content: 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 isinstance(math.ceil(1.0), int)
      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 isinstance(math.floor(1.0), int)
      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
      assert math.isnan(math.log2(-1.5)) == True
      assert math.isnan(math.log2(NINF)) == True
      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
      assert math.isnan(math.sqrt(-1.0)) == True
  
  
  @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
  
  
  @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
      assert math.isnan(math.cos(INF)) == True
      assert math.isnan(math.cos(NINF)) == True
      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
      assert math.isnan(math.sin(INF)) == True
      assert math.isnan(math.sin(NINF)) == True
      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)
      assert math.isnan(math.tan(INF)) == True
      assert math.isnan(math.tan(NINF)) == True
      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
      assert math.isnan(math.acosh(-1.0)) == True
  
  
  @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)
      assert math.isnan(math.atanh(INF)) == True
      assert math.isnan(math.atanh(NAN)) == True
      assert math.isnan(math.atanh(NINF)) == 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
      assert math.log1p(-1.0) == NINF
  
  
  @test
  def test_trunc():
      assert isinstance(math.trunc(1.0), int)
      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)
      assert math.isnan(math.gamma(-1.0)) == True
      assert math.gamma(INF) == INF
      assert math.isnan(math.gamma(NINF)) == True
      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
      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)
      assert math.isnan(math.remainder(INF, 1.0)) == True
      assert math.isnan(math.remainder(NINF, 1.0)) == True
      assert math.isnan(math.remainder(NAN, 1.0)) == True
  
  
  @test
  def test_gcd():
      assert math.gcd(0, 0) == 0
      assert math.gcd(1, 0) == 1
      assert math.gcd(-1, 0) == 1
      assert math.gcd(0, 1) == 1
      assert math.gcd(0, -1) == 1
      assert math.gcd(7, 1) == 1
      assert math.gcd(7, -1) == 1
      assert math.gcd(-23, 15) == 1
      assert math.gcd(120, 84) == 12
      assert math.gcd(84, -120) == 12
      assert math.gcd(Int[128]('1216342683557601535506311712'), Int[128]('436522681849110124616458784')) == Int[128](32)
  
      x = 43461
      y = 1064
      for c in (652560, 576559230):
          a = x * c
          b = y * c
          assert math.gcd(a, b) == c
          assert math.gcd(b, a) == c
          assert math.gcd(-a, b) == c
          assert math.gcd(b, -a) == c
          assert math.gcd(a, -b) == c
          assert math.gcd(-b, a) == c
          assert math.gcd(-a, -b) == c
          assert math.gcd(-b, -a) == c
  
      assert math.gcd() == 0
      assert math.gcd(120) == 120
      assert math.gcd(-120) == 120
      assert math.gcd(120, 84, 102) == 6
      assert math.gcd(120, 1, 84) == 1
  
  
  @test
  def test_lcm():
      assert math.lcm(0, 0) == 0
      assert math.lcm(1, 0) == 0
      assert math.lcm(-1, 0) == 0
      assert math.lcm(0, 1) == 0
      assert math.lcm(0, -1) == 0
      assert math.lcm(7, 1) == 7
      assert math.lcm(7, -1) == 7
      assert math.lcm(-23, 15) == 345
      assert math.lcm(120, 84) == 840
      assert math.lcm(84, -120) == 840
      #assert math.lcm(1216342683557601535506311712, 436522681849110124616458784) == 16592536571065866494401400422922201534178938447014944
  
      x = 4346103
      y = 1064501
      for c in (8171, 58657):
          a = x * c
          b = y * c
          d = x * y * c
          assert math.lcm(a, b) == d
          assert math.lcm(b, a) == d
          assert math.lcm(-a, b) == d
          assert math.lcm(b, -a) == d
          assert math.lcm(a, -b) == d
          assert math.lcm(-b, a) == d
          assert math.lcm(-a, -b) == d
          assert math.lcm(-b, -a) == d
  
      assert math.lcm() == 1
      assert math.lcm(120) == 120
      assert math.lcm(-120) == 120
      assert math.lcm(120, 84, 102) == 14280
      assert math.lcm(120, 0, 84) == 0
  
  
  @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
  def test_fsum():
      assert math.fsum((42,)) == 42.0
      assert math.fsum((1,2,3)) == 6.0
      assert math.fsum((1,2,-3)) == 0.0
      assert math.fsum(()) == 0.0
      assert math.fsum([.1] * 10) == 1.0
  
      mant_dig = 53
      etiny = -1074
  
      def sum_exact(p):
          n = len(p)
          hi = 0.0
          if n > 0:
              hi = p[n-1]
              n -= 1
              while n > 0:
                  x = hi
                  y = p[n-1]
                  n -= 1
                  hi = x + y
                  yr = hi - x
                  lo = y - yr
                  if lo != 0.0:
                      break
  
              if n > 0 and ((lo < 0 and p[n-1] < 0) or (lo > 0 and p[n-1] > 0)):
                  y = lo * 2
                  x = hi + y
                  yr = x - hi
                  if y == yr:
                      hi = x
          return hi
  
      def msum(iterable):
          "Full precision summation using multiple floats for intermediate values"
          # Rounded x+y stored in hi with the round-off stored in lo.  Together
          # hi+lo are exactly equal to x+y.  The inner loop applies hi/lo summation
          # to each partial so that the list of partial sums remains exact.
          # Depends on IEEE-754 arithmetic guarantees.  See proof of correctness at:
          # www-2.cs.cmu.edu/afs/cs/project/quake/public/papers/robust-arithmetic.ps
  
          partials = []               # sorted, non-overlapping partial sums
          for x in iterable:
              i = 0
              for y in partials:
                  if abs(x) < abs(y):
                      x, y = y, x
                  hi = x + y
                  lo = y - (hi - x)
                  if lo:
                      partials[i] = lo
                      i += 1
                  x = hi
              partials[i:] = [x]
          return sum_exact(partials)
  
      @pure
      @llvm
      def float1() -> float:
          ret double 0x401DF11F45F4E61A
  
      @pure
      @llvm
      def float2() -> float:
          ret double 0xBFE62A2AF1BD3624
  
      @pure
      @llvm
      def float3() -> float:
          ret double 0x7C95555555555555
  
      test_values = [
          ([], 0.0),
          ([0.0], 0.0),
          ([1e100, 1.0, -1e100, 1e-100, 1e50, -1.0, -1e50], 1e-100),
          ([2.0**53, -0.5, -2.0**-54], 2.0**53-1.0),
          ([2.0**53, 1.0, 2.0**-100], 2.0**53+2.0),
          ([2.0**53+10.0, 1.0, 2.0**-100], 2.0**53+12.0),
          ([2.0**53-4.0, 0.5, 2.0**-54], 2.0**53-3.0),
          ([1./n for n in range(1, 1001)], float1()),
          ([(-1.)**n/n for n in range(1, 1001)], float2()),
          ([1e16, 1., 1e-16], 10000000000000002.0),
          ([1e16-2., 1.-2.**-53, -(1e16-2.), -(1.-2.**-53)], 0.0),
          # exercise code for resizing partials array
          ([2.**n - 2.**(n+50) + 2.**(n+52) for n in range(-1074, 972, 2)] +
           [-2.**1022],
           float3()),
          ]
  
      # Telescoping sum, with exact differences (due to Sterbenz)
      terms = [1.7**i for i in range(1001)]
      test_values.append((
          [terms[i+1] - terms[i] for i in range(1000)] + [-terms[1000]],
          -terms[0]
      ))
  
      for i, (vals, expected) in enumerate(test_values):
          try:
              actual = math.fsum(vals)
          except OverflowError:
              # self.fail("test %d failed: got OverflowError, expected %r "
              #           "for math.fsum(%.100r)" % (i, expected, vals))
              assert False
          except ValueError:
              # self.fail("test %d failed: got ValueError, expected %r "
              #           "for math.fsum(%.100r)" % (i, expected, vals))
              assert False
  
          assert actual == expected
  
      from random import random, gauss, shuffle
      for j in range(10000):
          vals = [7, 1e100, -7, -1e100, -9e-20, 8e-20] * 10
          s = 0.
          for i in range(200):
              v = gauss(0, random()) ** 7 - s
              s += v
              vals.append(v)
          shuffle(vals)
          assert msum(vals) == math.fsum(vals)
  
  
  @test
  def test_prod():
      is_nan = lambda x: math.isnan(x)
      prod = math.prod
      assert prod(()) == 1
      assert prod((), start=5) == 5
      assert prod(list(range(2,8))) == 5040
      assert prod(iter(list(range(2,8)))) == 5040
      assert prod(range(1, 10), start=10) == 3628800
  
      assert prod([1, 2, 3, 4, 5]) == 120
      assert prod([1.0, 2.0, 3.0, 4.0, 5.0]) == 120.0
      assert prod([1, 2, 3, 4.0, 5.0]) == 120.0
      assert prod([1.0, 2.0, 3.0, 4, 5]) == 120.0
  
      # Test overflow in fast-path for integers
      assert prod([1, 1, 2**32, 1, 1]) == 2**32
      # Test overflow in fast-path for floats
      assert prod([1.0, 1.0, 2**32, 1, 1]) == float(2**32)
  
      # Some odd cases
      assert prod([2, 3], start='ab') == 'abababababab'
      assert prod([2, 3], start=[1, 2]) == [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2]
      assert prod((), start={2: 3}) == {2:3}
  
      #with self.assertRaises(TypeError):
      #    prod([10, 20], 1)     # start is a keyword-only argument
  
      assert prod([0, 1, 2, 3]) == 0
      assert prod([1, 0, 2, 3]) == 0
      assert prod([1, 2, 3, 0]) == 0
  
      def _naive_prod(iterable, start=1):
          for elem in iterable:
              start *= elem
          return start
  
      iterable = range(1, 13)
      assert prod(iterable) == _naive_prod(iterable)
      iterable = range(-12, -1)
      assert prod(iterable) == _naive_prod(iterable)
      iterable = range(-11, 5)
      assert prod(iterable) == 0
  
      # Big floats
  
      iterable = [float(x) for x in range(1, 123)]
      assert prod(iterable) == _naive_prod(iterable, 1.0)
      iterable = [float(x) for x in range(-123, -1)]
      assert prod(iterable) == _naive_prod(iterable, 1.0)
      iterable = [float(x) for x in range(-1000, 1000)]
      assert is_nan(prod(iterable))
  
      # Float tests
  
      assert is_nan(prod([1, 2, 3, float("nan"), 2, 3]))
      assert is_nan(prod([1, 0, float("nan"), 2, 3]))
      assert is_nan(prod([1, float("nan"), 0, 3]))
      assert is_nan(prod([1, float("inf"), float("nan"),3]))
      assert is_nan(prod([1, float("-inf"), float("nan"),3]))
      assert is_nan(prod([1, float("nan"), float("inf"),3]))
      assert is_nan(prod([1, float("nan"), float("-inf"),3]))
  
      assert prod([1, 2, 3, float('inf'),-3,4]) == float('-inf')
      assert prod([1, 2, 3, float('-inf'),-3,4]) == float('inf')
  
      assert is_nan(prod([1,2,0,float('inf'), -3, 4]))
      assert is_nan(prod([1,2,0,float('-inf'), -3, 4]))
      assert is_nan(prod([1, 2, 3, float('inf'), -3, 0, 3]))
      assert is_nan(prod([1, 2, 3, float('-inf'), -3, 0, 2]))
  
      # Type preservation
  
      assert type(prod([1, 2, 3, 4, 5, 6])) is int
      assert type(prod([1, 2.0, 3, 4, 5, 6])) is float
      assert type(prod(range(1, 10000))) is int
      assert type(prod(range(1, 10000), start=1.0)) is float
      #assert type(prod([1, decimal.Decimal(2.0), 3, 4, 5, 6])) is decimal.Decimal
  
      # Tuples
  
      assert prod((42,)) == 42
      assert prod((-3.5, 4.0)) == -14.0
      assert prod((3, 9, 3, 7, 1)) == 567
      assert prod((1, 2.5, 3)) == 7.5
      assert prod((2.5, 1, 3, 1.0, 1)) == 7.5
      assert prod((2, 3), start='ab') == 'abababababab'
  
  
  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_lcm()
  test_frexp()
  test_modf()
  test_isclose()
  test_fsum()
  test_prod()
  
  
  # 32-bit float ops
  
  NAN32 = math.nan32
  INF32 = math.inf32
  NINF32 = -math.inf32
  
  
  def close32(a: float32, b: float32, epsilon: float32 = 1e-5f32):
      return abs(a - b) <= epsilon
  
  
  @test
  def test_float32_isnan():
      assert math.isnan(float32(float("nan"))) == True
      assert math.isnan(4.0f32) == False
  
  
  @test
  def test_float32_isinf():
      assert math.isinf(float32(float("inf"))) == True
      assert math.isinf(7.0f32) == False
  
  
  @test
  def test_float32_isfinite():
      assert math.isfinite(1.4f32) == True
      assert math.isfinite(0.0f32) == True
      assert math.isfinite(NAN32) == False
      assert math.isfinite(INF32) == False
      assert math.isfinite(NINF32) == False
  
  
  @test
  def test_float32_ceil():
      assert isinstance(math.ceil(1.0f32), int)
      assert math.ceil(3.3f32) == 4
      assert math.ceil(0.5f32) == 1
      assert math.ceil(1.0f32) == 1
      assert math.ceil(1.5f32) == 2
      assert math.ceil(-0.5f32) == 0
      assert math.ceil(-1.0f32) == -1
      assert math.ceil(-1.5f32) == -1
  
  
  @test
  def test_float32_floor():
      assert isinstance(math.floor(1.0f32), int)
      assert math.floor(3.3f32) == 3
      assert math.floor(0.5f32) == 0
      assert math.floor(1.0f32) == 1
      assert math.floor(1.5f32) == 1
      assert math.floor(-0.5f32) == -1
      assert math.floor(-1.0f32) == -1
      assert math.floor(-1.5f32) == -2
  
  
  @test
  def test_float32_fabs():
      assert math.fabs(-1.0f32) == 1.0f32
      assert math.fabs(0.0f32) == 0.0f32
      assert math.fabs(1.0f32) == 1.0f32
  
  
  @test
  def test_float32_fmod():
      assert math.fmod(10.0f32, 1.0f32) == 0.0f32
      assert math.fmod(10.0f32, 0.5f32) == 0.0f32
      assert math.fmod(10.0f32, 1.5f32) == 1.0f32
      assert math.fmod(-10.0f32, 1.0f32) == -0.0f32
      assert math.fmod(-10.0f32, 0.5f32) == -0.0f32
      assert math.fmod(-10.0f32, 1.5f32) == -1.0f32
  
  
  @test
  def test_float32_exp():
      assert math.exp(0.0f32) == 1.0f32
      assert math.exp(-1.0f32) == 1.0f32 / math.e32
      assert math.exp(1.0f32) == math.e32
  
  
  @test
  def test_float32_expm1():
      assert math.expm1(0.0f32) == 0.0f32
      assert close32(math.expm1(1.0f32), 1.7182818284590453f32)
      assert close32(math.expm1(3.0f32), 19.085536923187668f32)
      assert close32(math.expm1(5.0f32), 147.4131591025766f32)
      assert math.expm1(INF32) == INF32
      assert math.expm1(NINF32) == -1.0f32
      assert math.isnan(math.expm1(NAN32)) == True
  
  
  @test
  def test_float32_ldexp():
      assert math.ldexp(0.0f32, 1) == 0.0f32
      assert math.ldexp(1.0f32, 1) == 2.0f32
      assert math.ldexp(1.0f32, -1) == 0.5f32
      assert math.ldexp(-1.0f32, 1) == -2.0f32
      assert math.ldexp(0.0f32, 1) == 0.0f32
      assert math.ldexp(1.0f32, -1000000) == 0.0f32
      assert math.ldexp(-1.0f32, -1000000) == -0.0f32
      assert math.ldexp(INF32, 30) == INF32
      assert math.ldexp(NINF32, -213) == NINF32
      assert math.isnan(math.ldexp(NAN32, 0)) == True
  
  
  @test
  def test_float32_log():
      assert math.log(1.0f32 / math.e32) == -1.0f32
      assert math.log(1.0f32) == 0.0f32
      assert close32(math.log(math.e32), 1.0f32)
  
  
  @test
  def test_float32_log2():
      assert math.log2(1.0f32) == 0.0f32
      assert math.log2(2.0f32) == 1.0f32
      assert math.log2(4.0f32) == 2.0f32
      assert math.log2(2.0f32 ** 50.0f32) == 50.0f32
      assert math.isnan(math.log2(-1.5f32)) == True
      assert math.isnan(math.log2(NINF32)) == True
      assert math.isnan(math.log2(NAN32)) == True
  
  
  @test
  def test_float32_log10():
      assert math.log10(0.1f32) == -1.0f32
      assert math.log10(1.0f32) == 0.0f32
      assert math.log10(10.0f32) == 1.0f32
      assert math.log10(10000.0f32) == 4.0f32
  
  
  @test
  def test_float32_degrees():
      assert math.degrees(math.pi32) == 180.0f32
      assert math.degrees(math.pi32 / 2.0f32) == 90.0f32
      assert math.degrees(-math.pi32 / 4.0f32) == -45.0f32
      assert math.degrees(0.0f32) == 0.0f32
  
  
  @test
  def test_float32_radians():
      assert math.radians(180.0f32) == math.pi32
      assert math.radians(90.0f32) == math.pi32 / 2.0f32
      assert math.radians(-45.0f32) == -math.pi32 / 4.0f32
      assert math.radians(0.0f32) == 0.0f32
  
  
  @test
  def test_float32_sqrt():
      assert math.sqrt(4.0f32) == 2.0f32
      assert math.sqrt(0.0f32) == 0.0f32
      assert math.sqrt(1.0f32) == 1.0f32
      assert math.isnan(math.sqrt(-1.0f32)) == True
  
  
  @test
  def test_float32_pow():
      assert math.pow(0.0f32, 1.0f32) == 0.0f32
      assert math.pow(1.0f32, 0.0f32) == 1.0f32
      assert math.pow(2.0f32, 1.0f32) == 2.0f32
      assert math.pow(2.0f32, -1.0f32) == 0.5f32
      assert math.pow(-0.0f32, 3.0f32) == -0.0f32
      assert math.pow(-0.0f32, 2.3f32) == 0.0f32
      assert math.pow(-0.0f32, 0.0f32) == 1.0f32
      assert math.pow(-0.0f32, -0.0f32) == 1.0f32
      assert math.pow(-2.0f32, 2.0f32) == 4.0f32
      assert math.pow(-2.0f32, 3.0f32) == -8.0f32
      assert math.pow(-2.0f32, -3.0f32) == -0.125f32
      assert math.pow(INF32, 1.0f32) == INF32
      assert math.pow(NINF32, 1.0f32) == NINF32
      assert math.pow(1.0f32, INF32) == 1.0f32
      assert math.pow(1.0f32, NINF32) == 1.0f32
      assert math.isnan(math.pow(NAN32, 1.0f32)) == True
      assert math.isnan(math.pow(2.0f32, NAN32)) == True
      assert math.isnan(math.pow(0.0f32, NAN32)) == True
      assert math.pow(1.0f32, NAN32) == 1.0f32
  
  
  @test
  def test_float32_acos():
      assert close32(math.acos(-1.0f32), math.pi32)
      assert close32(math.acos(0.0f32), math.pi32 / 2.0f32)
      assert math.acos(1.0f32) == 0.0f32
      assert math.isnan(math.acos(NAN32)) == True
  
  
  @test
  def test_float32_asin():
      assert close32(math.asin(-1.0f32), -math.pi32 / 2.0f32)
      assert math.asin(0.0f32) == 0.0f32
      assert close32(math.asin(1.0f32), math.pi32 / 2.0f32)
      assert math.isnan(math.asin(NAN32)) == True
  
  
  @test
  def test_float32_atan():
      assert math.atan(-1.0f32) == -math.pi32 / 4.0f32
      assert math.atan(0.0f32) == 0.0f32
      assert close32(math.atan(1.0f32), math.pi32 / 4.0f32)
      assert close32(math.atan(INF32), math.pi32 / 2.0f32)
      assert close32(math.atan(NINF32), -math.pi32 / 2.0f32)
      assert math.isnan(math.atan(NAN32)) == True
  
  
  @test
  def test_float32_atan2():
      assert math.atan2(-1.0f32, 0.0f32) == -math.pi32 / 2.0f32
      assert math.atan2(-1.0f32, 1.0f32) == -math.pi32 / 4.0f32
      assert math.atan2(0.0f32, 1.0f32) == 0.0f32
      assert math.atan2(1.0f32, 1.0f32) == math.pi32 / 4.0f32
      assert math.atan2(1.0f32, 0.0f32) == math.pi32 / 2.0f32
      assert math.atan2(-0.0f32, 0.0f32) == -0.0f32
      assert math.atan2(-0.0f32, 2.3f32) == -0.0f32
      assert close32(math.atan2(0.0f32, -2.3f32), math.pi32)
      assert math.atan2(INF32, NINF32) == math.pi32 * 3.0f32 / 4.0f32
      assert math.atan2(INF32, 2.3f32) == math.pi32 / 2.0f32
      assert math.isnan(math.atan2(NAN32, 0.0f32)) == True
  
  
  @test
  def test_float32_cos():
      assert math.cos(0.0f32) == 1.0f32
      assert close32(math.cos(math.pi32 / 2.0f32), 6.123233995736766e-17f32)
      assert close32(math.cos(-math.pi32 / 2.0f32), 6.123233995736766e-17f32)
      assert math.cos(math.pi32) == -1.0f32
      assert math.isnan(math.cos(INF32)) == True
      assert math.isnan(math.cos(NINF32)) == True
      assert math.isnan(math.cos(NAN32)) == True
  
  
  @test
  def test_float32_sin():
      assert math.sin(0.0f32) == 0.0f32
      assert math.sin(math.pi32 / 2.0f32) == 1.0f32
      assert math.sin(-math.pi32 / 2.0f32) == -1.0f32
      assert math.isnan(math.sin(INF32)) == True
      assert math.isnan(math.sin(NINF32)) == True
      assert math.isnan(math.sin(NAN32)) == True
  
  
  @test
  def test_float32_hypot():
      assert math.hypot(12.0f32, 5.0f32) == 13.0f32
      assert math.hypot(12.0f32 / 32.0f32, 5.0f32 / 32.0f32) == 13.0f32 / 32.0f32
      assert math.hypot(0.0f32, 0.0f32) == 0.0f32
      assert math.hypot(-3.0f32, 4.0f32) == 5.0f32
      assert math.hypot(3.0f32, 4.0f32) == 5.0f32
  
  
  @test
  def test_float32_tan():
      assert math.tan(0.0f32) == 0.0f32
      assert close32(math.tan(math.pi32 / 4.0f32), 0.9999999999999999f32)
      assert close32(math.tan(-math.pi32 / 4.0f32), -0.9999999999999999f32)
      assert math.isnan(math.tan(INF32)) == True
      assert math.isnan(math.tan(NINF32)) == True
      assert math.isnan(math.tan(NAN32)) == True
  
  
  @test
  def test_float32_cosh():
      assert math.cosh(0.0f32) == 1.0f32
      assert close32(math.cosh(2.0f32) - 2.0f32 * math.cosh(1.0f32) ** 2.0f32, -1.0f32)
      assert math.cosh(INF32) == INF32
      assert math.cosh(NINF32) == INF32
      assert math.isnan(math.cosh(NAN32)) == True
  
  
  @test
  def test_float32_sinh():
      assert math.sinh(0.0f32) == 0.0f32
      assert math.sinh(1.0f32) + math.sinh(-1.0f32) == 0.0f32
      assert math.sinh(INF32) == INF32
      assert math.sinh(NINF32) == NINF32
      assert math.isnan(math.sinh(NAN32)) == True
  
  
  @test
  def test_float32_tanh():
      assert math.tanh(0.0f32) == 0.0f32
      assert math.tanh(1.0f32) + math.tanh(-1.0f32) == 0.0f32
      assert math.tanh(INF32) == 1.0f32
      assert math.tanh(NINF32) == -1.0f32
      assert math.isnan(math.tanh(NAN32)) == True
  
  
  @test
  def test_float32_acosh():
      assert math.acosh(1.0f32) == 0.0f32
      assert close32(math.acosh(2.0f32), 1.3169578969248166f32)
      assert math.acosh(INF32) == INF32
      assert math.isnan(math.acosh(NAN32)) == True
      assert math.isnan(math.acosh(-1.0f32)) == True
  
  
  @test
  def test_float32_asinh():
      assert math.asinh(0.0f32) == 0.0f32
      assert close32(math.asinh(1.0f32), 0.881373587019543f32)
      assert close32(math.asinh(-1.0f32), -0.881373587019543f32)
      assert math.asinh(INF32) == INF32
      assert math.isnan(math.asinh(NAN32)) == True
      assert math.asinh(NINF32) == NINF32
  
  
  @test
  def test_float32_atanh():
      assert math.atanh(0.0f32) == 0.0f32
      assert close32(math.atanh(0.5f32), 0.5493061443340549f32)
      assert close32(math.atanh(-0.5f32), -0.5493061443340549f32)
      assert math.isnan(math.atanh(INF32)) == True
      assert math.isnan(math.atanh(NAN32)) == True
      assert math.isnan(math.atanh(NINF32)) == True
  
  
  @test
  def test_float32_copysign():
      assert math.copysign(1.0f32, -0.0f32) == -1.0f32
      assert math.copysign(1.0f32, 42.0f32) == 1.0f32
      assert math.copysign(1.0f32, -42.0f32) == -1.0f32
      assert math.copysign(3.0f32, 0.0f32) == 3.0f32
      assert math.copysign(INF32, 0.0f32) == INF32
      assert math.copysign(INF32, -0.0f32) == NINF32
      assert math.copysign(NINF32, 0.0f32) == INF32
      assert math.copysign(NINF32, -0.0f32) == NINF32
      assert math.copysign(1.0f32, INF32) == 1.0f32
      assert math.copysign(1.0f32, NINF32) == -1.0f32
      assert math.copysign(INF32, INF32) == INF32
      assert math.copysign(INF32, NINF32) == NINF32
      assert math.copysign(NINF32, INF32) == INF32
      assert math.copysign(NINF32, NINF32) == NINF32
      assert math.isnan(math.copysign(NAN32, 1.0f32)) == True
      assert math.isnan(math.copysign(NAN32, INF32)) == True
      assert math.isnan(math.copysign(NAN32, NINF32)) == True
      assert math.isnan(math.copysign(NAN32, NAN32)) == True
  
  
  @test
  def test_float32_log1p():
      assert close32(math.log1p(2.0f32), 1.0986122886681098f32)
      assert close32(math.log1p(2.0f32 ** 90.0f32), 62.383246250395075f32)
      assert math.log1p(INF32) == INF32
      assert math.log1p(-1.0f32) == NINF32
  
  
  @test
  def test_float32_trunc():
      assert isinstance(math.trunc(1.0f32), int)
      assert math.trunc(1.0f32) == 1
      assert math.trunc(-1.0f32) == -1
      assert math.trunc(1.5f32) == 1
      assert math.trunc(-1.5f32) == -1
      assert math.trunc(1.99999f32) == 1
      assert math.trunc(-1.99999f32) == -1
      assert math.trunc(0.99999f32) == 0
      assert math.trunc(-100.999f32) == -100
  
  
  @test
  def test_float32_erf():
      assert close32(math.erf(1.0f32), 0.8427007929497148f32)
      assert math.erf(0.0f32) == 0.0f32
      assert close32(math.erf(3.0f32), 0.9999779095030015f32)
      assert math.erf(256.0f32) == 1.0f32
      assert math.erf(INF32) == 1.0f32
      assert math.erf(NINF32) == -1.0f32
      assert math.isnan(math.erf(NAN32)) == True
  
  
  @test
  def test_float32_erfc():
      assert math.erfc(0.0f32) == 1.0f32
      assert close32(math.erfc(1.0f32), 0.15729920705028516f32)
      assert close32(math.erfc(2.0f32), 0.0046777349810472645f32)
      assert close32(math.erfc(-1.0f32), 1.8427007929497148f32)
      assert math.erfc(INF32) == 0.0f32
      assert math.erfc(NINF32) == 2.0f32
      assert math.isnan(math.erfc(NAN32)) == True
  
  
  @test
  def test_float32_gamma():
      assert close32(math.gamma(6.0f32), 120.0f32)
      assert close32(math.gamma(1.0f32), 1.0f32)
      assert close32(math.gamma(2.0f32), 1.0f32)
      assert close32(math.gamma(3.0f32), 2.0f32)
      assert math.isnan(math.gamma(-1.0f32)) == True
      assert math.gamma(INF32) == INF32
      assert math.isnan(math.gamma(NINF32)) == True
      assert math.isnan(math.gamma(NAN32)) == True
  
  
  @test
  def test_float32_lgamma():
      assert math.lgamma(1.0f32) == 0.0f32
      assert math.lgamma(2.0f32) == 0.0f32
      assert math.lgamma(-1.0f32) == INF32
      assert math.lgamma(INF32) == INF32
      assert math.lgamma(NINF32) == INF32
      assert math.isnan(math.lgamma(NAN32)) == True
  
  
  @test
  def test_float32_remainder():
      assert math.remainder(2.0f32, 2.0f32) == 0.0f32
      assert math.remainder(-4.0f32, 1.0f32) == -0.0f32
      assert close32(math.remainder(-3.8f32, 1.0f32), 0.20000000000000018f32)
      assert close32(math.remainder(3.8f32, 1.0f32), -0.20000000000000018f32)
      assert math.isnan(math.remainder(INF32, 1.0f32)) == True
      assert math.isnan(math.remainder(NINF32, 1.0f32)) == True
      assert math.isnan(math.remainder(NAN32, 1.0f32)) == True
  
  
  @test
  def test_float32_frexp():
      assert math.frexp(-2.0f32) == (-0.5f32, 2)
      assert math.frexp(-1.0f32) == (-0.5f32, 1)
      assert math.frexp(0.0f32) == (0.0f32, 0)
      assert math.frexp(1.0f32) == (0.5f32, 1)
      assert math.frexp(2.0f32) == (0.5f32, 2)
      assert math.frexp(INF32)[0] == INF32
      assert math.frexp(NINF32)[0] == NINF32
      assert math.isnan(math.frexp(NAN32)[0]) == True
  
  
  @test
  def test_float32_modf():
      assert math.modf(1.5f32) == (0.5f32, 1.0f32)
      assert math.modf(-1.5f32) == (-0.5f32, -1.0f32)
      assert math.modf(math.inf32) == (0.0f32, INF32)
      assert math.modf(-math.inf32) == (-0.0f32, NINF32)
      modf_nan = math.modf(NAN32)
      assert math.isnan(modf_nan[0]) == True
      assert math.isnan(modf_nan[1]) == True
  
  
  @test
  def test_float32_isclose():
      assert math.isclose(1.0f32 + 1.0f32, 1.000000000001f32 + 1.0f32) == True
      assert math.isclose(2.90909324093284f32, 2.909093240932844234234234234f32) == True
      assert math.isclose(2.90909324093284f32, 2.9f32) == False
      assert math.isclose(2.90909324093284f32, 2.90909324f32) == True
      assert math.isclose(2.909094f32, 2.909095f32) == False
      assert math.isclose(NAN32, 2.9f32) == False
      assert math.isclose(2.9f32, NAN32) == False
      assert math.isclose(INF32, INF32) == True
      assert math.isclose(NINF32, NINF32) == True
      assert math.isclose(NINF32, INF32) == False
      assert math.isclose(INF32, NINF32) == False
  
  
  test_float32_isnan()
  test_float32_isinf()
  test_float32_isfinite()
  test_float32_ceil()
  test_float32_floor()
  test_float32_fabs()
  test_float32_fmod()
  test_float32_exp()
  test_float32_expm1()
  test_float32_ldexp()
  test_float32_log()
  test_float32_log2()
  test_float32_log10()
  test_float32_degrees()
  test_float32_radians()
  test_float32_sqrt()
  test_float32_pow()
  test_float32_acos()
  test_float32_asin()
  test_float32_atan()
  test_float32_atan2()
  test_float32_cos()
  test_float32_sin()
  test_float32_hypot()
  test_float32_tan()
  test_float32_cosh()
  test_float32_sinh()
  test_float32_tanh()
  test_float32_acosh()
  test_float32_asinh()
  test_float32_atanh()
  test_float32_copysign()
  test_float32_log1p()
  test_float32_trunc()
  test_float32_erf()
  test_float32_erfc()
  test_float32_gamma()
  test_float32_lgamma()
  test_float32_remainder()
  test_float32_frexp()
  test_float32_modf()
  test_float32_isclose()
  