System and method for evaluating paging behavior

• US 3,921,153 A
• Filed: 08/02/1973
• Issued: 11/18/1975
• Est. Priority Date: 08/02/1973
• Status: Expired due to Term

• Current Assignee: Laszlo A. Belady, Robert I. Roth
• Original Assignee: Laszlo A. Belady, Robert I. Roth
• Inventors: Belady, Laszlo A., Roth, Robert I.
• Primary Examiner(s): Zache, Raulfe B.
• Application Number:
  US05/385,222
• Time in Patent Office: 838 Days
• Field of Search: 340/172.5 444/1
• US Class Current: 711/1
• CPC Class Codes: G06F 12/08 in hierarchically structured memory systems, e.g. virtual memory systems

Abstract

The system and method disclosed herein effect the determination of the minimum memory capacities for the pages of a page reference.

Claims

1. A system for use in data processing apparatus which is operated as a paging machine and wherein a program is considered as a page reference string, for determining the minimum memory capacities for the pages of said string, said data processing apparatus including means for maintaining a first list of the names of the pages of said program weighted in accordance with a least recently used (LRU) criterion, said first list being constituted by the names of said pages and LRU integers respectively therewith having one of the different discrete values of 1 to n, wherein n is equal to the total number of said pages in said program, said system comprising:

means for maintaining a second list of said names, said second list being constituted by an ordered sequence of n addresses, each of said addresses respectively having one of the different discrete values of 1 to n, there being located at each of said addresses, a different integer, C, associated therewith from which the minimum memory capacity (MMC) of said page can be determined, each of the integers in said second list having a different discrete value of 1 to n;

means responsive to said means for maintaining said second list for determining said minimium memory capacity (MMC) of a given referenced page comprising;

means responsive to the referencing of said given page for dividing said second list into a first group of addresses having the values of 1 to (l-1) respectively, and a second group of addresses having the values of l to n respectively, wherein l is equal to the integer associated with said referenced page in said first list, means responsive to said means for dividing said second list for ascertaining the address, k, in said second group whereat there is present the lowest value MMC integer;

means responsive to said means for ascertaining said address, k, for making the series of addresses in said second group which are included in the subgroup containing addresses l, (l+1), . . . , (k-1) which have the following values, viz. (l+a), (l+b), (l+c), . . . , to address (k-1), if necessary, wherein (l+a) has the smallest address value greater than l such that C(l+a) <

C(l), wherein (l+b) has the smallest address value greater than (l+a) such that C(l+b) <

C(l+a), etc., wherein C(i) is the value of integer, C, at location i. means responsive to said means for dividing said second list for generating the smallest missing number in the groiup of integers comprising 2 to (Cmax+1) wherein Cmax is the largest integer C of those contained at addresses 2 to (l-1), said generated smallest missing number being the minimum memory capacity of said referenced page, means responsive to said means for dividing said second list for incrementing each of the addresses 2 to (l-1) of said first group by 1 whereby they respectively have the address values of 3 to l, means responsive to said means for generating said smallest missing number for assigning the address value of 2 to said generated smallest missing number, and means responsive to said means for marking said series of addresses for assigning to each of the series of said marked addresses, the value of the next address in said series, the highest value address in said series being assigned the value of k, said integer originally at said address k being discarded.

2. In a data processing apparatus which is operated as a paging machine and wherein a program is considered as a page reference string, said data processing apparatus including, primary storage for containing a portion, m, of the pages of said program and secondary storage for containing the remainder, (n-m), pages of said program wherein n is the total number of pages in said program, means responsive to the occurrence of a page exception for effecting the exchanging of a page in primary storage for the page in secondary storage causing said page exception, means for maintaining a first list of the names of the pages of said program weighted in accordance with a least recently used (LRU) criterion, said first list being constituted by the names of said pages and (LRU) weighting integers respectively having one of the different discrete values of 1 to n, associated with each of said names according to said criterion, said first list comprising a first portion comprising means for containing the names of those pages in primary storage and having LRU weightings of 1 to m and the respective LRU integers associated therewith, and a second portion comprising the names of the remaining pages of said program and which have the LRU weightings of (m+1) to n and their respective associated integers in a location in said storage, said data processing apparatus further including means for effecting changes of information in said first and second portions of said first list, a system for determining the minimum memory capacities (MMC) for the pages of said page reference string comprising:

means for maintaining a second list of said names, said second list being constituted by n addresses, each of said addresses respectively having one of the different discrete values of 1 to n, there being located at each of said addresses a different one of said page names and an integer, C, associated with each of said page means from which the minimum memory capacity (MMC) of the page can be determined, each of the integers in said second list having a different discrete value of 1 to n, said second list comprising a first component comprising means for containing the integers, C, at addresses 1 to m of said second list and a second component comprising means for maintaining said total second list in said storage;

first means responsive to said means for maintaining said second list of said names for determining said minimum memory capacity of a given referenced page comprising;

means responsive to the referencing of a page which is present in primary storage for dividing said first component of said second list into a first group of addresses having the values of 1 to (l-1) respectively, and a second group of addresses having the values of l to m, respectively, wherein l is equal to the LRU weighting associated with said referenced page in said first portion of said first list, means responsive to said means for dividing said first component of said second list for ascertaining the address, k, in said second group whereat there is present the lowest value minimum memory capacity integer, means responsive to said means for ascertaining said address, k, for marking the series of addresses in said second group which are included in the subgroup containing addresses l, (l+1), . . . , (k-l) which have the following values, viz. (l+a), (l+b), (l+c), . . . , to address (k-l), if necessary, wherein (l+a) has the smallest address value greater than l such that C(l+a) <

C(l), wherein (l+b) has the smallest address value greater than (l+a) such that C(l+b) <

C (l+a), etc., wherein C(i) is the value of integer, C, at address i, in said second group of addresses, means responsive to said means for dividing said first component of said second list for generating the smallest missing number in the group of integers comprising 2 to (Cmax+1) wherein Cmax is the largest integer, C, of those contained at addresses 2 to (l-1) in said first group of addresses, said generated smallest missing number being the minimum memory capacity of said referenced page, means responsive to said means for dividing said first component of said second list for incrementing each of the addresses 2 to (l-1) of said first group by 1 whereby they respectively have the address values of 3 to l, means responsive to said means for generating said smallest missing number for assigning the address value of 2 to said generated smallest missing number, and means responsive to said means for marking said series of addresses for assigning to each of the series of said marked addresses, the value of the next address in said series, the highest value address in said series being assigned the value of k, said integer originally at said address k being discarded.

3. In the data processing system as defined in claim 2 wherein, in response to the occurrence of a page exception, there is activated said means to effect an exchange between said primary and secondary storage of the page in said primary storage having the LRU weighting of m associated therewith and the page in secondary storage causing said page exception, said system further including:

means responsive to said page exception for updating said second component of said second list, said updating means effecting the operations of bringing the information at the lst to mth addresses in said second component into conformity with the information in said lst to mth addresses in said first component, the adding of any missing integer and the deleting any duplicate integer in said (m+1)th to nth addresses in said second component;

there being actuated in response to the updating of said second component of said second list and the occurrence of said page exception to cause the page name of said page closing said exception to be placed into said first portion of said first list and assigned as LRU weighting integer of 1, the page name of said page being removed from primary storage into secondary Storage being placed into said second portion with its associated LRU integer being changed from m to (m+1), the remaining LRU integers in said first portion, i.e., those which have the LRU integer values of 1 to (m-1) immediately prior to the occurrence of said page exception being respectively incremented by 1, those LRU integers in said second portion of said first list which had the respective LRU integer values of (m+1) to one less than the LRU integer value of the page causing said exception immediately prior to the occurring of said page exception being incremented by 1;

second means responsive to the updating of said second component of said second list for determining said minimum memory capacity of said page causing said page exception, said second means effecting the operations of dividing said second component into a first group of addresses having the values of 1 to (l-1), respectively and a second group of addresses having the values of l to n, respectively, wherein l is equal to the LRU weighting which was associated with said page causing said exception immediately prior to the occurrence of said exception, ascertaining the address, k, in said second group whereat there is present the lowest value minimum memory capacity (MMC) integer, marking the series of addresses in said second group which are included in the subgroup containing addresses l, (l+1), . . . , (k-1), which have the following values, viz. wherein (l+a), (l+b), (l+c), . . . , to address (k-1), if necessary, wherein (l+a) has the smallest address value greater than l such that C(l+a) <

C(l), wherein (l+b) has the smallest address value greater than (l+a) such that C(l+b) <

C(l+a), etc., wherein C(i) is the value of integer, C, at address i, in said second group of addresses, shifting the contents in addresses 2 to (l-1) down by 1 respectively, generating the smallest missing number in the group 2 to (Cmax+1), wherein Cmax is the largest value integer, C, at addresses 2 to (l-1) of said second component, placing said smallest missing number at address 2 of said second component, and respectively shifting the contents of said marked addresses into the next address in said series; and

means responsive to said means for updating said second component of said second list for updating said first component of said second list, said last-named means effecting the operation of bringing the information at the lst to mth addresses in said first component into conformity with the information at the lst to mth addresses of said second component.

4. In data processing apparatus as defined in claim 3 wherein:

said first portion of said first list comprises a stack of at least m registers, each of said registers being capable of having contents of a value of at least m, and means for incrementing said contents of said registers; and

wherein said first component of said second list comprises a stack of a quantity of at least m registers capable of having contents of at least n, and means for shifting the contents of a register in said stack into any of the other registers of said stack.

5. In a data processing operation as defined in claim 4 wherein said means for generating said smallest missing number comprises:

an additional register capable of containing any quantity from 2 to n, means for comparing the contents of said additional register with the respective contents of said registers of said first component at addresses 2 to (l-1), whereby upon the successive comparisons of increasing values of the contents in said additional register with the numbers in the series, 2 to (Cmax+1), the value in said additioNal register which does not result in a finding of equality in said comparisons is said generated smallest missing number.

6. In a data processing apparatus which is operated as a paging machine and wherein a program is considered as a page reference string, said data processing apparatus including, primary storage for containing a portion, m, of the pages of said program and secondary storage for containing the remainder, (n-m), of the pages of said program wherein n is the total of the pages of said program, and means responsive to the occurrence of a page exception for effecting the exchanging of a page in primary storage for the page in secondary storage causing said page exception, a system for determining the minimum memory capacities (MMC) for the pages of said page reference string comprising:

means for maintaining a first list of the names of the pages of said program weighted in accordance with a least recently used (LRU) criterion, said first list being constituted by the names of said pages and least recently used (LRU) weighting integers respectively having one of the differrnt discrete values of 1 to n, associated with each of said names according to said criterion, said first list comprising a first portion comprising means for containing the names of those pages in primary storage having associated LRU weighting integers of 1 to m and the respective LRU weighting integers associated therewith, and a second portion comprising the names of the remaining pages of said program and which have the LRU weighting of (m+1) to n and their respective associated LRU weighting integers in a location in said storage;

means in circuit with said means for maintaining said first list for effecting changes of information in said first and second portions of said first list;

means for maintaining a second list of said names, said second list being constituted by an ordered sequence of lst to nth addresses, there being located at each of said addresses a different integer, C, from which the minimum memory capacity (MMC) of the page can be determined, each of the integers in said second list having a different discrete value of 1 to n, said second list comprising a first component comprising means for containing the names of the pages in primary storage and their associated MMC integers, C, at addresses 1 to m of said second list and a second component comprising means for maintaining said total second list in said storage;

first means for determining said mimimum memory capacity (MMC) of a given referenced page comprising;

means responsive to the referencing of a page which is present in primary storage for dividing said first component of said second list into a first group of addresses having the values of 1 to (l-1) respectively, and a second group of addresses having the values of l to m respectively, wherein l is equal to the LRU weighting associated with said referenced page in said first portion of said first list, means responsive to said means for dividing said first component of said second list for ascertaining the address, k, in said second group whereat there is present the lowest value minimum memory capacity (MMC) integer, means responsive to said means for ascertaining said address, k, for marking the series of addresses in said second group which are included in the subgroup containing addresses l, (l-1), . . . , (k-1) which have the following values, viz., (l+a), (l+b), (l+c), . . . , to address (k-1), if necessary, wherein (l+a) has the smallest address value greater than l such that C(l+a) <

C(l), wherein (l+b) has the smallest address value greater than (l+a) such that C(l+b) <

C(l+a), etc., wherein C(i) is the value of integer C at address i, in said second group of addresses, means responsive to said means for dividing said first component of said second list for generating the smallest missing number in the group of integers comprising 2 to (Cmax+

     1) wherein Cmax is the largest integer, C, of those contained at addresses 2 to (l-1) in the first group of addresses, said generated smallest missing number being the minimum memory capacity of said referenced page, means responsive to said means for dividing said first component of said second list for incrementing each of said first group of addresses by 1 whereby they respectively have the address value of 3 to l, means responsive to said means for generating said smallest missing number for assigning the address value of 2 to said generated smallest missing number, and means responsive to said means for marking said series of addresses for assigning to each of the series of said marked addresses, the value of the next address in said series, the highest value address in said series being assigned the value of k, said integer originally at said address k being discarded.

7. In a data processing system as defined in claim 6 wherein, in response to the occurrence of a page exception, there is actuated said means to effect an exchange between said primary and secondary storage of the page in said primary storage having the highest LRU weighting integer associated therewith and the page in secondary storage causing said page exception, said system further including:

means responsive to said page exception for updating said second list to bring the page names and their associated MMC integers into said component of said second list into conformity with said first component of said second list, and, where necessary, to remove redundant integers from and to insert missing integers into said second list;

means responsive to said page exception and the updating of said second list for updating said first and second portions of said first list, said updating including the placing of the page name of the page causing said page exception with an LRU weighting integer of 1 into said first portion of said first list, the page name of said page being removed from primary storage into secondary storage being placed into said second portion with its associated LRU integer being changed from m to (m+1), the remaining integers in said first portion of said first list, i.e., those which had the LRU integer values of 1 to (m-1) immediately preceding said page exception being respectively incremented by 1, those LRU integers in said second portion of said first list which, prior to the occurrence of said page exception, had the respective values of (m+1) to the LRU integer value which is one less than the LRU integer value of the page causing said page exception being respectively incremented by 1;

second means responsive to the updating of said second component of said second list and the updating of said first list for determininng said minimum memory capacity of said page causing said page exception, said second means effecting, the dividing of said second component of said second list into a first group of addresses having the values of 1 to (l-1), respectively, and a second group of addresses having the values of l to n respectively, wherein l is equal to the LRU weighting which was associated with the page causing the exception immediately prior to the occurrence of the page exception, the ascertaining the address, k, in the second group whereat there is present the lowest value minimum memory capacity integer, the marking of the series of addresses in the second group which are included in the subgroup containing addresses, l, (l+1), . . . , (k-1), which have the following values, viz. (l+a), (l+B), (l+c), . . . , to address (k-1), if necessary, wherein (l+a) has the smallest address value greater than l such that C(l+a) <

C(l) wherein (l+b) has the smallest address value greater than (l+a) such that C(l+b) <

C(l+a), etc., wherein C(i) is the value of integer, C, at address i, in said second group of addresses, the shifting down of one address in said first group of those MMC integers in address postion 2 to (l-1), the generating of the smallest missing number in the group 2 to (Cmax+1) at addresses 2 to (l-1) in said first group of said total second list wherein Cmax is the largest value integer, C, at said last-named addresses, the placing of the generated smallest missing number into address 2 of said last-named addresses, said generated smallest missing number being the MMC of said page causing said exception, and the respective shifting of the contents at the marked address positions to the next position in said series, the contents at the highest value address in said series being shifted into address, k, the integer originally at address, k, being discarded; and

means responsive to the determining of the minimum memory capacity of the page causing said exception for updating the first component of said second list, said updating including the operation of inserting into the lst to mth addresses of said first component the corresponding information contained at the lst to mth addresses of said second component.

8. In a data processing apparatus as defined in claim 7 wherein:

said first portion of said first list comprises a stack of at leasat m registers, each of said registers being capable of having contents of the value of at least m, and means for incrementing said contents of said registers; and

wherein said first component of said second list comprises a stack of at least m registers, each of said registers being capable of having contents of the value of at least n, and means for shifting the contents of the registers in said last-named stack into any of the other registers of said stack.

9. In a data processing apparatus as defined in claim 8 wherein said means for generating said smallest missing number comprises:

an additional register capable of containing any quantity from 2 to at least n;

means for comparing the contents of said additional register with the respective contents of said registers of said first component representing addresses 2 to (l-1), whereby upon the successive comparisons of increasing values of contents in said additional register with the numbers in the series 2 to (Cmax+1), wherein Cmax is the largest value integer, C, at addresses 2 to (l-1), the value in said additional register which does not result in a finding of equality in said comparisons in said generated smallest missing number.