text: import sys
  import platform
  
  from numpy.testing import *
  import numpy.core.umath as ncu
  import numpy as np
  
  # TODO: branch cuts (use Pauli code)
  # TODO: conj 'symmetry'
  # TODO: FPU exceptions
  
  # At least on Windows the results of many complex functions are not conforming
  # to the C99 standard. See ticket 1574.
  # Ditto for Solaris (ticket 1642) and OS X on PowerPC.
  olderr = np.seterr(invalid='ignore', divide='ignore')
  try:
      functions_seem_flaky = ((np.exp(complex(np.inf, 0)).imag != 0)
                              or (np.log(complex(np.NZERO, 0)).imag != np.pi))
  finally:
      np.seterr(**olderr)
  # TODO: replace with a check on whether platform-provided C99 funcs are used
  skip_complex_tests = (not sys.platform.startswith('linux') or functions_seem_flaky)
  
  def platform_skip(func):
      return dec.skipif(skip_complex_tests,
          "Numpy is using complex functions (e.g. sqrt) provided by your"
          "platform's C library. However, they do not seem to behave according"
          "to C99 -- so C99 tests are skipped.")(func)
  
  
  class TestCexp(object):
      def test_simple(self):
          check = check_complex_value
          f = np.exp
  
          yield check, f, 1, 0, np.exp(1), 0, False
          yield check, f, 0, 1, np.cos(1), np.sin(1), False
  
          ref = np.exp(1) * np.complex(np.cos(1), np.sin(1))
          yield check, f, 1, 1, ref.real, ref.imag, False
  
      @platform_skip
      def test_special_values(self):
          # C99: Section G 6.3.1
  
          check = check_complex_value
          f = np.exp
  
          # cexp(+-0 + 0i) is 1 + 0i
          yield check, f, np.PZERO, 0, 1, 0, False
          yield check, f, np.NZERO, 0, 1, 0, False
  
          # cexp(x + infi) is nan + nani for finite x and raises 'invalid' FPU
          # exception
          yield check, f,  1, np.inf, np.nan, np.nan
          yield check, f, -1, np.inf, np.nan, np.nan
          yield check, f,  0, np.inf, np.nan, np.nan
  
          # cexp(inf + 0i) is inf + 0i
          yield check, f,  np.inf, 0, np.inf, 0
  
          # cexp(-inf + yi) is +0 * (cos(y) + i sin(y)) for finite y
          ref = np.complex(np.cos(1.), np.sin(1.))
          yield check, f,  -np.inf, 1, np.PZERO, np.PZERO
  
          ref = np.complex(np.cos(np.pi * 0.75), np.sin(np.pi * 0.75))
          yield check, f,  -np.inf, 0.75 * np.pi, np.NZERO, np.PZERO
  
          # cexp(inf + yi) is +inf * (cos(y) + i sin(y)) for finite y
          ref = np.complex(np.cos(1.), np.sin(1.))
          yield check, f,  np.inf, 1, np.inf, np.inf
  
          ref = np.complex(np.cos(np.pi * 0.75), np.sin(np.pi * 0.75))
          yield check, f,  np.inf, 0.75 * np.pi, -np.inf, np.inf
  
          # cexp(-inf + inf i) is +-0 +- 0i (signs unspecified)
          def _check_ninf_inf(dummy):
              msgform = "cexp(-inf, inf) is (%f, %f), expected (+-0, +-0)"
              err = np.seterr(invalid='ignore')
              try:
                  z = f(np.array(np.complex(-np.inf, np.inf)))
                  if z.real != 0 or z.imag != 0:
                      raise AssertionError(msgform %(z.real, z.imag))
              finally:
                  np.seterr(**err)
  
          yield _check_ninf_inf, None
  
          # cexp(inf + inf i) is +-inf + NaNi and raised invalid FPU ex.
          def _check_inf_inf(dummy):
              msgform = "cexp(inf, inf) is (%f, %f), expected (+-inf, nan)"
              err = np.seterr(invalid='ignore')
              try:
                  z = f(np.array(np.complex(np.inf, np.inf)))
                  if not np.isinf(z.real) or not np.isnan(z.imag):
                      raise AssertionError(msgform % (z.real, z.imag))
              finally:
                  np.seterr(**err)
  
          yield _check_inf_inf, None
  
          # cexp(-inf + nan i) is +-0 +- 0i
          def _check_ninf_nan(dummy):
              msgform = "cexp(-inf, nan) is (%f, %f), expected (+-0, +-0)"
              err = np.seterr(invalid='ignore')
              try:
                  z = f(np.array(np.complex(-np.inf, np.nan)))
                  if z.real != 0 or z.imag != 0:
                      raise AssertionError(msgform % (z.real, z.imag))
              finally:
                  np.seterr(**err)
  
          yield _check_ninf_nan, None
  
          # cexp(inf + nan i) is +-inf + nan
          def _check_inf_nan(dummy):
              msgform = "cexp(-inf, nan) is (%f, %f), expected (+-inf, nan)"
              err = np.seterr(invalid='ignore')
              try:
                  z = f(np.array(np.complex(np.inf, np.nan)))
                  if not np.isinf(z.real) or not np.isnan(z.imag):
                      raise AssertionError(msgform % (z.real, z.imag))
              finally:
                  np.seterr(**err)
  
          yield _check_inf_nan, None
  
          # cexp(nan + yi) is nan + nani for y != 0 (optional: raises invalid FPU
          # ex)
          yield check, f, np.nan, 1, np.nan, np.nan
          yield check, f, np.nan, -1, np.nan, np.nan
  
          yield check, f, np.nan,  np.inf, np.nan, np.nan
          yield check, f, np.nan, -np.inf, np.nan, np.nan
  
          # cexp(nan + nani) is nan + nani
          yield check, f, np.nan, np.nan, np.nan, np.nan
  
      @dec.knownfailureif(True, "cexp(nan + 0I) is wrong on most implementations")
      def test_special_values2(self):
          # XXX: most implementations get it wrong here (including glibc <= 2.10)
          # cexp(nan + 0i) is nan + 0i
          yield check, f, np.nan, 0, np.nan, 0
  
  class TestClog(TestCase):
      def test_simple(self):
          x = np.array([1+0j, 1+2j])
          y_r = np.log(np.abs(x)) + 1j * np.angle(x)
          y = np.log(x)
          for i in range(len(x)):
              assert_almost_equal(y[i], y_r[i])
  
      @platform_skip
      def test_special_values(self):
          xl = []
          yl = []
  
          # From C99 std (Sec 6.3.2)
          # XXX: check exceptions raised
          # --- raise for invalid fails.
  
          # clog(-0 + i0) returns -inf + i pi and raises the 'divide-by-zero'
          # floating-point exception.
          err = np.seterr(divide='raise')
          try:
              x = np.array([np.NZERO], dtype=np.complex)
              y = np.complex(-np.inf, np.pi)
              self.assertRaises(FloatingPointError, np.log, x)
              np.seterr(divide='ignore')
              assert_almost_equal(np.log(x), y)
          finally:
              np.seterr(**err)
  
          xl.append(x)
          yl.append(y)
  
          # clog(+0 + i0) returns -inf + i0 and raises the 'divide-by-zero'
          # floating-point exception.
          err = np.seterr(divide='raise')
          try:
              x = np.array([0], dtype=np.complex)
              y = np.complex(-np.inf, 0)
              self.assertRaises(FloatingPointError, np.log, x)
              np.seterr(divide='ignore')
              assert_almost_equal(np.log(x), y)
          finally:
              np.seterr(**err)
  
          xl.append(x)
          yl.append(y)
  
          # clog(x + i inf returns +inf + i pi /2, for finite x.
          x = np.array([complex(1, np.inf)], dtype=np.complex)
          y = np.complex(np.inf, 0.5 * np.pi)
          assert_almost_equal(np.log(x), y)
          xl.append(x)
          yl.append(y)
  
          x = np.array([complex(-1, np.inf)], dtype=np.complex)
          assert_almost_equal(np.log(x), y)
          xl.append(x)
          yl.append(y)
  
          # clog(x + iNaN) returns NaN + iNaN and optionally raises the
          # 'invalid' floating- point exception, for finite x.
          err = np.seterr(invalid='raise')
          try:
              x = np.array([complex(1., np.nan)], dtype=np.complex)
              y = np.complex(np.nan, np.nan)
              #self.assertRaises(FloatingPointError, np.log, x)
              np.seterr(invalid='ignore')
              assert_almost_equal(np.log(x), y)
          finally:
              np.seterr(**err)
  
          xl.append(x)
          yl.append(y)
  
          err = np.seterr(invalid='raise')
          try:
              x = np.array([np.inf + 1j * np.nan], dtype=np.complex)
              #self.assertRaises(FloatingPointError, np.log, x)
              np.seterr(invalid='ignore')
              assert_almost_equal(np.log(x), y)
          finally:
              np.seterr(**err)
  
          xl.append(x)
          yl.append(y)
  
          # clog(- inf + iy) returns +inf + ipi , for finite positive-signed y.
          x = np.array([-np.inf + 1j], dtype=np.complex)
          y = np.complex(np.inf, np.pi)
          assert_almost_equal(np.log(x), y)
          xl.append(x)
          yl.append(y)
  
          # clog(+ inf + iy) returns +inf + i0, for finite positive-signed y.
          x = np.array([np.inf + 1j], dtype=np.complex)
          y = np.complex(np.inf, 0)
          assert_almost_equal(np.log(x), y)
          xl.append(x)
          yl.append(y)
  
          # clog(- inf + i inf) returns +inf + i3pi /4.
          x = np.array([complex(-np.inf, np.inf)], dtype=np.complex)
          y = np.complex(np.inf, 0.75 * np.pi)
          assert_almost_equal(np.log(x), y)
          xl.append(x)
          yl.append(y)
  
          # clog(+ inf + i inf) returns +inf + ipi /4.
          x = np.array([complex(np.inf, np.inf)], dtype=np.complex)
          y = np.complex(np.inf, 0.25 * np.pi)
          assert_almost_equal(np.log(x), y)
          xl.append(x)
          yl.append(y)
  
          # clog(+/- inf + iNaN) returns +inf + iNaN.
          x = np.array([complex(np.inf, np.nan)], dtype=np.complex)
          y = np.complex(np.inf, np.nan)
          assert_almost_equal(np.log(x), y)
          xl.append(x)
          yl.append(y)
  
          x = np.array([complex(-np.inf, np.nan)], dtype=np.complex)
          assert_almost_equal(np.log(x), y)
          xl.append(x)
          yl.append(y)
  
          # clog(NaN + iy) returns NaN + iNaN and optionally raises the
          # 'invalid' floating-point exception, for finite y.
          x = np.array([complex(np.nan, 1)], dtype=np.complex)
          y = np.complex(np.nan, np.nan)
          assert_almost_equal(np.log(x), y)
          xl.append(x)
          yl.append(y)
  
          # clog(NaN + i inf) returns +inf + iNaN.
          x = np.array([complex(np.nan, np.inf)], dtype=np.complex)
          y = np.complex(np.inf, np.nan)
          assert_almost_equal(np.log(x), y)
          xl.append(x)
          yl.append(y)
  
          # clog(NaN + iNaN) returns NaN + iNaN.
          x = np.array([complex(np.nan, np.nan)], dtype=np.complex)
          y = np.complex(np.nan, np.nan)
          assert_almost_equal(np.log(x), y)
          xl.append(x)
          yl.append(y)
  
          # clog(conj(z)) = conj(clog(z)).
          xa = np.array(xl, dtype=np.complex)
          ya = np.array(yl, dtype=np.complex)
          err = np.seterr(divide='ignore')
          try:
              for i in range(len(xa)):
                  assert_almost_equal(np.log(np.conj(xa[i])), np.conj(np.log(xa[i])))
          finally:
              np.seterr(**err)
  
  class TestCsqrt(object):
  
      def test_simple(self):
          # sqrt(1)
          yield check_complex_value, np.sqrt, 1, 0, 1, 0
  
          # sqrt(1i)
          yield check_complex_value, np.sqrt, 0, 1, 0.5*np.sqrt(2), 0.5*np.sqrt(2), False
  
          # sqrt(-1)
          yield check_complex_value, np.sqrt, -1, 0, 0, 1
  
      def test_simple_conjugate(self):
          ref = np.conj(np.sqrt(np.complex(1, 1)))
          def f(z):
              return np.sqrt(np.conj(z))
          yield check_complex_value, f, 1, 1, ref.real, ref.imag, False
  
      #def test_branch_cut(self):
      #    _check_branch_cut(f, -1, 0, 1, -1)
  
      @platform_skip
      def test_special_values(self):
          check = check_complex_value
          f = np.sqrt
  
          # C99: Sec G 6.4.2
          x, y = [], []
  
          # csqrt(+-0 + 0i) is 0 + 0i
          yield check, f, np.PZERO, 0, 0, 0
          yield check, f, np.NZERO, 0, 0, 0
  
          # csqrt(x + infi) is inf + infi for any x (including NaN)
          yield check, f,  1, np.inf, np.inf, np.inf
          yield check, f, -1, np.inf, np.inf, np.inf
  
          yield check, f, np.PZERO, np.inf, np.inf, np.inf
          yield check, f, np.NZERO, np.inf, np.inf, np.inf
          yield check, f,   np.inf, np.inf, np.inf, np.inf
          yield check, f,  -np.inf, np.inf, np.inf, np.inf
          yield check, f,  -np.nan, np.inf, np.inf, np.inf
  
          # csqrt(x + nani) is nan + nani for any finite x
          yield check, f,  1, np.nan, np.nan, np.nan
          yield check, f, -1, np.nan, np.nan, np.nan
          yield check, f,  0, np.nan, np.nan, np.nan
  
          # csqrt(-inf + yi) is +0 + infi for any finite y > 0
          yield check, f, -np.inf, 1, np.PZERO, np.inf
  
          # csqrt(inf + yi) is +inf + 0i for any finite y > 0
          yield check, f, np.inf, 1, np.inf, np.PZERO
  
          # csqrt(-inf + nani) is nan +- infi (both +i infi are valid)
          def _check_ninf_nan(dummy):
              msgform = "csqrt(-inf, nan) is (%f, %f), expected (nan, +-inf)"
              z = np.sqrt(np.array(np.complex(-np.inf, np.nan)))
              #Fixme: ugly workaround for isinf bug.
              err = np.seterr(invalid='ignore')
              try:
                  if not (np.isnan(z.real) and np.isinf(z.imag)):
                      raise AssertionError(msgform % (z.real, z.imag))
              finally:
                  np.seterr(**err)
  
          yield _check_ninf_nan, None
  
          # csqrt(+inf + nani) is inf + nani
          yield check, f, np.inf, np.nan, np.inf, np.nan
  
          # csqrt(nan + yi) is nan + nani for any finite y (infinite handled in x
          # + nani)
          yield check, f, np.nan,       0, np.nan, np.nan
          yield check, f, np.nan,       1, np.nan, np.nan
          yield check, f, np.nan,  np.nan, np.nan, np.nan
  
          # XXX: check for conj(csqrt(z)) == csqrt(conj(z)) (need to fix branch
          # cuts first)
  
  class TestCpow(TestCase):
      def test_simple(self):
          x = np.array([1+1j, 0+2j, 1+2j, np.inf, np.nan])
          err = np.seterr(invalid='ignore')
          try:
              y_r = x ** 2
              y = np.power(x, 2)
              for i in range(len(x)):
                  assert_almost_equal(y[i], y_r[i])
          finally:
              np.seterr(**err)
  
      def test_scalar(self):
          x = np.array([1, 1j,         2,  2.5+.37j, np.inf, np.nan])
          y = np.array([1, 1j, -0.5+1.5j, -0.5+1.5j,      2,      3])
          lx = list(range(len(x)))
          # Compute the values for complex type in python
          p_r = [complex(x[i]) ** complex(y[i]) for i in lx]
          # Substitute a result allowed by C99 standard
          p_r[4] = complex(np.inf, np.nan)
          # Do the same with numpy complex scalars
          err = np.seterr(invalid='ignore')
          try:
              n_r = [x[i] ** y[i] for i in lx]
              for i in lx:
                  assert_almost_equal(n_r[i], p_r[i], err_msg='Loop %d\n' % i)
          finally:
              np.seterr(**err)
  
      def test_array(self):
          x = np.array([1, 1j,         2,  2.5+.37j, np.inf, np.nan])
          y = np.array([1, 1j, -0.5+1.5j, -0.5+1.5j,      2,      3])
          lx = list(range(len(x)))
          # Compute the values for complex type in python
          p_r = [complex(x[i]) ** complex(y[i]) for i in lx]
          # Substitute a result allowed by C99 standard
          p_r[4] = complex(np.inf, np.nan)
          # Do the same with numpy arrays
          err = np.seterr(invalid='ignore')
          try:
              n_r = x ** y
              for i in lx:
                  assert_almost_equal(n_r[i], p_r[i], err_msg='Loop %d\n' % i)
          finally:
              np.seterr(**err)
  
  class TestCabs(object):
      def test_simple(self):
          x = np.array([1+1j, 0+2j, 1+2j, np.inf, np.nan])
          y_r = np.array([np.sqrt(2.), 2, np.sqrt(5), np.inf, np.nan])
  
          olderr = np.seterr(invalid='ignore')
          try:
              y = np.abs(x)
          finally:
              np.seterr(**olderr)
  
          for i in range(len(x)):
              assert_almost_equal(y[i], y_r[i])
  
      def test_fabs(self):
          # Test that np.abs(x +- 0j) == np.abs(x) (as mandated by C99 for cabs)
          x = np.array([1+0j], dtype=np.complex)
          assert_array_equal(np.abs(x), np.real(x))
  
          x = np.array([complex(1, np.NZERO)], dtype=np.complex)
          assert_array_equal(np.abs(x), np.real(x))
  
          olderr = np.seterr(invalid='ignore')
          try:
              x = np.array([complex(np.inf, np.NZERO)], dtype=np.complex)
              assert_array_equal(np.abs(x), np.real(x))
          finally:
              np.seterr(**olderr)
  
          x = np.array([complex(np.nan, np.NZERO)], dtype=np.complex)
          assert_array_equal(np.abs(x), np.real(x))
  
      def test_cabs_inf_nan(self):
          x, y = [], []
  
          # cabs(+-nan + nani) returns nan
          x.append(np.nan)
          y.append(np.nan)
          yield check_real_value, np.abs,  np.nan, np.nan, np.nan
  
          x.append(np.nan)
          y.append(-np.nan)
          yield check_real_value, np.abs, -np.nan, np.nan, np.nan
  
          # According to C99 standard, if exactly one of the real/part is inf and
          # the other nan, then cabs should return inf
          x.append(np.inf)
          y.append(np.nan)
          yield check_real_value, np.abs,  np.inf, np.nan, np.inf
  
          x.append(-np.inf)
          y.append(np.nan)
          yield check_real_value, np.abs, -np.inf, np.nan, np.inf
  
          # cabs(conj(z)) == conj(cabs(z)) (= cabs(z))
          def f(a):
              return np.abs(np.conj(a))
          def g(a, b):
              return np.abs(np.complex(a, b))
  
          xa = np.array(x, dtype=np.complex)
          ya = np.array(x, dtype=np.complex)
          for i in range(len(xa)):
              ref = g(x[i], y[i])
              yield check_real_value, f, x[i], y[i], ref
  
  class TestCarg(object):
      def test_simple(self):
          check_real_value(ncu._arg, 1, 0, 0, False)
          check_real_value(ncu._arg, 0, 1, 0.5*np.pi, False)
  
          check_real_value(ncu._arg, 1, 1, 0.25*np.pi, False)
          check_real_value(ncu._arg, np.PZERO, np.PZERO, np.PZERO)
  
      @dec.knownfailureif(True,
          "Complex arithmetic with signed zero is buggy on most implementation")
      def test_zero(self):
          # carg(-0 +- 0i) returns +- pi
          yield check_real_value, ncu._arg, np.NZERO, np.PZERO,  np.pi, False
          yield check_real_value, ncu._arg, np.NZERO, np.NZERO, -np.pi, False
  
          # carg(+0 +- 0i) returns +- 0
          yield check_real_value, ncu._arg, np.PZERO, np.PZERO, np.PZERO
          yield check_real_value, ncu._arg, np.PZERO, np.NZERO, np.NZERO
  
          # carg(x +- 0i) returns +- 0 for x > 0
          yield check_real_value, ncu._arg, 1, np.PZERO, np.PZERO, False
          yield check_real_value, ncu._arg, 1, np.NZERO, np.NZERO, False
  
          # carg(x +- 0i) returns +- pi for x < 0
          yield check_real_value, ncu._arg, -1, np.PZERO,  np.pi, False
          yield check_real_value, ncu._arg, -1, np.NZERO, -np.pi, False
  
          # carg(+- 0 + yi) returns pi/2 for y > 0
          yield check_real_value, ncu._arg, np.PZERO, 1, 0.5 * np.pi, False
          yield check_real_value, ncu._arg, np.NZERO, 1, 0.5 * np.pi, False
  
          # carg(+- 0 + yi) returns -pi/2 for y < 0
          yield check_real_value, ncu._arg, np.PZERO, -1, 0.5 * np.pi, False
          yield check_real_value, ncu._arg, np.NZERO, -1,-0.5 * np.pi, False
  
      #def test_branch_cuts(self):
      #    _check_branch_cut(ncu._arg, -1, 1j, -1, 1)
  
      def test_special_values(self):
          # carg(-np.inf +- yi) returns +-pi for finite y > 0
          yield check_real_value, ncu._arg, -np.inf,  1,  np.pi, False
          yield check_real_value, ncu._arg, -np.inf, -1, -np.pi, False
  
          # carg(np.inf +- yi) returns +-0 for finite y > 0
          yield check_real_value, ncu._arg, np.inf,  1, np.PZERO, False
          yield check_real_value, ncu._arg, np.inf, -1, np.NZERO, False
  
          # carg(x +- np.infi) returns +-pi/2 for finite x
          yield check_real_value, ncu._arg, 1,  np.inf,  0.5 * np.pi, False
          yield check_real_value, ncu._arg, 1, -np.inf, -0.5 * np.pi, False
  
          # carg(-np.inf +- np.infi) returns +-3pi/4
          yield check_real_value, ncu._arg, -np.inf,  np.inf,  0.75 * np.pi, False
          yield check_real_value, ncu._arg, -np.inf, -np.inf, -0.75 * np.pi, False
  
          # carg(np.inf +- np.infi) returns +-pi/4
          yield check_real_value, ncu._arg, np.inf,  np.inf,  0.25 * np.pi, False
          yield check_real_value, ncu._arg, np.inf, -np.inf, -0.25 * np.pi, False
  
          # carg(x + yi) returns np.nan if x or y is nan
          yield check_real_value, ncu._arg, np.nan,      0, np.nan, False
          yield check_real_value, ncu._arg,      0, np.nan, np.nan, False
  
          yield check_real_value, ncu._arg, np.nan, np.inf, np.nan, False
          yield check_real_value, ncu._arg, np.inf, np.nan, np.nan, False
  
  def check_real_value(f, x1, y1, x, exact=True):
      z1 = np.array([complex(x1, y1)])
      if exact:
          assert_equal(f(z1), x)
      else:
          assert_almost_equal(f(z1), x)
  
  def check_complex_value(f, x1, y1, x2, y2, exact=True):
      err = np.seterr(invalid='ignore')
      z1 = np.array([complex(x1, y1)])
      z2 = np.complex(x2, y2)
      try:
          if exact:
              assert_equal(f(z1), z2)
          else:
              assert_almost_equal(f(z1), z2)
      finally:
          np.seterr(**err)
  
  if __name__ == "__main__":
      run_module_suite()
  