MPFR Functionality
==================

Testing of mpfr functionality is split into multiple files.

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

    test_mpfr_exp_log.txt
        Test exponentiation and logarithmic functions.

    test_mpfr_special.txt
        Test special functions

    test_mpfr_io.txt
        Test input/output and formating.

    test_mpfr_comp.txt
        Test comparisons.

    >>> import gmpy2 as G
    >>> from gmpy2 import mpz, mpq, mpfr
    >>> a = mpfr("12.34")
    >>> b = mpfr("45.67")
    >>> c = 12345678901234567890

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

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

    >>> a+1
    mpfr('13.34')
    >>> a+1.0
    mpfr('13.34')
    >>> a+mpz(1)
    mpfr('13.34')
    >>> a+mpq(1,1)
    mpfr('13.34')
    >>> 1+a
    mpfr('13.34')
    >>> 1.0+a
    mpfr('13.34')
    >>> mpz(1)+a
    mpfr('13.34')
    >>> mpq(1,1)+a
    mpfr('13.34')
    >>> a+b
    mpfr('58.010000000000005')
    >>> a+0
    mpfr('12.34')
    >>> 0+a
    mpfr('12.34')
    >>> b+a
    mpfr('58.010000000000005')
    >>> a+'b'
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    TypeError: unsupported operand type(s) for +: 'mpfr' and 'str'
    >>> 'b'+a
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    TypeError: Can't convert 'mpfr' object to str implicitly
    >>> a == 12.34
    True
    >>> b == 45.67
    True
    >>> a+b == 12.34+45.67
    True

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

    >>> a-1
    mpfr('11.34')
    >>> a-1.0
    mpfr('11.34')
    >>> a-(-1)
    mpfr('13.34')
    >>> a-(-1.0)
    mpfr('13.34')
    >>> a-b
    mpfr('-33.329999999999998')
    >>> b-a
    mpfr('33.329999999999998')
    >>> a-'b'
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    TypeError: unsupported operand type(s) for -: 'mpfr' and 'str'
    >>> 'b'-a
    Traceback (most recent call last):
      File "<stdin>", line 1, in <module>
    TypeError: unsupported operand type(s) for -: 'str' and 'mpfr'
    >>> a-b==12.34-45.67
    True

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

    >>> a*b
    mpfr('563.56780000000003')
    >>> a*0
    mpfr('0.0')
    >>> a*0.0
    mpfr('0.0')
    >>> a*1
    mpfr('12.34')
    >>> a*1.0
    mpfr('12.34')
    >>> a*(-1.0)
    mpfr('-12.34')
    >>> 0*a
    mpfr('0.0')
    >>> 0.0*a
    mpfr('0.0')
    >>> 1*a
    mpfr('12.34')
    >>> 1.0*a
    mpfr('12.34')
    >>> a*b
    mpfr('563.56780000000003')
    >>> a*b==12.34*45.67
    True

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

    >>> a//b
    mpfr('0.0')
    >>> a/b
    mpfr('0.27019925552879348')
    >>> b//a
    mpfr('3.0')
    >>> b/a
    mpfr('3.7009724473257699')
    >>> a/b==12.34/45.67
    True
    >>> a/0
    mpfr('inf')
    >>> a/(-0.0)
    mpfr('-inf')
    >>> a/b==12.34/45.67
    True

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

    >>> a%1
    mpfr('0.33999999999999986')
    >>> 12.34%1
    0.33999999999999986

Test divmod
-----------

    >>> divmod(12.34, 45.67)
    (0.0, 12.34)
    >>> divmod(a,b)
    (mpfr('0.0'), mpfr('12.34'))
    >>> divmod(b,a)
    (mpfr('3.0'), mpfr('8.6500000000000021'))
    >>> divmod(45.67,12.34)==divmod(b,a)
    True


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

    >>> import pickle
    >>> pickle.loads(pickle.dumps(a))
    mpfr('12.34')
    >>> pickle.loads(pickle.dumps(mpfr("inf")))
    mpfr('inf')
    >>> pickle.loads(pickle.dumps(mpfr("-inf")))
    mpfr('-inf')
    >>> pickle.loads(pickle.dumps(mpfr("nan")))
    mpfr('nan')
    >>> pickle.loads(pickle.dumps(mpfr(0)))
    mpfr('0.0')


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')
    >>> mpfr(0) * float('Inf')
    mpfr('nan')
    >>> mpfr(0) * float('-Inf')
    mpfr('nan')
    >>> float('Inf') * mpfr(0)
    mpfr('nan')
    >>> float('-Inf') * mpfr(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') / mpfr(0)
    mpfr('nan')
    >>> float('nan') / mpfr(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('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') * mpfr(0)
    mpfr('nan')
    >>> mpfr('-Inf') * mpfr(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') / mpfr(0)
    mpfr('nan')
    >>> mpfr('nan') / mpfr(0)
    mpfr('nan')

    >>> divmod(a, float('Inf'))
    (mpfr('0.0'), mpfr('12.34'))
    >>> divmod(a, float('-Inf'))
    (mpfr('-1.0'), mpfr('-inf'))
    >>> divmod(-a, float('Inf'))
    (mpfr('-1.0'), mpfr('inf'))
    >>> divmod(-a, float('-Inf'))
    (mpfr('0.0'), mpfr('-12.34'))
    >>> divmod(a, float('nan'))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(-a, float('nan'))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr(0), float('Inf'))
    (mpfr('0.0'), mpfr('0.0'))
    >>> divmod(mpfr(0), float('-Inf'))
    (mpfr('-0.0'), mpfr('-0.0'))
    >>> divmod(mpfr(0), float('nan'))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(float('Inf'), a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(float('-Inf'), a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(float('Inf'), -a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(float('-Inf'), -a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(float('nan'), a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(float('nan'), -a)
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(float('Inf'), mpfr(0))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(float('-Inf'), mpfr(0))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(float('nan'), mpfr(0))
    (mpfr('nan'), mpfr('nan'))

    >>> divmod(a, mpfr('Inf'))
    (mpfr('0.0'), mpfr('12.34'))
    >>> 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('-12.34'))
    >>> divmod(a, mpfr('nan'))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(-a, mpfr('nan'))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr(0), mpfr('Inf'))
    (mpfr('0.0'), mpfr('0.0'))
    >>> divmod(mpfr(0), mpfr('-Inf'))
    (mpfr('-0.0'), mpfr('-0.0'))
    >>> divmod(mpfr(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'), mpfr(0))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('-Inf'), mpfr(0))
    (mpfr('nan'), mpfr('nan'))
    >>> divmod(mpfr('nan'), mpfr(0))
    (mpfr('nan'), mpfr('nan'))