omega/examples/floor_bound


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#
# Test floor/ceiling variable definitions in loop bounds
# Notes:
#   intFloor, intCeil are strict mathematical definition,
#   intMod(a,b) always has input b>0 and returns [0,b).
#

symbolic m, n;

# loop is strided
#
is := {[i]: exists (alpha: i = 4alpha && m <= 3i <= n)};
codegen is;

# only one single floor/ceiling variable in bound
#
is := {[i]: exists (lb: m-4 < 4*lb <= m && lb <= i <= n)};
codegen is;

# the floor/ceiling variable in bound has coefficient
#
is := {[i]: exists (lb: m-4 < 4*lb <= m && 4*lb <= i <= n)};
codegen is;

# mutiple floor/ceiling variables in bound
#
is := {[i]:exists (alpha,beta: m-4<4alpha<=m && m-3<3beta<=m &&
           4alpha+3*beta<=i<=n )};
codegen is;

# non-tight floor/ceiling definition
#
is := {[i]: exists (ub: n-2 < 3*ub <= n && m <= i <= 5*ub)};
codegen is;

# chain floor/ceiling definitions
#
is := {[i]: exists (alpha, beta: beta-4<4alpha<=beta &&
            m-8<8beta<=m && 4alpha<=i<=n )};
codegen is;

# one complicated case
#
is := {[i]: exists (alpha, beta: beta-4<4alpha<=beta &&
            m-7<8beta<=m && 4alpha<=i<=n )};
codegen is;