def test_multi_equal():
x, y, z = te.var("x"), te.var("y"), te.var("z")
problem = [
tvm.tir.LE(x, 6),
tvm.tir.GE(x, 6),
tvm.tir.GE(x - z * y, 0),
tvm.tir.LE(x - z * y, 0),
]
solution = arith.solve_linear_inequalities(problem, [x, y, z])
assert solution.ranges[x].min == 6
assert solution.ranges[x].extent == 1
assert len(solution.relations) == 3
assert ir.structural_equal(solution.relations[0], x == z * y)
assert isinstance(solution.relations[1], tvm.tir.LE)
assert solution.relations[1].b == 0
assert isinstance(solution.relations[2], tvm.tir.LE)
assert solution.relations[2].b == 0
# (z*y - 6) <= 0 && (6 - z*y) <= 0
ana = tvm.arith.Analyzer()
assert ana.simplify(solution.relations[1].a + solution.relations[2].a) == 0
assert ir.structural_equal(solution.relations[1].a, (z * y - 6)) or ir.structural_equal(
solution.relations[2].a, (z * y - 6)
)
solution = arith.solve_linear_inequalities(problem, [x, y, z], deskew_range=True)
assert solution.src_to_dst[y] == y
assert solution.src_to_dst[z] == z
assert solution.src_to_dst[x] == 6
def _check(variables, formulas, coef=(-5, 5), bounds=(-20, 20)):
vs = [te.var("x" + str(i)) for i in range(variables)]
fs = []
for i in range(formulas):
s1 = sum([v * random.randint(coef[0], coef[1]) for v in vs])
s1 += random.randint(coef[0], coef[1])
s2 = sum([v * random.randint(coef[0], coef[1]) for v in vs])
s2 += random.randint(coef[0], coef[1])
op = random.choice([
tir.expr.EQ, tir.expr.LE, tir.expr.LT, tir.expr.GE, tir.expr.GT
])
fs.append(op(s1, s2))
vranges = {v: tvm.ir.expr.Range(bounds[0], bounds[1] + 1) for v in vs}
before = te.all(tir.const(1, 'bool'), *fs)
after = arith._ffi_api.SolveInequalitiesAsCondition(vs, vranges, fs)
after = te.all(tir.const(1, 'bool'), *after)
testing.check_bool_expr_is_true(before == after, vranges)
solution = arith.solve_linear_inequalities(fs,
vs,
vranges,
deskew_range=True)
testing.check_int_constraints_trans_consistency(solution)
def test_dual_variable():
x, y = te.var("x"), te.var("y")
variables = [x, y]
ranges = {
x: tvm.ir.Range(-100, 100),
y: tvm.ir.Range(0, 10),
}
problem = [
tvm.tir.LE(x + y, 20),
tvm.tir.GE(x - y, 10),
]
# solution as conditions
solution = arith._ffi_api.SolveInequalitiesAsCondition(
variables, ranges, problem)
assert ir.structural_equal(solution[0], x >= (y + 10))
assert ir.structural_equal(solution[1], x <= (20 - y))
assert ir.structural_equal(solution[2], y >= 0)
assert ir.structural_equal(solution[3], y <= 5)
# solve and get the ranges
solution = arith.solve_linear_inequalities(problem, variables, ranges)
# 0 <= y <=5
assert solution.ranges[y].min == 0
assert solution.ranges[y].extent == 6
# y + 10 <= x <= 20 - y
assert ir.structural_equal(solution.ranges[x].min, y + 10)
assert solution.ranges[x].extent == 11 # max(10 - 2y)
# deskew the solved ranges to be starting from zero
solution = arith.solve_linear_inequalities(problem,
variables,
ranges,
deskew_range=True)
[x_new, y_new] = solution.dst.variables
[rel] = solution.dst.relations
assert ir.structural_equal(rel, (y_new * 2) + x_new <= 10)
assert ir.structural_equal(solution.dst.ranges[x_new].min, 0)
assert ir.structural_equal(solution.dst.ranges[x_new].extent, 11)
assert ir.structural_equal(solution.dst.ranges[y_new].min, 0)
assert ir.structural_equal(solution.dst.ranges[y_new].extent, 6)
assert ir.structural_equal(solution.src_to_dst[x], x_new + (y_new + 10))
assert ir.structural_equal(solution.src_to_dst[y], y_new)
assert ir.structural_equal(solution.dst_to_src[x_new], x - y - 10)
assert ir.structural_equal(solution.dst_to_src[y_new], y)
def test_no_solution():
x = te.var("x0")
vranges = {x: tvm.ir.Range.from_min_extent(-20, 41)}
problem = [-x - 4 <= -5 * x + 2, x * 4 + 5 <= x * 5]
solution = arith.solve_linear_inequalities(problem, [x], vranges, deskew_range=True)
assert list(solution.dst.variables) == []
[rel] = solution.dst.relations
assert ir.structural_equal(rel, False)
assert len(solution.src_to_dst) == 0
assert len(solution.dst_to_src) == 0
solution = arith.solve_linear_inequalities(problem, [x], vranges)
assert len(solution.variables) == 0
assert len(solution.ranges) == 0
[rel] = solution.relations
assert not rel
def test_equal():
x, y = te.var("x"), te.var("y")
problem = [
tvm.tir.GE(x + y, 10),
tvm.tir.GE(x - y, 2),
tvm.tir.LE(x, 6),
]
solution = arith.solve_linear_inequalities(problem, [x, y])
assert solution.ranges[x].min == 6
assert solution.ranges[x].extent == 1
assert solution.ranges[y].min == 4
assert solution.ranges[y].extent == 1
solution = arith.solve_linear_inequalities(problem, [x, y], deskew_range=True)
assert len(solution.dst.variables) == 0
assert len(solution.dst.ranges) == 0
assert len(solution.dst.relations) == 0
assert solution.src_to_dst[x] == 6
assert solution.src_to_dst[y] == 4
def test_multi_equal():
x, y, z = te.var("x"), te.var("y"), te.var("z")
problem = [
tvm.tir.LE(x, 6),
tvm.tir.GE(x, 6),
tvm.tir.GE(x - z * y, 0),
tvm.tir.LE(x - z * y, 0),
]
solution = arith.solve_linear_inequalities(problem, [x, y, z])
assert solution.ranges[x].min == 6
assert solution.ranges[x].extent == 1
assert len(solution.relations) == 3
assert ir.structural_equal(solution.relations[0], x == z * y)
assert ir.structural_equal(solution.relations[1], z * y - 6 <= 0)
assert ir.structural_equal(solution.relations[2], 6 - z * y <= 0)
solution = arith.solve_linear_inequalities(problem, [x, y, z],
deskew_range=True)
assert solution.src_to_dst[y] == y
assert solution.src_to_dst[z] == z
assert solution.src_to_dst[x] == 6