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951 // When we have a pair of subscripts of the form [c1] and [c2],
952 // where c1 and c2 are both loop invariant, we attack it using
984 // When we have a pair of subscripts of the form [c1 + a*i] and [c2 + a*i],
985 // where i is an induction variable, c1 and c2 are loop invariant,
993 // c1 + a*i = c2 + a*i'
997 // d = i' - i = (c1 - c2)/a
1122 // When we have a pair of subscripts of the form [c1 + a*i] and [c2 - a*i],
1123 // where i is an induction variable, c1 and c2 are loop invariant,
1127 // Given c1 + a*i = c2 - a*i', we can look for the intersection of
1130 // c1 + a*i = c2 - a*i
1131 // 2a*i = c2 - c1
1132 // i = (c2 - c1)/2a
1136 // If i = 0 (i.e., if c1 = c2), there's a dependence with distance = 0.
1355 // When we have a pair of subscripts of the form [c1 + a1*i] and [c2 + a2*i],
1356 // where i is an induction variable, c1 and c2 are loop invariant, and a1
1553 // When we have a pair of subscripts of the form [c1] and [c2 + a*i],
1554 // where i is an induction variable, c1 and c2 are loop invariant,
1560 // c1 = c2 + a*i
1564 // (c1 - c2)/a = i
1664 // When we have a pair of subscripts of the form [c1 + a*i] and [c2],
1665 // where i is an induction variable, c1 and c2 are loop invariant,
1671 // c1 + a*i = c2
1675 // i = (c2 - c1)/a
1772 // Things of the form [c1 + a*i] and [c2 + b*j],
1773 // where i and j are induction variable, c1 and c2 are loop invariant,
1888 // When we have a pair of subscripts of the form [c1 + a1*i] and [c2 + a2*j]
1889 // where i and j are induction variables and c1 and c2 are loop invariants,
1894 // For a dependence to exist, c1 + a1*i must equal c2 + a2*j for some
1898 // c1 + a1*i = c2 + a2*j
1899 // a1*i - a2*j = c2 - c1
1901 // To test for a dependence, we compute c2 - c1 and make sure it's in the
1906 // a1*0 - a2*N2 <= c2 - c1 <= a1*N1 - a2*0
1907 // -a2*N2 <= c2 - c1 <= a1*N1
1910 // a1*0 - a2*0 <= c2 - c1 <= a1*N1 - a2*N2
1911 // 0 <= c2 - c1 <= a1*N1 - a2*N2
1914 // a1*N1 - a2*N2 <= c2 - c1 <= a1*0 - a2*0
1915 // a1*N1 - a2*N2 <= c2 - c1 <= 0
1918 // a1*N1 - a2*0 <= c2 - c1 <= a1*0 - a2*N2
1919 // a1*N1 <= c2 - c1 <= -a2*N2
1924 const SCEV *C1,
1933 DEBUG(dbgs() << "\t C1 = " << *C1 << "\n");
1939 const SCEV *C2_C1 = SE->getMinusSCEV(C2, C1);
1940 const SCEV *C1_C2 = SE->getMinusSCEV(C1, C2);
1941 DEBUG(dbgs() << "\t C2 - C1 = " << *C2_C1 << "\n");
1942 DEBUG(dbgs() << "\t C1 - C2 = " << *C1_C2 << "\n");
1947 // make sure that c2 - c1 <= a1*N1
1956 // make sure that -a2*N2 <= c2 - c1, or a2*N2 >= c1 - c2
1968 // make sure that c2 - c1 <= a1*N1 - a2*N2
1978 // make sure that 0 <= c2 - c1
1989 // make sure that a1*N1 - a2*N2 <= c2 - c1
1999 // make sure that c2 - c1 <= 0
2008 // make sure that a1*N1 <= c2 - c1
2017 // make sure that c2 - c1 <= -a2*N2, or c1 - c2 >= a2*N2
2032 // When we have a pair of subscripts of the form [c1 + a1*i] and [c2 - a2*i]
2033 // where i is an induction variable, c1 and c2 are loop invariant, and a1 and
2098 // When we have a pair of subscripts of the form [c1 + a1*i] and [c2 + a2*j]
2099 // where i and j are induction variables, c1 and c2 are loop invariant,
2107 // [c1 + a1*i + a2*j][c2].