/edk2/AppPkg/Applications/Python/Python-2.7.2/Lib/test/test_long_future.py

from __future__ import division

# When true division is the default, get rid of this and add it to

# test_long.py instead.  In the meantime, it's too obscure to try to

# trick just part of test_long into using future division.



import sys

import random

import math

import unittest

from test.test_support import run_unittest



# decorator for skipping tests on non-IEEE 754 platforms

requires_IEEE_754 = unittest.skipUnless(

    float.__getformat__("double").startswith("IEEE"),

    "test requires IEEE 754 doubles")



DBL_MAX = sys.float_info.max

DBL_MAX_EXP = sys.float_info.max_exp

DBL_MIN_EXP = sys.float_info.min_exp

DBL_MANT_DIG = sys.float_info.mant_dig

DBL_MIN_OVERFLOW = 2**DBL_MAX_EXP - 2**(DBL_MAX_EXP - DBL_MANT_DIG - 1)



# pure Python version of correctly-rounded true division

def truediv(a, b):

    """Correctly-rounded true division for integers."""

    negative = a^b < 0

    a, b = abs(a), abs(b)



    # exceptions:  division by zero, overflow

    if not b:

        raise ZeroDivisionError("division by zero")

    if a >= DBL_MIN_OVERFLOW * b:

        raise OverflowError("int/int too large to represent as a float")



   # find integer d satisfying 2**(d - 1) <= a/b < 2**d

    d = a.bit_length() - b.bit_length()

    if d >= 0 and a >= 2**d * b or d < 0 and a * 2**-d >= b:

        d += 1



    # compute 2**-exp * a / b for suitable exp

    exp = max(d, DBL_MIN_EXP) - DBL_MANT_DIG

    a, b = a << max(-exp, 0), b << max(exp, 0)

    q, r = divmod(a, b)



    # round-half-to-even: fractional part is r/b, which is > 0.5 iff

    # 2*r > b, and == 0.5 iff 2*r == b.

    if 2*r > b or 2*r == b and q % 2 == 1:

        q += 1



    result = math.ldexp(float(q), exp)

    return -result if negative else result



class TrueDivisionTests(unittest.TestCase):

    def test(self):

        huge = 1L << 40000

        mhuge = -huge

        self.assertEqual(huge / huge, 1.0)

        self.assertEqual(mhuge / mhuge, 1.0)

        self.assertEqual(huge / mhuge, -1.0)

        self.assertEqual(mhuge / huge, -1.0)

        self.assertEqual(1 / huge, 0.0)

        self.assertEqual(1L / huge, 0.0)

        self.assertEqual(1 / mhuge, 0.0)

        self.assertEqual(1L / mhuge, 0.0)

        self.assertEqual((666 * huge + (huge >> 1)) / huge, 666.5)

        self.assertEqual((666 * mhuge + (mhuge >> 1)) / mhuge, 666.5)

        self.assertEqual((666 * huge + (huge >> 1)) / mhuge, -666.5)

        self.assertEqual((666 * mhuge + (mhuge >> 1)) / huge, -666.5)

        self.assertEqual(huge / (huge << 1), 0.5)

        self.assertEqual((1000000 * huge) / huge, 1000000)



        namespace = {'huge': huge, 'mhuge': mhuge}



        for overflow in ["float(huge)", "float(mhuge)",

                         "huge / 1", "huge / 2L", "huge / -1", "huge / -2L",

                         "mhuge / 100", "mhuge / 100L"]:

            # If the "eval" does not happen in this module,

            # true division is not enabled

            with self.assertRaises(OverflowError):

                eval(overflow, namespace)



        for underflow in ["1 / huge", "2L / huge", "-1 / huge", "-2L / huge",

                         "100 / mhuge", "100L / mhuge"]:

            result = eval(underflow, namespace)

            self.assertEqual(result, 0.0, 'expected underflow to 0 '

                             'from {!r}'.format(underflow))



        for zero in ["huge / 0", "huge / 0L", "mhuge / 0", "mhuge / 0L"]:

            with self.assertRaises(ZeroDivisionError):

                eval(zero, namespace)



    def check_truediv(self, a, b, skip_small=True):

        """Verify that the result of a/b is correctly rounded, by

        comparing it with a pure Python implementation of correctly

        rounded division.  b should be nonzero."""



        a, b = long(a), long(b)



        # skip check for small a and b: in this case, the current

        # implementation converts the arguments to float directly and

        # then applies a float division.  This can give doubly-rounded

        # results on x87-using machines (particularly 32-bit Linux).

        if skip_small and max(abs(a), abs(b)) < 2**DBL_MANT_DIG:

            return



        try:

            # use repr so that we can distinguish between -0.0 and 0.0

            expected = repr(truediv(a, b))

        except OverflowError:

            expected = 'overflow'

        except ZeroDivisionError:

            expected = 'zerodivision'



        try:

            got = repr(a / b)

        except OverflowError:

            got = 'overflow'

        except ZeroDivisionError:

            got = 'zerodivision'



        self.assertEqual(expected, got, "Incorrectly rounded division {}/{}: "

                         "expected {}, got {}".format(a, b, expected, got))



    @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

        for m in [1, 2, 4, 7, 8, 16, 17, 32, 12345, 7**100,

                  -1, -2, -5, -23, -67891, -41**50]:

            for n in range(-10, 10):

                self.check_truediv(2**DBL_MANT_DIG*m + n, m)



        # test round-half-to-even, subnormal result

        for n in range(-20, 20):

            self.check_truediv(n, 2**1076)



        # largeish random divisions: a/b where |a| <= |b| <=

        # 2*|a|; |ans| is between 0.5 and 1.0, so error should

        # always be bounded by 2**-54 with equality possible only

        # if the least significant bit of q=ans*2**53 is zero.

        for M in [10**10, 10**100, 10**1000]:

            for i in range(1000):

                a = random.randrange(1, M)

                b = random.randrange(a, 2*a+1)

                self.check_truediv(a, b)

                self.check_truediv(-a, b)

                self.check_truediv(a, -b)

                self.check_truediv(-a, -b)



        # and some (genuinely) random tests

        for _ in range(10000):

            a_bits = random.randrange(1000)

            b_bits = random.randrange(1, 1000)

            x = random.randrange(2**a_bits)

            y = random.randrange(1, 2**b_bits)

            self.check_truediv(x, y)

            self.check_truediv(x, -y)

            self.check_truediv(-x, y)

            self.check_truediv(-x, -y)





def test_main():

    run_unittest(TrueDivisionTests)



if __name__ == "__main__":

    test_main()