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'))
