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youknowdot
8573d916fc
Propagate dialect lookup errors except AttributeError, retry integer logarithms after float overflow, and update the decimal conversion diagnostic. Exercise the final reference contracts without implementation-specific branches. Assisted-by: OpenAI Codex:model identifier unavailable
469 lines
13 KiB
Python
469 lines
13 KiB
Python
import itertools
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import math
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from testutils import assert_raises, skip_if_unsupported
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NAN = float("nan")
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INF = float("inf")
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NINF = float("-inf")
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# assert(math.exp(2) == math.exp(2.0))
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# assert(math.exp(True) == math.exp(1.0))
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#
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# class Conversible():
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# def __float__(self):
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# print("Converting to float now!")
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# return 1.1111
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#
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# assert math.log(1.1111) == math.log(Conversible())
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# A logarithm can fit in a float even when its integer base cannot.
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assert math.isclose(math.log(2**4000, 2**2000), 2.0)
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assert math.isclose(math.log(2.0, 2**2000), 1.0 / 2000)
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for value in (1, 8.0, INF, NAN):
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assert_raises(ZeroDivisionError, math.log, value, 1)
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assert_raises(TypeError, math.log, object(), 1)
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assert_raises(ValueError, math.log, 8, -(2**2000))
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log_conversions = []
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class LogFloat:
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def __init__(self, name, value):
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self.name = name
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self.value = value
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def __float__(self):
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log_conversions.append(self.name)
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return self.value
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assert math.isclose(math.log(LogFloat("x", 8.0), LogFloat("base", 2.0)), 3.0)
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assert log_conversions == ["x", "base"]
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log_conversions.clear()
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assert_raises(ValueError, math.log, -1, LogFloat("base", 2.0))
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assert log_conversions == []
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class LogFloatOverflow:
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def __float__(self):
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log_conversions.append("float")
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raise OverflowError("float conversion failed")
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def __index__(self):
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log_conversions.append("index")
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return 2**2000
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class LogIndexOnly:
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def __index__(self):
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return 2**2000
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for logarithm in (math.log, math.log2, math.log10):
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log_conversions.clear()
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assert math.isclose(logarithm(LogFloatOverflow()), logarithm(2**2000))
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assert log_conversions == ["float", "index"]
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assert math.isclose(logarithm(LogIndexOnly()), logarithm(2**2000))
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for error_type in (TypeError, ValueError, RuntimeError):
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error = error_type("float conversion failed")
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class FailedFloat(LogFloatOverflow):
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def __float__(self):
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raise error
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with assert_raises(error_type) as caught:
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logarithm(FailedFloat())
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assert caught.exception is error
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error = RuntimeError("index conversion failed")
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class FailedIndex(LogFloatOverflow):
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def __index__(self):
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raise error
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with assert_raises(RuntimeError) as caught:
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logarithm(FailedIndex())
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assert caught.exception is error
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class NegativeIndex(LogFloatOverflow):
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def __index__(self):
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return -1
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assert_raises(ValueError, logarithm, NegativeIndex())
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class InvalidIndex(LogFloatOverflow):
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def __index__(self):
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return 1.0
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assert_raises(TypeError, logarithm, InvalidIndex())
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class NoIndex:
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__float__ = LogFloatOverflow.__float__
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assert_raises(OverflowError, logarithm, NoIndex())
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class SuccessfulFloat:
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def __float__(self):
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return 8.0
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def __index__(self):
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raise AssertionError("successful float conversion must not retry index")
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assert logarithm(SuccessfulFloat()) == logarithm(8.0)
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assert math.isclose(math.log(8, LogFloatOverflow()), 3 / 2000)
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assert math.isclose(math.log(8, LogIndexOnly()), 3 / 2000)
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class LogInt(int):
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def __float__(self):
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raise AssertionError("integer logarithms use the native integer value")
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assert math.isclose(math.log(LogInt(2**4000), LogInt(2**2000)), 2.0)
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# roundings
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assert int.__trunc__
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assert int.__floor__
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assert int.__ceil__
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# assert float.__trunc__
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def float_floor_exists():
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assert float.__floor__
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def float_ceil_exists():
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assert float.__ceil__
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skip_if_unsupported(3, 9, float_floor_exists)
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skip_if_unsupported(3, 9, float_ceil_exists)
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assert math.trunc(2) == 2
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assert math.ceil(3) == 3
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assert math.floor(4) == 4
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assert math.trunc(2.2) == 2
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assert math.ceil(3.3) == 4
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assert math.floor(4.4) == 4
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assert isinstance(math.trunc(2.2), int)
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assert isinstance(math.ceil(3.3), int)
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assert isinstance(math.floor(4.4), int)
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class A(object):
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def __trunc__(self):
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return 2
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def __ceil__(self):
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return 3
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def __floor__(self):
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return 4
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assert math.trunc(A()) == 2
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assert math.ceil(A()) == 3
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assert math.floor(A()) == 4
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class A(object):
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def __trunc__(self):
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return 2.2
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def __ceil__(self):
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return 3.3
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def __floor__(self):
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return 4.4
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assert math.trunc(A()) == 2.2
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assert math.ceil(A()) == 3.3
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assert math.floor(A()) == 4.4
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class A(object):
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def __trunc__(self):
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return "trunc"
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def __ceil__(self):
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return "ceil"
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def __floor__(self):
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return "floor"
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assert math.trunc(A()) == "trunc"
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assert math.ceil(A()) == "ceil"
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assert math.floor(A()) == "floor"
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with assert_raises(TypeError):
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math.trunc(object())
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with assert_raises(TypeError):
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math.ceil(object())
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with assert_raises(TypeError):
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math.floor(object())
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with assert_raises(TypeError) as cm:
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math.floor("1.5")
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assert str(cm.exception) == "must be real number, not str"
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with assert_raises(TypeError) as cm:
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math.ceil(None)
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assert str(cm.exception) == "must be real number, not NoneType"
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assert math.floor(-0.5) == -1 and math.ceil(-0.5) == 0
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with assert_raises(OverflowError):
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math.floor(INF)
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with assert_raises(ValueError):
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math.ceil(NAN)
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class FloatFloor(float):
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def __floor__(self):
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return "sub floor"
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def __ceil__(self):
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return "sub ceil"
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assert math.floor(FloatFloor(1.5)) == "sub floor"
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assert math.ceil(FloatFloor(1.5)) == "sub ceil"
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isclose = math.isclose
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def assertIsClose(a, b, *args, **kwargs):
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assert isclose(a, b, *args, **kwargs) == True, "%s and %s should be close!" % (a, b)
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def assertIsNotClose(a, b, *args, **kwargs):
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assert isclose(a, b, *args, **kwargs) == False, "%s and %s should not be close!" % (
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a,
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b,
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)
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def assertAllClose(examples, *args, **kwargs):
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for a, b in examples:
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assertIsClose(a, b, *args, **kwargs)
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def assertAllNotClose(examples, *args, **kwargs):
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for a, b in examples:
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assertIsNotClose(a, b, *args, **kwargs)
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# test_negative_tolerances: ValueError should be raised if either tolerance is less than zero
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assert_raises(ValueError, lambda: isclose(1, 1, rel_tol=-1e-100))
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assert_raises(ValueError, lambda: isclose(1, 1, rel_tol=1e-100, abs_tol=-1e10))
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# test_identical: identical values must test as close
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identical_examples = [
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(2.0, 2.0),
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(0.1e200, 0.1e200),
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(1.123e-300, 1.123e-300),
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(12345, 12345.0),
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(0.0, -0.0),
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(345678, 345678),
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]
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assertAllClose(identical_examples, rel_tol=0.0, abs_tol=0.0)
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# test_eight_decimal_places: examples that are close to 1e-8, but not 1e-9
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eight_decimal_places_examples = [
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(1e8, 1e8 + 1),
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(-1e-8, -1.000000009e-8),
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(1.12345678, 1.12345679),
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]
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assertAllClose(eight_decimal_places_examples, rel_tol=1e-08)
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assertAllNotClose(eight_decimal_places_examples, rel_tol=1e-09)
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# test_near_zero: values close to zero
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near_zero_examples = [(1e-9, 0.0), (-1e-9, 0.0), (-1e-150, 0.0)]
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# these should not be close to any rel_tol
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assertAllNotClose(near_zero_examples, rel_tol=0.9)
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# these should be close to abs_tol=1e-8
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assertAllClose(near_zero_examples, abs_tol=1e-8)
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# test_identical_infinite: these are close regardless of tolerance -- i.e. they are equal
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assertIsClose(INF, INF)
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assertIsClose(INF, INF, abs_tol=0.0)
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assertIsClose(NINF, NINF)
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assertIsClose(NINF, NINF, abs_tol=0.0)
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# test_inf_ninf_nan(self): these should never be close (following IEEE 754 rules for equality)
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not_close_examples = [
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(NAN, NAN),
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(NAN, 1e-100),
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(1e-100, NAN),
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(INF, NAN),
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(NAN, INF),
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(INF, NINF),
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(INF, 1.0),
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(1.0, INF),
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(INF, 1e308),
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(1e308, INF),
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]
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# use largest reasonable tolerance
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assertAllNotClose(not_close_examples, abs_tol=0.999999999999999)
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# test_zero_tolerance: test with zero tolerance
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zero_tolerance_close_examples = [(1.0, 1.0), (-3.4, -3.4), (-1e-300, -1e-300)]
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assertAllClose(zero_tolerance_close_examples, rel_tol=0.0)
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zero_tolerance_not_close_examples = [
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(1.0, 1.000000000000001),
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(0.99999999999999, 1.0),
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(1.0e200, 0.999999999999999e200),
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]
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assertAllNotClose(zero_tolerance_not_close_examples, rel_tol=0.0)
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# test_asymmetry: test the asymmetry example from PEP 485
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assertAllClose([(9, 10), (10, 9)], rel_tol=0.1)
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# test_integers: test with integer values
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integer_examples = [(100000001, 100000000), (123456789, 123456788)]
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assertAllClose(integer_examples, rel_tol=1e-8)
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assertAllNotClose(integer_examples, rel_tol=1e-9)
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# test_decimals: test with Decimal values
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# test_fractions: test with Fraction values
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assert math.copysign(1, 42) == 1.0
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assert math.copysign(0.0, 42) == 0.0
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assert math.copysign(1.0, -42) == -1.0
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assert math.copysign(3, 0.0) == 3.0
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assert math.copysign(4.0, -0.0) == -4.0
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assert_raises(TypeError, math.copysign)
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# copysign should let us distinguish signs of zeros
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assert math.copysign(1.0, 0.0) == 1.0
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assert math.copysign(1.0, -0.0) == -1.0
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assert math.copysign(INF, 0.0) == INF
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assert math.copysign(INF, -0.0) == NINF
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assert math.copysign(NINF, 0.0) == INF
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assert math.copysign(NINF, -0.0) == NINF
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# and of infinities
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assert math.copysign(1.0, INF) == 1.0
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assert math.copysign(1.0, NINF) == -1.0
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assert math.copysign(INF, INF) == INF
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assert math.copysign(INF, NINF) == NINF
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assert math.copysign(NINF, INF) == INF
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assert math.copysign(NINF, NINF) == NINF
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assert math.isnan(math.copysign(NAN, 1.0))
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assert math.isnan(math.copysign(NAN, INF))
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assert math.isnan(math.copysign(NAN, NINF))
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assert math.isnan(math.copysign(NAN, NAN))
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# copysign(INF, NAN) may be INF or it may be NINF, since
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# we don't know whether the sign bit of NAN is set on any
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# given platform.
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assert math.isinf(math.copysign(INF, NAN))
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# similarly, copysign(2., NAN) could be 2. or -2.
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assert abs(math.copysign(2.0, NAN)) == 2.0
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assert str(math.frexp(0.0)) == str((+0.0, 0))
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assert str(math.frexp(-0.0)) == str((-0.0, 0))
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assert math.frexp(1) == (0.5, 1)
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assert math.frexp(1.5) == (0.75, 1)
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assert_raises(TypeError, lambda: math.frexp(None))
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assert str(math.ldexp(+0.0, 0)) == str(0.0)
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assert str(math.ldexp(-0.0, 0)) == str(-0.0)
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assert math.ldexp(0.5, 1) == 1
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assert math.ldexp(0.75, 1) == 1.5
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assert_raises(TypeError, lambda: math.ldexp(None, None))
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assert math.frexp(INF) == (INF, 0)
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assert str(math.frexp(NAN)) == str((NAN, 0))
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assert_raises(TypeError, lambda: math.frexp(None))
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assert math.gcd(0, 0) == 0
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assert math.gcd(1, 0) == 1
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assert math.gcd(0, 1) == 1
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assert math.gcd(1, 1) == 1
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assert math.gcd(-1, 1) == 1
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assert math.gcd(1, -1) == 1
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assert math.gcd(-1, -1) == 1
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assert math.gcd(125, -255) == 5
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assert_raises(TypeError, lambda: math.gcd(1.1, 2))
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assert math.factorial(0) == 1
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assert math.factorial(1) == 1
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assert math.factorial(2) == 2
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assert math.factorial(3) == 6
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assert math.factorial(10) == 3628800
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assert math.factorial(20) == 2432902008176640000
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assert_raises(ValueError, lambda: math.factorial(-1))
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if hasattr(math, "nextafter"):
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try:
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assert math.nextafter(4503599627370496.0, -INF) == 4503599627370495.5
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assert math.nextafter(4503599627370496.0, INF) == 4503599627370497.0
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assert math.nextafter(9223372036854775808.0, 0.0) == 9223372036854774784.0
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assert math.nextafter(-9223372036854775808.0, 0.0) == -9223372036854774784.0
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assert math.nextafter(4503599627370496, -INF) == 4503599627370495.5
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assert math.nextafter(2.0, 2.0) == 2.0
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assert math.isnan(math.nextafter(NAN, 1.0))
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except NotImplementedError:
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# WASM
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pass
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assert math.modf(1.25) == (0.25, 1.0)
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assert math.modf(-1.25) == (-0.25, -1.0)
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assert math.modf(2.56) == (0.56, 2.0)
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assert math.modf(-2.56) == (-0.56, -2.0)
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assert math.modf(1) == (0.0, 1.0)
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assert math.modf(INF) == (0.0, INF)
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assert math.modf(NINF) == (-0.0, NINF)
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modf_nan = math.modf(NAN)
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assert math.isnan(modf_nan[0])
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assert math.isnan(modf_nan[1])
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assert math.fmod(10, 1) == 0.0
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assert math.fmod(10, 0.5) == 0.0
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assert math.fmod(10, 1.5) == 1.0
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assert math.fmod(-10, 1) == -0.0
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assert math.fmod(-10, 0.5) == -0.0
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assert math.fmod(-10, 1.5) == -1.0
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assert math.isnan(math.fmod(NAN, 1.0)) == True
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assert math.isnan(math.fmod(1.0, NAN)) == True
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assert math.isnan(math.fmod(NAN, NAN)) == True
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assert_raises(ValueError, lambda: math.fmod(1.0, 0.0))
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assert_raises(ValueError, lambda: math.fmod(INF, 1.0))
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assert_raises(ValueError, lambda: math.fmod(NINF, 1.0))
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assert_raises(ValueError, lambda: math.fmod(INF, 0.0))
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assert math.fmod(3.0, INF) == 3.0
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assert math.fmod(-3.0, INF) == -3.0
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assert math.fmod(3.0, NINF) == 3.0
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assert math.fmod(-3.0, NINF) == -3.0
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assert math.fmod(0.0, 3.0) == 0.0
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assert math.fmod(0.0, NINF) == 0.0
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assert math.gamma(1) == 1.0
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# sumprod compares the two lengths as it goes; it must not drain either
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# argument first.
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assert_raises(ValueError, lambda: math.sumprod(itertools.count(), [1, 2, 3]))
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assert_raises(ValueError, lambda: math.sumprod([1, 2, 3], itertools.count()))
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assert math.sumprod(iter([1, 2, 3]), iter([4, 5, 6])) == 32
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# perm/comb reject a k above 2**63 - 1 instead of computing, and perm(n) is factorial(n).
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for f in [
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lambda: math.perm(2**63),
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lambda: math.perm(2**64 + 1, 2**63),
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lambda: math.comb(2**64 + 1, 2**63),
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]:
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assert_raises(OverflowError, f)
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assert_raises(
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ValueError,
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lambda: math.perm(-1),
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_msg="factorial() not defined for negative values",
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)
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assert math.perm(5) == math.perm(5, None) == 120
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assert math.perm(2**64, 0) == 1
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assert math.comb(2**64, 2**64 - 1) == 2**64
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