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+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# # 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 };
+#
+#
+# # original code without mmap
+# #
+#
+# codegen
+# IS_INIT, IS_COPY, IS_CALC
+# given (KNOWN join ex_0_5v);
+for(t2 = 0; t2 <= N-1; t2++) {
+ s1(1,t2,1,0,0);
+}
+for(t2 = 0; t2 <= T-1; t2++) {
+ for(t4 = 0; t4 <= N-1; t4++) {
+ s2(2,t2,0,t4,1);
+ }
+ for(t4 = 1; t4 <= N-2; t4++) {
+ s3(2,t2,1,t4,1);
+ }
+}
+
+#
+#