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FH2?, ./2?^IK?, >mtJ¤0o2 F>$Y]:sY],1K 8-b-,ZYIK?, >M,10_2 V V V V \_, >GFHA908IFHghY_4H,1gh,10_2:B25F7[¨0}:B0]\Y],1KMLj[9K?g:s0]./,*[BL2 ,*2Pb-[qgqF`\I\¨4H,4: 69,1K/>1m V User processes Library Library User space Kernel space Kernel extension FHA9^IK@, »¦n ,">M6I>M2?,1gþ:BK. F72@, ./2?^IK?, >|[BL´ +ncC)m ¬ V V M M 300 | overhead in dropping unnecessary messages M M | M 250 M M M M M M M | time in usecs 200 150 | 100 | M M MNM M M 50 | 0 || | | | | | | | 0 200 400 600 800 1000 1200 1400 packet size in bytes F7A¨^IK?,&I»En ,[Bv9,1K , :9\[BL¦\_K?[9YIY_FH0IA¥:s0Z^I0I0I, ./, >?>?:BK?6Zg, >?>?:BA9,9m V V 3000 | one-way latency 2500 | | time in usecs 2000 1500 | 1000 | 500 | 0 || | | | | | | | 0 200 400 600 800 1000 1200 1400 packet size in bytes F7A¨^IK?,"z]»En ,[90I,1ijbc: 6q4`:B2?,10]./6Z[BL¦´D+)ncC)m V O O 10 | effective bandwidth O O OO O OO O OPOPO OPO OPO O O O OPO O O O OQO O O O O O O O O O O O O O O 8 | 6 | bandwidth in Mbits/sec 4 | 2 | 0 || | | | | | 0 10 20 30 40 50 message size in MBytes FHA9^IK?, »~n ,*,/u, ./2MFHv9,"X]:B0]\_bF\_2 [BL¦´D+)ncC)m T V V R R R T S | 4 processors (slow subset) S 64.0 S 4 processors (fast subset) R T T T S 32.0 | 8 processors T R S 16.0 | R T S | R 8.0 T R T S R T | S R 4.0 T R T R T R R S R R T R T T T T | 2.0 S S S | S S S S 1.0 S 0.5 || | | | | | | | | | | | | | | time (in msecs) per MPI_Bcast, in log scale 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Log (message size in bytes) FHA9^IK?,"xI»¦n ,*2MFHgh,"[BL¦ V V y ¬ U U 8 | 4 processors (slow subset) V V 4 processors (fast subset) U | W W 7 W 8 processors | 6 U W V 5 | U | 4 W V U W U | 3 W U W U U V U U W U W W W W | time (in msecs) per MPI_Bcast 2 V V V V | V V V 1 V 0 || | | | | | | | | | | 2 3 4 5 6 7 8 9 10 11 12 Log (message size in bytes) FHA9^IK?,§3»¦n ,*2MFHgh,"[BL¦ V V X X Z 1024 | 4 processors (slow subset) Y Y 4 processors (fast subset) | X Z Z 512 8 processors Z Y | Z 256 X Y | X 128 Z Y | X 64 Z Y | X 32 Z Y X | 16 Z Y Z Z X | Z Z Z Z Z X 8 Z X Y X X X X | X X Y Y 4 Y Y Y Y Y Y 2 | 1 || | | | | | | | | | | | | | | 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 time (in msecs) per MPI_Allgather, in log scale Log (message size in bytes) FHA9^IK?, »En ,"2MFHgh,*[sL' ¹ V V V ¬ V [ [ 14 | 4 processors (slow subset) \ \ 4 processors (fast subset) ] ] ] 12 | 8 processors 10 | ] ] | [ 8 ] ] ] ] [ ] | 6 ] [ \ [ [ [ | [ [ 4 [ \ \ \ \ \ \ \ \ | time (in msecs) per MPI_Allgather 2 0 || | | | | | | | | 2 3 4 5 6 7 8 9 10 Log (message size in bytes) FHA9^IK?, »En ,"2MFHgh,*[sL' V V V ¬ V ¬I | 800 ^ 700 | ^ 600 | ^ | 500 ^ ^ 400 | ^ 300 | ^ 200 | 100 | msec per all-to-all broadcast of 64 KByte message 0 || | | | | | | 2 3 4 5 6 7 8 Number of processors F7A¨^IK?, yI»*n ,2MFHgh,h[BLc<}C'J c4l4HA3:B2 ,1KO¤|47A¨[9KMFH2 g 85¦}Ö RD:¨>*:La^I0]./2MFH[90¢[BL2 ,03^IgqX],1K[BL V V V ¬ V b[¨K?>52:B2MFH[90]>~^]>GFH0IAZ>G4H[®b¶>M^IX]>M,12 m _ _ | 450 _ 4 processors 400 | | _ _ 350 _ _`_ _ _ _ 300 | 250 | 200 | 150 | 100 | 50 | 0 || | | | | | | | | | | | | | | | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 K msec per all-to-all broadcast of 64 KByte message FHA9^IK?, »En ,*2MFHgh,[BL¦<}C'J c4l4HA3:B2 ,1K*:9>c:&La^I0]./2MFH[90=[BL¦^]>GFH0IA¥>G4H[Bbe>M^IX]>5,12 m 9 V V a a b 4 processors (slow subset) a b b | 4 processors (fast subset) c a 64.0 b c c 8 processors | c a 32.0 b | c a 16.0 b a c | 8.0 b c a a c a | c b 4.0 a c a c b a a c a a b c c 2.0 | b b | b b b 1.0 b 0.5 || | | | | | | | | | | | | | 2 3 4 5 6 7 8 9 10 11 12 13 14 15 time (in msecs) per MPI_Scatter, in log scale Log (message size in bytes) FHA9^IK?, »¦n ,*2MFHgh,[BL ¬ V V ¬9¬ d d | 9 4 processors (slow subset) d f e e | 4 processors (fast subset) f 8 f 8 processors e 7 | | f 6 d | d 5 f d | 4 f e d | f d f 3 e d d f d d f e f | time (in msecs) per MPI_Scatter 2 e e e | e e 1 e 0 || | | | | | | | | | 2 3 4 5 6 7 8 9 10 11 Log (message size in bytes) FHA9^IK?, ²»¦n ,*2MFHgh,[BL V V | i 256.0 g h g g | 4 processors (slow subset) i g h h 128.0 h 4 processors (fast subset) i | i i h 64.0 8 processors g i | h g 32.0 i g | h 16.0 i h | g 8.0 i g | h i 4.0 g g i g | g g g g g i h i 2.0 i i h i h | h h h h 1.0 h 0.5 || | | | | | | | | | | | | | | 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 time (in msecs) per MPI_Gather, in log scale Log (message size in bytes) FHA9^IK@, z]»En ,*25F7g,"[BL¦ V V V j j | 12 4 processors (slow subset) l k k 4 processors (fast subset) l l 10 | 8 processors k | 8 j l 6 | | 4 j k l j j l j time (in msecs) per MPI_Gather | j j j j j l k l l l k 2 l k k k k k k 0 || | | | | | | | | | 2 3 4 5 6 7 8 9 10 11 Log (message size in bytes) FHA9^IK@, »En ,*25F7g,"[BL¦ T V V V ¬ m m 5 | slow subset m n n m fast subsetm m m m | 4 m | 3 n n n n n 2 | n n | time (in msecs) per MPI_Barrier 1 0 || | | | | | | 2 3 4 5 6 7 8 Number of workstations F7A¨^IK?, x²»n ,*2MFHgh,"[BL¦ V V o o 0.9 | 4407 vector length p p o | 1102 vector length 0.8 0.7 | time in secs 0.6 | o 0.5 | 0.4 | o 0.3 | | 0.2 p p | 0.1 p 0.0 || | | | 1 2 3 4 number of processors F7A¨^IK?, 3»QC),1KMLa[¨K?g:B0]./,=[BL>5Y]:BK>M,=g:B2?KMFl Iijv9, ./2?[9K$gq^_4H2MFHY_4F`.1:B25F7[¨0 :9>:QLj^I0]./2MFH[90[BL*0_^Ig&X;,1KZ[BL YIK?[./, >@>M[9K>~Lj[9Kc2Mb-[qv9, ./2?[9K~4H,10IA92 >|^]>GFH0IA$[9^IKD V q q 3.0 | 4407 vector length r r | 2.8 1102 vector length q speedup 2.6 | r 2.4 | 2.2 | 2.0 | 1.8 | q | 1.6 r 1.4 | 1.2 | q r 1.0 || | | | 1 2 3 4 number of processors F7A¨^IK?, »)¨9Y],1, \_^IYq[BLW>MY]:BK/>M,Eg:B2?K5F Iijv9, ./2?[¨Kgq^_4725F7Y_4lF`.1:B2MFH[90$:9>:~Lj^I0]./2MFH[90q[BLI03^IgqX],1K)[BLIYIK?[I./, >?>M[9K> ¹ La[9K|2Pb-[qv9, ./2?[¨K¦4H,10IA92 >c^]>GFH0IA$[9^IKD V z ¬ s s 6 | MPL on UDP protocol t t t MPI-CCL on URTP protocol 5 | s time in secs 4 | s 3 | t s 2 | t 1 | 0 || | | | 1 2 3 4 number of processors F7A¨^IK?, »C),1K5La[9K@g:B0]./,*[BL¦\_,10]>M,"g$:B2?KMFl Iijg:B2?KMFl Zgq^_4725F7Y_4lF`.1:B2MFH[90¢^]>GFH0IA[9^IK <}C'J¤iM³c³-«p[90´ +)ncC YIK?[92?[I./[B4v9,1K>M^]>2 :B2c^]>GFH0IA$JP©-<Ö V V ¬9¹ ¬¨¹ u u 8.000 | 128 by 128 matrix u v v 64 by 64 matrix | w 4.000 w 32 by 32 matrix u 2.000 | u 1.000 | v 0.500 | v 0.250 | time in secs, log scale v 0.125 | | 0.062 w w | 0.031 w | | | | 1 2 3 4 number of processors F7A¨^IK?, yI»QC),1KMLa[¨K?g:B0]./,=[BL&\_,10]>M,Qg:B2?K5F Iijg:B2@KMFl og&^_4H2MFHY_4lF`.1:B2MFH[90¡:9>$:QLj^I0]./2MFH[90t[BL"0_^Ig&X;,1KZ[BL ¬ YIK?[./, 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ONFN8+-*¯"Ã*¦-R)' +-, ./,/FHv9, \_¸°FH0]\_[®b ©:¨>M,BO¤gZR"ûÖF3' \_[90I,zû ' ä ,/4`>M, â ¨96> ¨9,10]\;³¦2?KM4jOP+c¦"8]g=8_FjR)' ¸k: FH2? 0]\Iµ [9^IX_4H,BOP\_,/4`: 698<}:® ²+-, ./v_¸k: FH21R&' ä ä K?,12?^IK@0O¤XIYR)' ä FHA9^IK?, »)DYIY_4lF`.1:B2MFH[90w³:®44¤»-+-, ./vm ¬9T ¬9¹ :B0]\¨4H,BO?R V â \_[h^I0_2MFl4OG0I[&g[9K?,*Y]:9.@9,12>/R â ¨96I>?+-, ./v;OP²K?,1, ©~^_LN>18;g>MA²R)' >5b-FH2. OGg>MA]mÏ2M6_Y],BR V â n C~n*» .1:9>M,"C~n .1:9>M,"©|³¦¨3n*» ý :B0]\¨4H,B¨3¯DµOGg>MAIR)'²XIK?, :B[' .1:9>M,"+c¦"» ý :B0]\¨4H, +c¦V*OGg>MAIR)';XIK?, :B[' .1:9>M,**³-Îq» ý :B0]\¨4H,1*³ÎO¤g$>MAIR)'IXIK@, :B' ä ä K?,12?^IK?05' ä FHA9^IK?, x²»-¨BFHA90]: 4ý :B0]\¨4H,1K » :B0]\¨4H,9m ¬ V ýD:B0]\¨4H,1*³-ÎO¤g>MAIR â g ûÊg>MA]m>5[9^IK./,' FLûÊg>MA]m./[¨^I032Q' #"ûͨ9,10_2?¸°F70]\_[BbD©-:9>5,BO¤gZR)' FlLcO¤J¤0I¸°FH0]\_[Bb*OjF¤8 #/R?R¦2 ,10 V â FlF ûÖJ¤0]. OjF¤8+-*¯"Ã*¦-R)' ²K?,1,B¨9,10]\I©~^_LPOGg8#18_FlFjR)' ¨9,10_2?¸°FH0]\_[BbD©-:9>M,BO¤gZR.û±µ , . 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O¤,98+-¯íæR)' FlLcO¤J¤0I¸°FH0]\_[Bb*O¤,98 #/R:B0]\=OM+-, ./,/FHv9, \;O¤g8;,1,BRÖ ¯ ´ ««)R?R¦2 ,10 V ¨96I>/¨9,10]\;³¦2@KM4jOP+c¦V"8;g8I,BR&' 4`:û±« :9>M2?*.?¨, \;O¤gZR)' FlLcO?O¤,°4`:£t.@3¸°FH0]\_[Bb*R¦[9KOP+-*¯"Ã*¦+-*¯"Ã*¦ ,z°4`:¨t*.@3¸°FH0]\_[Bb*R?R¦2 ,10 V â , : ûɵ , . O¤,98]+¯íæR)' ¨96I>/¨9,10]\;³¦2@KM4jO¤*³Îq8;g8_, :_R)' « :9>M2?*.?¨, \;O¤gZR û±, :³' ä n [3[3¦~:BKM4H6;O¤gZR ûÉy³' ¦) IY], ./2@, \;O¤gZR"ûÖ,' K?,12?^IK@05' ä FHA9^IK?, »Eý :B0]\¨4H, ¦) IY], ./2?, \¢OP.1: 4l4H, \=X36Zý :B0]\¨4H,B¨3¯DµRm ¬9 9y ýD:B0]\¨4H,B¨3¯ µO¤g>MA²R â g ûÊg>MA]m>5[9^IK./,' FLûÊg>MA]m./[¨^I032Q' #"ûÉ+-, ./,/FHv9, \_¸°FH0]\_[BbD©-:9>M,BO¤gZR&' FlLcO¤J¤0I¸°FH0]\_[Bb*OjF¤8 #/R:B0]\=OP+, ./,/F7v¨, \;O¤g8²FaR.Öe¯ ´D««R?R2 ,10 V â +, ./,/F7v¨, \;O¤g8²FaR"û±:9\I\_K?, >@>/O¤g>MA²R)' ,û˦) IY], ./2?, \;OGgZR)' FlLcO¤,]Ö-FjR¦2 ,10}ý :B0]\¨4H, ¦) IY], ./2?, \;O¤g=8#18I,BR)' V ,/4`>M, â n[_[3¦~:BKM4H6]OGgZR û±J¤0]. OMn[_[3¦¦:sKM4H6]O¤gR8I+c¦VDµ ,/4`: 6]R&' FlLcOPn[_[3¦~:BKM4H6]OGgZRVÖey_R¦2 ,10 V â ¨96I>/¨9,10]\;³¦2?K54aOM+c¦V"8;g8I,BR)' «:¨>M2?*.?9, \;OGgZR ûɵ , . O¤,98]+¯íæR)' ä ä ä ,/4`>M,&²K?,1,BO¤g>5AIR)' K?,12?^IK@05' ä FHA9^IK?,q9yI»EýD:s0]\¨47,B¨3¯ µOM.1: 4l47, \=X_6 :s0]\¨47,BR/m V IK?,1,B¨9,10]\I©~^_LMO¤g81# 8_FlFjR â \_[hb Fl4H,$Ol#ÖtFFjR V â ²K?,1,BO?¨9,10_21O¤g8#/R?R)' #"û±JG0]. Ol#18]+-*¯"Ã*¦-R)' ä K?,12?^IK@05' ä F7A¨^IK?,& »²K?,1,B¨9,10]\I©~^_LcOjLjK?,1, >-XI^_u,1K>/Rm