MPZ Functionality
=================

Testing of mpz functionality is split into multiple files.

    test_mpz.txt
        Test basic functionality and stuff not covered anywhere else.

    test_mpz_functions.txt
        Test mpz functions, including error messages.

    test_mpz_io.txt
        Test input/output and formating.

    test_mpz_comp.txt
        Test comparisons.

    >>> 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)
    >>> c = 12345678901234567890

Test elementary operations
==========================

Test addition
-------------

    >>> a+1
    mpz(124)
    >>> a+(-1)
    mpz(122)
    >>> 1+a
    mpz(124)
    >>> (-1)+a
    mpz(122)
    >>> a+b
    mpz(579)
    >>> b+a
    mpz(579)
    >>> a+'b'
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    TypeError: unsupported operand type(s) for +: 'mpz' and 'str'
    >>> 'b'+a
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    TypeError: ** message detail varies **
    >>> print(a+c)
    12345678901234568013
    >>> print(c+a)
    12345678901234568013


Test subtraction
----------------

    >>> a-1
    mpz(122)
    >>> a-(-1)
    mpz(124)
    >>> 1-a
    mpz(-122)
    >>> (-1)-a
    mpz(-124)
    >>> a-b
    mpz(-333)
    >>> b-a
    mpz(333)
    >>> a-'b'
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    TypeError: unsupported operand type(s) for -: 'mpz' and 'str'
    >>> 'b'-a
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    TypeError: ** message detail varies **
    >>> print(a-c)
    -12345678901234567767
    >>> print(c-a)
    12345678901234567767

Test multiplication
-------------------

    >>> a*b
    mpz(56088)
    >>> b*a
    mpz(56088)
    >>> a*0
    mpz(0)
    >>> 0*a
    mpz(0)
    >>> a*123
    mpz(15129)
    >>> 123*a
    mpz(15129)
    >>> print(a*c)
    1518518504851851850470
    >>> print(c*a)
    1518518504851851850470
    >>> a*'b'
    'bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb'
    >>> 'b'*a
    'bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb'

Test division
-------------

    >>> a//b
    mpz(0)
    >>> a/b
    mpfr('0.26973684210526316')
    >>> b//a
    mpz(3)
    >>> b/a
    mpfr('3.7073170731707319')
    >>> (a*b)//b
    mpz(123)
    >>> (a*b)//a
    mpz(456)
    >>> a//0
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    ZeroDivisionError: division or modulo by zero
    >>> a/0
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    ZeroDivisionError: division or modulo by zero
    >>> a/0.0
    mpfr('inf')
    >>> print(c//a)
    100371373180768844
    >>> a**10//c
    mpz(64)

Test modulo
-----------

    >>> a%b
    mpz(123)
    >>> b%a
    mpz(87)
    >>> divmod(a,b)
    (mpz(0), mpz(123))
    >>> divmod(b,a)
    (mpz(3), mpz(87))
    >>> divmod(a,0)
    Traceback (most recent call last):
      ...
    ZeroDivisionError: division or modulo by zero
    >>> divmod(a,mpz(0))
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    ZeroDivisionError: division or modulo by zero
    >>> divmod(123,mpz(0))
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    ZeroDivisionError: division or modulo by zero
    >>> divmod(b,123)
    (mpz(3), mpz(87))
    >>> divmod(a,c)
    (mpz(0), mpz(123))
    >>> divmod(a,int(c))
    (mpz(0), mpz(123))
    >>> print("%s %s" % divmod(a*(c-1),c))
    122 12345678901234567767
    >>> print("%s %s" % divmod(a*(c-1),int(c)))
    122 12345678901234567767
    >>> divmod(a*(c-1),-c)
    (mpz(-123), mpz(-123))
    >>> divmod(a*(c-1),-int(c))
    (mpz(-123), mpz(-123))
    >>> print("%s %s" % divmod(int(a*(c-1)),-int(c)))
    -123 -123

Test miscellaneous
------------------

    >>> a+True
    mpz(124)
    >>> a+False
    mpz(123)
    >>> a*False
    mpz(0)
    >>> a//True
    mpz(123)
    >>> abs(-a) == a
    True
    >>> print(pow(a,10))
    792594609605189126649
    >>> pow(a,7,b)
    mpz(99)
    >>> G.sign(b-a)
    1
    >>> G.sign(b-b)
    0
    >>> G.sign(a-b)
    -1
    >>> G.sign(a)
    1
    >>> G.sign(-a)
    -1
    >>> z=b-b; G.sign(z)
    0

Test pickle
-----------

    >>> import pickle
    >>> pickle.loads(pickle.dumps(G.mpz(12346789)))
    mpz(12346789)
    >>> pickle.loads(pickle.dumps(G.mpz(-12346789)))
    mpz(-12346789)
    >>> pickle.loads(pickle.dumps(G.mpz(0)))
    mpz(0)

Test mpz.__index__
------------------

    >>> range(333)[a]
    123
    >>> range(333)[b]
    Traceback (innermost last):
      ...
    IndexError: range object index out of range

Test operations involving NaN/Inf
---------------------------------

    >>> a + float('Inf')
    mpfr('inf')
    >>> float('Inf') + a
    mpfr('inf')
    >>> a + float('-Inf')
    mpfr('-inf')
    >>> float('-Inf') + a
    mpfr('-inf')
    >>> a + float('nan')
    mpfr('nan')
    >>> float('nan') + a
    mpfr('nan')

    >>> a - float('Inf')
    mpfr('-inf')
    >>> float('Inf') - a
    mpfr('inf')
    >>> a - float('-Inf')
    mpfr('inf')
    >>> float('-Inf') - a
    mpfr('-inf')
    >>> a - float('nan')
    mpfr('nan')
    >>> float('nan') - a
    mpfr('nan')

    >>> a * float('Inf')
    mpfr('inf')
    >>> float('Inf') * a
    mpfr('inf')
    >>> a * float('-Inf')
    mpfr('-inf')
    >>> float('-Inf') * a
    mpfr('-inf')
    >>> -a * float('Inf')
    mpfr('-inf')
    >>> float('Inf') * -a
    mpfr('-inf')
    >>> -a * float('-Inf')
    mpfr('inf')
    >>> float('-Inf') * -a
    mpfr('inf')
    >>> a * float('nan')
    mpfr('nan')
    >>> float('nan') * a
    mpfr('nan')
    >>> G.mpz(0) * float('Inf')
    mpfr('nan')
    >>> G.mpz(0) * float('-Inf')
    mpfr('nan')
    >>> float('Inf') * G.mpz(0)
    mpfr('nan')
    >>> float('-Inf') * G.mpz(0)
    mpfr('nan')
    >>> a / float('Inf')
    mpfr('0.0')
    >>> -a / float('Inf')
    mpfr('-0.0')
    >>> float('Inf') / a
    mpfr('inf')
    >>> float('Inf') / -a
    mpfr('-inf')
    >>> a / float('-Inf')
    mpfr('-0.0')
    >>> -a / float('-Inf')
    mpfr('0.0')
    >>> float('-Inf') / a
    mpfr('-inf')
    >>> float('-Inf') / -a
    mpfr('inf')
    >>> a / float('nan')
    mpfr('nan')
    >>> float('nan') / a
    mpfr('nan')
    >>> float('nan') / G.mpz(0)
    mpfr('nan')
    >>> float('nan') / G.mpz(0)
    mpfr('nan')

    >>> a - mpfr('Inf')
    mpfr('-inf')
    >>> mpfr('Inf') - a
    mpfr('inf')
    >>> a - mpfr('-Inf')
    mpfr('inf')
    >>> mpfr('-Inf') - a
    mpfr('-inf')
    >>> a - mpfr('nan')
    mpfr('nan')
    >>> mpfr('nan') - a
    mpfr('nan')
    >>> a * mpfr('Inf')
    mpfr('inf')
    >>> mpfr('Inf') * a
    mpfr('inf')
    >>> a * mpfr('-Inf')
    mpfr('-inf')
    >>> mpfr('-Inf') * a
    mpfr('-inf')
    >>> -a * mpfr('Inf')
    mpfr('-inf')
    >>> mpfr('Inf') * -a
    mpfr('-inf')
    >>> -a * mpfr('-Inf')
    mpfr('inf')
    >>> mpfr('-Inf') * -a
    mpfr('inf')
    >>> a * mpfr('nan')
    mpfr('nan')
    >>> mpfr('nan') * a
    mpfr('nan')
    >>> G.mpz(0) * mpfr('Inf')
    mpfr('nan')
    >>> G.mpz(0) * mpfr('-Inf')
    mpfr('nan')
    >>> mpfr('Inf') * G.mpz(0)
    mpfr('nan')
    >>> mpfr('-Inf') * G.mpz(0)
    mpfr('nan')
    >>> a / mpfr('Inf')
    mpfr('0.0')
    >>> -a / mpfr('Inf')
    mpfr('-0.0')
    >>> mpfr('Inf') / a
    mpfr('inf')
    >>> mpfr('Inf') / -a
    mpfr('-inf')
    >>> a / mpfr('-Inf')
    mpfr('-0.0')
    >>> -a / mpfr('-Inf')
    mpfr('0.0')
    >>> mpfr('-Inf') / a
    mpfr('-inf')
    >>> mpfr('-Inf') / -a
    mpfr('inf')
    >>> a / mpfr('nan')
    mpfr('nan')
    >>> mpfr('nan') / a
    mpfr('nan')
    >>> mpfr('nan') / G.mpz(0)
    mpfr('nan')
    >>> mpfr('nan') / G.mpz(0)
    mpfr('nan')

    >>> divmod(a, mpfr('Inf'))
    (mpfr('0.0'), mpfr('123.0'))
    >>> divmod(a, mpfr('-Inf'))
    (mpfr('-1.0'), mpfr('-inf'))
    >>> divmod(-a, mpfr('Inf'))
    (mpfr('-1.0'), mpfr('inf'))
    >>> divmod(-a, mpfr('-Inf'))
    (mpfr('0.0'), mpfr('-123.0'))
    >>> divmod(a, mpfr('nan'))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(-a, mpfr('nan'))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(G.mpz(0), mpfr('Inf'))
    (mpfr('0.0'), mpfr('0.0'))
    >>> divmod(G.mpz(0), mpfr('-Inf'))
    (mpfr('-0.0'), mpfr('-0.0'))
    >>> divmod(G.mpz(0), mpfr('nan'))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('Inf'), a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('-Inf'), a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('Inf'), -a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('-Inf'), -a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('nan'), a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('nan'), -a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('Inf'), G.mpz(0))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('-Inf'), G.mpz(0))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('nan'), G.mpz(0))
    (mpfr('nan'), mpfr('nan'))

    >>> divmod(a, mpfr('Inf'))
    (mpfr('0.0'), mpfr('123.0'))
    >>> divmod(a, mpfr('-Inf'))
    (mpfr('-1.0'), mpfr('-inf'))
    >>> divmod(-a, mpfr('Inf'))
    (mpfr('-1.0'), mpfr('inf'))
    >>> divmod(-a, mpfr('-Inf'))
    (mpfr('0.0'), mpfr('-123.0'))
    >>> divmod(a, mpfr('nan'))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(-a, mpfr('nan'))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(G.mpz(0), mpfr('Inf'))
    (mpfr('0.0'), mpfr('0.0'))
    >>> divmod(G.mpz(0), mpfr('-Inf'))
    (mpfr('-0.0'), mpfr('-0.0'))
    >>> divmod(G.mpz(0), mpfr('nan'))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('Inf'), a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('-Inf'), a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('Inf'), -a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('-Inf'), -a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('nan'), a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('nan'), -a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('Inf'), G.mpz(0))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('-Inf'), G.mpz(0))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('nan'), G.mpz(0))
    (mpfr('nan'), mpfr('nan'))

Test bit operations
-------------------

    >>> ~a
    mpz(-124)
    >>> a&b
    mpz(72)
    >>> a|b
    mpz(507)
    >>> a^b
    mpz(435)
    >>> a<<1
    mpz(246)
    >>> a>>1
    mpz(61)
    >>> a<<-1
    Traceback (innermost last):
      ...
    ValueError: negative shift count
    >>> a>>-2
    Traceback (innermost last):
      ...
    ValueError: negative shift count
    >>> a<<0
    mpz(123)
    >>> a>>0
    mpz(123)

Test conversions
----------------

    >>> int(G.mpz(-3))
    -3