Rafid Ahmed - db.in.tum.dedb.in.tum.de/.../seminarHauptspeicherdbs/slides/04-cuckoo-hashing.pdf ·...

Fakultät für InformatikTechnische Universität München

SIMD-Accelerated Hash Tables: Cuckoo Hashing

Rafid Ahmed

Seminar: Techniques for implementing main memory database


Cuckoo Hashing[1] :

4 4

72

16 19

72

2

16

16

45

68

53

T1 T2

alternate position for older key is vacant

if not the procedure recurses until an empty slot is found or enters a cycle

Two locations must be checked for

lookup

Two locations must be checked for

deletion

Inserting a new key may push an

older key to another position:

SIMD-Accelerated Hash Tables: Cuckoo Hashing 1

--


Worst-Case Time Complexity of Hash Tables:


LinearProbingOperations Double

HashingRandomHashing

SeparateChaining

CuckooHashing

Search

Insertion

Deletion

O(n)

O(n)

O(n)

O(n)

O(n)

O(n)

O(n)

O(n)

O(n)

O(n)

O(n)

O(n)

O(1)

O(1)

O(n)


SIMD (Single Instruction Multiple Data):

+ +

= =

3 15 25 1 33 46 89 6

23 3 16 77 45 3 7 12

26 18 41 78 78 49 96 18

+

=

6

12

18

Scalar operation SIMD operation

Input vecotr 1

O(f(n)) O(f(n)/W)

Input vector 2

Output vector

SIMD Register



Fundamental Vector Operations:

2 9 0 5 11 10 3 9

54 29 19 67 93 71 23 29

memory

index vector

output vector

547419 23 11 67 99 77 21 71 9329

Gather:


__m256i _mm256_i32gather_epi64 (__int64 const* base_addr, __m128i vindex, const int scale)



Selective Gather:


__m256i _mm256_mask_i32gather_epi64 (__m256i src, __int64 const* base_addr, __m128i vindex, __m256i mask, const int scale)

2 9 0 5 11 10 3 9

63 29 19 59 93 13 23 29

63 34 45 59 78 13 89 19

memory

index vector

output vector

source vector

mask

547419 23 11 67 99 77 21 71 9329

0 1 1 0 1 0 1 1

3 15 25 1 33 46 89 6

memory

vector

mask

15 25 33 89 6

0 1 1 0 1 0 1 1



Selective Store :


__m256i _mm256_permutevar8x32_epi32 (__m256i a, __m256i idx)

void _mm256_maskstore_epi32 (int* mem_addr, __m256i mask, __m256i a)


Cuckoo Hash tables:

Scalar Hash tables :k

k1p1

p2k2

h1 h2

T1 T2

Branching

Branchless [2]


- conditionally accesssecond location

- access both locations


Cuckoo Hash tables:

k

k1k3p1p3

k2 k4p2 p4

h1 h2

T1 T2

Vector Hash tables (Horizontal)[3] :


- Hash buckets

- Building

- Contiguous Keys

- Contiguous Payloads

- loop unrolling

- Probing techniques

- SIMD masking


Cuckoo Hash tables:

k3

k2

k7

k9

p3

k1

k5

k4

k6

p1p6

p5

p4

p9

p2

p7

h1 h2

k1

k3

k4

k7

T1 T2

Vector Hash tables (Vertical)[4] :


Blending

Selective

-

-gather all bucketsgenerate masks fromcomparing keys

-

-

gather �rst bucketper key

selectively gather secondbucket for keys that did notmatch

j 0for i 0 to |S| - 1 step W do k Skeys[i] v Spayloads[i] h1 (k f1) >> |T| h2 (k f2) >> |T| kT Tkeys[h1] vT Tpayloads[h1] m k = kT

kT m Tkeys[h2] vT m Tpayloads[h2] m k = kT

RSkeys[j] m k RSS_payloads[j] m v RSR_payloads[j] m vT

j j + |m|end for


Vertical (Selective) Cuckoo Hashing - Probing[4] :


load input tuples

calculate 1st hash value

calculate 2nd hash value

gather 1st hash bucket

compare hash bucket key with probe key

selectively gather 2nd hash bucket

again compare hash bucket key with probe key

selectively store matches


Results:

Cuckoo Hashing - Probing (30% Selectivity) Benchmark:


0

1

2

3

4

5

6

7

8

4 KB 16 KB 64 KB 256 KB 1 MB 4 MB 16 MB 64 MB

Thro

ughp

ut (G

B/s)

Hash table size

Scalar (Branching) Scalar (Branchless)

Run on (4 X 3500 MHz CPU s) CPU Caches: L1 Data 32K (x4) L1 Instruction 32K (x4) L2 Uni�ed 256K (x4) L3 Uni�ed 6144K (x1)


Results:



0

1

2

3

4

5

6

7

8


Thro

ughp

ut (G

B/s)

Hash table size

Scalar (Branching) Scalar (Branchless) Vector (Horizontal)



Results:



0

1

2

3

4

5

6

7

8


Thro

ughp

ut (G

B/s)

Hash table size

Scalar (Branching) Scalar (Branchless) Vector (Horizontal) Vector (Blending_4)

Vector (Blending_8)



Results:



0

1

2

3

4

5

6

7

8


Thro

ughp

ut (G

B/s)

Hash table size


Vector (Blending_8) Vector (Selec�ve_4) Vector (Selec�ve_8)



Results:



0.

2

4.

6

8

10

12

14

16


Thro

ughp

ut (G

B/s)

Hash table size

Scalar (Branching) Scalar (Branchless)



Results:



0.

2

4.

6

8

10

12

14

16


Thro

ughp

ut (G

B/s)

Hash table size

Scalar (Branching) Scalar (Branchless) Vector (Horizontal)



Results:



0.

2

4.

6

8

10

12

14

16


Thro

ughp

ut (G

B/s)

Hash table size


Vector (Blending_8)



Results:



0.

2

4.

6

8

10

12

14

16


Thro

ughp

ut (G

B/s)

Hash table size


Vector (Blending_8) Vector (Selec�ve_4) Vector (Selec�ve_8)



Summary:


For both selectivity rate, vertically vectorized code performs about 1.8x fasterthan horizontal vector and scalar implementation

-


Sources:

O. Polychroniou, A. Raghavan, K. A. Ross. Rethinking SIMD Vectorization forIn-Memory Databases

K. A. Ross. E�cient hash probes on modern processors.

M. Zukowski et al. Architecture-conscious hashing.

R. Pagh et al. Cuckoo hashing.[1]

[2]

[3]

[4]


Rafid Ahmed - db.in.tum.dedb.in.tum.de/.../seminarHauptspeicherdbs/slides/04-cuckoo-hashing.pdf ·...

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