math.pi

[casevh]

Unfortunately, your fraction only provides 53 bits of accuracy, not the 64 bits required by long double.

This computation is not correct, because when you write a=gmpy2.mpfr(8552228672519733982877442985294966266405.0), the python interpreter converts the number to float, which loses precision. You need to use some string "8552228672519733982877442985294966266405.0".

The following code using the bigfloat library confirms Skaperen's values

>>> from bigfloat import *
>>> with precision(133):
...  print(const_pi().as_integer_ratio())
... 
(8552228672519733982877442985294966266405, 2722258935367507707706996859454145691648)

You are correct. I had meant to keep the values as integers.

@Skaperen, please accept my apologies.

casevh