[PATCH] grub-mkconfig linux: Fix quadratic algorithm for sorting menu items

[PATCH] grub-mkconfig linux: Fix quadratic algorithm for sorting menu items

[Mathieu Desnoyers]

The current implementation of the 10_linux script implements its menu
items sorting in bash with a quadratic algorithm, calling "sed", "sort",
head, and grep to compare versions between individual lines, which is
annoyingly slow for kernel developers who can easily end up with 50-100
kernels in /boot.

As an example, on a Intel(R) Core(TM) i7-8650U CPU @ 1.90GHz, running:

  /usr/sbin/grub-mkconfig > /dev/null

With 44 kernels in /boot, this command takes 10-15 seconds to complete.
After this fix, the same command runs in 5 seconds.

With 116 kernels in /boot, this command takes 40 seconds to complete.
After this fix, the same command runs in 8 seconds.

For reference, the quadratic algorithm here is:

while [ "x$list" != "x" ] ; do      <--- outer loop
  linux=`version_find_latest $list`
    version_find_latest()
      for i in "$@" ; do            <--- inner loop
        version_test_gt()
          fork+exec sed
            version_test_numeric()
              version_sort
                fork+exec sort
              fork+exec head -n 1
              fork+exec grep
  list=`echo $list | tr ' ' '\n' | fgrep -vx "$linux" | tr '\n' ' '`
    tr
    fgrep
    tr

So all commands executed under version_test_gt() are executed
O(n^2) times where n is the number of kernel images in /boot.

I notice that the same quadratic sorting is done for other supported
OSes, so I suspect similar gains can be obtained there, but I limit the
scope of this patch to Linux because this is the platform on which I can
test.

Signed-off-by: Mathieu Desnoyers <mathieu.desnoyers@efficios.com>
---
 util/grub-mkconfig_lib.in | 18 ++++++++++++++++++
 util/grub.d/10_linux.in   | 12 ++++++++----
 2 files changed, 26 insertions(+), 4 deletions(-)

diff --git a/util/grub-mkconfig_lib.in b/util/grub-mkconfig_lib.in
index 301d1ac22..f1a09f4c9 100644
--- a/util/grub-mkconfig_lib.in
+++ b/util/grub-mkconfig_lib.in
@@ -218,6 +218,24 @@ version_sort ()
    esac
 }
 
+version_reverse_sort ()
+{
+  case $version_reverse_sort_sort_has_v in
+    yes)
+      LC_ALL=C sort -r -V;;
+    no)
+      LC_ALL=C sort -r -n;;
+    *)
+      if sort -r -V </dev/null > /dev/null 2>&1; then
+        version_reverse_sort_sort_has_v=yes
+        LC_ALL=C sort -r -V
+      else
+        version_reverse_sort_sort_has_v=no
+        LC_ALL=C sort -r -n
+      fi;;
+   esac
+}
+
 version_test_numeric ()
 {
   version_test_numeric_a="$1"
diff --git a/util/grub.d/10_linux.in b/util/grub.d/10_linux.in
index ca068038e..23d4bb741 100644
--- a/util/grub.d/10_linux.in
+++ b/util/grub.d/10_linux.in
@@ -195,9 +195,15 @@ title_correction_code=
 # yet, so it's empty. In a submenu it will be equal to '\t' (one tab).
 submenu_indentation=""
 
+# Perform a reverse version sort on the entire list.
+# Temporarily replace the '.old' suffix by ' 1' and append ' 2' for all
+# other files to order the '.old' files after their non-old counterpart
+# in reverse-sorted order.
+
+reverse_sorted_list=$(echo $list | tr ' ' '\n' | sed -e 's/$/ 2/' | sed -e 's/.old 2/ 1/' | version_reverse_sort | sed 's/ 1$/.old/' | sed 's/ 2$//')
+
 is_top_level=true
-while [ "x$list" != "x" ] ; do
-  linux=`version_find_latest $list`
+for linux in $reverse_sorted_list; do
   gettext_printf "Found linux image: %s\n" "$linux" >&2
   basename=`basename $linux`
   dirname=`dirname $linux`
@@ -293,8 +299,6 @@ while [ "x$list" != "x" ] ; do
     linux_entry "${OS}" "${version}" recovery \
                 "${GRUB_CMDLINE_LINUX_RECOVERY} ${GRUB_CMDLINE_LINUX}"
   fi
-
-  list=`echo $list | tr ' ' '\n' | fgrep -vx "$linux" | tr '\n' ' '`
 done
 
 # If at least one kernel was found, then we need to
-- 
2.30.2

Re: [PATCH] grub-mkconfig linux: Fix quadratic algorithm for sorting menu items

[Paul Menzel]

Dear Mathieu,


Am 02.05.22 um 16:14 schrieb Mathieu Desnoyers:
> The current implementation of the 10_linux script implements its menu
> items sorting in bash with a quadratic algorithm, calling "sed", "sort",
> head, and grep to compare versions between individual lines, which is
> annoyingly slow for kernel developers who can easily end up with 50-100
> kernels in /boot.
> 
> As an example, on a Intel(R) Core(TM) i7-8650U CPU @ 1.90GHz, running:
> 
>    /usr/sbin/grub-mkconfig > /dev/null
> 
> With 44 kernels in /boot, this command takes 10-15 seconds to complete.
> After this fix, the same command runs in 5 seconds.
> 
> With 116 kernels in /boot, this command takes 40 seconds to complete.
> After this fix, the same command runs in 8 seconds.
> 
> For reference, the quadratic algorithm here is:
> 
> while [ "x$list" != "x" ] ; do      <--- outer loop
>    linux=`version_find_latest $list`
>      version_find_latest()
>        for i in "$@" ; do            <--- inner loop
>          version_test_gt()
>            fork+exec sed
>              version_test_numeric()
>                version_sort
>                  fork+exec sort
>                fork+exec head -n 1
>                fork+exec grep
>    list=`echo $list | tr ' ' '\n' | fgrep -vx "$linux" | tr '\n' ' '`
>      tr
>      fgrep
>      tr
> 
> So all commands executed under version_test_gt() are executed
> O(n^2) times where n is the number of kernel images in /boot.
> 
> I notice that the same quadratic sorting is done for other supported
> OSes, so I suspect similar gains can be obtained there, but I limit the
> scope of this patch to Linux because this is the platform on which I can
> test.

Wow, thank you very much. Can you add a paragraph describing the new 
algorithm, and what runtime it has O(n)?


Kind regards,

Paul


> Signed-off-by: Mathieu Desnoyers <mathieu.desnoyers@efficios.com>
> ---
>   util/grub-mkconfig_lib.in | 18 ++++++++++++++++++
>   util/grub.d/10_linux.in   | 12 ++++++++----
>   2 files changed, 26 insertions(+), 4 deletions(-)
> 
> diff --git a/util/grub-mkconfig_lib.in b/util/grub-mkconfig_lib.in
> index 301d1ac22..f1a09f4c9 100644
> --- a/util/grub-mkconfig_lib.in
> +++ b/util/grub-mkconfig_lib.in
> @@ -218,6 +218,24 @@ version_sort ()
>      esac
>   }
>   
> +version_reverse_sort ()
> +{
> +  case $version_reverse_sort_sort_has_v in
> +    yes)
> +      LC_ALL=C sort -r -V;;
> +    no)
> +      LC_ALL=C sort -r -n;;
> +    *)
> +      if sort -r -V </dev/null > /dev/null 2>&1; then
> +        version_reverse_sort_sort_has_v=yes
> +        LC_ALL=C sort -r -V
> +      else
> +        version_reverse_sort_sort_has_v=no
> +        LC_ALL=C sort -r -n
> +      fi;;
> +   esac
> +}
> +
>   version_test_numeric ()
>   {
>     version_test_numeric_a="$1"
> diff --git a/util/grub.d/10_linux.in b/util/grub.d/10_linux.in
> index ca068038e..23d4bb741 100644
> --- a/util/grub.d/10_linux.in
> +++ b/util/grub.d/10_linux.in
> @@ -195,9 +195,15 @@ title_correction_code=
>   # yet, so it's empty. In a submenu it will be equal to '\t' (one tab).
>   submenu_indentation=""
>   
> +# Perform a reverse version sort on the entire list.
> +# Temporarily replace the '.old' suffix by ' 1' and append ' 2' for all
> +# other files to order the '.old' files after their non-old counterpart
> +# in reverse-sorted order.
> +
> +reverse_sorted_list=$(echo $list | tr ' ' '\n' | sed -e 's/$/ 2/' | sed -e 's/.old 2/ 1/' | version_reverse_sort | sed 's/ 1$/.old/' | sed 's/ 2$//')
> +
>   is_top_level=true
> -while [ "x$list" != "x" ] ; do
> -  linux=`version_find_latest $list`
> +for linux in $reverse_sorted_list; do
>     gettext_printf "Found linux image: %s\n" "$linux" >&2
>     basename=`basename $linux`
>     dirname=`dirname $linux`
> @@ -293,8 +299,6 @@ while [ "x$list" != "x" ] ; do
>       linux_entry "${OS}" "${version}" recovery \
>                   "${GRUB_CMDLINE_LINUX_RECOVERY} ${GRUB_CMDLINE_LINUX}"
>     fi
> -
> -  list=`echo $list | tr ' ' '\n' | fgrep -vx "$linux" | tr '\n' ' '`
>   done
>   
>   # If at least one kernel was found, then we need to

Re: [PATCH] grub-mkconfig linux: Fix quadratic algorithm for sorting menu items

[Mathieu Desnoyers]

----- On May 3, 2022, at 4:47 AM, Paul Menzel pmenzel@molgen.mpg.de wrote:

> Dear Mathieu,
> 
> 
> Am 02.05.22 um 16:14 schrieb Mathieu Desnoyers:
>> The current implementation of the 10_linux script implements its menu
>> items sorting in bash with a quadratic algorithm, calling "sed", "sort",
>> head, and grep to compare versions between individual lines, which is
>> annoyingly slow for kernel developers who can easily end up with 50-100
>> kernels in /boot.
>> 
>> As an example, on a Intel(R) Core(TM) i7-8650U CPU @ 1.90GHz, running:
>> 
>>    /usr/sbin/grub-mkconfig > /dev/null
>> 
>> With 44 kernels in /boot, this command takes 10-15 seconds to complete.
>> After this fix, the same command runs in 5 seconds.
>> 
>> With 116 kernels in /boot, this command takes 40 seconds to complete.
>> After this fix, the same command runs in 8 seconds.
>> 
>> For reference, the quadratic algorithm here is:
>> 
>> while [ "x$list" != "x" ] ; do      <--- outer loop
>>    linux=`version_find_latest $list`
>>      version_find_latest()
>>        for i in "$@" ; do            <--- inner loop
>>          version_test_gt()
>>            fork+exec sed
>>              version_test_numeric()
>>                version_sort
>>                  fork+exec sort
>>                fork+exec head -n 1
>>                fork+exec grep
>>    list=`echo $list | tr ' ' '\n' | fgrep -vx "$linux" | tr '\n' ' '`
>>      tr
>>      fgrep
>>      tr
>> 
>> So all commands executed under version_test_gt() are executed
>> O(n^2) times where n is the number of kernel images in /boot.
>> 
>> I notice that the same quadratic sorting is done for other supported
>> OSes, so I suspect similar gains can be obtained there, but I limit the
>> scope of this patch to Linux because this is the platform on which I can
>> test.
> 
> Wow, thank you very much. Can you add a paragraph describing the new
> algorithm, and what runtime it has O(n)?

How does the following paragraph sound ?

^^^^^^^^
Here is the improved algorithm proposed:

- Prepare a list with all the relevant information for ordering by a single
  sort(1) execution. This is done by renaming ".old" suffixes by " 1" and
  by suffixing all other files with " 2", thus making sure the ".old" entries
  will follow the non-old entries in reverse-sorted-order.
- Call version_reverse_sort on the list (sort -r -V): A single execution of
  sort(1) will reverse-sort the list in O(n*log(n)) with a merge sort.
- Replace the " 1" suffixes by ".old", and remove the " 2" suffixes.
- Iterate on the reverse-sorted list to output each menu entry item.

Therefore, the algorithm proposed has O(n*log(n)) complexity compared to
the prior O(n^2) complexity. Moreover, the constant time required for each
list entry is much less because sorting is done within a single execution
of sort(1) rather than requiring O(n^2) executions of sed(1), sort(1),
head(1), and grep(1) in sub-shells.
^^^^^^^^^

Please let me know if you want me to re-send an updated patch or if you want
to add the text to the current patch's commit message as it is committed.

Thanks,

Mathieu


> 
> 
> Kind regards,
> 
> Paul
> 
> 
>> Signed-off-by: Mathieu Desnoyers <mathieu.desnoyers@efficios.com>
>> ---
>>   util/grub-mkconfig_lib.in | 18 ++++++++++++++++++
>>   util/grub.d/10_linux.in   | 12 ++++++++----
>>   2 files changed, 26 insertions(+), 4 deletions(-)
>> 
>> diff --git a/util/grub-mkconfig_lib.in b/util/grub-mkconfig_lib.in
>> index 301d1ac22..f1a09f4c9 100644
>> --- a/util/grub-mkconfig_lib.in
>> +++ b/util/grub-mkconfig_lib.in
>> @@ -218,6 +218,24 @@ version_sort ()
>>      esac
>>   }
>>   
>> +version_reverse_sort ()
>> +{
>> +  case $version_reverse_sort_sort_has_v in
>> +    yes)
>> +      LC_ALL=C sort -r -V;;
>> +    no)
>> +      LC_ALL=C sort -r -n;;
>> +    *)
>> +      if sort -r -V </dev/null > /dev/null 2>&1; then
>> +        version_reverse_sort_sort_has_v=yes
>> +        LC_ALL=C sort -r -V
>> +      else
>> +        version_reverse_sort_sort_has_v=no
>> +        LC_ALL=C sort -r -n
>> +      fi;;
>> +   esac
>> +}
>> +
>>   version_test_numeric ()
>>   {
>>     version_test_numeric_a="$1"
>> diff --git a/util/grub.d/10_linux.in b/util/grub.d/10_linux.in
>> index ca068038e..23d4bb741 100644
>> --- a/util/grub.d/10_linux.in
>> +++ b/util/grub.d/10_linux.in
>> @@ -195,9 +195,15 @@ title_correction_code=
>>   # yet, so it's empty. In a submenu it will be equal to '\t' (one tab).
>>   submenu_indentation=""
>>   
>> +# Perform a reverse version sort on the entire list.
>> +# Temporarily replace the '.old' suffix by ' 1' and append ' 2' for all
>> +# other files to order the '.old' files after their non-old counterpart
>> +# in reverse-sorted order.
>> +
>> +reverse_sorted_list=$(echo $list | tr ' ' '\n' | sed -e 's/$/ 2/' | sed -e
>> 's/.old 2/ 1/' | version_reverse_sort | sed 's/ 1$/.old/' | sed 's/ 2$//')
>> +
>>   is_top_level=true
>> -while [ "x$list" != "x" ] ; do
>> -  linux=`version_find_latest $list`
>> +for linux in $reverse_sorted_list; do
>>     gettext_printf "Found linux image: %s\n" "$linux" >&2
>>     basename=`basename $linux`
>>     dirname=`dirname $linux`
>> @@ -293,8 +299,6 @@ while [ "x$list" != "x" ] ; do
>>       linux_entry "${OS}" "${version}" recovery \
>>                   "${GRUB_CMDLINE_LINUX_RECOVERY} ${GRUB_CMDLINE_LINUX}"
>>     fi
>> -
>> -  list=`echo $list | tr ' ' '\n' | fgrep -vx "$linux" | tr '\n' ' '`
>>   done
>>   
> >   # If at least one kernel was found, then we need to

-- 
Mathieu Desnoyers
EfficiOS Inc.
http://www.efficios.com

Re: [PATCH] grub-mkconfig linux: Fix quadratic algorithm for sorting menu items

[Paul Menzel]

Dear Mathieu,


Am 03.05.22 um 16:42 schrieb Mathieu Desnoyers:
> ----- On May 3, 2022, at 4:47 AM, Paul Menzel pmenzel@molgen.mpg.de wrote:

>> Am 02.05.22 um 16:14 schrieb Mathieu Desnoyers:
>>> The current implementation of the 10_linux script implements its menu
>>> items sorting in bash with a quadratic algorithm, calling "sed", "sort",
>>> head, and grep to compare versions between individual lines, which is
>>> annoyingly slow for kernel developers who can easily end up with 50-100
>>> kernels in /boot.
>>>
>>> As an example, on a Intel(R) Core(TM) i7-8650U CPU @ 1.90GHz, running:
>>>
>>>     /usr/sbin/grub-mkconfig > /dev/null
>>>
>>> With 44 kernels in /boot, this command takes 10-15 seconds to complete.
>>> After this fix, the same command runs in 5 seconds.
>>>
>>> With 116 kernels in /boot, this command takes 40 seconds to complete.
>>> After this fix, the same command runs in 8 seconds.
>>>
>>> For reference, the quadratic algorithm here is:
>>>
>>> while [ "x$list" != "x" ] ; do      <--- outer loop
>>>     linux=`version_find_latest $list`
>>>       version_find_latest()
>>>         for i in "$@" ; do            <--- inner loop
>>>           version_test_gt()
>>>             fork+exec sed
>>>               version_test_numeric()
>>>                 version_sort
>>>                   fork+exec sort
>>>                 fork+exec head -n 1
>>>                 fork+exec grep
>>>     list=`echo $list | tr ' ' '\n' | fgrep -vx "$linux" | tr '\n' ' '`
>>>       tr
>>>       fgrep
>>>       tr
>>>
>>> So all commands executed under version_test_gt() are executed
>>> O(n^2) times where n is the number of kernel images in /boot.
>>>
>>> I notice that the same quadratic sorting is done for other supported
>>> OSes, so I suspect similar gains can be obtained there, but I limit the
>>> scope of this patch to Linux because this is the platform on which I can
>>> test.
>>
>> Wow, thank you very much. Can you add a paragraph describing the new
>> algorithm, and what runtime it has O(n)?
> 
> How does the following paragraph sound ?
> 
> ^^^^^^^^
> Here is the improved algorithm proposed:
> 
> - Prepare a list with all the relevant information for ordering by a single
>    sort(1) execution. This is done by renaming ".old" suffixes by " 1" and
>    by suffixing all other files with " 2", thus making sure the ".old" entries
>    will follow the non-old entries in reverse-sorted-order.
> - Call version_reverse_sort on the list (sort -r -V): A single execution of
>    sort(1) will reverse-sort the list in O(n*log(n)) with a merge sort.
> - Replace the " 1" suffixes by ".old", and remove the " 2" suffixes.
> - Iterate on the reverse-sorted list to output each menu entry item.
> 
> Therefore, the algorithm proposed has O(n*log(n)) complexity compared to
> the prior O(n^2) complexity. Moreover, the constant time required for each
> list entry is much less because sorting is done within a single execution
> of sort(1) rather than requiring O(n^2) executions of sed(1), sort(1),
> head(1), and grep(1) in sub-shells.
> ^^^^^^^^^

Sounds perfect. Thank you.

> Please let me know if you want me to re-send an updated patch or if you want
> to add the text to the current patch's commit message as it is committed.

As the maintainers are pretty busy, I guess it’s better you send a v2.

[…]


Kind regards,

Paul

Re: [PATCH] grub-mkconfig linux: Fix quadratic algorithm for sorting menu items

[Mihai Moldovan]

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Just a nit, feel free to ignore it...


* On 5/3/22 4:42 PM, Mathieu Desnoyers wrote:
> How does the following paragraph sound ?
> 
> ^^^^^^^^
> Here is the improved algorithm proposed:
> 
> - Prepare a list with all the relevant information for ordering by a single
>   sort(1) execution. This is done by renaming ".old" suffixes by " 1" and
>   by suffixing all other files with " 2", thus making sure the ".old" entries
>   will follow the non-old entries in reverse-sorted-order.
> - Call version_reverse_sort on the list (sort -r -V): A single execution of
>   sort(1) will reverse-sort the list in O(n*log(n)) with a merge sort.

This is correct for GNU coreutils's sort, but nothing (I'm mostly thinking of
SUS/POSIX here) mandates that the sort utility must either use merge sort or
have O(n*log(n)) time complexity.

Given that you're using version sort, which is a GNU extension, it probably
can't be anything than GNU sort anyway, though, so the point still holds by
implicity.

However, this also means that you're adding a hidden dependency upon GNU
coreutils sort here, which will hit systems traditionally not using the GNU
userland by default, most prominently BSDs (which, I might add, seem not to use
GRUB by default and generally either discourage it or have thrown it out of
their package management systems).



Mihai


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Re: [PATCH] grub-mkconfig linux: Fix quadratic algorithm for sorting menu items

[Oskari Pirhonen]

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On Tue, May 03, 2022 at 07:15:47PM +0200, Mihai Moldovan wrote:
> Just a nit, feel free to ignore it...
> 
> 
> * On 5/3/22 4:42 PM, Mathieu Desnoyers wrote:
> > How does the following paragraph sound ?
> > 
> > ^^^^^^^^
> > Here is the improved algorithm proposed:
> > 
> > - Prepare a list with all the relevant information for ordering by a single
> >   sort(1) execution. This is done by renaming ".old" suffixes by " 1" and
> >   by suffixing all other files with " 2", thus making sure the ".old" entries
> >   will follow the non-old entries in reverse-sorted-order.
> > - Call version_reverse_sort on the list (sort -r -V): A single execution of
> >   sort(1) will reverse-sort the list in O(n*log(n)) with a merge sort.
> 
> This is correct for GNU coreutils's sort, but nothing (I'm mostly thinking of
> SUS/POSIX here) mandates that the sort utility must either use merge sort or
> have O(n*log(n)) time complexity.
> 
> Given that you're using version sort, which is a GNU extension, it probably
> can't be anything than GNU sort anyway, though, so the point still holds by
> implicity.
> 
> However, this also means that you're adding a hidden dependency upon GNU
> coreutils sort here, which will hit systems traditionally not using the GNU
> userland by default, most prominently BSDs (which, I might add, seem not to use
> GRUB by default and generally either discourage it or have thrown it out of
> their package management systems).

The existing `version_sort()` function in grub-mkconfig_lib.in uses the
same logic for detecting the existence of `sort -V` with a fallback to
`sort -n`. I don't think it adds any new hidden dependencies.

    version_sort ()
    {
      case $version_sort_sort_has_v in
        yes)
          LC_ALL=C sort -V;;
        no)
          LC_ALL=C sort -n;;
        *)
          if sort -V </dev/null > /dev/null 2>&1; then
            version_sort_sort_has_v=yes
            LC_ALL=C sort -V
          else
            version_sort_sort_has_v=no
            LC_ALL=C sort -n
          fi;;
       esac
    }

- Oskari


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Re: [PATCH] grub-mkconfig linux: Fix quadratic algorithm for sorting menu items

[Mihai Moldovan]

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* On 5/4/22 2:54 AM, Oskari Pirhonen wrote:
> The existing `version_sort()` function in grub-mkconfig_lib.in uses the
> same logic for detecting the existence of `sort -V` with a fallback to
> `sort -n`. I don't think it adds any new hidden dependencies.

Right, there are fallbacks in both places for sort versions not supporting the
version sort extension, so that's probably fine then. Nevermind.



Mihai



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Re: [PATCH] grub-mkconfig linux: Fix quadratic algorithm for sorting menu items

[Mathieu Desnoyers]

----- On May 3, 2022, at 1:15 PM, Mihai Moldovan ionic@ionic.de wrote:

> Just a nit, feel free to ignore it...
> 
> 
> * On 5/3/22 4:42 PM, Mathieu Desnoyers wrote:
>> How does the following paragraph sound ?
>> 
>> ^^^^^^^^
>> Here is the improved algorithm proposed:
>> 
>> - Prepare a list with all the relevant information for ordering by a single
>>   sort(1) execution. This is done by renaming ".old" suffixes by " 1" and
>>   by suffixing all other files with " 2", thus making sure the ".old" entries
>>   will follow the non-old entries in reverse-sorted-order.
>> - Call version_reverse_sort on the list (sort -r -V): A single execution of
>>   sort(1) will reverse-sort the list in O(n*log(n)) with a merge sort.
> 
> This is correct for GNU coreutils's sort, but nothing (I'm mostly thinking of
> SUS/POSIX here) mandates that the sort utility must either use merge sort or
> have O(n*log(n)) time complexity.
> 
> Given that you're using version sort, which is a GNU extension, it probably
> can't be anything than GNU sort anyway, though, so the point still holds by
> implicity.

I'm using the same sort already used in version_sort(). It uses sort -V if available,
but there is a fallback to sort if -V is not available. Therefore, nothing implies
a version sort, so nothing implies a GNU extension. So your point about other sort
not necessarily being O(nlog(n)) merge sort is valid. I will remove this statement
from the next patch version commit message.

Thanks,

Mathieu

-- 
Mathieu Desnoyers
EfficiOS Inc.
http://www.efficios.com