Recently, a correspondent mentioned float.as_integer_ratio()
, new in Python 2.6, noting that typical floating point implementations are essentially rational approximations of real numbers. Intrigued, I had to try π:
>>> float.as_integer_ratio(math.pi);
(884279719003555L, 281474976710656L)
I was mildly surprised not to see the more accurate result due to Arima,:
(428224593349304L, 136308121570117L)
For example, this code:
#! /usr/bin/env python
from decimal import *
getcontext().prec = 36
print "python: ",Decimal(884279719003555) / Decimal(281474976710656)
print "Arima: ",Decimal(428224593349304) / Decimal(136308121570117)
print "Wiki: 3.14159265358979323846264338327950288"
produces this output:
python: 3.14159265358979311599796346854418516
Arima: 3.14159265358979323846264338327569743
Wiki: 3.14159265358979323846264338327950288
Certainly, the result is correct given the precision afforded by 64-bit floating-point numbers, but it leads me to ask: How can I find out more about the implementation limitations of as_integer_ratio()
? Thanks for any guidance.
Additional links: Stern-Brocot tree and Python source.
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