University:
Boston University
Course:
GRS CS 910 | Directed Study: Systems
Academic year:

2023
Views:

289

Pages:

18
Author:

pisturaqftp

!"#$%&'()*$+&,-.$)/#,-0),$ ! !"#$%&'()*$+&,-.$)/#,-0),$&($1&2#*$34$ ! Cost to apply this matrix to a vector?! ! Bytes moved to/from memory?! ! Floating-point operations?! !"#$%&'()*+",-./0*%+1'2#%3'0%4&*' Spin-project (from 4 to 2 independent spin components), once per direction:! 8 x 12 = 96 flops! SU(3) multiply, once per direction: 8 x 132 = 1056 flops! Accumulate to the output spinor:! 7 x 24 = 168 flops! Altogether, this gives 1320 flops per site.! !"#$%&'()*+",-./0*%+1'2)*)'(%./(/&*' ! ! 3%'0)++4'%5*'*6/'!"#$%&'()*+",-./0*%+'7+%850*9'7/+'$"*/9':/' (5$*1' ;/)8'%&/'$7"&%+'7/+'8"+/0<%&9'=%+')'*%*)#'%='>','?@'A'BC?'D%)*$' Read one gauge matrix per direction, for a total of! 8 x 18 = 144 floats! Write one output spinor, consisting of 24 floats! Altogether, we must transfer 360 floats from memory, or 1440 bytes in single precision.! !"#$%&'()"*"&#'+(,--.%&/()"#.( ! ! 0&(1-2'3&("3#$%4'#453'67(4$'(1"%&()-8*'&'#.(%6(-9'&( )"&2:%24$(4-(1'1-3;7(3"4$'3(4$"&(3":(<-"=&/(>-%&4( 4$3-5/$>54?( 04(:"6&@4("*:";6(*%.'(4$%6+( (Cartoon by John McCalpin, author of the STREAM benchmark)! •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“Gulftown”! • • !"#$%&'$("&')*+,& • .",'+&-"/&$,0")1#0"23)14&"556"781#9" • :;:<"=1%%1'8"#+$8-1-#'+-" • 50$+&4">?"@$,0&A":B"CD" • >:E>BA"."F"/?BG"HD9"I":JBG"HD" • -*,&./(01&2345& • 67&.891&:$:(;<&=>"?@A?#B& • 7*"#'"BKK"LD"/J."LD"1-"+&$%1-M,9" 5:1! “Fermi”! CD!E!F&.$G(;H$&.I'&J+,& • 2KG",'+&-" • ?;G"=1%%1'8"#+$8-1-#'+-" • 50$+&4">B"@$,0&A"<.K"HD" • >:E5CEN&OA":P"F":JB"HD"I"BKKG"HD" • -6J)&./(01&2345& • -KK&.891&:$:(;<&=>"?@A?#B& • :;P"LD"/7*"#'"."LD"18"Q&-%$"R$+1$8#9" 7.5:1! !"#$%&$'()*+#,'-"&#',) ! ! • 5:1! Recall that in single precision, the Wilson matrix-vector product has a byte/flop ratio of just over 1 (slightly lower for clover).! We're entirely constrained by memory bandwidth. On the GPU, flops are virtually free.! • !"#$%&'()$*+,-$ ./$%01)$232'45$6789:;9<=$ • 7.5:1! • !.>?$%&'()$*+,-$ !@@$%01)$232'45$6789:;9<=$ !"#$%&%'()$*+&(,(-*)$ (GeForce GTX 480)! !"#$%&'()'*++,-)%+(./0% Serial on CPU and Data Parallel on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