Method test_correctly_rounded_true_division

Lib/test/test_long.py:875–964

(self)

    @unittest.expectedFailure  # TODO: RUSTPYTHON
    @support.requires_IEEE_754
    def test_correctly_rounded_true_division(self):
        # more stringent tests than those above, checking that the
        # result of true division of ints is always correctly rounded.
        # This test should probably be considered CPython-specific.

        # Exercise all the code paths not involving Gb-sized ints.
        # ... divisions involving zero
        self.check_truediv(123, 0)
        self.check_truediv(-456, 0)
        self.check_truediv(0, 3)
        self.check_truediv(0, -3)
        self.check_truediv(0, 0)
        # ... overflow or underflow by large margin
        self.check_truediv(671 * 12345 * 2**DBL_MAX_EXP, 12345)
        self.check_truediv(12345, 345678 * 2**(DBL_MANT_DIG - DBL_MIN_EXP))
        # ... a much larger or smaller than b
        self.check_truediv(12345*2**100, 98765)
        self.check_truediv(12345*2**30, 98765*7**81)
        # ... a / b near a boundary: one of 1, 2**DBL_MANT_DIG, 2**DBL_MIN_EXP,
        #                 2**DBL_MAX_EXP, 2**(DBL_MIN_EXP-DBL_MANT_DIG)
        bases = (0, DBL_MANT_DIG, DBL_MIN_EXP,
                 DBL_MAX_EXP, DBL_MIN_EXP - DBL_MANT_DIG)
        for base in bases:
            for exp in range(base - 15, base + 15):
                self.check_truediv(75312*2**max(exp, 0), 69187*2**max(-exp, 0))
                self.check_truediv(69187*2**max(exp, 0), 75312*2**max(-exp, 0))

        # overflow corner case
        for m in [1, 2, 7, 17, 12345, 7**100,
                  -1, -2, -5, -23, -67891, -41**50]:
            for n in range(-10, 10):
                self.check_truediv(m*DBL_MIN_OVERFLOW + n, m)
                self.check_truediv(m*DBL_MIN_OVERFLOW + n, -m)

        # check detection of inexactness in shifting stage
        for n in range(250):
            # (2**DBL_MANT_DIG+1)/(2**DBL_MANT_DIG) lies halfway
            # between two representable floats, and would usually be
            # rounded down under round-half-to-even.  The tiniest of
            # additions to the numerator should cause it to be rounded
            # up instead.
            self.check_truediv((2**DBL_MANT_DIG + 1)*12345*2**200 + 2**n,
                           2**DBL_MANT_DIG*12345)

        # 1/2731 is one of the smallest division cases that's subject
        # to double rounding on IEEE 754 machines working internally with
        # 64-bit precision.  On such machines, the next check would fail,
        # were it not explicitly skipped in check_truediv.
        self.check_truediv(1, 2731)

        # a particularly bad case for the old algorithm:  gives an
        # error of close to 3.5 ulps.
        self.check_truediv(295147931372582273023, 295147932265116303360)
        for i in range(1000):
            self.check_truediv(10**(i+1), 10**i)
            self.check_truediv(10**i, 10**(i+1))

        # test round-half-to-even behaviour, normal result