" CS"#$I&"'$B ") Lo op sk ewing Used - - PDF document

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cs i b lo op sk ewing used with lo op in terc hange to
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" CS"#$I&"'$B ") Lo op sk ewing Used - - PDF document

Jan 26, 2024 314 likes •393 views

" CS"#$I&"'$B ") Lo op sk ewing Used with lo op in terc hange to exploit parallelism in w a v efron t computations5 do i # $% n'( do j#$% m'( a,i%j-#a,i'(%j-. a,i %j '(- .a ,i. (% j-.

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SLIDE 1 CS"#$I&"'$B ") ! " # Lo
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sk ewing Used with lo
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in terc hange to exploit parallelism in w a v efron t computations5 do i # $% n'( do j#$% m'( a,i%j-#a,i'(%j-. a,i %j '(- .a ,i. (% j-. a, i%j .(
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enddo enddo Dep endence 789:;9 7:98; do i # $% n'( do j#i.$% i.m'( j1#j'i/ a,i%j1-#a,i'(%j1- .a, i% j1' (- .a, i. (%j 1- .a, i% j1. (-/ enddo enddo Sk ew ed co de< Dep endence 7898;9 7:98; CS* UCSB T ao Y ang
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SLIDE 2 CS"#$I&"'$B "' ! " # Original iteration space Sk ew ed space

i j i j

do j#$% m'n)* do i # max.*%j)m'/0% min.n)/%j)*0 j1#j)i2 a3i%j14#a3i)/%j14 'a3 i% j1) /4 'a3 i' /%j 14 'a3 i% j1' /42 enddo enddo Sk ew ed and in terc hanged co de Dep endence '()*+) '()(+, Inner lo
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can b e executed in parallel, CS) UCSB T ao Y ang
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SLIDE 3 CS"#$I&"'$B ") ! " # Strip mining Adjust the gran ularit y
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an
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eration2 do i # $% n a(i)#a(i)*c enddo TN#/n0123412 do TI#$% TN% 12 a(TI6TI*17)#a(TI 6TI *1 7)* c enddo do i # TN% n a(i)#a(i)*c enddo CS* UCSB T ao Y ang
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SLIDE 4 CS"#$I&"'$B ") ! " # Lo
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tiling F
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i$% to n F
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j$% to n u new i$j $ )!*+,u i*+$j
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i +$j
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i$j *+
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i$j + ./ EndF
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EndF
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Iteration space partitioning CS, UCSB T ao Y ang
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SLIDE 5 CS"#$I&"'$B ") ! " # T ransformation pro cess Step $% In tro duce con trol v ariables% F
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bi # $ to p F
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i # &b i $'# ( $ to b i # F
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bj # $ to p F
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j # &b j $'# ( $ to b j # u new i%j # )&*+&u i*+%j ( u i +%j ( u i%j *+ ( u i%j + ', EndF
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EndF
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EndF
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EndF
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Step 3% In terc hange lo
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F
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bi # $ to p F
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bj # $ to p F
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i # &b i $'# ( $ to b i # F
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j # &b j $'# ( $ to b j # u new i%j # )&*+&u i*+%j ( u i +%j ( u i%j *+ ( u i%j + ', EndF
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EndF
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EndF
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EndF
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CS, UCSB T ao Y ang
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SLIDE 6 CS"#$I&"'$B ") ! " # Tiling for matrix m ultiplication for i ! to n do for j ! to n do for k ! to n do c$i% j % c$i% j % & a$i% k % b$k % j %' Endfor Endfor Endfor CS* UCSB T ao Y ang