content: import operator as op
  import math
  
  NAN = math.nan
  INF = math.inf
  NINF = -math.inf
  
  @test
  def test_py_numerics_int():
      one = 1
      iz = 0
      fz = 0.0
      n = 0
  
      # through function (not optimized / pre-evaluated)
      assert op.floordiv(-5, 2) == -3
      assert op.floordiv(-5, 2.0) == -3.0
      assert op.truediv(-5, 2) == -2.5
      assert op.truediv(-5, 2.0) == -2.5
      assert op.mod(-10, 3) == 2
      assert op.mod(-1, 0.3) == 0.19999999999999996
      assert divmod(-10, 3) == (-4, 2)
      assert divmod(-1, 0.3) == (-4.0, 0.19999999999999996)
  
      # with vars (evaluated in IR)
      a = -5
      b = 2
      c = 2.0
      d = -10
      e = 3
      f = -1
      g = 0.3
      assert a // b == -3
      assert a // c == -3.0
      assert a / b == -2.5
      assert a / c == -2.5
      assert d % e == 2
      assert f % g == 0.19999999999999996
  
      # constant (evaluated statically by parser)
      assert -5 // 2 == -3
      assert -10 % 3 == 2
  
      # errors
      try:
          print(one // fz)
          assert False
      except ZeroDivisionError as e:
          assert str(e) == 'float floor division by zero'
          n += 1
  
      try:
          print(one // iz)
          assert False
      except ZeroDivisionError as e:
          assert str(e) == 'integer division or modulo by zero'
          n += 1
  
      try:
          print(one / fz)
          assert False
      except ZeroDivisionError as e:
          assert str(e) == 'float division by zero'
          n += 1
  
      try:
          print(one / iz)
          assert False
      except ZeroDivisionError as e:
          assert str(e) == 'division by zero'
          n += 1
  
      try:
          print(one % fz)
          assert False
      except ZeroDivisionError as e:
          assert str(e) == 'float modulo'
          n += 1
  
      try:
          print(one % iz)
          assert False
      except ZeroDivisionError as e:
          assert str(e) == 'integer division or modulo by zero'
          n += 1
  
      try:
          print(divmod(one, iz))
          assert False
      except ZeroDivisionError as e:
          assert str(e) == 'integer division or modulo by zero'
          n += 1
  
      try:
          print(divmod(one, fz))
          assert False
      except ZeroDivisionError as e:
          assert str(e) == 'float divmod()'
          n += 1
  
      assert n == 8
  
  @test
  def test_py_numerics_float():
      one = 1.0
      iz = 0
      fz = 0.0
      n = 0
  
      # through function (not optimized / pre-evaluated)
      assert op.floordiv(-5.6, 2) == -3.0
      assert op.floordiv(-5.6, 2.0) == -3.0
      assert op.truediv(-5.6, 2) == -2.8
      assert op.truediv(-5.6, 2.0) == -2.8
      assert op.mod(-10.0, 3) == 2.0
      assert op.mod(-1.0, 0.3) == 0.19999999999999996
      assert divmod(-10.0, 3) == (-4.0, 2.0)
      assert divmod(-1.0, 0.3) == (-4.0, 0.19999999999999996)
  
      # with vars (evaluated in IR)
      a = -5.6
      b = 2
      c = 2.0
      d = -10.0
      e = 3
      f = -1.0
      g = 0.3
      assert a // b == -3
      assert a // c == -3.0
      assert a / b == -2.8
      assert a / c == -2.8
      assert d % e == 2
      assert f % g == 0.19999999999999996
  
      try:
          print(one // fz)
          assert False
      except ZeroDivisionError as e:
          assert str(e) == 'float floor division by zero'
          n += 1
  
      try:
          print(one // iz)
          assert False
      except ZeroDivisionError as e:
          assert str(e) == 'float floor division by zero'
          n += 1
  
      try:
          print(one / fz)
          assert False
      except ZeroDivisionError as e:
          assert str(e) == 'float division by zero'
          n += 1
  
      try:
          print(one / iz)
          assert False
      except ZeroDivisionError as e:
          assert str(e) == 'float division by zero'
          n += 1
  
      try:
          print(one % fz)
          assert False
      except ZeroDivisionError as e:
          assert str(e) == 'float modulo'
          n += 1
  
      try:
          print(one % iz)
          assert False
      except ZeroDivisionError as e:
          assert str(e) == 'float modulo'
          n += 1
  
      try:
          print(divmod(one, iz))
          assert False
      except ZeroDivisionError as e:
          assert str(e) == 'float divmod()'
          n += 1
  
      try:
          print(divmod(one, fz))
          assert False
      except ZeroDivisionError as e:
          assert str(e) == 'float divmod()'
          n += 1
  
      assert n == 8
  
  
  import math
  
  NAN = math.nan
  INF = math.inf
  NINF = -math.inf
  
  
  def close(a: float, b: float, epsilon: float = 1e-7):
      return abs(a - b) <= epsilon
  
  
  @test
  def test_isnan():
      assert math.isnan(float("nan")) == True
      assert math.isnan(4.0) == False
  
  
  @test
  def test_isinf():
      assert math.isinf(float("inf")) == True
      assert math.isinf(7.0) == False
  
  
  @test
  def test_isfinite():
      assert math.isfinite(1.4) == True
      assert math.isfinite(0.0) == True
      assert math.isfinite(NAN) == False
      assert math.isfinite(INF) == False
      assert math.isfinite(NINF) == False
  
  
  @test
  def test_ceil():
      assert math.ceil(3.3) == 4
      assert math.ceil(0.5) == 1
      assert math.ceil(1.0) == 1
      assert math.ceil(1.5) == 2
      assert math.ceil(-0.5) == 0
      assert math.ceil(-1.0) == -1
      assert math.ceil(-1.5) == -1
  
  
  @test
  def test_floor():
      assert math.floor(3.3) == 3
      assert math.floor(0.5) == 0
      assert math.floor(1.0) == 1
      assert math.floor(1.5) == 1
      assert math.floor(-0.5) == -1
      assert math.floor(-1.0) == -1
      assert math.floor(-1.5) == -2
  
  
  @test
  def test_fabs():
      assert math.fabs(-1.0) == 1
      assert math.fabs(0.0) == 0
      assert math.fabs(1.0) == 1
  
  
  @test
  def test_fmod():
      assert math.fmod(10.0, 1.0) == 0.0
      assert math.fmod(10.0, 0.5) == 0.0
      assert math.fmod(10.0, 1.5) == 1.0
      assert math.fmod(-10.0, 1.0) == -0.0
      assert math.fmod(-10.0, 0.5) == -0.0
      assert math.fmod(-10.0, 1.5) == -1.0
  
  
  @test
  def test_exp():
      assert math.exp(0.0) == 1
      assert math.exp(-1.0) == 1 / math.e
      assert math.exp(1.0) == math.e
  
  
  @test
  def test_expm1():
      assert math.expm1(0.0) == 0
      assert close(math.expm1(1.0), 1.7182818284590453)
      assert close(math.expm1(3.0), 19.085536923187668)
      assert close(math.expm1(5.0), 147.4131591025766)
      assert math.expm1(INF) == INF
      assert math.expm1(NINF) == -1
      assert math.isnan(math.expm1(NAN)) == True
  
  
  @test
  def test_ldexp():
      assert math.ldexp(0.0, 1) == 0.0
      assert math.ldexp(1.0, 1) == 2.0
      assert math.ldexp(1.0, -1) == 0.5
      assert math.ldexp(-1.0, 1) == -2.0
      assert math.ldexp(0.0, 1) == 0.0
      assert math.ldexp(1.0, -1000000) == 0.0
      assert math.ldexp(-1.0, -1000000) == -0.0
      assert math.ldexp(INF, 30) == INF
      assert math.ldexp(NINF, -213) == NINF
      assert math.isnan(math.ldexp(NAN, 0)) == True
  
  
  @test
  def test_log():
      assert math.log(1.0 / math.e) == -1
      assert math.log(1.0) == 0
      assert math.log(math.e) == 1
  
  
  @test
  def test_log2():
      assert math.log2(1.0) == 0.0
      assert math.log2(2.0) == 1.0
      assert math.log2(4.0) == 2.0
      assert math.log2(2.0 ** 1023) == 1023.0
      try:
          math.log2(-1.5)
          assert False
      except ValueError as e:
          assert str(e) == 'math domain error'
      try:
          math.log2(NINF)
          assert False
      except ValueError as e:
          assert str(e) == 'math domain error'
      assert math.isnan(math.log2(NAN)) == True
  
  
  @test
  def test_log10():
      assert math.log10(0.1) == -1
      assert math.log10(1.0) == 0
      assert math.log10(10.0) == 1
      assert math.log10(10000.0) == 4
  
  
  @test
  def test_degrees():
      assert math.degrees(math.pi) == 180.0
      assert math.degrees(math.pi / 2) == 90.0
      assert math.degrees(-math.pi / 4) == -45.0
      assert math.degrees(0.0) == 0.0
  
  
  @test
  def test_radians():
      assert math.radians(180.0) == math.pi
      assert math.radians(90.0) == math.pi / 2
      assert math.radians(-45.0) == -math.pi / 4
      assert math.radians(0.0) == 0.0
  
  
  @test
  def test_sqrt():
      assert math.sqrt(4.0) == 2
      assert math.sqrt(0.0) == 0
      assert math.sqrt(1.0) == 1
      try:
          math.sqrt(-1.0)
          assert False
      except ValueError as e:
          assert str(e) == 'math domain error'
  
  
  @test
  def test_pow():
      assert math.pow(0.0, 1.0) == 0
      assert math.pow(1.0, 0.0) == 1
      assert math.pow(2.0, 1.0) == 2
      assert math.pow(2.0, -1.0) == 0.5
      assert math.pow(-0.0, 3.0) == -0.0
      assert math.pow(-0.0, 2.3) == 0.0
      assert math.pow(-0.0, 0.0) == 1
      assert math.pow(-0.0, -0.0) == 1
      assert math.pow(-2.0, 2.0) == 4.0
      assert math.pow(-2.0, 3.0) == -8.0
      assert math.pow(-2.0, -3.0) == -0.125
      assert math.pow(INF, 1.0) == INF
      assert math.pow(NINF, 1.0) == NINF
      assert math.pow(1.0, INF) == 1
      assert math.pow(1.0, NINF) == 1
      assert math.isnan(math.pow(NAN, 1.0)) == True
      assert math.isnan(math.pow(2.0, NAN)) == True
      assert math.isnan(math.pow(0.0, NAN)) == True
      assert math.pow(1.0, NAN) == 1
      try:
          math.pow(10.0, 400.0)
          assert False
      except OverflowError as e:
          assert str(e) == 'math range error'
  
  
  @test
  def test_acos():
      assert math.acos(-1.0) == math.pi
      assert math.acos(0.0) == math.pi / 2
      assert math.acos(1.0) == 0
      assert math.isnan(math.acos(NAN)) == True
  
  
  @test
  def test_asin():
      assert math.asin(-1.0) == -math.pi / 2
      assert math.asin(0.0) == 0
      assert math.asin(1.0) == math.pi / 2
      assert math.isnan(math.asin(NAN)) == True
  
  
  @test
  def test_atan():
      assert math.atan(-1.0) == -math.pi / 4
      assert math.atan(0.0) == 0
      assert math.atan(1.0) == math.pi / 4
      assert math.atan(INF) == math.pi / 2
      assert math.atan(NINF) == -math.pi / 2
      assert math.isnan(math.atan(NAN)) == True
  
  
  @test
  def test_atan2():
      assert math.atan2(-1.0, 0.0) == -math.pi / 2
      assert math.atan2(-1.0, 1.0) == -math.pi / 4
      assert math.atan2(0.0, 1.0) == 0
      assert math.atan2(1.0, 1.0) == math.pi / 4
      assert math.atan2(1.0, 0.0) == math.pi / 2
      assert math.atan2(-0.0, 0.0) == -0
      assert math.atan2(-0.0, 2.3) == -0
      assert math.atan2(0.0, -2.3) == math.pi
      assert math.atan2(INF, NINF) == math.pi * 3 / 4
      assert math.atan2(INF, 2.3) == math.pi / 2
      assert math.isnan(math.atan2(NAN, 0.0)) == True
  
  
  @test
  def test_cos():
      assert math.cos(0.0) == 1
      assert close(math.cos(math.pi / 2), 6.123233995736766e-17)
      assert close(math.cos(-math.pi / 2), 6.123233995736766e-17)
      assert math.cos(math.pi) == -1
  
      try:
          math.cos(INF)
          assert False
      except ValueError as e:
          assert str(e) == 'math domain error'
  
      try:
          math.cos(NINF)
          assert False
      except ValueError as e:
          assert str(e) == 'math domain error'
  
      assert math.isnan(math.cos(NAN)) == True
  
  
  @test
  def test_sin():
      assert math.sin(0.0) == 0
      assert math.sin(math.pi / 2) == 1
      assert math.sin(-math.pi / 2) == -1
  
      try:
          math.sin(INF)
          assert False
      except ValueError as e:
          assert str(e) == 'math domain error'
  
      try:
          math.sin(NINF)
          assert False
      except ValueError as e:
          assert str(e) == 'math domain error'
  
      assert math.isnan(math.sin(NAN)) == True
  
  
  @test
  def test_hypot():
      assert math.hypot(12.0, 5.0) == 13
      assert math.hypot(12.0 / 32.0, 5.0 / 32) == 13 / 32
      assert math.hypot(0.0, 0.0) == 0
      assert math.hypot(-3.0, 4.0) == 5
      assert math.hypot(3.0, 4.0) == 5
  
  
  @test
  def test_tan():
      assert math.tan(0.0) == 0
      assert close(math.tan(math.pi / 4), 0.9999999999999999)
      assert close(math.tan(-math.pi / 4), -0.9999999999999999)
  
      try:
          math.tan(INF)
          assert False
      except ValueError as e:
          assert str(e) == 'math domain error'
  
      try:
          math.tan(NINF)
          assert False
      except ValueError as e:
          assert str(e) == 'math domain error'
  
      assert math.isnan(math.tan(NAN)) == True
  
  
  @test
  def test_cosh():
      assert math.cosh(0.0) == 1
      assert math.cosh(2.0) - 2 * math.cosh(1.0) ** 2 == -1
      assert math.cosh(INF) == INF
      assert math.cosh(NINF) == INF
      assert math.isnan(math.cosh(NAN)) == True
  
  
  @test
  def test_sinh():
      assert math.sinh(0.0) == 0
      assert math.sinh(1.0) + math.sinh(-1.0) == 0
      assert math.sinh(INF) == INF
      assert math.sinh(NINF) == NINF
      assert math.isnan(math.sinh(NAN)) == True
  
  
  @test
  def test_tanh():
      assert math.tanh(0.0) == 0
      assert math.tanh(1.0) + math.tanh(-1.0) == 0
      assert math.tanh(INF) == 1
      assert math.tanh(NINF) == -1
      assert math.isnan(math.tanh(NAN)) == True
  
  
  @test
  def test_acosh():
      assert math.acosh(1.0) == 0
      assert close(math.acosh(2.0), 1.3169578969248166)
      assert math.acosh(INF) == INF
      assert math.isnan(math.acosh(NAN)) == True
      try:
          math.acosh(-1.0)
          assert False
      except ValueError as e:
          assert str(e) == 'math domain error'
  
  
  @test
  def test_asinh():
      assert math.asinh(0.0) == 0
      assert close(math.asinh(1.0), 0.881373587019543)
      assert close(math.asinh(-1.0), -0.881373587019543)
      assert math.asinh(INF) == INF
      assert math.isnan(math.asinh(NAN)) == True
      assert math.asinh(NINF) == NINF
  
  
  @test
  def test_atanh():
      assert math.atanh(0.0) == 0
      assert close(math.atanh(0.5), 0.5493061443340549)
      assert close(math.atanh(-0.5), -0.5493061443340549)
  
      try:
          math.atanh(INF)
          assert False
      except ValueError as e:
          assert str(e) == 'math domain error'
  
      try:
          math.atanh(NINF)
          assert False
      except ValueError as e:
          assert str(e) == 'math domain error'
  
      assert math.isnan(math.atanh(NAN)) == True
  
  
  @test
  def test_copysign():
      assert math.copysign(1.0, -0.0) == -1
      assert math.copysign(1.0, 42.0) == 1
      assert math.copysign(1.0, -42.0) == -1
      assert math.copysign(3.0, 0.0) == 3
      assert math.copysign(INF, 0.0) == INF
      assert math.copysign(INF, -0.0) == NINF
      assert math.copysign(NINF, 0.0) == INF
      assert math.copysign(NINF, -0.0) == NINF
      assert math.copysign(1.0, INF) == 1
      assert math.copysign(1.0, NINF) == -1
      assert math.copysign(INF, INF) == INF
      assert math.copysign(INF, NINF) == NINF
      assert math.copysign(NINF, INF) == INF
      assert math.copysign(NINF, NINF) == NINF
      assert math.isnan(math.copysign(NAN, 1.0)) == True
      assert math.isnan(math.copysign(NAN, INF)) == True
      assert math.isnan(math.copysign(NAN, NINF)) == True
      assert math.isnan(math.copysign(NAN, NAN)) == True
  
  
  @test
  def test_log1p():
      assert close(math.log1p(2.0), 1.0986122886681098)
      assert close(math.log1p(2.0 ** 90), 62.383246250395075)
      assert close(math.log1p(2.0 ** 300), 207.94415416798358)
      assert math.log1p(INF) == INF
      try:
          math.log1p(-1.0)
          assert False
      except ValueError as e:
          assert str(e) == 'math domain error'
  
  
  @test
  def test_trunc():
      assert math.trunc(1.0) == 1
      assert math.trunc(-1.0) == -1
      assert math.trunc(1.5) == 1
      assert math.trunc(-1.5) == -1
      assert math.trunc(1.99999999) == 1
      assert math.trunc(-1.99999999) == -1
      assert math.trunc(0.99999999) == 0
      assert math.trunc(-100.999) == -100
  
  
  @test
  def test_erf():
      assert close(math.erf(1.0), 0.8427007929497148)
      assert math.erf(0.0) == 0
      assert close(math.erf(3.0), 0.9999779095030015)
      assert math.erf(256.0) == 1.0
      assert math.erf(INF) == 1.0
      assert math.erf(NINF) == -1.0
      assert math.isnan(math.erf(NAN)) == True
  
  
  @test
  def test_erfc():
      assert math.erfc(0.0) == 1.0
      assert close(math.erfc(1.0), 0.15729920705028516)
      assert close(math.erfc(2.0), 0.0046777349810472645)
      assert close(math.erfc(-1.0), 1.8427007929497148)
      assert math.erfc(INF) == 0.0
      assert math.erfc(NINF) == 2.0
      assert math.isnan(math.erfc(NAN)) == True
  
  
  @test
  def test_gamma():
      assert close(math.gamma(6.0), 120.0)
      assert close(math.gamma(1.0), 1.0)
      assert close(math.gamma(2.0), 1.0)
      assert close(math.gamma(3.0), 2.0)
      try:
          math.gamma(-1.0)
          assert False
      except ValueError as e:
          assert str(e) == 'math domain error'
      assert math.gamma(INF) == INF
      try:
          math.gamma(NINF)
          assert False
      except ValueError as e:
          assert str(e) == 'math domain error'
      assert math.isnan(math.gamma(NAN)) == True
  
  
  @test
  def test_lgamma():
      assert math.lgamma(1.0) == 0.0
      assert math.lgamma(2.0) == 0.0
      #assert math.lgamma(-1.0) == INF  # Python's custom lgamma gives math domain error
      assert math.lgamma(INF) == INF
      assert math.lgamma(NINF) == INF
      assert math.isnan(math.lgamma(NAN)) == True
  
  
  @test
  def test_remainder():
      assert math.remainder(2.0, 2.0) == 0.0
      assert math.remainder(-4.0, 1.0) == -0.0
      assert close(math.remainder(-3.8, 1.0), 0.20000000000000018)
      assert close(math.remainder(3.8, 1.0), -0.20000000000000018)
      try:
          math.remainder(INF, 1.0)
          assert False
      except ValueError as e:
          assert str(e) == 'math domain error'
      try:
          math.remainder(NINF, 1.0)
          assert False
      except ValueError as e:
          assert str(e) == 'math domain error'
      assert math.isnan(math.remainder(NAN, 1.0)) == True
  
  
  @test
  def test_gcd():
      assert math.gcd(0.0, 0.0) == 0
      assert math.gcd(1.0, 0.0) == 1
      assert math.gcd(-1.0, 0.0) == 1
      assert math.gcd(0.0, -1.0) == 1
      assert math.gcd(0.0, 1.0) == 1
      assert math.gcd(7.0, 1.0) == 1
      assert math.gcd(7.0, -1.0) == 1
      assert math.gcd(-23.0, 15.0) == 1
      assert math.gcd(120.0, 84.0) == 12
      assert math.gcd(84.0, -120.0) == 12
  
  
  @test
  def test_frexp():
      assert math.frexp(-2.0) == (-0.5, 2)
      assert math.frexp(-1.0) == (-0.5, 1)
      assert math.frexp(0.0) == (0.0, 0)
      assert math.frexp(1.0) == (0.5, 1)
      assert math.frexp(2.0) == (0.5, 2)
      assert math.frexp(INF)[0] == INF
      assert math.frexp(NINF)[0] == NINF
      assert math.isnan(math.frexp(NAN)[0]) == True
  
  
  @test
  def test_modf():
      assert math.modf(1.5) == (0.5, 1.0)
      assert math.modf(-1.5) == (-0.5, -1.0)
      assert math.modf(math.inf) == (0.0, INF)
      assert math.modf(-math.inf) == (-0.0, NINF)
      modf_nan = math.modf(NAN)
      assert math.isnan(modf_nan[0]) == True
      assert math.isnan(modf_nan[1]) == True
  
  
  @test
  def test_isclose():
      assert math.isclose(1.0 + 1.0, 1.000000000001 + 1.0) == True
      assert math.isclose(2.90909324093284, 2.909093240932844234234234234) == True
      assert math.isclose(2.90909324093284, 2.9) == False
      assert math.isclose(2.90909324093284, 2.90909324) == True
      assert math.isclose(2.90909324, 2.90909325) == False
      assert math.isclose(NAN, 2.9) == False
      assert math.isclose(2.9, NAN) == False
      assert math.isclose(INF, INF) == True
      assert math.isclose(NINF, NINF) == True
      assert math.isclose(NINF, INF) == False
      assert math.isclose(INF, NINF) == False
  
  test_py_numerics_int()
  test_py_numerics_float()
  
  test_isnan()
  test_isinf()
  test_isfinite()
  test_ceil()
  test_floor()
  test_fabs()
  test_fmod()
  test_exp()
  test_expm1()
  test_ldexp()
  test_log()
  test_log2()
  test_log10()
  test_degrees()
  test_radians()
  test_sqrt()
  test_pow()
  test_acos()
  test_asin()
  test_atan()
  test_atan2()
  test_cos()
  test_sin()
  test_hypot()
  test_tan()
  test_cosh()
  test_sinh()
  test_tanh()
  test_acosh()
  test_asinh()
  test_atanh()
  test_copysign()
  test_log1p()
  test_trunc()
  test_erf()
  test_erfc()
  test_gamma()
  test_lgamma()
  test_remainder()
  test_gcd()
  test_frexp()
  test_modf()
  test_isclose()
  