Created
April 25, 2019 12:16
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Loop interchange rough analysis
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def show_iv(iv) | |
"(%s)"%(iv.collect{|x|x.to_s}.join(",")) | |
end | |
def sub_iv(iv0, iv1) | |
iv0.zip(iv1).collect{|x0,x1| x0 - x1} | |
end | |
def add_dependence(iv, ds, us, du_lst) | |
us.each do |u| | |
du_lst.reverse.each do |iv_, ds_, us_| | |
unless ds_.index(u).nil? then | |
dv = sub_iv(iv, iv_) | |
printf " Flow: %s, %s -> %s, d:%s\n", u, show_iv(iv_), show_iv(iv), show_iv(dv) | |
break | |
end | |
end | |
end | |
ds.each do |d| | |
du_lst.reverse.each do |iv_, ds_, us_| | |
unless us_.index(d).nil? then | |
dv = sub_iv(iv, iv_) | |
printf " Anti: %s, %s -> %s, d:%s\n", d, show_iv(iv_), show_iv(iv), show_iv(dv) | |
break | |
end | |
end | |
end | |
du_lst.push [iv, ds, us] | |
end | |
N = 4 | |
du_lst = [] | |
(2..N).each do |i| | |
(2..N).each do |j| | |
(2..(N-1)).each do |k| | |
iv = [i-2,j-2,k-2] | |
str0 = "A[#{i},#{j},#{k}]" | |
str1 = "A[#{i-1},#{j-1},#{k-1}]" | |
str2 = "A[#{i-1},#{j-1},#{k+1}]" | |
printf "%s: %s = (%s + %s)/2\n", show_iv(iv), str0, str1, str2 | |
add_dependence(iv, [str0], [str1,str2], du_lst) | |
end | |
end | |
end | |
printf "\n\n----\n\n" | |
du_lst = [] | |
(2..N).each do |i| | |
(2..(N-1)).each do |k| | |
(2..N).each do |j| | |
iv = [i-2,k-2,j-2] | |
str0 = "A[#{i},#{j},#{k}]" | |
str1 = "A[#{i-1},#{j-1},#{k-1}]" | |
str2 = "A[#{i-1},#{j-1},#{k+1}]" | |
printf "%s: %s = (%s + %s)/2\n", show_iv(iv), str0, str1, str2 | |
add_dependence(iv, [str0], [str1,str2], du_lst) | |
end | |
end | |
end | |
printf "\n\n----\n\n" | |
du_lst = [] | |
(2..(N-1)).each do |k| | |
(2..N).each do |i| | |
(2..N).each do |j| | |
iv = [k-2,i-2,j-2] | |
str0 = "A[#{i},#{j},#{k}]" | |
str1 = "A[#{i-1},#{j-1},#{k-1}]" | |
str2 = "A[#{i-1},#{j-1},#{k+1}]" | |
printf "%s: %s = (%s + %s)/2\n", show_iv(iv), str0, str1, str2 | |
add_dependence(iv, [str0], [str1,str2], du_lst) | |
end | |
end | |
end |
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(0,0,0): A[2,2,2] = (A[1,1,1] + A[1,1,3])/2 | |
(0,0,1): A[2,2,3] = (A[1,1,2] + A[1,1,4])/2 | |
(0,1,0): A[2,3,2] = (A[1,2,1] + A[1,2,3])/2 | |
(0,1,1): A[2,3,3] = (A[1,2,2] + A[1,2,4])/2 | |
(0,2,0): A[2,4,2] = (A[1,3,1] + A[1,3,3])/2 | |
(0,2,1): A[2,4,3] = (A[1,3,2] + A[1,3,4])/2 | |
(1,0,0): A[3,2,2] = (A[2,1,1] + A[2,1,3])/2 | |
(1,0,1): A[3,2,3] = (A[2,1,2] + A[2,1,4])/2 | |
(1,1,0): A[3,3,2] = (A[2,2,1] + A[2,2,3])/2 | |
Flow: A[2,2,3], (0,0,1) -> (1,1,0), d:(1,1,-1) | |
(1,1,1): A[3,3,3] = (A[2,2,2] + A[2,2,4])/2 | |
Flow: A[2,2,2], (0,0,0) -> (1,1,1), d:(1,1,1) | |
(1,2,0): A[3,4,2] = (A[2,3,1] + A[2,3,3])/2 | |
Flow: A[2,3,3], (0,1,1) -> (1,2,0), d:(1,1,-1) | |
(1,2,1): A[3,4,3] = (A[2,3,2] + A[2,3,4])/2 | |
Flow: A[2,3,2], (0,1,0) -> (1,2,1), d:(1,1,1) | |
(2,0,0): A[4,2,2] = (A[3,1,1] + A[3,1,3])/2 | |
(2,0,1): A[4,2,3] = (A[3,1,2] + A[3,1,4])/2 | |
(2,1,0): A[4,3,2] = (A[3,2,1] + A[3,2,3])/2 | |
Flow: A[3,2,3], (1,0,1) -> (2,1,0), d:(1,1,-1) | |
(2,1,1): A[4,3,3] = (A[3,2,2] + A[3,2,4])/2 | |
Flow: A[3,2,2], (1,0,0) -> (2,1,1), d:(1,1,1) | |
(2,2,0): A[4,4,2] = (A[3,3,1] + A[3,3,3])/2 | |
Flow: A[3,3,3], (1,1,1) -> (2,2,0), d:(1,1,-1) | |
(2,2,1): A[4,4,3] = (A[3,3,2] + A[3,3,4])/2 | |
Flow: A[3,3,2], (1,1,0) -> (2,2,1), d:(1,1,1) | |
---- | |
(0,0,0): A[2,2,2] = (A[1,1,1] + A[1,1,3])/2 | |
(0,0,1): A[2,3,2] = (A[1,2,1] + A[1,2,3])/2 | |
(0,0,2): A[2,4,2] = (A[1,3,1] + A[1,3,3])/2 | |
(0,1,0): A[2,2,3] = (A[1,1,2] + A[1,1,4])/2 | |
(0,1,1): A[2,3,3] = (A[1,2,2] + A[1,2,4])/2 | |
(0,1,2): A[2,4,3] = (A[1,3,2] + A[1,3,4])/2 | |
(1,0,0): A[3,2,2] = (A[2,1,1] + A[2,1,3])/2 | |
(1,0,1): A[3,3,2] = (A[2,2,1] + A[2,2,3])/2 | |
Flow: A[2,2,3], (0,1,0) -> (1,0,1), d:(1,-1,1) | |
(1,0,2): A[3,4,2] = (A[2,3,1] + A[2,3,3])/2 | |
Flow: A[2,3,3], (0,1,1) -> (1,0,2), d:(1,-1,1) | |
(1,1,0): A[3,2,3] = (A[2,1,2] + A[2,1,4])/2 | |
(1,1,1): A[3,3,3] = (A[2,2,2] + A[2,2,4])/2 | |
Flow: A[2,2,2], (0,0,0) -> (1,1,1), d:(1,1,1) | |
(1,1,2): A[3,4,3] = (A[2,3,2] + A[2,3,4])/2 | |
Flow: A[2,3,2], (0,0,1) -> (1,1,2), d:(1,1,1) | |
(2,0,0): A[4,2,2] = (A[3,1,1] + A[3,1,3])/2 | |
(2,0,1): A[4,3,2] = (A[3,2,1] + A[3,2,3])/2 | |
Flow: A[3,2,3], (1,1,0) -> (2,0,1), d:(1,-1,1) | |
(2,0,2): A[4,4,2] = (A[3,3,1] + A[3,3,3])/2 | |
Flow: A[3,3,3], (1,1,1) -> (2,0,2), d:(1,-1,1) | |
(2,1,0): A[4,2,3] = (A[3,1,2] + A[3,1,4])/2 | |
(2,1,1): A[4,3,3] = (A[3,2,2] + A[3,2,4])/2 | |
Flow: A[3,2,2], (1,0,0) -> (2,1,1), d:(1,1,1) | |
(2,1,2): A[4,4,3] = (A[3,3,2] + A[3,3,4])/2 | |
Flow: A[3,3,2], (1,0,1) -> (2,1,2), d:(1,1,1) | |
---- | |
(0,0,0): A[2,2,2] = (A[1,1,1] + A[1,1,3])/2 | |
(0,0,1): A[2,3,2] = (A[1,2,1] + A[1,2,3])/2 | |
(0,0,2): A[2,4,2] = (A[1,3,1] + A[1,3,3])/2 | |
(0,1,0): A[3,2,2] = (A[2,1,1] + A[2,1,3])/2 | |
(0,1,1): A[3,3,2] = (A[2,2,1] + A[2,2,3])/2 | |
(0,1,2): A[3,4,2] = (A[2,3,1] + A[2,3,3])/2 | |
(0,2,0): A[4,2,2] = (A[3,1,1] + A[3,1,3])/2 | |
(0,2,1): A[4,3,2] = (A[3,2,1] + A[3,2,3])/2 | |
(0,2,2): A[4,4,2] = (A[3,3,1] + A[3,3,3])/2 | |
(1,0,0): A[2,2,3] = (A[1,1,2] + A[1,1,4])/2 | |
Anti: A[2,2,3], (0,1,1) -> (1,0,0), d:(1,-1,-1) | |
(1,0,1): A[2,3,3] = (A[1,2,2] + A[1,2,4])/2 | |
Anti: A[2,3,3], (0,1,2) -> (1,0,1), d:(1,-1,-1) | |
(1,0,2): A[2,4,3] = (A[1,3,2] + A[1,3,4])/2 | |
(1,1,0): A[3,2,3] = (A[2,1,2] + A[2,1,4])/2 | |
Anti: A[3,2,3], (0,2,1) -> (1,1,0), d:(1,-1,-1) | |
(1,1,1): A[3,3,3] = (A[2,2,2] + A[2,2,4])/2 | |
Flow: A[2,2,2], (0,0,0) -> (1,1,1), d:(1,1,1) | |
Anti: A[3,3,3], (0,2,2) -> (1,1,1), d:(1,-1,-1) | |
(1,1,2): A[3,4,3] = (A[2,3,2] + A[2,3,4])/2 | |
Flow: A[2,3,2], (0,0,1) -> (1,1,2), d:(1,1,1) | |
(1,2,0): A[4,2,3] = (A[3,1,2] + A[3,1,4])/2 | |
(1,2,1): A[4,3,3] = (A[3,2,2] + A[3,2,4])/2 | |
Flow: A[3,2,2], (0,1,0) -> (1,2,1), d:(1,1,1) | |
(1,2,2): A[4,4,3] = (A[3,3,2] + A[3,3,4])/2 | |
Flow: A[3,3,2], (0,1,1) -> (1,2,2), d:(1,1,1) |
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