def test_apply_loop_invariant_optimisation_constant_evaluation():
variables = {
'v1': Variable('v1', scalar=False),
'v2': Variable('v2', scalar=False),
'i1': Variable('i1', scalar=False, dtype=int),
'N': Constant('N', 10),
's1': Variable('s1', scalar=True, dtype=float),
's2': Variable('s2', scalar=True, dtype=float),
'exp': DEFAULT_FUNCTIONS['exp']
}
statements = [
Statement('v1', '=', 'v1 * (1 + 2 + 3)', '', np.float),
Statement('v1', '=', 'exp(N)*v1', '', np.float),
Statement('v1', '=', 'exp(0)*v1', '', np.float),
]
scalar, vector = optimise_statements([], statements, variables)
# exp(N) should be pulled out of the vector statements, the rest should be
# evaluated in place
assert len(scalar) == 1
assert scalar[0].expr == 'exp(N)'
assert len(vector) == 3
expr = vector[0].expr.replace(' ', '')
assert expr == '_lio_1*v1' or 'v1*_lio_1'
expr = vector[1].expr.replace(' ', '')
assert expr == '6.0*v1' or 'v1*6.0'
assert vector[2].expr == 'v1'
def test_apply_loop_invariant_optimisation_no_optimisation():
variables = {
'v1': Variable('v1', scalar=False),
'v2': Variable('v2', scalar=False),
'N': Constant('N', 10),
's1': Variable('s1', scalar=True, dtype=float),
's2': Variable('s2', scalar=True, dtype=float),
'rand': DEFAULT_FUNCTIONS['rand']
}
statements = [
# This hould not be simplified to 0!
Statement('v1', '=', 'rand() - rand()', '', np.float),
Statement('v1', '=', '3*rand() - 3*rand()', '', np.float),
Statement('v1', '=', '3*rand() - ((1+2)*rand())', '', np.float),
# This should not pull out rand()*N
Statement('v1', '=', 's1*rand()*N', '', np.float),
Statement('v1', '=', 's2*rand()*N', '', np.float),
# This is not important mathematically, but it would change the numbers
# that are generated
Statement('v1', '=', '0*rand()*N', '', np.float),
Statement('v1', '=', '0/rand()*N', '', np.float)
]
scalar, vector = optimise_statements([], statements, variables)
for vs in vector[:3]:
assert vs.expr.count(
'rand()'
) == 2, 'Expression should still contain two rand() calls, but got ' + str(
vs)
for vs in vector[3:]:
assert vs.expr.count(
'rand()'
) == 1, 'Expression should still contain a rand() call, but got ' + str(
vs)
def test_apply_loop_invariant_optimisation_constant_evaluation():
variables = {'v1': Variable('v1', scalar=False),
'v2': Variable('v2', scalar=False),
'i1': Variable('i1', scalar=False, dtype=int),
'N': Constant('N', 10),
's1': Variable('s1', scalar=True, dtype=float),
's2': Variable('s2', scalar=True, dtype=float),
'exp': DEFAULT_FUNCTIONS['exp']
}
statements = [
Statement('v1', '=', 'v1 * (1 + 2 + 3)', '', np.float),
Statement('v1', '=', 'exp(N)*v1', '', np.float),
Statement('v1', '=', 'exp(0)*v1', '', np.float),
]
scalar, vector = optimise_statements([], statements, variables)
# exp(N) should be pulled out of the vector statements, the rest should be
# evaluated in place
assert len(scalar) == 1
assert scalar[0].expr == 'exp(N)'
assert len(vector) == 3
expr = vector[0].expr.replace(' ', '')
assert expr == '_lio_1*v1' or 'v1*_lio_1'
expr = vector[1].expr.replace(' ', '')
assert expr == '6.0*v1' or 'v1*6.0'
assert vector[2].expr == 'v1'
def test_apply_loop_invariant_optimisation_integer():
variables = {
'v': Variable('v', scalar=False),
'N': Constant('N', 10),
'b': Variable('b', scalar=True, dtype=int),
'c': Variable('c', scalar=True, dtype=int),
'd': Variable('d', scalar=True, dtype=int),
'y': Variable('y', scalar=True, dtype=float),
'z': Variable('z', scalar=True, dtype=float),
'w': Variable('w', scalar=True, dtype=float),
}
statements = [
Statement('v', '=', 'v % (2*3*N)', '', np.float32),
# integer version doesn't get rewritten but float version does
Statement('a', ':=', 'b//(c//d)', '', int),
Statement('x', ':=', 'y/(z/w)', '', float),
]
scalar, vector = optimise_statements([], statements, variables)
assert len(scalar) == 3
assert np.issubdtype(scalar[0].dtype, np.signedinteger)
assert scalar[0].var == '_lio_1'
expr = scalar[0].expr.replace(' ', '')
assert expr == '6*N' or expr == 'N*6'
assert np.issubdtype(scalar[1].dtype, np.signedinteger)
assert scalar[1].var == '_lio_2'
expr = scalar[1].expr.replace(' ', '')
assert expr == 'b//(c//d)'
assert np.issubdtype(scalar[2].dtype, np.floating)
assert scalar[2].var == '_lio_3'
expr = scalar[2].expr.replace(' ', '')
assert expr == '(y*w)/z' or expr == '(w*y)/z'
def test_apply_loop_invariant_optimisation_no_optimisation():
variables = {'v1': Variable('v1', scalar=False),
'v2': Variable('v2', scalar=False),
'N': Constant('N', 10),
's1': Variable('s1', scalar=True, dtype=float),
's2': Variable('s2', scalar=True, dtype=float),
'rand': DEFAULT_FUNCTIONS['rand']
}
statements = [
# This hould not be simplified to 0!
Statement('v1', '=', 'rand() - rand()', '', np.float),
Statement('v1', '=', '3*rand() - 3*rand()', '', np.float),
Statement('v1', '=', '3*rand() - ((1+2)*rand())', '', np.float),
# This should not pull out rand()*N
Statement('v1', '=', 's1*rand()*N', '', np.float),
Statement('v1', '=', 's2*rand()*N', '', np.float),
# This is not important mathematically, but it would change the numbers
# that are generated
Statement('v1', '=', '0*rand()*N', '', np.float),
Statement('v1', '=', '0/rand()*N', '', np.float)
]
scalar, vector = optimise_statements([], statements, variables)
for vs in vector[:3]:
assert vs.expr.count('rand()') == 2, 'Expression should still contain two rand() calls, but got ' + str(vs)
for vs in vector[3:]:
assert vs.expr.count('rand()') == 1, 'Expression should still contain a rand() call, but got ' + str(vs)
def test_apply_loop_invariant_optimisation_boolean():
variables = {'v1': Variable('v1', scalar=False),
'v2': Variable('v2', scalar=False),
'N': Constant('N', 10),
'b': Variable('b', scalar=True, dtype=bool),
'c': Variable('c', scalar=True, dtype=bool),
'int': DEFAULT_FUNCTIONS['int'],
'foo': Function(lambda x: None,
arg_units=[Unit(1)], return_unit=Unit(1),
arg_types=['boolean'], return_type='float',
stateless=False)
}
# The calls for "foo" cannot be pulled out, since foo is marked as stateful
statements = [Statement('v1', '=', '1.0*int(b and c)', '', np.float32),
Statement('v1', '=', '1.0*foo(b and c)', '', np.float32),
Statement('v2', '=', 'int(not b and True)', '', np.float32),
Statement('v2', '=', 'foo(not b and True)', '', np.float32)
]
scalar, vector = optimise_statements([], statements, variables)
assert len(scalar) == 4
assert scalar[0].expr == '1.0 * int(b and c)'
assert scalar[1].expr == 'b and c'
assert scalar[2].expr == 'int((not b) and True)'
assert scalar[3].expr == '(not b) and True'
assert len(vector) == 4
assert vector[0].expr == '_lio_1'
assert vector[1].expr == 'foo(_lio_2)'
assert vector[2].expr == '_lio_3'
assert vector[3].expr == 'foo(_lio_4)'
def test_apply_loop_invariant_optimisation_integer():
variables = {'v': Variable('v', scalar=False),
'N': Constant('N', 10),
'b': Variable('b', scalar=True, dtype=int),
'c': Variable('c', scalar=True, dtype=int),
'd': Variable('d', scalar=True, dtype=int),
'y': Variable('y', scalar=True, dtype=float),
'z': Variable('z', scalar=True, dtype=float),
'w': Variable('w', scalar=True, dtype=float),
}
statements = [Statement('v', '=', 'v % (2*3*N)', '', np.float32),
# integer version doesn't get rewritten but float version does
Statement('a', ':=', 'b//(c//d)', '', int),
Statement('x', ':=', 'y/(z/w)', '', float),
]
scalar, vector = optimise_statements([], statements, variables)
assert len(scalar) == 3
assert np.issubdtype(scalar[0].dtype, np.signedinteger)
assert scalar[0].var == '_lio_1'
expr = scalar[0].expr.replace(' ', '')
assert expr=='6*N' or expr=='N*6'
assert np.issubdtype(scalar[1].dtype, np.signedinteger)
assert scalar[1].var == '_lio_2'
expr = scalar[1].expr.replace(' ', '')
assert expr=='b//(c//d)'
assert np.issubdtype(scalar[2].dtype, np.floating)
assert scalar[2].var == '_lio_3'
expr = scalar[2].expr.replace(' ', '')
assert expr=='(y*w)/z' or expr=='(w*y)/z'
def test_apply_loop_invariant_optimisation_boolean():
variables = {'v1': Variable('v1', scalar=False),
'v2': Variable('v2', scalar=False),
'N': Constant('N', 10),
'b': Variable('b', scalar=True, dtype=bool),
'c': Variable('c', scalar=True, dtype=bool),
'int': DEFAULT_FUNCTIONS['int'],
'foo': Function(lambda x: None,
arg_units=[Unit(1)], return_unit=Unit(1),
arg_types=['boolean'], return_type='float',
stateless=False)
}
# The calls for "foo" cannot be pulled out, since foo is marked as stateful
statements = [Statement('v1', '=', '1.0*int(b and c)', '', np.float32),
Statement('v1', '=', '1.0*foo(b and c)', '', np.float32),
Statement('v2', '=', 'int(not b and True)', '', np.float32),
Statement('v2', '=', 'foo(not b and True)', '', np.float32)
]
scalar, vector = optimise_statements([], statements, variables)
assert len(scalar) == 4
assert scalar[0].expr == '1.0 * int(b and c)'
assert scalar[1].expr == 'b and c'
assert scalar[2].expr == 'int((not b) and True)'
assert scalar[3].expr == '(not b) and True'
assert len(vector) == 4
assert vector[0].expr == '_lio_1'
assert vector[1].expr == 'foo(_lio_2)'
assert vector[2].expr == '_lio_3'
assert vector[3].expr == 'foo(_lio_4)'
def test_apply_loop_invariant_optimisation():
variables = {'v': Variable('v', scalar=False),
'w': Variable('w', scalar=False),
'dt': Constant('dt', dimensions=second.dim, value=0.1*ms),
'tau': Constant('tau', dimensions=second.dim, value=10*ms),
'exp': DEFAULT_FUNCTIONS['exp']}
statements = [Statement('v', '=', 'dt*w*exp(-dt/tau)/tau + v*exp(-dt/tau)', '', np.float32),
Statement('w', '=', 'w*exp(-dt/tau)', '', np.float32)]
scalar, vector = optimise_statements([], statements, variables)
# The optimisation should pull out at least exp(-dt / tau)
assert len(scalar) >= 1
assert np.issubdtype(scalar[0].dtype, np.floating)
assert scalar[0].var == '_lio_1'
assert len(vector) == 2
assert all('_lio_' in stmt.expr for stmt in vector)
def test_apply_loop_invariant_optimisation():
variables = {'v': Variable('v', scalar=False),
'w': Variable('w', scalar=False),
'dt': Constant('dt', dimensions=second.dim, value=0.1*ms),
'tau': Constant('tau', dimensions=second.dim, value=10*ms),
'exp': DEFAULT_FUNCTIONS['exp']}
statements = [Statement('v', '=', 'dt*w*exp(-dt/tau)/tau + v*exp(-dt/tau)', '', np.float32),
Statement('w', '=', 'w*exp(-dt/tau)', '', np.float32)]
scalar, vector = optimise_statements([], statements, variables)
# The optimisation should pull out at least exp(-dt / tau)
assert len(scalar) >= 1
assert np.issubdtype(scalar[0].dtype, np.floating)
assert scalar[0].var == '_lio_1'
assert len(vector) == 2
assert all('_lio_' in stmt.expr for stmt in vector)
def test_apply_loop_invariant_optimisation_simplification():
variables = {
'v1': Variable('v1', scalar=False),
'v2': Variable('v2', scalar=False),
'i1': Variable('i1', scalar=False, dtype=int),
'N': Constant('N', 10)
}
statements = [
# Should be simplified to 0.0
Statement('v1', '=', 'v1 - v1', '', np.float),
Statement('v1', '=', 'N*v1 - N*v1', '', np.float),
Statement('v1', '=', 'v1*N * 0', '', np.float),
Statement('v1', '=', 'v1 * 0', '', np.float),
Statement('v1', '=', 'v1 * 0.0', '', np.float),
Statement('v1', '=', '0.0 / (v1*N)', '', np.float),
# Should be simplified to 0
Statement('i1', '=', 'i1*N * 0', '', np.int),
Statement('i1', '=', '0 * i1', '', np.int),
Statement('i1', '=', '0 * i1*N', '', np.int),
Statement('i1', '=', 'i1 * 0', '', np.int),
# Should be simplified to v1*N
Statement('v2', '=', '0 + v1*N', '', np.float),
Statement('v2', '=', 'v1*N + 0.0', '', np.float),
Statement('v2', '=', 'v1*N - 0', '', np.float),
Statement('v2', '=', 'v1*N - 0.0', '', np.float),
Statement('v2', '=', '1 * v1*N', '', np.float),
Statement('v2', '=', '1.0 * v1*N', '', np.float),
Statement('v2', '=', 'v1*N / 1.0', '', np.float),
Statement('v2', '=', 'v1*N / 1', '', np.float),
# Should be simplified to i1
Statement('i1', '=', 'i1*1', '', int),
Statement('i1', '=', 'i1//1', '', int),
Statement('i1', '=', 'i1+0', '', int),
Statement('i1', '=', '0+i1', '', int),
Statement('i1', '=', 'i1-0', '', int),
# Should *not* be simplified (because it would change the type,
# important for integer division, for example)
Statement('v1', '=', 'i1*1.0', '', float),
Statement('v1', '=', '1.0*i1', '', float),
Statement('v1', '=', 'i1/1.0', '', float),
Statement('v1', '=', 'i1/1', '', float),
Statement('v1', '=', 'i1+0.0', '', float),
Statement('v1', '=', '0.0+i1', '', float),
Statement('v1', '=', 'i1-0.0', '', float),
## Should *not* be simplified, flooring division by 1 changes the value
Statement('v1', '=', 'v2//1.0', '', float),
Statement('i1', '=', 'i1//1.0', '', float) # changes type
]
scalar, vector = optimise_statements([], statements, variables)
assert len(scalar) == 0
for s in vector[:6]:
assert s.expr == '0.0'
for s in vector[6:10]:
assert s.expr == '0', s.expr # integer
for s in vector[10:18]:
expr = s.expr.replace(' ', '')
assert expr == 'v1*N' or expr == 'N*v1'
for s in vector[18:23]:
expr = s.expr.replace(' ', '')
assert expr == 'i1'
for s in vector[23:27]:
expr = s.expr.replace(' ', '')
assert expr == '1.0*i1' or expr == 'i1*1.0' or expr == 'i1/1.0'
for s in vector[27:30]:
expr = s.expr.replace(' ', '')
assert expr == '0.0+i1' or expr == 'i1+0.0'
for s in vector[30:31]:
expr = s.expr.replace(' ', '')
assert expr == 'v2//1.0' or expr == 'v2//1'
for s in vector[31:]:
expr = s.expr.replace(' ', '')
assert expr == 'i1//1.0'
def test_apply_loop_invariant_optimisation_simplification():
variables = {'v1': Variable('v1', scalar=False),
'v2': Variable('v2', scalar=False),
'i1': Variable('i1', scalar=False, dtype=int),
'N': Constant('N', 10)
}
statements = [
# Should be simplified to 0.0
Statement('v1', '=', 'v1 - v1', '', np.float),
Statement('v1', '=', 'N*v1 - N*v1', '', np.float),
Statement('v1', '=', 'v1*N * 0', '', np.float),
Statement('v1', '=', 'v1 * 0', '', np.float),
Statement('v1', '=', 'v1 * 0.0', '', np.float),
Statement('v1', '=', '0.0 / (v1*N)', '', np.float),
# Should be simplified to 0
Statement('i1', '=', 'i1*N * 0', '', np.int),
Statement('i1', '=', '0 * i1', '', np.int),
Statement('i1', '=', '0 * i1*N', '', np.int),
Statement('i1', '=', 'i1 * 0', '', np.int),
# Should be simplified to v1*N
Statement('v2', '=', '0 + v1*N', '', np.float),
Statement('v2', '=', 'v1*N + 0.0', '', np.float),
Statement('v2', '=', 'v1*N - 0', '', np.float),
Statement('v2', '=', 'v1*N - 0.0', '', np.float),
Statement('v2', '=', '1 * v1*N', '', np.float),
Statement('v2', '=', '1.0 * v1*N', '', np.float),
Statement('v2', '=', 'v1*N / 1.0', '', np.float),
Statement('v2', '=', 'v1*N / 1', '', np.float),
# Should be simplified to i1
Statement('i1', '=', 'i1*1', '', int),
Statement('i1', '=', 'i1//1', '', int),
Statement('i1', '=', 'i1+0', '', int),
Statement('i1', '=', '0+i1', '', int),
Statement('i1', '=', 'i1-0', '', int),
# Should *not* be simplified (because it would change the type,
# important for integer division, for example)
Statement('v1', '=', 'i1*1.0', '', float),
Statement('v1', '=', '1.0*i1', '', float),
Statement('v1', '=', 'i1/1.0', '', float),
Statement('v1', '=', 'i1/1' , '', float),
Statement('v1', '=', 'i1+0.0', '', float),
Statement('v1', '=', '0.0+i1', '', float),
Statement('v1', '=', 'i1-0.0', '', float),
## Should *not* be simplified, flooring division by 1 changes the value
Statement('v1', '=', 'v2//1.0', '', float),
Statement('i1', '=', 'i1//1.0', '', float) # changes type
]
scalar, vector = optimise_statements([], statements, variables)
assert len(scalar) == 0
for s in vector[:6]:
assert s.expr == '0.0'
for s in vector[6:10]:
assert s.expr == '0',s.expr # integer
for s in vector[10:18]:
expr = s.expr.replace(' ', '')
assert expr == 'v1*N' or expr == 'N*v1'
for s in vector[18:23]:
expr = s.expr.replace(' ', '')
assert expr == 'i1'
for s in vector[23:27]:
expr = s.expr.replace(' ', '')
assert expr == '1.0*i1' or expr == 'i1*1.0' or expr == 'i1/1.0'
for s in vector[27:30]:
expr = s.expr.replace(' ', '')
assert expr == '0.0+i1' or expr == 'i1+0.0'
for s in vector[30:31]:
expr = s.expr.replace(' ', '')
assert expr == 'v2//1.0' or expr == 'v2//1'
for s in vector[31:]:
expr = s.expr.replace(' ', '')
assert expr == 'i1//1.0'