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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 };
+#
+#
+# # Lets try to build up the equivalent of the time skewing transformation,
+# # IS_Trans := { [2,t,1,i,1] -> [2,tb,1,x,1,y,1] :
+# # 1000*tb<=t-1<=1000*(tb+1)-1 && y=t-1000*tb && x=y+i };
+# # for both statements together, right from the diagram in the new TOPLAS stuff.
+#
+# # original code without mmap
+# #
+#
+# # First, look at it as a wider space
+#
+# WIDEN := { [2, t, s, i , 1] -> [2, 2t+s, 0, i, 1] : 0<=s<=1 };
+#
+# TSKEW := { [2, t, 0, i , 1] -> [2, tb, t+i, tt, 1] :
+# 1000*tb+tt = t and 0 <= tt < 1000 };
+#
+#
+# TSKEW_2LOOPS := WIDEN join TSKEW;
+#
+# # print this for the paper
+#
+# # I think this should work but it blows up codegen:
+# # codegen
+# # IS_INIT, TSKEW_2LOOPS : IS_COPY, TSKEW_2LOOPS : IS_CALC
+# # given (KNOWN join ex_0_5v);
+#
+# # So we fake it as follows,
+# # relying on the fact that neither "t" nor "s" is used in any statement
+#
+# WIDEN0 := { [2, t, 0, i , 1] -> [2, 2t, 0, i, 1] };
+#
+# WIDEN1 := { [2, t, 1, i , 1] -> [2, 2t+1, 0, i, 1] };
+#
+#
+# codegen
+# IS_INIT, TSKEW : (IS_COPY join WIDEN0) , TSKEW : (IS_CALC join WIDEN1)
+# given (KNOWN join ex_0_5v);
+for(t2 = 0; t2 <= N-1; t2++) {
+ s1(1,t2,1,0,0);
+}
+for(t2 = 0; t2 <= intDiv(T-1,500); t2++) {
+ for(t3 = 1000*t2; t3 <= min(1000*t2+N+997,N+2*T-3); t3++) {
+ if (intMod(-N+t3+1,2) == 0 && 1000*t2 <= -N+t3+1) {
+ s2(2,t3-N+1,0,N-1,1);
+ }
+ for(t4 = max(-1000*t2-N+t3+2,0); t4 <= min(-1000*t2+2*T-1,-1000*t2+t3-1,999); t4++) {
+ if (intMod(t4,2) == 0) {
+ s2(2,t4+1000*t2,0,t3-t4+-1000*t2,1);
+ }
+ if (intMod(t4+1,2) == 0) {
+ s3(2,t4+1000*t2,0,t3-t4+-1000*t2,1);
+ }
+ }
+ if (intMod(t3,2) == 0 && 2*T >= t3+2 && 1000*t2 >= t3-998) {
+ s2(2,t3,0,0,1);
+ }
+ }
+}
+
+#
+#