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70
400
4 CSHIFTs
50
300
4 OVERLAP_CSHIFTs
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Optimized program
200
40
30
20
Original program
100
10
0
64
128
192
256
320
384
Subgrid size (squared)
448
512
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256
320
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100
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25
4 CSHIFTs
4 OVERLAP_CSHIFTs
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Execution time (ms)
80
Optimized program
20
15
60
10
Original program
40
5
Optimized program
20
0
8
16
32
48
64
80
Subgrid size (squared)
96
112
128
8
16
32
48
64
80
Subgrid size (squared)
96
112
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Optimized program
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150
100
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50
Original program
20
Optimized program
0
4
6
8
10
12
14
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16
18
0
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8
10
12
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Subgrid size (squared)
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10000
CSHIFT specification
Execution time (ms)
8000
exceeded
memory
Purdue Problem 9
6000
4000
2000
0
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128
192
256
320
384
Subgrid size (squared)
448
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v@m…mˆkXjt„…sUv-s ' v&‰5fG{Dg’ Š-‹ ’ ŠŒ kGgp{lg qC{lgsGjC„ZorqCs$}¦$fG”G&v@wpqChlgqC{l{|q}r{Dg:y™gp{lg/sw:gCm,hlkqChqt”G”gCqC{
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hlkGgqt{l{|qp} # jIsG-} ‹p! jtyhlkGg/o qC{lg(fGsXv@J8fGg ŠŒ kGv@m…g *gCw:hDv-†8gp&}iwEfGh3m\hDkGg&j8j5”‡qC@qCsw:g  Ž
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88µµ
88µµ
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88µµ
88µµ
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5º ±*³n´± º ³nW´ ¶ ]³ ¸€¼ ,¶ 5¼*º ³¸¼ W¶ ‘»–º³ ¸
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5¼*³ uº¼³ Gº8»¸ º8¸
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v-srkqt6y ŠŒ kXv@m-j8jI”
{DfGsmmˆv-‰IsGv ®wpqtsuhl&} y>qImˆhlg/{…hlkqCs
hlkXg‚jI{lv&‰5v-s–qt]j5srorq5w3kGv&sGgCmWhDkqth…k–q†8g q
{lgpxqthlv&†8gp-} mnorqt&$orqIw kXv-sGg‡qtxqtsw:g  ƒŽ Š,' j5{qt{|w kXv-hlgw:hlfG{DgCmń…v&hlkƒv-smnhl{lf–w:hlv&j5s$¢>-gp†8g/$”qC{3qC<¢
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hljƒ{lgp‰Iv@mˆhDgp{3m # wpqCs
‡ggpËugCw:fGhDgCv-sr”qC{3qC--g/ Š
2MK 8 ¥_a` 6 Wc T^ ¤V®^ V
Œ jroigCqImˆfG{DghDkGg(”gp{ˆy™jI{lorqCsw:g‡j8j¡mˆhƒmˆfX”G”G-v&gC ‡u}
gq5w3k¨mˆhlg/”jty…jIfG{ mˆhDgpsw:v&¤w:jIoi”Gv&@qthDv-jIs
mˆhl{|qthDgp‰5} # „g{3qCs
q mˆgph,jCy]hlgCmnh3mWjIsrqts ! ¢F”G{Djuw:gCmDmˆj5{Ê ) ¢ Š gmnh3qC{lhlg‡$}(‰IgpsGgp{|qthDv-sG‰
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j5fG{ ?87E9 H89@AG254 †8gp{|mˆv-jIs Š g(hlkXgps¨mˆfw/w:gCmlmnv-†8gp&}iqC”G”G&v-gC
hDkGghD{3qts–mMy™j5{DorqthDv-jIs¨q5m~j5fGhD-v&sGgC
v-sihDkGg”G{lgCwEgC$v-sX‰mnfG‡mngCw:hlv&j5sUqts– o¦gCq5mnfG{lgC(hlkXg~gpËugCw:fGhDv-j5s¦hlv-o¦g ŠŒ kGg{lgmˆfG&h3mqC{lg mˆkXjt„…s
v-s ' v-‰IfG{lg ’ Š “ Š
gEy™j5{lgqtsqC-}u%pv-sX‰hDkGg{DgCmˆfG&h3mv&s ' v&‰5fG{Dg(’ Š “ # v&h\vxmd„j5{lhDk$„…kXv--ghDjiw:jIoi”qC{lgv-hhljihDkGg
{lgCmnfG-h|m\mnkGjC„…sv-s ' v-‰5fX{lg(’ Š-‹ y™j5{hlkGg ) {lj5‡X-gpo ’ƒw:ju$g Š fX{ j5{lv&‰5v&sqtx£ ) ÊW†8gp{|mˆv-jIs
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jI”$¢
hlv-o¦v-%CqChlv-jIshljUhlkGg¦w:ju$g # qImmnkGjC„…s—v&s ' v-‰5fX{lg¦’ Š-‹ ŠŒ kXv@m‚{DgCmˆfX-hlg v&sPq
{lgC$f–w:hlv&j5s
v-srgpËugCw:fGhDv-j5s¦hlv-o¦g # gCJ‘fXv-†Iqt&gps$h,hDjiq(mn”®g/gC$fG”Ujty ‹5Š ! “ Š j5suhlgpËuh…”qC{lhlv&hlv&j5sGv&sG‰(„…qIm\qC”G”G-v&gC
sGgpËuh # qIm‚mnkGjC„…sv&s ' v-‰IfG{lgƒ’ Š-‹ Š(Œ kGvxm~j5”GhDv-oiv&%CqthDv-j5s qt&-jC„gCUmlwpqC@qC{lv-%qthlv&j5shDj o¦gp{l‰Ig(qt&
hlkGgrwEj5oi”GfXh3qthDv-jIsPv-suhlj q
mˆv&sG‰5&gi-j8jI”€sGgCmˆh # {lgCmnfG-hDv-sG‰Uv-sžq ‹ {lgCufw:hlv&j5s¨v-sPg/Ë$gCwEfGhlv&j5s
hlv-o¦g~jC†8gp{…hlkGg ”G{lg/†$v&j5fm†8gp{|mˆv&j5s Š h…hlkXv@m…”®jIv-suh\„gkqp†8g‚{DgC$fwEgC hDkGggpË$gw:fGhlv&j5srhlv&oig~jCy
hlkGgj5{Dv-‰Iv-sqC”G{ljI‰5{3qCo ‡$} # qmn”gpgC$fG”Ujty Š Š
gihDkGgpsžqt”G”G&v-gCj5fX{(w:jIoiofXsGv@wEqthDv-j5sUfGsGv&j5sGv&sG‰
jI”Ghlv&oiv-%CqChlv&j5s # qImmnkGjC„…s—v&s ' v-‰5fX{lg
’ Š-‹ ŠrŒ kGvxm~{lgCmnfG-h|m«v&sjIsG-}
y™jIfG{(wEj5oioƒfGsGv&wpqChlv-jIs
jI”®g/{3qthDv-jIsm‚‡gpv&sG‰r”®g/{ˆy™j5{DoigC # qCs {Dg:¢
$fw:gCm~hDkGg(gpËugCw:fGhDv-j5shDv-oig‡u}
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v-s 8gCwEhlv-jIs¨’ Š {DgC$fwEgC
hlkGg(g/Ë$gCwEfGhlv&j5s
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jCy Š-‹ ’
gmˆh…mnj5oig/j5sGg…hDkGv-s (hDkqth„g…kqp†8gzw kXj8mˆg/siÊ
m]Ë$&kG”$yaw:j5o¦”Gv-&gp{¤qImq mˆhl{|qp„QorqCs # „g
kqp†8gƒw:j5&-gCw:hDgCrmˆjIoig(qIG$v-hDv-jIsqt¤”gp{ny™j5{DorqtswEgsufGo‡gp{|m Š g(‰IgpsGgp{|qthlgqhlkGv&{3
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qC{l{|q}¨mn}$suh3qC˨mˆv&oiv-xqt{hljrhlkGg ¢>”j5v&s$h
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88µµ
88µµ
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5º ±*³n´± º ³³nW´ ¶ ]³ ¸€¼ ,¶ 5¼*º ³¸¼ W¶ ‘»–º³ ¸
¹± ¼ W¶ ųG»º8¸
¹
±± ¼¼ WW¶¶ Å
5¼*³ uº¼³ Gº8»¸ º8¸
¹
¹± ¼ W¶ 5¼*º³ u¼º8¸
¹
±
¼ W¶ ‘»–º³ G»º8¸
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aº—
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5¼*¼*ºº³³ u¼–¸ ²X¸
aº—
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,¶ ]³ ¸P
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²¹
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± ®² ¼ W¶ ų u¼ ¸
²¹±®² ¼ W¶ 5¼*º³ u¼º8¸
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‘¼*»–ºº³³ uu¼¼º8¸¸
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¾± °¼ W¶ ųu¼–²X¸
¾
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5¼*³ uº¼ ³ *u¼–¸ ²X¸
¾
¾± °¼ W¶ 5¼*º³ u¼*¸
¾
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-
-
-
-
‹‹
500
Original program
Offset arrays
Execution time (ms)
400
Context Partitioning
300
Communication Unioning
Memory Optimizations
200
100
0
64
128
192
256
320
384
Subgrid size (squared)
448
512
…À @Á * ˆm Åà Dh 3{CÄ Cq Æ lh pg : I‰ È } Ij s 8) Dh l{ pg Ij $” G‡ >¢ - …„ /g o @v ˆm g (’ D{ Cg…„ ˆm GkGf pg& 3h rs Wm pg ™y D{uË 5j Cg o :w Gf Dh nm Cglh pg s Ij Ew s -v  tq Ew s5j io G” ) &v ¢ @ Cq lhŠ -v Ij s
v-suhlgp{Dv-j5{gp&gpoigpsuh3m,jtyhlkGg(o qthl{Dv-Ë*.®hDkqthzv@m # gp-gpo¦gps$h|m +)d¢ ‹ v-sgq5w3k$v&oigpsmnv-j5s Š ‰I{3qC”Gk
w:j5oi”–qt{lv&sG‰iv&h3m\gpËugCw:fXhlv-jIs
hDv-oighlj¦hlkGg(jIhlkGgp{hn„j ’¢>”®jIv-suh mˆhlg/sw:v-¥mˆ”gCwEv *wpqChlv&j5sm\vxm\‰5v&†8gps
v-s ' v-‰IfG{lg ’ Š ‹IŠŒ kXgÊ Ëu-kG”uy,w:jIoi”Gv&-gp{,„…qImfmˆg v-sUqC-w/q5mˆgm Š
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ofGsXv@wpqChlv-jIs # ”G{lg/†8gps$h,hDkGg~‰5g/sGgp{3qChlv&j5srjty¥v-suhl{|qt”G{Djuw:gCmlmnj5{w:jI”$}uv-sX‰ # qCsij5”GhDv-oiv&%pg…hlkXgw:j5oƒ¢
”GfGh3qChlv&j5s(y™j5{¤hDkGgqt{D{3qp}‘¢Mmˆ}usuh3qt˃mnhlgps–w:v- Š ÊFsy>qIw:h # hDkGv@m¥mˆ”gCw:v *wpqthDv-jIs(jty*hlkGg 8g/{lsGgpu”G{Dju$fw:gC
”®g/{ˆy™j5{Dorqts–w:g,s$fGoƒ‡gp{3mhlkqCh¤hl{|q5w 8gC\jIfG{¤‡gCmˆh]”gp{ˆy™jI{lorqCsw:g,sufGo‡gp{|m–y™jI{¤qC-u”G{ljI‡G-gpo mˆv-%/gCm
gpËGwEgp”GhhDkGg@qC{l‰5gmˆh # „…kXgp{lg„gkqI
q ‹ “ Ÿq5$†IqCs$h|qt‰5g Š
Œ kXv@m~$g/oij5smnhl{|qthlgm\hlkGg ”G{ljI‡G-g/o „…v&hlk¨w:jIoi”Gv&-gp{…jI”Ghlv&oiv-%CqChlv&j5sm‡qImˆgC
fX”®jIs”–qthlhDgp{ls
orqth|w kGv&sG‰ Š kGgps¨hlkGg¦w:jIoi”Gv-&gp{v@mqC‡G-gƒhljUorqth|w k¨qr”qthDhlgp{Dsv&shDkGgifmngp{ "m~”G{ljI‰5{3qCo # v&h
wpqtsU”G{lju$f–w:ggpËXw:gp&-gpsuh,w:juug Š fXh…v<y¥hlkGgfmngp{ "m”G{ljI‰5{3qCo $gp†uv@qthDgCm…mˆ&v-‰Ik$hD-} # hlkGg w:jIoi”Gv-&gp{
wpqtsGsXj5h…orqCh3w3kƒq‚”qChlhlg/{lsrqCshlkXgw:ju$gv-h”G{lju$f–w:gCmWvxm¤oigC$v&juw:{lgqCh‡gCmˆh Š ÊFhv@m¤v&oi”j5{lh|qtsuh
hljsXj5hlghlk–qthhDkGgzmˆhlg/sw:v-–w:j5oi”Xv-@qChlv&j5sƒmˆhD{3qChlgp‰I}hDkqth„g…kqp†8g”G{lgCmngpsuhlgC(kqts–$-gCm,qC-hlkG{Dgpg
mˆ”gCw:v *wpqthDv-jIsmjtyzhlkGgU’p¢F”j5v&s$hƒmnhlgps–w:v-gCJ‘f–qt-&}„gp- ŠŒ kqChvxm‚‡gCwpqCfmˆgrj5fX{iqC-‰5jI{lv&hlkGo v@m
‡q5mngC fG”jIs hDkGg qtsqC-}Xmˆvxm…qtsij5”Xhlv-o¦v-%CqChlv-jIsjCy¤hDkGg‡q5mng w:j5smnhl{Dfw:h3mfX”®jIs
„…kGvxw k mˆhlg/sw:v-xm
qt{lg(‡XfGv-&h Š fG{zqt&‰5jI{lv-hDkGo vxm~$gCmnv-‰IsGgC hDjikqCs$-g(hDkGg&jC„gCmnh~w:jIoioijIs
ugpsGj5o¦v-sqChlj5{ Uq
y™j5{lo v-suhlj(„…kGvxw krj5fX{~w:jIoi”Gv&-gp{,w/qts
hD{3qCsmMy™jI{lo qt&mˆhDgpsw:v&w:jIoi”GfGh|qthDv-j5s–m Š
"
$#
#
‹
10000
exceeded
memory
CSHIFT specification
Purdue Problem 9
8000
Execution time (ms)
Array syntax
6000
4000
2000
0
64
128
192
256
320
384
Subgrid size (squared)
448
512
À…Á Â*Ã]ÄtÆ : È *É j5oi”qC{lvxmˆj5srjCy,hlkG{Dgpg’p¢F”j5v&s$hzmˆhDgpsw:v&mn”®gw:v *w/qthlv&j5sm Š
2 2 W^DT ¤ _
sXg\jCyhlkXg {|mˆhorq lj5{¥g *j5{lh|mWhDjmn”gCw:v ®wpqt&-}(qIG${DgCmlm,hlkGgw:jIoi”Gv&@qthDv-jIs(jty]mnhlgps–w:v-wEj5oi”Gfu¢
h3qthDv-jIsmy™jI{q $v@mnhl{Dv-‡GfGhDgC‘¢>oigpoƒj5{D}‚o q5w3kGv-sGg„…qImhDkGgzmˆhlg/sw:v-–w:j5oi”Xv--g/{ y™jI{WhDkGg ¢ # qtxmˆj
$sGjC„…sžq5m~hlkXgƒw:j5su†8j5&fGhlv&j5swEj5oi”Gv&-gp{ © # # ’5ª Š Œ kGgp}Ugp-v&oiv-sqChlgCihDkGg(v-suhl{|qt”G{Djuw:gCmlmnj5{
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