Python default behavior of str(x)

Question

I am depending on some code that uses the Decimal class because it needs precision to a certain number of decimal places. Some of the functions allow inputs to be floats because of the way that it interfaces with other parts of the codebase. To convert them to decimal objects, it uses things like

mydec = decimal.Decimal(str(x))

where x is the float taken as input. My question is, does anyone know what the standard is for the 'str' method as applied to floats?

For example, take the number 2.1234512. It is stored internally as 2.12345119999999999 because of how floats are represented.

>>> x = 2.12345119999999999
>>> x
2.1234511999999999
>>> str(x)
'2.1234512'

Ok, str(x) in this case is doing something like '%.6f' % x. This is a problem with the way my code converts to decimals. Take the following:

>>> d = decimal.Decimal('2.12345119999999999')
>>> ds = decimal.Decimal(str(2.12345119999999999))
>>> d - ds
Decimal('-1E-17')

So if I have the float, 2.12345119999999999, and I want to pass it to Decimal, converting it to a string using str() gets me the wrong answer. I need to know what are the rules for str(x) that determine what the formatting will be, because I need to determine whether this code needs to be re-written to avoid this error (note that it might be OK, because, for example, the code might round to the 10th decimal place once we have a decimal object)

There must be some set of rules in python's docs that hopefully someone here can point me to. Thanks!

Answer 1

In the Python source, look in "Include/floatobject.h". The precision for the string conversion is set a few lines from the top after an comment with some explanation of the choice:

/* The str() precision PyFloat_STR_PRECISION is chosen so that in most cases,
   the rounding noise created by various operations is suppressed, while
   giving plenty of precision for practical use. */

#define PyFloat_STR_PRECISION 12

You have the option of rebuilding, if you need something different. Any changes will change formatting of floats and complex numbers. See ./Objects/complexobject.c and ./Objects/floatobject.c. Also, you can compare the difference between how repr and str convert doubles in these two files.