Parallel Sorting Algorithms: Unlimited, Fixed, and Scalable Approaches, Study notes of Computer Science

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Parallel Sorting

Three solutions to sorting in parallel:• Unlimited parallelism — similar to bubble sort• Fixed parallelism — 26 threads, one per letter• Scalable parallelism — Batcher’s Bitonic Sort

Using Unlimited Parallelism Dog^

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Art

Eel

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Fun

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Dog

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Fun

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Fun

Swaping Pairs

void

swap_pairs(int start) {

forall(i

in(start...n

stride

by

{ rec

temp; bool

done

= true;

if

(strcmp(L

[i].x, L

[i+1].x)

>^

0)^

temp

=^

L[i];

L[i]

=^

L[i+1];

L[i+1]

= temp; done

=^

false;

} if

(!start) continue

= !(&&/done);

Fixed Parallelism

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Bun

counts['C']++counts['C']++

counts['A']++counts['C']++

counts['B']++counts['B']++

counts['A']

Art

counts['B'] Bus

Bun

counts['C'] Cog

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Cel

Art

Bun

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Cel

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Local Sorting

rec[]

localSort(int index, int

myCount)

rec

temp[] = new rec[myCount]; int

j^

for

(int i = 0; i < n

; i++)

if^

(letRank(L

[i].x[0])

index)

temp[j++] = L

[i];

alphabetizeInPlace(temp, myCount);return

temp;

Scalable Parallelism

Batcher’s Setup

rec L

[n]; int t

int m

=^

log2(t

int size

n^

/^

t;

typedef

struct

{ char x[MAXLEN];

int

home;

key;

key BufK

[m

][size

];

bool free'[m

]^

= false, ready'[m

];

Assume

L^ localized into equal contiguous segments

Assume

BufK

localized by first index

Batcher’s Thread Outline

forall

(index

in(0..t

-1))

{

rec

myL[size

]^ = localize(L

),^

inputCopy[size

];

key

Kn[][]

=^

localize(BufK

),^

K[size

];

for

(int

i^

=^ 0;

i^

<^ size

;^ i++)

{

K[i].x

=^

myL[i].x;

K[i].home

=^

localToGobal(myL,

i,

0);

} alphabetizeInPlace(K,

size

,^ bit(index,

/*

up

or

down

*/);

....

/*

main

loop

*/

for

(int

i^

=^ 0;

i^

<^ size

;^ i++)

inputCopy[i]

=^

L[K[i].home];

barrier;for

(int

i^

=^ 0; i

<^

size

;^ i++)

myL[i]

=^

inputCopy[i];

}

Batcher’s Merge

void merge(int index, int d, int p, key

Kn[][],

key

K[])

{ for (int i = 0;

i < size

; i++) {

bool want;int cmp;cmp = strcmp(Kn[index][i].x, K[i].x);if (bit(index, d) == bit(index, p))want = (cmp

0);

elsewant = (cmp

< 0);

if (want)K[i] = Kn[i];} }^