > + THE IMAGE CHECKSUM > + > +The CRC-32 is calculated over the entire file using an initial > +remainder of 0x. The checksum is appended to the file Run-on sentences. Use period (full stop) or semi-colon at end of above sentence. If using a period, capitalize the next word. Thanks. > +therefore the CRC of the file up to the limit specified in the syssize > +field of the header is always 0. > + > THE KERNEL COMMAND LINE > > The kernel command line has become an important way for the boot --- ~Randy -- To unsubscribe from this list: send the line "unsubscribe linux-kernel" in the body of a message to [EMAIL PROTECTED] More majordomo info at http://vger.kernel.org/majordomo-info.html Please read the FAQ at http://www.tux.org/lkml/
Re: [PATCH] x86: add a crc32 checksum to the kernel image.
* Ian Campbell <[EMAIL PROTECTED]> wrote: > > * Please don't use "unsigned long" to represent a 32-bit number. > > Fixed. thanks, applied. Ingo -- To unsubscribe from this list: send the line "unsubscribe linux-kernel" in the body of a message to [EMAIL PROTECTED] More majordomo info at http://vger.kernel.org/majordomo-info.html Please read the FAQ at http://www.tux.org/lkml/
Re: [PATCH] x86: add a crc32 checksum to the kernel image.
On Thu, 2008-01-31 at 17:16 -0800, H. Peter Anvin wrote: > David Newall wrote: > > Isn't a crc32 calculation already defined? Yes; in lib/crc32.c. One is > > surely enough. > > As long as it can be included in user-space code we should use that one. I don't think it can. There is a main function surrounded by #ifdef UNITTEST which might once have worked but now there is far too much kernel gunk in there (as you might expect). If I can work up the enthusiasm I might break out the core algorithm into a separate file that can be used in both the kernel and userspace. Ian. -- Ian Campbell Current Noise: Reverend Bizarre - Cirith Ungol "Would I turn on the gas if my pal Mugsy were in there?" "You might, rabbit, you might!" -- Looney Tunes, Bugs and Thugs (1954, Friz Freleng) -- To unsubscribe from this list: send the line "unsubscribe linux-kernel" in the body of a message to [EMAIL PROTECTED] More majordomo info at http://vger.kernel.org/majordomo-info.html Please read the FAQ at http://www.tux.org/lkml/
Re: [PATCH] x86: add a crc32 checksum to the kernel image.
On Thu, 2008-01-31 at 14:10 -0800, H. Peter Anvin wrote:
> Hm. I have some minor concerns about this:
>
> * The classical length field is only available in multiples of 16 (I
> realize your patches change that to some degree, but I'd hate to make
> the guarantee that the image payload is the last thing in the image --
> it loses flexibility for the future.) The end of the image isn't
> available in all cases, so this would require padding it out to a
> 16-byte boundary before appending the CRC32. An mmap is guaranteed to
> be zero-padded out to the next page boundary, so explicitly rounding sz
> up (instead of when calculating sys_size) should do the job.
Peter in a followup mail:
> Thinking about this more carefully, we should probably have it rounded
> up to a 16-byte boundary *including* the CRC32, so the CRC32 is
> included in the notional image.
Agreed.
Peter in the first mail again:
> * I believe it is recommended to store the inverse of the crc32, not the
> crc32 itself - it catches more errors. This is also the reason to start
> out with ~0 rather than 0.
If you store the inverted checksum then the complete file will always
sum to 0xdebb20e3 rather than zero.
However I'm told that inverting the checksum only protects extra zeroes
after the CRC. Given that we checksum over a known length and don't
especially care about trailing zeroes in any case I think it is nicer if
the file checksums to zero.
> * Please don't use "unsigned long" to represent a 32-bit number.
Fixed.
---
>From 1c614383dc9cb0c7791ebab386dc012db336b28c Mon Sep 17 00:00:00 2001
From: Ian Campbell <[EMAIL PROTECTED]>
Date: Fri, 1 Feb 2008 09:01:22 +
Subject: [PATCH] x86: add a crc32 checksum to the kernel image.
Signed-off-by: Ian Campbell <[EMAIL PROTECTED]>
Cc: Thomas Gleixner <[EMAIL PROTECTED]>
Cc: Ingo Molnar <[EMAIL PROTECTED]>
Cc: H. Peter Anvin <[EMAIL PROTECTED]>
---
Documentation/i386/boot.txt |7 +++
arch/x86/boot/tools/build.c | 88 ++-
2 files changed, 94 insertions(+), 1 deletions(-)
diff --git a/Documentation/i386/boot.txt b/Documentation/i386/boot.txt
index b5f5ba1..f853d49 100644
--- a/Documentation/i386/boot.txt
+++ b/Documentation/i386/boot.txt
@@ -531,6 +531,13 @@ Protocol: 2.08+
The length of the compressed payload.
+ THE IMAGE CHECKSUM
+
+The CRC-32 is calculated over the entire file using an initial
+remainder of 0x. The checksum is appended to the file
+therefore the CRC of the file up to the limit specified in the syssize
+field of the header is always 0.
+
THE KERNEL COMMAND LINE
The kernel command line has become an important way for the boot
diff --git a/arch/x86/boot/tools/build.c b/arch/x86/boot/tools/build.c
index b424874..2ba22e8 100644
--- a/arch/x86/boot/tools/build.c
+++ b/arch/x86/boot/tools/build.c
@@ -50,6 +50,75 @@ typedef unsigned long u32;
u8 buf[SETUP_SECT_MAX*512];
int is_big_kernel;
+/*--*/
+
+static const unsigned int crctab32[] = {
+ 0xU, 0x77073096U, 0xee0e612cU, 0x990951baU, 0x076dc419U,
+ 0x706af48fU, 0xe963a535U, 0x9e6495a3U, 0x0edb8832U, 0x79dcb8a4U,
+ 0xe0d5e91eU, 0x97d2d988U, 0x09b64c2bU, 0x7eb17cbdU, 0xe7b82d07U,
+ 0x90bf1d91U, 0x1db71064U, 0x6ab020f2U, 0xf3b97148U, 0x84be41deU,
+ 0x1adad47dU, 0x6ddde4ebU, 0xf4d4b551U, 0x83d385c7U, 0x136c9856U,
+ 0x646ba8c0U, 0xfd62f97aU, 0x8a65c9ecU, 0x14015c4fU, 0x63066cd9U,
+ 0xfa0f3d63U, 0x8d080df5U, 0x3b6e20c8U, 0x4c69105eU, 0xd56041e4U,
+ 0xa2677172U, 0x3c03e4d1U, 0x4b04d447U, 0xd20d85fdU, 0xa50ab56bU,
+ 0x35b5a8faU, 0x42b2986cU, 0xdbbbc9d6U, 0xacbcf940U, 0x32d86ce3U,
+ 0x45df5c75U, 0xdcd60dcfU, 0xabd13d59U, 0x26d930acU, 0x51de003aU,
+ 0xc8d75180U, 0xbfd06116U, 0x21b4f4b5U, 0x56b3c423U, 0xcfba9599U,
+ 0xb8bda50fU, 0x2802b89eU, 0x5f058808U, 0xc60cd9b2U, 0xb10be924U,
+ 0x2f6f7c87U, 0x58684c11U, 0xc1611dabU, 0xb6662d3dU, 0x76dc4190U,
+ 0x01db7106U, 0x98d220bcU, 0xefd5102aU, 0x71b18589U, 0x06b6b51fU,
+ 0x9fbfe4a5U, 0xe8b8d433U, 0x7807c9a2U, 0x0f00f934U, 0x9609a88eU,
+ 0xe10e9818U, 0x7f6a0dbbU, 0x086d3d2dU, 0x91646c97U, 0xe6635c01U,
+ 0x6b6b51f4U, 0x1c6c6162U, 0x856530d8U, 0xf262004eU, 0x6c0695edU,
+ 0x1b01a57bU, 0x8208f4c1U, 0xf50fc457U, 0x65b0d9c6U, 0x12b7e950U,
+ 0x8bbeb8eaU, 0xfcb9887cU, 0x62dd1ddfU, 0x15da2d49U, 0x8cd37cf3U,
+ 0xfbd44c65U, 0x4db26158U, 0x3ab551ceU, 0xa3bc0074U, 0xd4bb30e2U,
+ 0x4adfa541U, 0x3dd895d7U, 0xa4d1c46dU, 0xd3d6f4fbU, 0x4369e96aU,
+ 0x346ed9fcU, 0xad678846U, 0xda60b8d0U, 0x44042d73U, 0x33031de5U,
+ 0xaa0a4c5fU, 0xdd0d7cc9U, 0x5005713cU, 0x270241aaU, 0xbe0b1010U,
+ 0xc90c2086U, 0x5768b525U, 0x206f85b3U, 0xb966d409U, 0xce61e49fU,
+ 0x5edef90eU, 0x29d9c998U, 0xb0d09822U,
Re: [PATCH] x86: add a crc32 checksum to the kernel image.
H. Peter Anvin wrote: > David Newall wrote: >> Isn't a crc32 calculation already defined? Yes; in lib/crc32.c. One is >> surely enough. > > As long as it can be included in user-space code we should use that one. You're right. I misread the patch. I thought the calculation was being added to kernel code. -- To unsubscribe from this list: send the line "unsubscribe linux-kernel" in the body of a message to [EMAIL PROTECTED] More majordomo info at http://vger.kernel.org/majordomo-info.html Please read the FAQ at http://www.tux.org/lkml/
Re: [PATCH] x86: add a crc32 checksum to the kernel image.
David Newall wrote: Isn't a crc32 calculation already defined? Yes; in lib/crc32.c. One is surely enough. As long as it can be included in user-space code we should use that one. -hpa -- To unsubscribe from this list: send the line "unsubscribe linux-kernel" in the body of a message to [EMAIL PROTECTED] More majordomo info at http://vger.kernel.org/majordomo-info.html Please read the FAQ at http://www.tux.org/lkml/
Re: [PATCH] x86: add a crc32 checksum to the kernel image.
Isn't a crc32 calculation already defined? Yes; in lib/crc32.c. One is surely enough. -- To unsubscribe from this list: send the line "unsubscribe linux-kernel" in the body of a message to [EMAIL PROTECTED] More majordomo info at http://vger.kernel.org/majordomo-info.html Please read the FAQ at http://www.tux.org/lkml/
Re: [PATCH] x86: add a crc32 checksum to the kernel image.
H. Peter Anvin wrote: Hm. I have some minor concerns about this: * The classical length field is only available in multiples of 16 (I realize your patches change that to some degree, but I'd hate to make the guarantee that the image payload is the last thing in the image -- it loses flexibility for the future.) The end of the image isn't available in all cases, so this would require padding it out to a 16-byte boundary before appending the CRC32. An mmap is guaranteed to be zero-padded out to the next page boundary, so explicitly rounding sz up (instead of when calculating sys_size) should do the job. Thinking about this more carefully, we should probably have it rounded up to a 16-byte boundary *including* the CRC32, so the CRC32 is included in the notional image. -hpa -- To unsubscribe from this list: send the line "unsubscribe linux-kernel" in the body of a message to [EMAIL PROTECTED] More majordomo info at http://vger.kernel.org/majordomo-info.html Please read the FAQ at http://www.tux.org/lkml/
Re: [PATCH] x86: add a crc32 checksum to the kernel image.
Ian Campbell wrote: Signed-off-by: Ian Campbell <[EMAIL PROTECTED]> Cc: Thomas Gleixner <[EMAIL PROTECTED]> Cc: Ingo Molnar <[EMAIL PROTECTED]> Cc: H. Peter Anvin <[EMAIL PROTECTED]> --- Documentation/i386/boot.txt |5 +++ arch/x86/boot/tools/build.c | 78 +++ 2 files changed, 83 insertions(+), 0 deletions(-) diff --git a/Documentation/i386/boot.txt b/Documentation/i386/boot.txt index b5f5ba1..ad201f0 100644 --- a/Documentation/i386/boot.txt +++ b/Documentation/i386/boot.txt @@ -531,6 +531,11 @@ Protocol: 2.08+ The length of the compressed payload. + THE IMAGE CHECKSUM + +The CRC-32 checksum of the entire file is appended to the end of the +file. The CRC of the file including these trailing bytes is therefore 0. + Hm. I have some minor concerns about this: * The classical length field is only available in multiples of 16 (I realize your patches change that to some degree, but I'd hate to make the guarantee that the image payload is the last thing in the image -- it loses flexibility for the future.) The end of the image isn't available in all cases, so this would require padding it out to a 16-byte boundary before appending the CRC32. An mmap is guaranteed to be zero-padded out to the next page boundary, so explicitly rounding sz up (instead of when calculating sys_size) should do the job. * I believe it is recommended to store the inverse of the crc32, not the crc32 itself - it catches more errors. This is also the reason to start out with ~0 rather than 0. * Please don't use "unsigned long" to represent a 32-bit number. -hpa -- To unsubscribe from this list: send the line "unsubscribe linux-kernel" in the body of a message to [EMAIL PROTECTED] More majordomo info at http://vger.kernel.org/majordomo-info.html Please read the FAQ at http://www.tux.org/lkml/
[PATCH] x86: add a crc32 checksum to the kernel image.
Signed-off-by: Ian Campbell <[EMAIL PROTECTED]>
Cc: Thomas Gleixner <[EMAIL PROTECTED]>
Cc: Ingo Molnar <[EMAIL PROTECTED]>
Cc: H. Peter Anvin <[EMAIL PROTECTED]>
---
Documentation/i386/boot.txt |5 +++
arch/x86/boot/tools/build.c | 78 +++
2 files changed, 83 insertions(+), 0 deletions(-)
diff --git a/Documentation/i386/boot.txt b/Documentation/i386/boot.txt
index b5f5ba1..ad201f0 100644
--- a/Documentation/i386/boot.txt
+++ b/Documentation/i386/boot.txt
@@ -531,6 +531,11 @@ Protocol: 2.08+
The length of the compressed payload.
+ THE IMAGE CHECKSUM
+
+The CRC-32 checksum of the entire file is appended to the end of the
+file. The CRC of the file including these trailing bytes is therefore 0.
+
THE KERNEL COMMAND LINE
The kernel command line has become an important way for the boot
diff --git a/arch/x86/boot/tools/build.c b/arch/x86/boot/tools/build.c
index b424874..9c34032 100644
--- a/arch/x86/boot/tools/build.c
+++ b/arch/x86/boot/tools/build.c
@@ -50,6 +50,75 @@ typedef unsigned long u32;
u8 buf[SETUP_SECT_MAX*512];
int is_big_kernel;
+/*--*/
+
+static const unsigned int crctab32[] = {
+ 0xU, 0x77073096U, 0xee0e612cU, 0x990951baU, 0x076dc419U,
+ 0x706af48fU, 0xe963a535U, 0x9e6495a3U, 0x0edb8832U, 0x79dcb8a4U,
+ 0xe0d5e91eU, 0x97d2d988U, 0x09b64c2bU, 0x7eb17cbdU, 0xe7b82d07U,
+ 0x90bf1d91U, 0x1db71064U, 0x6ab020f2U, 0xf3b97148U, 0x84be41deU,
+ 0x1adad47dU, 0x6ddde4ebU, 0xf4d4b551U, 0x83d385c7U, 0x136c9856U,
+ 0x646ba8c0U, 0xfd62f97aU, 0x8a65c9ecU, 0x14015c4fU, 0x63066cd9U,
+ 0xfa0f3d63U, 0x8d080df5U, 0x3b6e20c8U, 0x4c69105eU, 0xd56041e4U,
+ 0xa2677172U, 0x3c03e4d1U, 0x4b04d447U, 0xd20d85fdU, 0xa50ab56bU,
+ 0x35b5a8faU, 0x42b2986cU, 0xdbbbc9d6U, 0xacbcf940U, 0x32d86ce3U,
+ 0x45df5c75U, 0xdcd60dcfU, 0xabd13d59U, 0x26d930acU, 0x51de003aU,
+ 0xc8d75180U, 0xbfd06116U, 0x21b4f4b5U, 0x56b3c423U, 0xcfba9599U,
+ 0xb8bda50fU, 0x2802b89eU, 0x5f058808U, 0xc60cd9b2U, 0xb10be924U,
+ 0x2f6f7c87U, 0x58684c11U, 0xc1611dabU, 0xb6662d3dU, 0x76dc4190U,
+ 0x01db7106U, 0x98d220bcU, 0xefd5102aU, 0x71b18589U, 0x06b6b51fU,
+ 0x9fbfe4a5U, 0xe8b8d433U, 0x7807c9a2U, 0x0f00f934U, 0x9609a88eU,
+ 0xe10e9818U, 0x7f6a0dbbU, 0x086d3d2dU, 0x91646c97U, 0xe6635c01U,
+ 0x6b6b51f4U, 0x1c6c6162U, 0x856530d8U, 0xf262004eU, 0x6c0695edU,
+ 0x1b01a57bU, 0x8208f4c1U, 0xf50fc457U, 0x65b0d9c6U, 0x12b7e950U,
+ 0x8bbeb8eaU, 0xfcb9887cU, 0x62dd1ddfU, 0x15da2d49U, 0x8cd37cf3U,
+ 0xfbd44c65U, 0x4db26158U, 0x3ab551ceU, 0xa3bc0074U, 0xd4bb30e2U,
+ 0x4adfa541U, 0x3dd895d7U, 0xa4d1c46dU, 0xd3d6f4fbU, 0x4369e96aU,
+ 0x346ed9fcU, 0xad678846U, 0xda60b8d0U, 0x44042d73U, 0x33031de5U,
+ 0xaa0a4c5fU, 0xdd0d7cc9U, 0x5005713cU, 0x270241aaU, 0xbe0b1010U,
+ 0xc90c2086U, 0x5768b525U, 0x206f85b3U, 0xb966d409U, 0xce61e49fU,
+ 0x5edef90eU, 0x29d9c998U, 0xb0d09822U, 0xc7d7a8b4U, 0x59b33d17U,
+ 0x2eb40d81U, 0xb7bd5c3bU, 0xc0ba6cadU, 0xedb88320U, 0x9abfb3b6U,
+ 0x03b6e20cU, 0x74b1d29aU, 0xead54739U, 0x9dd277afU, 0x04db2615U,
+ 0x73dc1683U, 0xe3630b12U, 0x94643b84U, 0x0d6d6a3eU, 0x7a6a5aa8U,
+ 0xe40ecf0bU, 0x9309ff9dU, 0x0a00ae27U, 0x7d079eb1U, 0xf00f9344U,
+ 0x8708a3d2U, 0x1e01f268U, 0x6906c2feU, 0xf762575dU, 0x806567cbU,
+ 0x196c3671U, 0x6e6b06e7U, 0xfed41b76U, 0x89d32be0U, 0x10da7a5aU,
+ 0x67dd4accU, 0xf9b9df6fU, 0x8ebeeff9U, 0x17b7be43U, 0x60b08ed5U,
+ 0xd6d6a3e8U, 0xa1d1937eU, 0x38d8c2c4U, 0x4fdff252U, 0xd1bb67f1U,
+ 0xa6bc5767U, 0x3fb506ddU, 0x48b2364bU, 0xd80d2bdaU, 0xaf0a1b4cU,
+ 0x36034af6U, 0x41047a60U, 0xdf60efc3U, 0xa867df55U, 0x316e8eefU,
+ 0x4669be79U, 0xcb61b38cU, 0xbc66831aU, 0x256fd2a0U, 0x5268e236U,
+ 0xcc0c7795U, 0xbb0b4703U, 0x220216b9U, 0x5505262fU, 0xc5ba3bbeU,
+ 0xb2bd0b28U, 0x2bb45a92U, 0x5cb36a04U, 0xc2d7ffa7U, 0xb5d0cf31U,
+ 0x2cd99e8bU, 0x5bdeae1dU, 0x9b64c2b0U, 0xec63f226U, 0x756aa39cU,
+ 0x026d930aU, 0x9c0906a9U, 0xeb0e363fU, 0x72076785U, 0x05005713U,
+ 0x95bf4a82U, 0xe2b87a14U, 0x7bb12baeU, 0x0cb61b38U, 0x92d28e9bU,
+ 0xe5d5be0dU, 0x7cdcefb7U, 0x0bdbdf21U, 0x86d3d2d4U, 0xf1d4e242U,
+ 0x68ddb3f8U, 0x1fda836eU, 0x81be16cdU, 0xf6b9265bU, 0x6fb077e1U,
+ 0x18b74777U, 0x88085ae6U, 0xff0f6a70U, 0x66063bcaU, 0x11010b5cU,
+ 0x8f659effU, 0xf862ae69U, 0x616bffd3U, 0x166ccf45U, 0xa00ae278U,
+ 0xd70dd2eeU, 0x4e048354U, 0x3903b3c2U, 0xa7672661U, 0xd06016f7U,
+ 0x4969474dU, 0x3e6e77dbU, 0xaed16a4aU, 0xd9d65adcU, 0x40df0b66U,
+ 0x37d83bf0U, 0xa9bcae53U, 0xdebb9ec5U, 0x47b2cf7fU, 0x30b5ffe9U,
+ 0xbdbdf21cU, 0xcabac28aU, 0x53b39330U, 0x24b4a3a6U, 0xbad03605U,
+ 0xcdd70693U, 0x54de5729U, 0x23d967bfU, 0xb3667a2eU, 0xc4614ab8U,
+ 0x5d681b02U, 0x2a6f2b94U, 0xb40bbe37U, 0xc30c8ea1U, 0x5a05df1bU,
+ 0x2d02ef8dU
+};
+
+
