text: """
  These routines are not well-tested. They are also old.
  OB says that it is not important to test them well because Scalar Ops
  are rarely used by themselves, instead they are the basis for Tensor Ops
  (which should be checked thoroughly). Moreover, Scalar will be changed
  to use numpy's scalar routines.
  If you do want to rewrite these tests, bear in mind:
    * You don't need to use Composite.
    * FunctionGraph and DualLinker are old, use theano.compile.function.function instead.
  """
  import numpy as np
  import pytest
  
  import tests.unittest_tools as utt
  import theano
  from theano import gof
  from theano.gof import FunctionGraph
  from theano.scalar.basic import (
      ComplexError,
      Composite,
      InRange,
      Scalar,
      add,
      and_,
      arccos,
      arccosh,
      arcsin,
      arcsinh,
      arctan,
      arctan2,
      arctanh,
      cast,
      complex64,
      constant,
      cos,
      cosh,
      deg2rad,
      div_proxy,
      eq,
      exp,
      exp2,
      expm1,
      float16,
      float32,
      floats,
      int8,
      int32,
      ints,
      inv,
      invert,
      log,
      log1p,
      log2,
      log10,
      mul,
      neq,
      rad2deg,
      sin,
      sinh,
      sqrt,
      switch,
      tan,
      tanh,
      true_div,
      uint8,
  )
  
  
  def test_mul_add_div_proxy():
      x, y, z = floats("xyz")
      e = mul(add(x, y), div_proxy(x, y))
      g = FunctionGraph([x, y], [e])
      fn = gof.DualLinker().accept(g).make_function()
      assert fn(1.0, 2.0) == 1.5
  
  
  class TestComposite:
      def test_composite_clone_float32(self):
          def has_f16(comp):
              if any(v.type == float16 for v in comp.fgraph.variables):
                  return True
              return False
  
          w = int8()
          x = float16()
          y = float32()
          cz = Composite([x, y], [tanh(x + cast(y, "float16"))])
          c = Composite(
              [w, x, y],
              [
                  cz(x, y)
                  - cz(x, y) ** 2
                  + cast(x, "int16")
                  + cast(x, "float32")
                  + cast(w, "float16")
                  - constant(np.float16(1.0))
              ],
          )
          assert has_f16(c)
          nc = c.clone_float32()
          assert not has_f16(nc)
  
          v = uint8()
          w = float16()
          x = float16()
          y = float16()
          z = float16()
  
          c = Composite([v, w, x, y, z], [switch(v, mul(w, x, y), z)])
  
          assert has_f16(c)
          nc = c.clone_float32()
          assert not has_f16(nc)
  
      def test_straightforward(self):
          x, y, z = floats("xyz")
          e = mul(add(x, y), div_proxy(x, y))
          C = Composite([x, y], [e])
          c = C.make_node(x, y)
          # print c.c_code(['x', 'y'], ['z'], dict(id = 0))
          g = FunctionGraph([x, y], [c.out])
          fn = gof.DualLinker().accept(g).make_function()
          assert fn(1.0, 2.0) == 1.5
  
      def test_flatten(self):
          # Test that we flatten multiple Composite.
          x, y, z = floats("xyz")
          C = Composite([x, y], [x + y])
          CC = Composite([x, y], [C(x * y, y)])
          assert not isinstance(CC.outputs[0].owner.op, Composite)
  
          # Test with multiple outputs
          CC = Composite([x, y, z], [C(x * y, y), C(x * z, y)])
          # We don't flatten that case.
          assert isinstance(CC.outputs[0].owner.op, Composite)
  
      def test_with_constants(self):
          x, y, z = floats("xyz")
          e = mul(add(70.0, y), div_proxy(x, y))
          C = Composite([x, y], [e])
          c = C.make_node(x, y)
          assert "70.0" in c.op.c_code(c, "dummy", ["x", "y"], ["z"], dict(id=0))
          # print c.c_code(['x', 'y'], ['z'], dict(id = 0))
          g = FunctionGraph([x, y], [c.out])
          fn = gof.DualLinker().accept(g).make_function()
          assert fn(1.0, 2.0) == 36.0
  
      def test_many_outputs(self):
          x, y, z = floats("xyz")
          e0 = x + y + z
          e1 = x + y * z
          e2 = x / y
          C = Composite([x, y, z], [e0, e1, e2])
          c = C.make_node(x, y, z)
          # print c.c_code(['x', 'y', 'z'], ['out0', 'out1', 'out2'], dict(id = 0))
          g = FunctionGraph([x, y, z], c.outputs)
          fn = gof.DualLinker().accept(g).make_function()
          assert fn(1.0, 2.0, 3.0) == [6.0, 7.0, 0.5]
  
      def test_composite_printing(self):
          x, y, z = floats("xyz")
          e0 = x + y + z
          e1 = x + y * z
          e2 = x / y
          e3 = x // 5
          e4 = -x
          e5 = x - y
          e6 = x ** y + (-z)
          e7 = x % 3
          C = Composite([x, y, z], [e0, e1, e2, e3, e4, e5, e6, e7])
          c = C.make_node(x, y, z)
          g = FunctionGraph([x, y, z], c.outputs)
          gof.DualLinker().accept(g).make_function()
  
          assert str(g) == (
              "[*1 -> Composite{((i0 + i1) + i2),"
              " (i0 + (i1 * i2)), (i0 / i1), "
              "(i0 // Constant{5}), "
              "(-i0), (i0 - i1), ((i0 ** i1) + (-i2)),"
              " (i0 % Constant{3})}(x, y, z), "
              "*1::1, *1::2, *1::3, *1::4, *1::5, *1::6, *1::7]"
          )
  
      def test_make_node_continue_graph(self):
          # This is a test for a bug (now fixed) that disabled the
          # local_gpu_elemwise_0 optimization and printed an
          # optimization warning on the terminal.
  
          # We test that Composite.make_node accept as inputs Variable
          # some that represent existing computation.
  
          si0 = theano.scalar.int8()
          si1 = theano.scalar.int8()
          si2 = theano.scalar.float32()
          sout = (si0 * si1) / si2
          sop = theano.scalar.Composite([si0, si1, si2], [sout])
          si0 = theano.scalar.int8()
          si1 = theano.scalar.int8()
          si2 = theano.scalar.float32()
          si3 = theano.scalar.float32()
          sop.make_node(si0 * si3, si1, si2)
  
  
  class TestLogical:
      def test_gt(self):
          x, y, z = floats("xyz")
          fn = gof.DualLinker().accept(FunctionGraph([x, y], [x > y])).make_function()
          for a, b in ((3.0, 9), (3, 0.9), (3, 3)):
              assert fn(a, b) == (a > b)
  
      def test_lt(self):
          x, y, z = floats("xyz")
          fn = gof.DualLinker().accept(FunctionGraph([x, y], [x < y])).make_function()
          for a, b in ((3.0, 9), (3, 0.9), (3, 3)):
              assert fn(a, b) == (a < b)
  
      def test_le(self):
          x, y, z = floats("xyz")
          fn = gof.DualLinker().accept(FunctionGraph([x, y], [x <= y])).make_function()
          for a, b in ((3.0, 9), (3, 0.9), (3, 3)):
              assert fn(a, b) == (a <= b)
  
      def test_ge(self):
          x, y, z = floats("xyz")
          fn = gof.DualLinker().accept(FunctionGraph([x, y], [x >= y])).make_function()
          for a, b in ((3.0, 9), (3, 0.9), (3, 3)):
              assert fn(a, b) == (a >= b)
  
      def test_eq(self):
          x, y, z = floats("xyz")
          fn = gof.DualLinker().accept(FunctionGraph([x, y], [eq(x, y)])).make_function()
          for a, b in ((3.0, 9), (3, 0.9), (3, 3)):
              assert fn(a, b) == (a == b)
  
      def test_neq(self):
          x, y, z = floats("xyz")
          fn = gof.DualLinker().accept(FunctionGraph([x, y], [neq(x, y)])).make_function()
          for a, b in ((3.0, 9), (3, 0.9), (3, 3)):
              assert fn(a, b) == (a != b)
  
      def test_or(self):
          x, y, z = ints("xyz")
          fn = gof.DualLinker().accept(FunctionGraph([x, y], [x | y])).make_function()
          for a, b in ((0, 1), (0, 0), (1, 0), (1, 1)):
              assert fn(a, b) == (a | b), (a, b)
  
      def test_xor(self):
          x, y, z = ints("xyz")
          fn = gof.DualLinker().accept(FunctionGraph([x, y], [x ^ y])).make_function()
          for a, b in ((0, 1), (0, 0), (1, 0), (1, 1)):
              assert fn(a, b) == (a ^ b), (a, b)
  
      def test_and(self):
          x, y, z = ints("xyz")
          fn = (
              gof.DualLinker().accept(FunctionGraph([x, y], [and_(x, y)])).make_function()
          )
          for a, b in ((0, 1), (0, 0), (1, 0), (1, 1)):
              assert fn(a, b) == (a & b), (a, b)
  
          x, y, z = ints("xyz")
          fn = gof.DualLinker().accept(FunctionGraph([x, y], [x & y])).make_function()
          for a, b in ((0, 1), (0, 0), (1, 0), (1, 1)):
              assert fn(a, b) == (a & b), (a, b)
  
      def test_not(self):
          x, y, z = ints("xyz")
          fn = gof.DualLinker().accept(FunctionGraph([x, y], [invert(x)])).make_function()
          for a, b in ((0, 1), (0, 0), (1, 0), (1, 1)):
              assert fn(a, b) == ~a, (a,)
  
          x, y, z = ints("xyz")
          fn = gof.DualLinker().accept(FunctionGraph([x, y], [~x])).make_function()
          for a, b in ((0, 1), (0, 0), (1, 0), (1, 1)):
              assert fn(a, b) == ~a, (a,)
  
  
  class TestUpgradeToFloat:
      # Test for Ops whose output has to be floating point, even when all
      # inputs are ints.
      # In particular, when the inputs are int8, the output should be
      # at least float32, not float16.
  
      unary_ops_vals = [
          (inv, list(range(-127, 0)) + list(range(1, 127))),
          (sqrt, list(range(0, 128))),
          (log, list(range(1, 128))),
          (log2, list(range(1, 128))),
          (log10, list(range(1, 128))),
          (log1p, list(range(0, 128))),
          (exp, list(range(-127, 89))),
          (exp2, list(range(-127, 89))),
          (expm1, list(range(-127, 89))),
          (deg2rad, list(range(-127, 128))),
          (rad2deg, list(range(-127, 128))),
          (cos, list(range(-127, 128))),
          (arccos, list(range(-1, 2))),
          (cosh, list(range(-89, 90))),
          (arccosh, list(range(1, 128))),
          (sin, list(range(-127, 128))),
          (arcsin, list(range(-1, 2))),
          (sinh, list(range(-89, 90))),
          (arcsinh, list(range(-127, 128))),
          (tan, list(range(-3, 4))),
          (arctan, list(range(-127, 128))),
          (tanh, list(range(-127, 128))),
          (arctanh, [0]),
      ]
  
      binary_ops_vals = [(arctan2, list(range(-127, 128)), list(range(-127, 128)))]
  
      @staticmethod
      def _test_unary(unary_op, x_range):
          xi = int8("xi")
          xf = float32("xf")
  
          ei = unary_op(xi)
          fi = theano.function([xi], ei)
  
          ef = unary_op(xf)
          ff = theano.function([xf], ef)
  
          for x_val in x_range:
              outi = fi(x_val)
              outf = ff(x_val)
  
              assert outi.dtype == outf.dtype, "incorrect dtype"
              assert np.allclose(outi, outf), "insufficient precision"
  
      @staticmethod
      def _test_binary(binary_op, x_range, y_range):
          xi = int8("xi")
          yi = int8("yi")
          xf = float32("xf")
          yf = float32("yf")
  
          ei = binary_op(xi, yi)
          fi = theano.function([xi, yi], ei)
  
          ef = binary_op(xf, yf)
          ff = theano.function([xf, yf], ef)
  
          for x_val in x_range:
              for y_val in y_range:
                  outi = fi(x_val, y_val)
                  outf = ff(x_val, y_val)
  
                  assert outi.dtype == outf.dtype, "incorrect dtype"
                  assert np.allclose(outi, outf), "insufficient precision"
  
      def test_true_div(self):
          # true_div's upcast policy is not exactly "upgrade_to_float",
          # so the test is a little bit different
          x_range = list(range(-127, 128))
          y_range = list(range(-127, 0)) + list(range(1, 127))
  
          xi = int8("xi")
          yi = int8("yi")
          xf = Scalar(theano.config.floatX)("xf")
          yf = Scalar(theano.config.floatX)("yf")
  
          ei = true_div(xi, yi)
          fi = theano.function([xi, yi], ei)
  
          ef = true_div(xf, yf)
          ff = theano.function([xf, yf], ef)
  
          for x_val in x_range:
              for y_val in y_range:
                  outi = fi(x_val, y_val)
                  outf = ff(x_val, y_val)
  
                  assert outi.dtype == outf.dtype, "incorrect dtype"
                  assert np.allclose(outi, outf), "insufficient precision"
  
      def test_unary(self):
          # Automatically define all individual unary tests
          for unary_op, x_range in self.unary_ops_vals:
              self._test_unary(unary_op, x_range)
  
      def test_binary(self):
          # Automatically define all individual binary tests
          for binary_op, x_range, y_range in self.binary_ops_vals:
              self._test_binary(binary_op, x_range, y_range)
  
  
  def test_mod_complex_fail():
      # Make sure % fails on complex numbers.
      x = complex64()
      y = int32()
      with pytest.raises(ComplexError):
          x % y
  
  
  def test_grad_gt():
      x = float32(name="x")
      y = float32(name="y")
      z = x > y
      g = theano.gradient.grad(z, y)
      assert g.eval({y: 1.0}) == 0.0
  
  
  def test_grad_switch():
  
      # This is a code snippet from the mailing list
      # It caused an assert to be raised due to the
      # switch op's grad method not handling integer
      # inputs correctly
  
      x = theano.tensor.matrix()
      c = theano.tensor.matrix()
  
      s = theano.tensor.switch(c, x, 0)
      l = s.sum()
  
      theano.gradient.grad(l, x)
  
  
  def test_grad_identity():
      # Check that the grad method of Identity correctly handles int dytpes
      x = theano.tensor.imatrix("x")
      # tensor_copy is Elemwise{Identity}
      y = theano.tensor.tensor_copy(x)
      l = y.sum(dtype=theano.config.floatX)
      theano.gradient.grad(l, x)
  
  
  def test_grad_inrange():
      for bound_definition in [(True, True), (False, False)]:
          # Instantiate op, and then take the gradient
          op = InRange(*bound_definition)
          x = theano.tensor.fscalar("x")
          low = theano.tensor.fscalar("low")
          high = theano.tensor.fscalar("high")
          out = op(x, low, high)
          gx, glow, ghigh = theano.tensor.grad(out, [x, low, high])
  
          # We look if the gradient are equal to zero
          # if x is lower than the lower bound,
          # equal to the lower bound, between lower and higher bound,
          # equal to the higher bound and higher than the higher
          # bound.
          # Mathematically we should have an infinite gradient when
          # x is equal to the lower or higher bound but in that case
          # Theano defines the gradient to be zero for stability.
          f = theano.function([x, low, high], [gx, glow, ghigh])
          utt.assert_allclose(f(0, 1, 5), [0, 0, 0])
          utt.assert_allclose(f(1, 1, 5), [0, 0, 0])
          utt.assert_allclose(f(2, 1, 5), [0, 0, 0])
          utt.assert_allclose(f(5, 1, 5), [0, 0, 0])
          utt.assert_allclose(f(7, 1, 5), [0, 0, 0])
  
  
  def test_grad_abs():
      a = theano.tensor.fscalar("a")
      b = theano.tensor.nnet.relu(a)
      c = theano.grad(b, a)
      f = theano.function([a], c, mode=theano.Mode(optimizer=None))
      # Currently Theano return 0.5, but it isn't sure it won't change
      # in the futur.
      ret = f(0.0)
      assert ret == 0.5, ret
  
  
  def test_constant():
      c = constant(2, name="a")
      assert c.name == "a"
      assert c.dtype == "int8"
      c = constant(2, dtype="float32")
      assert c.name is None
      assert c.dtype == "float32"
  