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# This is the file facts.prew, which is prepended to the .prew files
# for the particular code generation we want, defines things like the
# iteration space and dependences. Known facts are inserted by the
# Makefile.
#
# If you're looking at a .w file instead of facts.prew, then you should
# remember to edit the original .prew files, not the .w files.
#
# This facts.prew file describes the program
#
# for(i = 0; i <= N-1; i++) {
# cur[i]=...
# }
# for(t = 0; t < T; t++) {
# for(i = 0; i <= N-1; i++) {
# old[i]=cur[i];
# }
# for(i = 1; i <= N-2; i++) {
# cur[i] = (old[i-1]+old[i]+old[i]+old[i+1])*0.25;
# }
# }
# first, the spaces and memory maps
symbolic T, N;
IS_INIT := { [1,i,1,0,0] : 0<=i<=N-1 };
MM_INIT := { [1,i,1,0,0] -> [0,i] : 0<=i<=N-1 };
IS_COPY := { [2,t,0,i,1] : 0<=t<T && 0<=i<=N-1 };
MM_COPY := { [2,t,0,i,1] -> [t+1,i] : 0<=t<T && 0<=i<=N-1 };
IS_CALC := { [2,t,1,i,1] : 0<=t<T && 0< i< N-1 };
MM_CALC := { [2,t,1,i,1] -> [t+1,i] : 0<=t<T && 0< i< N-1 };
RESULTS := { [3,0,0,0,0] };
# memory-based Output and Flow/anti-dependences (among Assign (copy), and Calc)
FWD5 := {[x,t,y,i,z] -> [x',t',y',i',z'] :
(x'>x) or
(x'=x and t'>t) or
(x'=x and t'=t and y'>y) or
(x'=x and t'=t and y'=y and i'>i) or
(x'=x and t'=t and y'=y and i'=i and z'>z) };
FWD7 := {[x,t,y,i,z,a,b] -> [x',t',y',i',z',a',b'] :
(x'>x) or
(x'=x and t'>t) or
(x'=x and t'=t and y'>y) or
(x'=x and t'=t and y'=y and i'>i) or
(x'=x and t'=t and y'=y and i'=i and z'>z) or
(x'=x and t'=t and y'=y and i'=i and z'=z and a'>a) or
(x'=x and t'=t and y'=y and i'=i and z'=z and a'=a and b'>b) };
BWD5 := inverse FWD5;
BWD7 := inverse FWD7;
EQi := {[x,t,y,i,z] -> [x',t',y',i',z'] : i'=i };
# output deps
OAA := (IS_COPY * IS_COPY) intersection FWD5 intersection EQi;
OCC := (IS_CALC * IS_CALC) intersection FWD5 intersection EQi;
# combined flow/anti deps
FAC := (IS_COPY * IS_CALC) intersection FWD5 intersection {[2,t,0,i,1] -> [2,t',1,i',1] : (i'-1<=i<=i'+1)};
FCA := (IS_CALC * IS_COPY) intersection FWD5 intersection {[2,t,1,i,1] -> [2,t',0,i',1] : (i-1<=i'<=i+1)};
# total memory deps in the "core"
COREMEMDEPS := OAA union OCC union FAC union FCA;
# data flow for original code:
DF_12p1 := ( IS_INIT * IS_COPY ) intersection {[1,i,1,0,0] -> [2,0,0,i,1] : 0<i<N-1 };
DF_12p2 := ( IS_INIT * IS_COPY ) intersection {[1,0,1,0,0] -> [2,t,0,0,1] };
DF_12p3 := ( IS_INIT * IS_COPY ) intersection {[1,i,1,0,0] -> [2,t,0,i,1] : i=N-1 && N>1 };
DF_32 := ( IS_CALC * IS_COPY ) intersection {[2,t,1,i,1] -> [2,t+1,0,i,1]};
DF_23a := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i+1,1] };
DF_23b := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i,1] };
DF_23c := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i-1,1] };
# data flow for array expanded code,
# after forward substitution of "old[i] = cur[i]"
DF1Ia := { [1,i,1,0,0] -> [2,t,1,i+1,1] : t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
DF1Ib := { [1,i,1,0,0] -> [2,t,1,i+1,1] : t>0 && i=0 } restrictDomain IS_INIT restrictRange IS_CALC;
DF1C := { [2,t,1,i,1] -> [2,t+1,1,i+1,1] } restrictDomain IS_CALC restrictRange IS_CALC;
DF2I := { [1,i,1,0,0] -> [2,t,1,i,1] : t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
DF2C := { [2,t,1,i,1] -> [2,t+1,1,i+0,1] } restrictDomain IS_CALC restrictRange IS_CALC;
DF3Ia := { [1,i,1,0,0] -> [2,t,1,i-1,1] : t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
DF3Ib := { [1,i,1,0,0] -> [2,t,1,i-1,1] : t>0 && i=N-1 } restrictDomain IS_INIT restrictRange IS_CALC;
DF3C := { [2,t,1,i,1] -> [2,t+1,1,i-1,1] } restrictDomain IS_CALC restrictRange IS_CALC;
# total data flow
COREDATAFLOW := DF1C union DF2C union DF3C;
# arity expansion relations
ex_0_5v := { [] -> [a,b,c,d,e] };
ex_0_7v := { [] -> [a,b,c,d,e,f,g] };
ex_3_5 := { [a,b,c] -> [a,b,c,0,0] };
ex_3_7 := { [a,b,c] -> [a,b,c,0,0,0,0] };
ex_5_7 := { [a,b,c,d,e] -> [a,b,c,d,e,0,0] };
ex_5_3 := { [a,b,c,0,0] -> [a,b,c] };
ex_7_3 := { [a,b,c,0,0,0,0] -> [a,b,c] };
ex_7_5 := { [a,b,c,d,e,0,0] -> [a,b,c,d,e] };
# stuff used in skew and tskew
# Here is the description of time skewing from the current draft of the paper.
IS_Trans := { [2,t,1,i,1] -> [2,tb,1,s,1,tt,1] :
0<=tt<1000 && s=i+1*t && t=1000*tb+tt };
IS_Tinv := inverse IS_Trans;
# We use it to transform the iteration spaces
TS_IS_CALC := IS_CALC join IS_Trans;
# for some reason OC refuses do to this "join" but will do the reverse:
# TS_IS_INIT := ex_7_5 join IS_INIT;
TS_IS_INIT := IS_INIT join (inverse ex_7_5);
# Now we can update the data flow relations to correspond to the new I.S.'s
TS_DF1Ia := ex_7_5 join DF1Ia join IS_Trans;
TS_DF1Ib := ex_7_5 join DF1Ib join IS_Trans;
TS_DF1C := IS_Tinv join DF1C join IS_Trans;
TS_DF2I := ex_7_5 join DF2I join IS_Trans;
TS_DF2C := IS_Tinv join DF2C join IS_Trans;
TS_DF3Ia := ex_7_5 join DF3Ia join IS_Trans;
TS_DF3Ib := ex_7_5 join DF3Ib join IS_Trans;
TS_DF3C := IS_Tinv join DF3C join IS_Trans;
KNOWN := { [] : T >= 0 and N >= 4 };
IS_INIT_EXP := { [1,t,1,i,0] : (0=t && 0<=i<=N-1) ||
(1=t && 0=i) ||
(1=t && N-1=i) };
TSKEW := { [2, t, 1, i, 1] -> [2, tb, t+i, tt, 0] :
1000*tb+tt = t and 0 <= tt < 1000 };
codegen
IS_INIT_EXP, TSKEW : IS_CALC
given (KNOWN join ex_0_5v);
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