Python format default rounding when formatting float number

Question

I'm trying to solve some floating-point problems in my code in Python 2.7.10. When testing I've encountered a strange behaviour with the format method:

print "{}".format(0.3000000000004) # 13 decimals

Prints: 0.3

But:

print "{}".format(0.300000000004) # 12 decimals

Prints: 0.300000000004

Since I'm not specifying the format, why does it round the first number? Is there a default number of allowed decimal places?

Answer 1

Since you do not specify a format, the default type coercion to string is used. So this isn't really an issue with format. Python 2 truncates to a precision of 12 characters (excluding the leading zero, if any) for float.__str__, and after truncation in this case, all trailing zeros are cleaned up:

>>> str(0.3000000000004) # unlike str(0.3000000000014) -> '0.300000000001'
'0.3'

Adding the format_spec :f gives you the default precision of 6:

>>> '{:f}'.format(0.3000000000004)
'0.300000' 

Specify the width and precision or use repr to get a good representation:

>>> '{!r}'.format(0.3000000000004)
'0.3000000000004'

The behavior is different in Python 3 though:

>>> str(0.3000000000004)
'0.3000000000004'

---

The formatting of floats is handled by just one function float_repr in Python 3 (it does not have a special float_str function):

(reprfunc)float_repr,                       /* tp_repr */
...
(reprfunc)float_repr,                        /* tp_str */

whereas Python2.7 defines a separate handler float_str and float_repr for __str__ and __repr__ respectively:

(reprfunc)float_repr,                       /* tp_repr */
...
(reprfunc)float_str,                        /* tp_str */

The deciding variable here which I think is the reason for the precision loss beyond 12d.p. is PyFloat_STR_PRECISION (defined in Python 2):

#define PyFloat_STR_PRECISION 12

It reverses to a truncation for floats taking more than 12 characters in the default conversion.