Another Clock-pro approx

Hi,

I've been thinking on another clock-pro approximation.

Each page has 3 bits: hot/cold, test and referenced. Say we have 3 lists: T1, T2 and T3.
and variable: s

T1 will have hot and cold pages, T2 will only have cold pages and T3 will have the non-resident pages.
c will be the total number of resident pages; |T1| + |T2| + |T3| = 2c.

T1-rotation:

h/c test ref action

 0         0       0                T2-000  the page leaves T1, T2, and T3     
 0         0       1                T2-001   the page must be resident, do nothing          
 0       1       0           T2-000           test bit is cleared. if it is non-resident, it leaves T3
 0       1       1           T1-100           test bit is cleared
 1       0       0           T2-001           turn into cold page
 1       0       1           T1-100           ref bit is cleared
 1       1       0           <cannot happen>
 1       1       1           <cannot happen>

T2-rotation:

h/c test ref action

 0         0       0           <remove page from list> the pages leaves T1, T2 and T3
 0         0        1              T1-000  this page must be resident, free the page, the page leaves T1, T2, and T3   
 0         1        0              T3-010  if the page is resident, free the page, place it in T3. Otherwise, do nothing 
 0         1        1              T1-100   the page must be resident, move the page to T1, rotate T1 to a hot page into a cold one  

T3-rotation: frees up non-resident slots

So, on fault we rotate T2, unless empty then we start by rotating T1 until T2 contains at least 1 cold page.
If a T2 rotation creates a hot page, we rotate T1 to degrade a hot page to a cold page in order to keep the cold page target m_c. Every T1 rotation adds |T1| to s. While s > c, we subtract c from s and

turn T3 for each subtraction.

Compare to clock-pro:
T1-rotation <-> Hand_hot
T2-rotation <-> Hand_cold
T3-rotation <-> Hand_test

The normal m_c adaption rules can be applied.

Zoned edition:
This can be done per zone by having:
T1_i, T2_i, T3_j, s, t, u_j
where _i is the zone index and _j the non-resident bucket index.

Then each T1_i turn will add |T1_i| to s, each c in s will increment t by 1. On each non-resident bucket access we increment u_j until it equals t and for each increment we rotate the bucket.

Kind regards,

Peter Zijlstra

Hi, Peter,

I didn't see your explanation of the actions such as T2-000.
So I put my understanding at the below.

While setting three lists, do you indicate that a page can have 3 set of pointers, each for the links in one list?

If we don't restrict ourselves to the current active and inactive list data structure, can you point to us what major approximations we have to make on the original clock-pro policy so that the policy becomes acceptable in the kernel? (I understand that zoned data structure is one of the required adaptations.) The reason I'm asking the question is that I didn't see some major changes here in your approxiamtion? Once I understand the kernel required adaptations, I can work with you for a clock-pro approximation.

I have a clock-pro simulator in C code and powerpoint presentation slides explaining clock-pro operations. If you are interested in any of them, let me know.

Thanks.

Song

Quoted 8 lines · Peter Zijlstra

Hi,

I've been thinking on another clock-pro approximation.

Each page has 3 bits: hot/cold, test and referenced. Say we have 3 lists: T1, T2 and T3.
and variable: s

Quoted 3 lines

T1 will have hot and cold pages, T2 will only have cold pages and T3 will have the non-resident pages.
c will be the total number of resident pages; |T1| + |T2| + |T3| = 2c.

Do you mean |T1 U T2 U
T3| = 2c ?

Quoted 15 lines

T1-rotation:

h/c   test   ref       action
 0      0     0        T2-000   page is passed on to T2
 0      0     1        T2-001   page is passed on to T2
 0      1     0        T2-000   page to T2, clear test bit
 0      1     1        T1-100   make it hot
 1      0     0        T2-010   turn into cold page, start test period
 1      0     1        T1-100   keep it hot, clear ref bit
 1      1     0        <cannot happen>
 1      1     1        <cannot happen>

T2-rotation:

Quoted 8 lines

h/c   test   ref       action
 0      0     0        <remove page from list>
 0      0     1        T1-000  keep it cold, keep it resident.
 0      1     0        T3-010  make it non-resident
 0      1     1        T1-100  make it hot

T3-rotation: remove from non-resident list.

Quoted 5 lines

So, on fault we rotate T2, unless empty then we start by rotating T1 until T2 contains at least 1 cold page.
If a T2 rotation creates a hot page, we rotate T1 to degrade a hot page to a cold page in order to keep the cold page target m_c. Every T1 rotation adds |T1| to s. While s > c, we subtract c from s and

Does |T1| mean the total size if T1?

Can you explain why in more
detail?

Quoted 14 lines

turn T3 for each subtraction.

Compare to clock-pro:
T1-rotation <-> Hand_hot
T2-rotation <-> Hand_cold
T3-rotation <-> Hand_test

The normal m_c adaption rules can be applied.

Zoned edition:
This can be done per zone by having:
T1_i, T2_i, T3_j, s, t, u_j
where _i is the zone index and _j the non-resident bucket index.

Quoted 4 lines

Then each T1_i turn will add |T1_i| to s, each c in s will increment t by 1. On each non-resident bucket access we increment u_j until it equals t and for each increment we rotate the bucket.

Quoted 4 lines · Song Jiang

Hi, Peter,

I didn't see your explanation of the actions such as T2-000.
So I put my understanding at the below.

My bad, I keep forgetting to write half the stuff down, often the most important pieces appear missing ;-(

As I told Rik yesterday on IRC, the main idea behind it was to make T1 + T2 behave like 1 big SC-list and superimpose T3 thereon by coupling the rotation speed. And thus creating 1 virtual wheel as clock-pro has. The split in T1 and T2 acts as the hot hand and determines the length of the test period.

|T1| + |T2| <= c
|T1| + |T2| + |T3| <= 2c

Resident:
T1 can contain pages marked as both hot and cold.
T2 can only contain cold pages.

Non-resident:
T3 can only contain non-resident cold pages in their test period.

The actions presented like Tn-abc are to be read as: place page on the head of list Tn with the hot/cold bit set to a, the test bit set to b and the referenced bit set to c.

Quoted 2 lines

While setting three lists, do you indicate that a page can have 3 set of pointers, each for the links in one list?

No, a page can only be on 1 list at a time.

Quoted 8 lines

If we don't restrict ourselves to the current active and inactive list data structure, can you point to us what major approximations we have to make on the original clock-pro policy so that the policy becomes acceptable in the kernel? (I understand that zoned data structure is one of the required adaptations.) The reason I'm asking the question is that I didn't see some major changes here in your approxiamtion? Once I understand the kernel required adaptations, I can work with you for a clock-pro approximation.

Yes the zoned data structure is the most difficult. It gives rise to the fact that we have to split the resident from the non-resident page management. Each zone will have a resident part and all zones will share the non-resident part. This because a page leaving zone 1 could be faulted back in zone 2.

Another is that the pageout operation is async, ie. we start writeback against a page but until it is finished the page has to stay on the resident lists but as soon as writeback finishes and we have not yet had another reference we need to reclaim the page asap.

The last one, and I'm not quite sure on this one (Rik?), is that when we insert a page we're sure it is going to be referenced right after the context switch to userspace. Hence we effectively insert referenced pages.

Rik, any things missing here?

Quoted 19 lines

I have a clock-pro simulator in C code and powerpoint presentation slides explaining clock-pro operations. If you are interested in any of them, let me know.

Thanks.

Song

Quoted 8 lines · Peter Zijlstra

Hi,

I've been thinking on another clock-pro approximation.

Each page has 3 bits: hot/cold, test and referenced. Say we have 3 lists: T1, T2 and T3.
and variable: s

Quoted 5 lines

Quoted 3 lines

T1 will have hot and cold pages, T2 will only have cold pages and T3 will have the non-resident pages.
c will be the total number of resident pages; |T1| + |T2| + |T3| = 2c.

Do you mean |T1 U T2 U
T3| = 2c ?

See above.

New and improved actions:

Quoted 15 lines

Quoted 15 lines

T1-rotation:

h/c   test   ref       action
 0      0     0        T2-000   page is passed on to T2
 0      0     1        T2-001   page is passed on to T2
 0      1     0        T2-000   page to T2, clear test bit
 0      1     1        T1-100   make it hot
 1      0     0        T2-010   turn into cold page, start test period
 1      0     1        T1-100   keep it hot, clear ref bit
 1      1     0        <cannot happen>
 1      1     1        <cannot happen>

T2-rotation:

Quoted 8 lines

Quoted 8 lines

h/c   test   ref       action
 0      0     0        <remove page from list>
 0      0     1        T1-000  keep it cold, keep it resident.
 0      1     0        T3-010  make it non-resident
 0      1     1        T1-100  make it hot

T3-rotation: remove from non-resident list.

A fault will check the non-resident list and also remove the page if found.

Quoted 7 lines

Quoted 5 lines

So, on fault we rotate T2, unless empty then we start by rotating T1 until T2 contains at least 1 cold page.
If a T2 rotation creates a hot page, we rotate T1 to degrade a hot page to a cold page in order to keep the cold page target m_c. Every T1 rotation adds |T1| to s. While s > c, we subtract c from s and

Does |T1| mean the total size if T1?

Yes, |T1| is the size of T1.

Quoted 3 lines

Can you explain why in more
detail?

This because the hot hand pushes the test hand.

Hmmm, maybe it should not be every T1 rotation, but only rotations on hot pages that get accounted. Because at that point the hot page with the largest inter reference period will disappear and the test period changes.

So the idea is to couple to rotation speed of T3 to T1 and scale the respective sizes.

Quoted 14 lines

Quoted 14 lines

turn T3 for each subtraction.

Compare to clock-pro:
T1-rotation <-> Hand_hot
T2-rotation <-> Hand_cold
T3-rotation <-> Hand_test

The normal m_c adaption rules can be applied.

Zoned edition:
This can be done per zone by having:
T1_i, T2_i, T3_j, s, t, u_j
where _i is the zone index and _j the non-resident bucket index.

Quoted 4 lines

Quoted 4 lines

Then each T1_i turn will add |T1_i| to s, each c in s will increment t by 1. On each non-resident bucket access we increment u_j until it equals t and for each increment we rotate the bucket.

More thoughts, it should probably be: u_j = t/J. Where J is the total number of buckets.

Kind regards,

Peter Zijlstra

Peter,

Two obvious issues in the actions are
(1) test bits have never been set;
(2) pages in T3 have never been promoted into T1/T2.

I might have to take the responsibility for all the confusion in the understanding of why clock-pro works. (e.g. clock-pro can deal with access-once, loop accesses effectively). I should have put a pseudo code in the clock-pro paper. However, even with a pseudo code, the description of clock-pro would seem much more complicated than the idea behind it actually is. To get its idea without being bothered by all the details involved in the clock-pro description, my suggestion is that let's base our discussion/design on the original LIRS algorithm.
(see section 3 of the following paper
http://www.cs.wm.edu/hpcs/WWW/HTML/publications/papers/TR-05-11.pdf)

In the context of the LIRS algorithm, compare to clock-pro,

cold <--> HIR
hot <--> LIR

HAND_hot --> bottom of the LIRS stack (= last resident hot page). This is the most critical position in the stack, which serves as a criterion of hot/cold. A reference to a page above it (if the stack is vertically viewed) makes the page a hot one, otherwise, the page remains as a cold one. This is also the place where a hot page is demoted to a cold one.

HAND-cold --> last resident cold page (== bottom of stack
Q) where a victim page is going to be searched.

If we allow an unlimited number of non-resident stay in the stack, there is no need for a HAND_test. Actually HAND_hot serves the purpose. If we have a limit on that (say the memory size c), then the HAND-test points to the last non-resident cold page or last hot page, whichever is higher.

If we use separate lists for h/c pages (like active/inactive lists), we lose the chance for the comparison, and major performance advantages of clock-pro are lost.

Actually
CAR/CART have been shown in the aforementioned paper not be able to deal with loop access problem of LRU, and that is the reason.

It is fine to have a common non-resident page pool for the zoned memory, if we can also set their corresponding place-holders in a single list for each zone.

Let me know if the single list suggestion is feasible in the Linux kernel.

Quoted 160 lines · Song Jiang

Quoted 4 lines

Hi, Peter,

I didn't see your explanation of the actions such as T2-000.
So I put my understanding at the below.

My bad, I keep forgetting to write half the stuff down, often the most important pieces appear missing ;-(

As I told Rik yesterday on IRC, the main idea behind it was to make T1 + T2 behave like 1 big SC-list and superimpose T3 thereon by coupling the rotation speed. And thus creating 1 virtual wheel as clock-pro has. The split in T1 and T2 acts as the hot hand and determines the length of the test period.

|T1| + |T2| <= c
|T1| + |T2| + |T3| <= 2c

Resident:
T1 can contain pages marked as both hot and cold.
T2 can only contain cold pages.

Non-resident:
T3 can only contain non-resident cold pages in their test period.

The actions presented like Tn-abc are to be read as: place page on the head of list Tn with the hot/cold bit set to a, the test bit set to b and the referenced bit set to c.

Quoted 2 lines

While setting three lists, do you indicate that a page can have 3 set of pointers, each for the links in one list?

No, a page can only be on 1 list at a time.

Quoted 8 lines

If we don't restrict ourselves to the current active and inactive list data structure, can you point to us what major approximations we have to make on the original clock-pro policy so that the policy becomes acceptable in the kernel? (I understand that zoned data structure is one of the required adaptations.) The reason I'm asking the question is that I didn't see some major changes here in your approxiamtion? Once I understand the kernel required adaptations, I can work with you for a clock-pro approximation.

Yes the zoned data structure is the most difficult. It gives rise to the fact that we have to split the resident from the non-resident page management. Each zone will have a resident part and all zones will share the non-resident part. This because a page leaving zone 1 could be faulted back in zone 2.

Another is that the pageout operation is async, ie. we start writeback against a page but until it is finished the page has to stay on the resident lists but as soon as writeback finishes and we have not yet had another reference we need to reclaim the page asap.

The last one, and I'm not quite sure on this one (Rik?), is that when we insert a page we're sure it is going to be referenced right after the context switch to userspace. Hence we effectively insert referenced pages.

Rik, any things missing here?

Quoted 19 lines

I have a clock-pro simulator in C code and powerpoint presentation slides explaining clock-pro operations. If you are interested in any of them, let me know.

Thanks.

Song

Quoted 8 lines · Peter Zijlstra

Hi,

I've been thinking on another clock-pro approximation.

Each page has 3 bits: hot/cold, test and referenced. Say we have 3 lists: T1, T2 and T3.
and variable: s

Quoted 5 lines

Quoted 3 lines

T1 will have hot and cold pages, T2 will only have cold pages and T3 will have the non-resident pages.
c will be the total number of resident pages; |T1| + |T2| + |T3| = 2c.

Do you mean |T1 U T2 U
T3| = 2c ?

See above.

New and improved actions:

Quoted 15 lines

Quoted 15 lines

T1-rotation:

h/c   test   ref       action
 0      0     0        T2-000   page is passed on to T2
 0      0     1        T2-001   page is passed on to T2
 0      1     0        T2-000   page to T2, clear test bit
 0      1     1        T1-100   make it hot
 1      0     0        T2-010   turn into cold page, start test period
 1      0     1        T1-100   keep it hot, clear ref bit
 1      1     0        <cannot happen>
 1      1     1        <cannot happen>

T2-rotation:

Quoted 8 lines

Quoted 8 lines

h/c   test   ref       action
 0      0     0        <remove page from list>
 0      0     1        T1-000  keep it cold, keep it resident.
 0      1     0        T3-010  make it non-resident
 0      1     1        T1-100  make it hot

T3-rotation: remove from non-resident list.

A fault will check the non-resident list and also remove the page if found.

Quoted 7 lines

Quoted 5 lines

So, on fault we rotate T2, unless empty then we start by rotating T1 until T2 contains at least 1 cold page.
If a T2 rotation creates a hot page, we rotate T1 to degrade a hot page to a cold page in order to keep the cold page target m_c. Every T1 rotation adds |T1| to s. While s > c, we subtract c from s and

Does |T1| mean the total size if T1?

Yes, |T1| is the size of T1.

Quoted 3 lines

Can you explain why in more
detail?

This because the hot hand pushes the test hand.

Hmmm, maybe it should not be every T1 rotation, but only rotations on hot pages that get accounted. Because at that point the hot page with the largest inter reference period will disappear and the test period changes.

So the idea is to couple to rotation speed of T3 to T1 and scale the respective sizes.

Quoted 18 lines

Quoted 18 lines

turn T3 for each subtraction.

Compare to clock-pro:
T1-rotation <-> Hand_hot
T2-rotation <-> Hand_cold
T3-rotation <-> Hand_test

The normal m_c adaption rules can be applied.

Zoned edition:
This can be done per zone by having:
T1_i, T2_i, T3_j, s, t, u_j
where _i is the zone index and _j the non-resident bucket index.

Then each T1_i turn will add |T1_i| to s, each c in s will increment t by 1. On each non-resident bucket access we increment u_j until it equals t and for each increment we rotate the bucket.

Quoted 8 lines

More thoughts, it should probably be: u_j = t/J. Where J is the total number of buckets.

Kind regards,

Peter Zijlstra

Quoted 5 lines · Song Jiang

Peter,

Two obvious issues in the actions are
(1) test bits have never been set;
(2) pages in T3 have never been promoted into T1/T2.

Drad, more missing information:
On fault the new page is searched for in T3, if present T1-100 otherwise T1-010.

Quoted 4 lines

HAND-cold --> last resident cold page (== bottom of stack
Q) where a victim page is going to be searched.

Do you imply here that HAND-cold pushes HAND-hot? If so, then it is

possible to write this 2-hand clock as 2 lists, where the top one will always push its tail into the head of the botton, and the botton will puth into the head of the top one on reference.
This is exactly what I have done.

Quoted 3 lines

If we use separate lists for h/c pages (like active/inactive lists), we lose the chance for the comparison, and major performance advantages of clock-pro are lost.

Neither my proposal nor CART have h/c separarted lists. CARTs T1 list can contain both hot and cold pages as can mine.

Quoted 4 lines

Actually
CAR/CART have been shown in the aforementioned paper not be able to deal with loop access problem of LRU, and that is the reason.

I fixed that:
http://programming.kicks-ass.net/kernel-patches/cart/cart-cart-r.patch

Quoted 3 lines

Let me know if the single list suggestion is feasible in the Linux kernel.

Single list should not be a problem. However I still have some trouble with placing the page meta-data of non-resident pages on those lists.

Quoted 7 lines · Peter Zijlstra

Quoted 5 lines · Song Jiang

Peter,

Two obvious issues in the actions are
(1) test bits have never been set;
(2) pages in T3 have never been promoted into T1/T2.

Quoted 4 lines

Drad, more missing information:
On fault the new page is searched for in T3, if present T1-100 otherwise T1-010.

I am interested in rethinking the mechanism of clock-pro under your 3-digit code abstraction.

I put my comments in pairs of brackets.

(Please confirm: all T1 and T2 pages are resident.)

T1-rotation:

h/c test ref action
0 0 0 T2-000

0 0 1 T2-001

 0       1       0           T2-000 
 0       1       1           T1-100
 1       0       0           T2-001 [T1-010 because I don't see why 

we can artificially give it a ref. But we can give it a second
chance to test its next reuse in T1]

 1       0       1           T1-100
 1       1       0           <cannot happen>
 1       1       1           <cannot happen>

T2-rotation:

h/c test ref action

 0       0       0           <remove page from list>
 0       0       1           T1-000  [T1-010 to test its next reuse]

 0       1       0           T3-010 
 0       1       1           T1-100

T3-rotation:

    present:       T1-100
    not present:  T1-010

My obsevations:

(1) The test bits of all T1 cold pages are 1
(test bit is irrelevant to hot pages),
because once a T1 page with test bit 1 has its
test bit cleared, it either leaves T1 or
becomes a hot page.
So that in T1-rotation, the cases of 000, 001
cannot happen.

(2) The test bits of all T2 cold pages are 0,
because all T2 pages are from T1, and there are
no T1 actions generating a test bit.
So that in T2-rotation, the cases of 010, 011
cannot happen.

(3) The test bits of all T3 pages are designed
to be 1. (I will keep thinking how to really
achieve the design goal).

Considering the above, there is no need to
explictly use a test bit.

Quoted 6 lines

Quoted 4 lines

HAND-cold --> last resident cold page (== bottom of stack
Q) where a victim page is going to be searched.

Do you imply here that HAND-cold pushes HAND-hot? If so, then it is

HAND-hot pushes HAND-test, but not necessarily HAND-cold,
because a cold page that is turned from a hot page can stay below the HAND-hot in the LIRS stack.

Quoted 4 lines

possible to write this 2-hand clock as 2 lists, where the top one will always push its tail into the head of the botton, and the botton will puth into the head of the top one on reference.
This is exactly what I have done.

I have no issue with this.

Quoted 7 lines

Quoted 3 lines

If we use separate lists for h/c pages (like active/inactive lists), we lose the chance for the comparison, and major performance advantages of clock-pro are lost.

Neither my proposal nor CART have h/c separarted lists. CARTs T1 list can contain both hot and cold pages as can mine.

My fault in expressing. I actually mean multiple lists, not necessarily hot and cold pages have to be in seperate lists. To effectively set the test bits, I wonder we might have to put non-resident pages with resident pages in the same list. But I will keep thinking how to make them seperate without compromising the role of test period.

Quoted 7 lines

Quoted 3 lines

Let me know if the single list suggestion is feasible in the Linux kernel.

Single list should not be a problem. However I still have some trouble with placing the page meta-data of non-resident pages on those lists.

We should have a way out on this.