MPZ related input/output
========================

    >>> import gmpy2 as G
    >>> from gmpy2 import mpz, mpq, mpfr, mpc
    >>> from decimal import Decimal as D
    >>> from fractions import Fraction as F
    >>> a = mpz(123)
    >>> b = mpz(456)

Test mpz construction
---------------------

    >>> mpz(3.14)
    mpz(3)
    >>> mpz(mpq(17,3))
    mpz(5)
    >>> mpz(23)
    mpz(23)
    >>> mpz(-23)
    mpz(-23)
    >>> x=1000*1000*1000*1000*1000*1000*1000
    >>> print(mpz(x))
    1000000000000000000000
    >>> mpz(0.0)
    mpz(0)
    >>> mpz(0.0)
    mpz(0)
    >>> mpz(-0.0)
    mpz(0)
    >>> mpz(float("nan"))
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    ValueError: 'mpz' does not support NaN
    >>> mpz(float("inf"))
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    OverflowError: 'mpz' does not support Infinity
    >>> mpz(float("-inf"))
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    OverflowError: 'mpz' does not support Infinity
    >>> mpz("0")
    mpz(0)
    >>> mpz("-0")
    mpz(0)
    >>> mpz("hi")
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    ValueError: invalid digits
    >>> mpz("123456", 7)
    mpz(22875)
    >>> mpz("123456", base=3)
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    ValueError: invalid digits
    >>> mpz()
    mpz(0)
    >>> mpz(F(1,2))
    mpz(0)
    >>> mpz(F(-3,2))
    mpz(-1)
    >>> mpz(F(3,2))
    mpz(1)
    >>> mpz(D("0"))
    mpz(0)
    >>> mpz(D("-0"))
    mpz(0)
    >>> mpz(D("1"))
    mpz(1)
    >>> mpz(D("1e10")) == mpz(10000000000)
    True
    >>> mpz(D("nan"))
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
      File "/opt/local/lib/python3.2/decimal.py", line 1564, in __int__
        raise ValueError("Cannot convert NaN to integer")
    ValueError: Cannot convert NaN to integer
    >>> mpz(D("inf"))
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
      File "/opt/local/lib/python3.2/decimal.py", line 1566, in __int__
        raise OverflowError("Cannot convert infinity to integer")
    OverflowError: Cannot convert infinity to integer
    >>> mpz(D("-inf"))
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
      File "/opt/local/lib/python3.2/decimal.py", line 1566, in __int__
        raise OverflowError("Cannot convert infinity to integer")
    OverflowError: Cannot convert infinity to integer
    >>> G.mpz('043')
    mpz(43)
    >>> G.mpz('43',0)
    mpz(43)
    >>> G.mpz('0o43')
    mpz(35)
    >>> G.mpz('0x43')
    mpz(67)
    >>> G.mpz('0x43',10)
    Traceback (innermost last):
      ...
    ValueError: invalid digits
    >>> G.mpz('43')
    mpz(43)

Test format
-----------

    >>> str(a)
    '123'
    >>> repr(a)
    'mpz(123)'
    >>> hex(a)
    '0x7b'
    >>> oct(a) == ('0o173' if sys.version_info[0] == 3 else '0173')
    True
    >>> G.mpz('123')
    mpz(123)
    >>> G.mpz('1001001011',2)
    mpz(587)
    >>> bin(G.mpz('1001001011',2))
    '0b1001001011'
    >>> '1001001011' == G.mpz('1001001011',2).digits(2)
    True
    >>> for i in range(2,63):
    ...     print(a.digits(i))
    ...
    1111011
    11120
    1323
    443
    323
    234
    173
    146
    123
    102
    a3
    96
    8b
    83
    7b
    74
    6f
    69
    63
    5i
    5d
    58
    53
    4n
    4j
    4f
    4b
    47
    43
    3u
    3r
    3o
    3l
    3i
    3f
    3C
    39
    36
    33
    30
    2d
    2b
    2Z
    2X
    2V
    2T
    2R
    2P
    2N
    2L
    2J
    2H
    2F
    2D
    2B
    29
    27
    25
    23
    21
    1z
    >>> print(a.digits(63))
    Traceback (innermost last):
      ...
    ValueError: base must be either 0 or in the interval 2 ... 62
    >>> a.__format__()
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    TypeError: function takes exactly 1 argument (0 given)
    >>> a.__format__('')
    '123'
    >>> a.__format__('d')
    '123'
    >>> a.__format__('b')
    '1111011'
    >>> a.__format__('o')
    '173'
    >>> a.__format__('x')
    '7b'
    >>> a.__format__('#x')
    '0x7b'
    >>> a.__format__('#X')
    '0X7B'
    >>> a.__format__('#o')
    '0o173'
    >>> a.__format__('#15o')
    '          0o173'
    >>> a.__format__('<#15o')
    '0o173          '
    >>> a.__format__('^#15o')
    '     0o173     '
    >>> a.__format__('>#15o')
    '          0o173'
    >>> a.__format__('^ #15o')
    '     0o173     '
    >>> a.__format__('^#15o')
    '     0o173     '
    >>> a.__format__('^ #16o')
    '      0o173     '
    >>> a.__format__('#^16o')
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    ValueError: Invalid conversion specification
    >>> a.__format__('^#16o')
    '     0o173      '