DYNAMIC STORAGE ALLOCATION. Hanan Samet

Transcription

1 ds0 DYNAMIC STORAGE ALLOCATION Hanan Samet Compute Science Depatment and Cente fo Automation Reseach and Institute fo Advanced Compute Studies Univesity of Mayland College Pak, Mayland Copyight 1997 Hanan Samet These notes may not e epoduced y any means (mechanical o electonic o any othe) without the expess witten pemission of Hanan Samet

2 DYNAMIC STORAGE ALLOCATION ds1 Explicit allocation and deallocation ( feeing o lieating ) of locks of contiguous stoage locations Issues: 1. how to keep tack of availale space and its patitioning usually keep a linked list of availale locks a. elements location of stat of lock of lock pointe to next lock in list. how to ode (i.e., sot ) list y location (i.e., inceasing ode) y no ode. how to find a lock of consecutive locations if list soted y location, find fist one with s (fist fit) a. equies a seach. ut good if want to mege adjacent empty locks into lage ones upon stoage deallocation if list soted y, find smallest one with s (est fit) Ex: fist fit is supeio to est fit equest availale aeas fist fit availale aeas est fit stat 100, ,100

3 DYNAMIC STORAGE ALLOCATION ds1 Explicit allocation and deallocation ( feeing o lieating ) of locks of contiguous stoage locations Issues: 1. how to keep tack of availale space and its patitioning usually keep a linked list of availale locks a. elements location of stat of lock of lock pointe to next lock in list. how to ode (i.e., sot ) list y location (i.e., inceasing ode) y no ode. how to find a lock of consecutive locations if list soted y location, find fist one with s (fist fit) a. equies a seach. ut good if want to mege adjacent empty locks into lage ones upon stoage deallocation if list soted y, find smallest one with s (est fit) Ex: fist fit is supeio to est fit equest availale aeas fist fit availale aeas est fit stat 100, , , ,00

4 DYNAMIC STORAGE ALLOCATION z ds1 Explicit allocation and deallocation ( feeing o lieating ) of locks of contiguous stoage locations Issues: 1. how to keep tack of availale space and its patitioning usually keep a linked list of availale locks a. elements location of stat of lock of lock pointe to next lock in list. how to ode (i.e., sot ) list y location (i.e., inceasing ode) y no ode. how to find a lock of consecutive locations if list soted y location, find fist one with s (fist fit) a. equies a seach. ut good if want to mege adjacent empty locks into lage ones upon stoage deallocation if list soted y, find smallest one with s (est fit) Ex: fist fit is supeio to est fit equest availale aeas fist fit availale aeas est fit stat 100, , , , ,100 00,00

5 DYNAMIC STORAGE ALLOCATION 4 g z ds1 Explicit allocation and deallocation ( feeing o lieating ) of locks of contiguous stoage locations Issues: 1. how to keep tack of availale space and its patitioning usually keep a linked list of availale locks a. elements location of stat of lock of lock pointe to next lock in list. how to ode (i.e., sot ) list y location (i.e., inceasing ode) y no ode. how to find a lock of consecutive locations if list soted y location, find fist one with s (fist fit) a. equies a seach. ut good if want to mege adjacent empty locks into lage ones upon stoage deallocation if list soted y, find smallest one with s (est fit) Ex: fist fit is supeio to est fit equest availale aeas fist fit availale aeas est fit stat 100, , , , ,100 00, ,100 STUCK!

6 DYNAMIC STORAGE ALLOCATION 5 4 g z ds1 Explicit allocation and deallocation ( feeing o lieating ) of locks of contiguous stoage locations Issues: 1. how to keep tack of availale space and its patitioning usually keep a linked list of availale locks a. elements location of stat of lock of lock pointe to next lock in list. how to ode (i.e., sot ) list y location (i.e., inceasing ode) y no ode. how to find a lock of consecutive locations if list soted y location, find fist one with s (fist fit) a. equies a seach. ut good if want to mege adjacent empty locks into lage ones upon stoage deallocation if list soted y, find smallest one with s (est fit) Ex: fist fit is supeio to est fit equest availale aeas fist fit availale aeas est fit stat 100, , , , ,100 00, ,100 STUCK! Requests in ode of inceasing : fist fit is ette Requests in ode of deceasing : est fit is ette

7 DYNAMIC STORAGE ALLOCATION 6 v 5 4 g z ds1 Explicit allocation and deallocation ( feeing o lieating ) of locks of contiguous stoage locations Issues: 1. how to keep tack of availale space and its patitioning usually keep a linked list of availale locks a. elements location of stat of lock of lock pointe to next lock in list. how to ode (i.e., sot ) list y location (i.e., inceasing ode) y no ode. how to find a lock of consecutive locations if list soted y location, find fist one with s (fist fit) a. equies a seach. ut good if want to mege adjacent empty locks into lage ones upon stoage deallocation if list soted y, find smallest one with s (est fit) Ex: fist fit is supeio to est fit equest availale aeas fist fit availale aeas est fit stat 100, , , , ,100 00, ,100 STUCK! Requests in ode of inceasing : fist fit is ette Requests in ode of deceasing : est fit is ette Can give example whee est fit is ette than fist fit

8 FRAGMENTATION ds Fagmentation esults when too many small locks ae geneated Solutions: 1. can avoid y choosing a constant k and selecting lock a of s to satisfy the equest fo a lock of if s < k eliminates small locks speeds up seach in fist-fit method as list of locks is smalle. can avoid inspecting locks that ae too small in fist-fit y pefoming seach in a cicula manne so that it esumes whee the last lock was found. can also avoid y using compaction upon deallocation

9 LIBERATION ds 1. Want to etun stoage to the AVAIL list as soon as possile implies that can coalesce elements of AVAIL list into lage locks. Contast with methods ased on gaage collection which allocate stoage continuously until exhausting the AVAIL list followed y a pass fo stoage eclamation and compaction. Comining gaage collection with compaction stoage locations must e moved need to execise cae when moving pointe data pesence of elocation egistes oviates some of the polems, since the pointes could e offset addesses

10 LIBERATION WITH COALESCING Ex: assume a soted AVAIL list y memoy locations i.e., LINK(p) Ω LINK(p)>p fee ds4 next on AVAIL lieated next on AVAIL lieated next on AVAIL lieated Polem: each time the algoithm is invoked to lieate lock pointed at y p, we must seach though appoximately half the list to locate q such that LINK(q)>p

11 LIBERATION WITH COALESCING ds4 Ex: assume a soted AVAIL list y memoy locations i.e., LINK(p) Ω LINK(p)>p coalesce fom elow fee next on AVAIL lieated next on AVAIL lieated next on AVAIL lieated Polem: each time the algoithm is invoked to lieate lock pointed at y p, we must seach though appoximately half the list to locate q such that LINK(q)>p

12 LIBERATION WITH COALESCING z ds4 Ex: assume a soted AVAIL list y memoy locations i.e., LINK(p) Ω LINK(p)>p coalesce fom elow fee next on AVAIL lieated coalesce fom aove next on AVAIL lieated next on AVAIL lieated Polem: each time the algoithm is invoked to lieate lock pointed at y p, we must seach though appoximately half the list to locate q such that LINK(q)>p

13 LIBERATION WITH COALESCING 4 g z ds4 Ex: assume a soted AVAIL list y memoy locations i.e., LINK(p) Ω LINK(p)>p coalesce fom elow fee next on AVAIL lieated coalesce fom aove next on AVAIL lieated coalesce fom elow and aove next on AVAIL lieated Polem: each time the algoithm is invoked to lieate lock pointed at y p, we must seach though appoximately half the list to locate q such that LINK(q)>p

14 LIBERATION ALGORITHM ds5 Assume N consecutive wods stating at P0 ae eing lieated Algoithm: 1. seach though AVAIL until finding a node Q such that link(q) = P > P0. if P0+N = P then egin /* coalesce fom aove */ (P0) (P)+N; link(p0) link(p); end else egin link(p0) P; (P0) N; end;. if Q+(Q) = P0 then egin /* coalesce fom elow */ (Q) (Q)+(P); /* N was aleady accounted fo in step (aove) */ link(q) link(p0); end else link(q) P0;

15 LIBERATION USING DOUBLY-LINKED LISTS ds6 Data stuctue lock inuse=+ inuse }SIZE { wods inuse fee lock link link inuse= inuse=+ inuse inuse INUSE and SIZE fields 1. easy to locate immediately adjacent locks to detemine if coalescing is possile. oviate need to sot list of availale locks (AVAIL) in inceasing memoy. moe complex if sot AVAIL y lock as need to update Douly-linked AVAIL enales easy emoval of coalesced locks Ex: fee inuse= pev next + lieated + + pev + lieated + next pev next pev next + lieated +

16 LIBERATION USING DOUBLY-LINKED LISTS ds6 Data stuctue lock inuse=+ inuse }SIZE { wods inuse fee lock link link inuse= inuse=+ inuse inuse INUSE and SIZE fields 1. easy to locate immediately adjacent locks to detemine if coalescing is possile. oviate need to sot list of availale locks (AVAIL) in inceasing memoy. moe complex if sot AVAIL y lock as need to update Douly-linked AVAIL enales easy emoval of coalesced locks Ex: fee inuse= coalesce fom elow pev next + lieated pev + lieated + next pev next pev next + lieated +

17 LIBERATION USING DOUBLY-LINKED LISTS z ds6 Data stuctue lock inuse=+ inuse }SIZE { wods inuse fee lock link link inuse= inuse=+ inuse inuse INUSE and SIZE fields 1. easy to locate immediately adjacent locks to detemine if coalescing is possile. oviate need to sot list of availale locks (AVAIL) in inceasing memoy. moe complex if sot AVAIL y lock as need to update Douly-linked AVAIL enales easy emoval of coalesced locks Ex: fee inuse= coalesce fom elow pev next + lieated coalesce fom aove pev + lieated + next pev next pev next + lieated +

18 LIBERATION USING DOUBLY-LINKED LISTS 4 g z ds6 Data stuctue lock inuse=+ inuse }SIZE { wods inuse fee lock link link inuse= inuse=+ inuse inuse INUSE and SIZE fields 1. easy to locate immediately adjacent locks to detemine if coalescing is possile. oviate need to sot list of availale locks (AVAIL) in inceasing memoy. moe complex if sot AVAIL y lock as need to update Douly-linked AVAIL enales easy emoval of coalesced locks Ex: fee inuse= coalesce fom elow pev next + lieated coalesce fom aove pev + lieated + next coalesce fom elow and aove pev next pev next + lieated +

19 BUDDY SYSTEM ds7 Restict lock to e a powe of 1. all locks of k stat at location x whee x mod k = 0. given a lock stating at location x such that x mod k = 0 BUDDY k (x) = x + k if x mod k+1 = 0 BUDDY k (x) = x k if x mod k+1 = k Ex: BUDDY (10100) = only uddies can e meged 4. ty to coalesce uddies when stoage is deallocated k diffeent availale lock lists one fo each lock When equest a lock of k and none is availale: 1. split smallest lock j > k into a pai of locks of j 1. place lock on appopiate AVAIL list and ty again Data stuctue 1. douly-linked list (not cicula) FREE of availale locks indexed y k links stoed in actual locks FREE[k] points to fist availale lock of k. each lock contains INUSE it SIZE NEXT and PREV links fo FREE list Can get geate vaiety in lock s using Fionacci sequence of lock s so i = i 1 + i and now atio of successive lock s is / instead of 1/

20 EXAMPLE OF BUDDY ALGORITHM M = I S P N 0 16 Ω Ω ds8 k FREE[k] 0 Ω 1 Ω Ω Ω 4 0 initially, one lock of 16 stating at location 0 is availale

21 EXAMPLE OF BUDDY ALGORITHM M = I S P N 0 8 Ω Ω 0 4 Ω Ω 0 Ω Ω Ω Ω z ds8 k FREE[k] 0 Ω 1 Ω Ω 4 Ω Ω initially, one lock of 16 stating at location 0 is availale allocate a lock of

22 EXAMPLE OF BUDDY ALGORITHM M = I S P N 0 4 Ω Ω 0 Ω Ω Ω Ω Ω Ω 0 1 Ω Ω Ω Ω z ds8 k FREE[k] 0 Ω 1 Ω 10 Ω 4 1 Ω 8 Ω 4 0 Ω initially, one lock of 16 stating at location 0 is availale allocate a lock of allocate locks of 4,, in ode

23 EXAMPLE OF BUDDY ALGORITHM M = I S P N Ω Ω Ω Ω 0 0 Ω Ω Ω Ω Ω Ω Ω Ω 10 Ω Ω Ω Ω 4 g z ds8 k FREE[k] 0 Ω 1 Ω 10 Ω 4 1 Ω 8 Ω 4 0 Ω initially, one lock of 16 stating at location 0 is availale allocate a lock of allocate locks of 4,, in ode fee the lock at location

24 EXAMPLE OF BUDDY ALGORITHM 5 v 4 g z ds8 M = I S P N Ω Ω Ω Ω Ω Ω Ω Ω Ω Ω Ω Ω Ω Ω Ω 10 Ω Ω Ω 1 Ω Ω k FREE[k] 0 Ω 1 Ω 10 Ω 4 1 Ω 8 Ω 4 0 Ω initially, one lock of 16 stating at location 0 is availale allocate a lock of allocate locks of 4,, in ode fee the lock at location fee the lock at location 0 mege lock at 0 with its uddy at no futhe meging is possile as the uddy at 4 is in use

25 BUDDY ALGORITHM NOTES ds9 Assume stoage uns fom locations 0 to m 1 To eseve a lock of k : 1. find smallest j fo which FREE[j] Ω (assume this lock stats at location n). emove the lock at location n fom FREE[j]. while j>k do egin j j 1; add lock at location n+ j to FREE[j]; end; To lieate a lock of k stating at location n: while k m and NOT(INUSE(BUDDY k (n))) do egin emove BUDDY k (n) fom FREE[k]; k k+1; if BUDDY k (n)<n then n BUDDY k (n); end; INUSE flag only needs to e set in fist wod of each lock 1. all emaining elements (wods) have thei uddies within the same lock. no one outside the lock will look fo uddies within the lock

26 OVERFLOW ds10 At times, have moe stoage allocation equests than availale memoy Can pefom gaage collection with compaction ut will soon un out of memoy again Altenatively, emove locks to seconday stoage: 1. keep a douly-linked list of locks in use, soted accoding to fequency of use wheneve a lock is accessed, move it to font of list like a self-oganizing file Ex: stat A B C D. cicula list of locks and a ecently-used it indicating if the lock was accessed since the last time locks wee emoved to seconday stoage to emove a lock, mach down the list looking fo a 0 and eset all 1s that wee encounteed to 0 cuculating pointe ensues that a lock eset to 0 will not e checked again fo emoval until all othe locks have een checked Ex: stat A B C D E

27 OVERFLOW ds10 At times, have moe stoage allocation equests than availale memoy Can pefom gaage collection with compaction ut will soon un out of memoy again Altenatively, emove locks to seconday stoage: 1. keep a douly-linked list of locks in use, soted accoding to fequency of use wheneve a lock is accessed, move it to font of list like a self-oganizing file Ex: stat C A B C D accessing C causes it to move to the font. cicula list of locks and a ecently-used it indicating if the lock was accessed since the last time locks wee emoved to seconday stoage to emove a lock, mach down the list looking fo a 0 and eset all 1s that wee encounteed to 0 cuculating pointe ensues that a lock eset to 0 will not e checked again fo emoval until all othe locks have een checked Ex: stat A B C D E

28 OVERFLOW z ds10 At times, have moe stoage allocation equests than availale memoy Can pefom gaage collection with compaction ut will soon un out of memoy again Altenatively, emove locks to seconday stoage: 1. keep a douly-linked list of locks in use, soted accoding to fequency of use wheneve a lock is accessed, move it to font of list like a self-oganizing file Ex: stat C A B C D accessing C causes it to move to the font. cicula list of locks and a ecently-used it indicating if the lock was accessed since the last time locks wee emoved to seconday stoage to emove a lock, mach down the list looking fo a 0 and eset all 1s that wee encounteed to 0 cuculating pointe ensues that a lock eset to 0 will not e checked again fo emoval until all othe locks have een checked Ex: stat stat A 0 B 0 C D E lock D is the fist to e emoved

29 OVERFLOW 4 g z ds10 At times, have moe stoage allocation equests than availale memoy Can pefom gaage collection with compaction ut will soon un out of memoy again Altenatively, emove locks to seconday stoage: 1. keep a douly-linked list of locks in use, soted accoding to fequency of use wheneve a lock is accessed, move it to font of list like a self-oganizing file Ex: stat C A B C D accessing C causes it to move to the font. cicula list of locks and a ecently-used it indicating if the lock was accessed since the last time locks wee emoved to seconday stoage to emove a lock, mach down the list looking fo a 0 and eset all 1s that wee encounteed to 0 cuculating pointe ensues that a lock eset to 0 will not e checked again fo emoval until all othe locks have een checked Ex: stat stat A 0 B 0 1 C D E lock D is the fist to e emoved access lock A

30 OVERFLOW 5 v 4 g z ds10 At times, have moe stoage allocation equests than availale memoy Can pefom gaage collection with compaction ut will soon un out of memoy again Altenatively, emove locks to seconday stoage: 1. keep a douly-linked list of locks in use, soted accoding to fequency of use wheneve a lock is accessed, move it to font of list like a self-oganizing file Ex: stat C A B C D accessing C causes it to move to the font. cicula list of locks and a ecently-used it indicating if the lock was accessed since the last time locks wee emoved to seconday stoage to emove a lock, mach down the list looking fo a 0 and eset all 1s that wee encounteed to 0 cuculating pointe ensues that a lock eset to 0 will not e checked again fo emoval until all othe locks have een checked Ex: stat stat stat A 0 B 0 1 C D E 0 0 lock D is the fist to e emoved access lock A lock B is emoved next