BLIS Performs Devangi N. Parikh Science of High Performance - - PowerPoint PPT Presentation

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BLIS Performs Devangi N. Parikh Science of High Performance - - PowerPoint PPT Presentation

Dec 20, 2022 129 likes •311 views

BLIS Performs Devangi N. Parikh Science of High Performance Compu8ng The University of Texas at Aus8n ThunderX2 Architecture arm v8.1 Base frequency 2.0 GHz # sockets/node 2 # cores/socket 28 armv8a kernels in BLIS were wriOen by

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SLIDE 1

BLIS Performs

Devangi N. Parikh Science of High Performance Compu8ng The University of Texas at Aus8n

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SLIDE 2

ThunderX2

Architecture arm v8.1 Base frequency 2.0 GHz # sockets/node 2 # cores/socket 28

armv8a kernels in BLIS were wriOen by Fransisco D. Igual for cortexa57 architectures.

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SLIDE 3

DGEMM (armv8a)

200 400 600 800 1000 1200 1400 1600 1800 2000

matrix dimension m=n=k

2 4 6 8 10 12 14 16

GFLOPS DGEMM (single-threaded)

BLIS

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SLIDE 4

DGEMM – Other Libraries

200 400 600 800 1000 1200 1400 1600 1800 2000

matrix dimension m=n=k

2 4 6 8 10 12 14 16

GFLOPS DGEMM (single-threaded)

BLIS OpenBLAS ARMPL

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SLIDE 5

GEMM – Other Datatypes

200 400 600 800 1000 1200 1400 1600 1800 2000

matrix dimension m=n=k

5 10 15 20 25 30

GFLOPS SGEMM (single-threaded)

BLIS OpenBLAS ARMPL

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SLIDE 6

GEMM – Other Datatypes

200 400 600 800 1000 1200 1400 1600 1800 2000

matrix dimension m=n=k

5 10 15 20 25 30

GFLOPS CGEMM (single-threaded)

BLIS OpenBLAS ARMPL

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SLIDE 7

GEMM – Other Datatypes

200 400 600 800 1000 1200 1400 1600 1800 2000

matrix dimension m=n=k

2 4 6 8 10 12 14 16

GFLOPS ZGEMM (single-threaded)

BLIS OpenBLAS ARMPL

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SLIDE 8

Level 3

500 1000 1500 2000 5 10 15 20 25 30 GFLOPS SGEMM (single-threaded) 500 1000 1500 2000 5 10 15 GFLOPS DGEMM (single-threaded) 500 1000 1500 2000 5 10 15 20 25 30 GFLOPS CGEMM (single-threaded) 500 1000 1500 2000 matrix dimension m=n=k 5 10 15 GFLOPS ZGEMM (single-threaded) 500 1000 1500 2000 5 10 15 20 25 30 GFLOPS SSYRK (single-threaded) 500 1000 1500 2000 5 10 15 GFLOPS DSYRK (single-threaded) 500 1000 1500 2000 5 10 15 20 25 30 GFLOPS CSYRK (single-threaded) 500 1000 1500 2000 matrix dimension m=n=k 5 10 15 GFLOPS ZSYRK (single-threaded) 500 1000 1500 2000 5 10 15 20 25 30 GFLOPS SSYMM (single-threaded) 500 1000 1500 2000 5 10 15 GFLOPS DSYMM (single-threaded) 500 1000 1500 2000 5 10 15 20 25 30 GFLOPS CHEMM (single-threaded) 500 1000 1500 2000 matrix dimension m=n=k 5 10 15 GFLOPS ZHEMM (single-threaded) 500 1000 1500 2000 5 10 15 20 25 30 GFLOPS STRMM (single-threaded) 500 1000 1500 2000 5 10 15 GFLOPS DTRMM (single-threaded) 500 1000 1500 2000 5 10 15 20 25 30 GFLOPS CTRMM (single-threaded) 500 1000 1500 2000 matrix dimension m=n=k 5 10 15 GFLOPS ZTRMM (single-threaded) BLIS OpenBLAS ARMPL
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SLIDE 9

MulG-threaded BLIS (28 cores)

1000 2000 3000 4000 5000 200 400 600 800 GFLOPS SGEMM (multi-threaded) 1000 2000 3000 4000 5000 100 200 300 400 GFLOPS DGEMM (multi-threaded) 1000 2000 3000 4000 5000 200 400 600 800 GFLOPS CGEMM (multi-threaded) 1000 2000 3000 4000 5000 matrix dimension m=n=k 100 200 300 400 GFLOPS ZGEMM (multi-threaded) 1000 2000 3000 4000 5000 200 400 600 800 GFLOPS SSYRK (multi-threaded) 1000 2000 3000 4000 5000 100 200 300 400 GFLOPS DSYRK (multi-threaded) 1000 2000 3000 4000 5000 200 400 600 800 GFLOPS CSYRK (multi-threaded) 1000 2000 3000 4000 5000 matrix dimension m=n=k 100 200 300 400 GFLOPS ZSYRK (multi-threaded) 1000 2000 3000 4000 5000 200 400 600 800 GFLOPS SSYMM (multi-threaded) 1000 2000 3000 4000 5000 100 200 300 400 GFLOPS DSYMM (multi-threaded) 1000 2000 3000 4000 5000 200 400 600 800 GFLOPS CHEMM (multi-threaded) 1000 2000 3000 4000 5000 matrix dimension m=n=k 100 200 300 400 GFLOPS ZHEMM (multi-threaded) 1000 2000 3000 4000 5000 200 400 600 800 GFLOPS STRMM (multi-threaded) 1000 2000 3000 4000 5000 100 200 300 400 GFLOPS DTRMM (multi-threaded) 1000 2000 3000 4000 5000 200 400 600 800 GFLOPS CTRMM (multi-threaded) 1000 2000 3000 4000 5000 matrix dimension m=n=k 100 200 300 400 GFLOPS ZTRMM (multi-threaded) BLIS OpenBLAS ARMPL
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SLIDE 10

MulG-threaded BLIS (56 cores)

1000 2000 3000 4000 5000 500 1000 1500 GFLOPS SGEMM (multi-threaded) 1000 2000 3000 4000 5000 200 400 600 800 GFLOPS DGEMM (multi-threaded) 1000 2000 3000 4000 5000 500 1000 1500 GFLOPS CGEMM (multi-threaded) 1000 2000 3000 4000 5000 matrix dimension m=n=k 200 400 600 800 GFLOPS ZGEMM (multi-threaded) 1000 2000 3000 4000 5000 500 1000 1500 GFLOPS SSYRK (multi-threaded) 1000 2000 3000 4000 5000 200 400 600 800 GFLOPS DSYRK (multi-threaded) 1000 2000 3000 4000 5000 500 1000 1500 GFLOPS CSYRK (multi-threaded) 1000 2000 3000 4000 5000 matrix dimension m=n=k 200 400 600 800 GFLOPS ZSYRK (multi-threaded) 1000 2000 3000 4000 5000 500 1000 1500 GFLOPS SSYMM (multi-threaded) 1000 2000 3000 4000 5000 200 400 600 800 GFLOPS DSYMM (multi-threaded) 1000 2000 3000 4000 5000 500 1000 1500 GFLOPS CHEMM (multi-threaded) 1000 2000 3000 4000 5000 matrix dimension m=n=k 200 400 600 800 GFLOPS ZHEMM (multi-threaded) 1000 2000 3000 4000 5000 500 1000 1500 GFLOPS STRMM (multi-threaded) 1000 2000 3000 4000 5000 200 400 600 800 GFLOPS DTRMM (multi-threaded) 1000 2000 3000 4000 5000 500 1000 1500 GFLOPS CTRMM (multi-threaded) 1000 2000 3000 4000 5000 matrix dimension m=n=k 200 400 600 800 GFLOPS ZTRMM (multi-threaded) BLIS OpenBLAS ARMPL
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SLIDE 11

Other Architectures SkylakeX (single core)

500 1000 1500 2000 20 40 60 80 100 GFLOPS SGEMM (single-threaded) 500 1000 1500 2000 10 20 30 40 50 GFLOPS DGEMM (single-threaded) 500 1000 1500 2000 20 40 60 80 100 GFLOPS CGEMM (single-threaded) 500 1000 1500 2000 matrix dimension m=n=k 10 20 30 40 50 GFLOPS ZGEMM (single-threaded) 500 1000 1500 2000 20 40 60 80 100 GFLOPS SSYRK (single-threaded) 500 1000 1500 2000 10 20 30 40 50 GFLOPS DSYRK (single-threaded) 500 1000 1500 2000 20 40 60 80 100 GFLOPS CSYRK (single-threaded) 500 1000 1500 2000 matrix dimension m=n=k 10 20 30 40 50 GFLOPS ZSYRK (single-threaded) 500 1000 1500 2000 20 40 60 80 100 GFLOPS SSYMM (single-threaded) 500 1000 1500 2000 10 20 30 40 50 GFLOPS DSYMM (single-threaded) 500 1000 1500 2000 20 40 60 80 100 GFLOPS CHEMM (single-threaded) 500 1000 1500 2000 matrix dimension m=n=k 10 20 30 40 50 GFLOPS ZHEMM (single-threaded) 500 1000 1500 2000 20 40 60 80 100 GFLOPS STRMM (single-threaded) 500 1000 1500 2000 10 20 30 40 50 GFLOPS DTRMM (single-threaded) 500 1000 1500 2000 20 40 60 80 100 GFLOPS CTRMM (single-threaded) 500 1000 1500 2000 matrix dimension m=n=k 10 20 30 40 50 GFLOPS ZTRMM (single-threaded) BLIS OpenBLAS MKL
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SLIDE 12

Other Architectures SkylakeX (20 cores)

1000 2000 3000 4000 5000 500 1000 1500 2000 GFLOPS SGEMM (multi-threaded) 1000 2000 3000 4000 5000 200 400 600 800 1000 GFLOPS DGEMM (multi-threaded) 1000 2000 3000 4000 5000 500 1000 1500 2000 GFLOPS CGEMM (multi-threaded) 1000 2000 3000 4000 5000 matrix dimension m=n=k 200 400 600 800 1000 GFLOPS ZGEMM (multi-threaded) 1000 2000 3000 4000 5000 500 1000 1500 2000 GFLOPS SSYRK (multi-threaded) 1000 2000 3000 4000 5000 200 400 600 800 1000 GFLOPS DSYRK (multi-threaded) 1000 2000 3000 4000 5000 500 1000 1500 2000 GFLOPS CSYRK (multi-threaded) 1000 2000 3000 4000 5000 matrix dimension m=n=k 200 400 600 800 1000 GFLOPS ZSYRK (multi-threaded) 1000 2000 3000 4000 5000 500 1000 1500 2000 GFLOPS SSYMM (multi-threaded) 1000 2000 3000 4000 5000 200 400 600 800 1000 GFLOPS DSYMM (multi-threaded) 1000 2000 3000 4000 5000 500 1000 1500 2000 GFLOPS CHEMM (multi-threaded) 1000 2000 3000 4000 5000 matrix dimension m=n=k 200 400 600 800 1000 GFLOPS ZHEMM (multi-threaded) 1000 2000 3000 4000 5000 500 1000 1500 2000 GFLOPS STRMM (multi-threaded) 1000 2000 3000 4000 5000 200 400 600 800 1000 GFLOPS DTRMM (multi-threaded) 1000 2000 3000 4000 5000 500 1000 1500 2000 GFLOPS CTRMM (multi-threaded) 1000 2000 3000 4000 5000 matrix dimension m=n=k 200 400 600 800 1000 GFLOPS ZTRMM (multi-threaded) BLIS OpenBLAS MKL
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SLIDE 13

Other Architectures SkylakeX (40 cores)

1000 2000 3000 4000 5000 1000 2000 3000 4000 GFLOPS SGEMM (multi-threaded) 1000 2000 3000 4000 5000 500 1000 1500 2000 GFLOPS DGEMM (multi-threaded) 1000 2000 3000 4000 5000 1000 2000 3000 4000 GFLOPS CGEMM (multi-threaded) 1000 2000 3000 4000 5000 matrix dimension m=n=k 500 1000 1500 2000 GFLOPS ZGEMM (multi-threaded) 1000 2000 3000 4000 5000 1000 2000 3000 4000 GFLOPS SSYRK (multi-threaded) 1000 2000 3000 4000 5000 500 1000 1500 2000 GFLOPS DSYRK (multi-threaded) 1000 2000 3000 4000 5000 1000 2000 3000 4000 GFLOPS CSYRK (multi-threaded) 1000 2000 3000 4000 5000 matrix dimension m=n=k 500 1000 1500 2000 GFLOPS ZSYRK (multi-threaded) 1000 2000 3000 4000 5000 1000 2000 3000 4000 GFLOPS SSYMM (multi-threaded) 1000 2000 3000 4000 5000 500 1000 1500 2000 GFLOPS DSYMM (multi-threaded) 1000 2000 3000 4000 5000 1000 2000 3000 4000 GFLOPS CHEMM (multi-threaded) 1000 2000 3000 4000 5000 matrix dimension m=n=k 500 1000 1500 2000 GFLOPS ZHEMM (multi-threaded) 1000 2000 3000 4000 5000 1000 2000 3000 4000 GFLOPS STRMM (multi-threaded) 1000 2000 3000 4000 5000 500 1000 1500 2000 GFLOPS DTRMM (multi-threaded) 1000 2000 3000 4000 5000 1000 2000 3000 4000 GFLOPS CTRMM (multi-threaded) 1000 2000 3000 4000 5000 matrix dimension m=n=k 500 1000 1500 2000 GFLOPS ZTRMM (multi-threaded) BLIS OpenBLAS MKL
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SLIDE 14

Conclusion

BLIS instan8ates high-performance implementa8ons across virtually all level-3 opera8ons, parameter cases, and datatypes with just two microkernels.

  • sgemm
  • dgemm
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SLIDE 15

Thank you!

  • Thanks to Fransisco D. Igual for running

experiments on a frequency stable SkylakeX.

  • Thanks to Cavium and ARM for access to

ThunderX2.

(More plots on poster)

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SLIDE 16
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SLIDE 17

Details

  • ThunderX2
  • 2.0 GHz
  • 2 sockets
  • 28 cores/socket
  • Hardware threads turned off
  • OpenBLAS (commit 52d3f7a), built for target

THUNDERX2T99

  • ARMPL: armpl-18.4.0_ThunderX2CN99
  • 1 socket: JC_NT = 2; IC_NT = 14
  • 2 socket: JC_NT = 4; IC_NT = 14
  • SkylakeX
  • 1.7 GHz
  • 2 sockets
  • 20 cores/socket
  • Frequency throOling turned off
  • OpenBLAS (commit 4dd70d9)
  • MKL 18
  • 1 socket: JC_NT = 1; IC_NT = 20
  • 2 socket: JC_NT = 2; IC_NT = 20
  • Haswell
  • 3.2 GHz/3.0 GHz
  • 2 sockets
  • 12 cores/socket
  • MKL 11.3
  • 1 socket: JC_NT = 2; IC_NT = 6
  • 2 socket: JC_NT = 4; IC_NT = 6
  • For single-threaded experiments, each graphs plots GFLOPS as a

func8on of problem size--varied from 40 to 2000 in increments of 40--where all matrix operands' dimensions (m, n, k) are bound to the problem size. In other words, all matrices are square.

  • For mul8-threaded experiments, each graphs plots GFLOPS as a

func8on of problem size--varied from 200 to 5000 in increments of 200–where all matrix operands' dimensions (m, n, k) are bound to the problem size. In other words, all matrices are square.

  • The y-axis is scaled so that the top of the graphs correspond to

theore8cal peak for the clock rate.

  • All results are performed on random data, with each point of each

graph represen8ng the best (shortest run8me) of three trials.

  • I've omiOed legends from all graphs except one in the boOom-

right, only to minimize cluOer.

  • BLIS uses the 1M-induced methods for C,Z opera8ons (ThunderX2,

and SkylakeX)