Print extremely large long in scientific notation in python

Question

Is there a way to get python to print extremely large longs in scientific notation? I am talking about numbers on the order of 10^1000 or larger, at this size the standard print "%e" % num fails.

For example:

Python 2.6.2 (release26-maint, Apr 19 2009, 01:56:41) 
[GCC 4.3.3] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> print "%e" % 10**100
1.000000e+100
>>> print "%e" % 10**1000
Traceback (most recent call last):
  File "", line 1, in 
TypeError: float argument required, not long

It appears that python is trying to convert the long to a float and then print it, is it possible to get python to just print the long in scientific notation without converting it to a float?

Answer 1

gmpy to the rescue...:

>>> import gmpy
>>> x = gmpy.mpf(10**1000)
>>> x.digits(10, 0, -1, 1)
'1.e1000'

I'm biased, of course, as the original author and still a committer of gmpy, but I do think it eases tasks such as this one that can be quite a chore without it (I don't know a simple way to do it without some add-on, and gmpy's definitely the add-on I'd choose here;-).

Answer 2

No need to use a third party library. Here's a solution in Python3, that works for large integers.

def ilog(n, base):
    """
    Find the integer log of n with respect to the base.

    >>> import math
    >>> for base in range(2, 16 + 1):
    ...     for n in range(1, 1000):
    ...         assert ilog(n, base) == int(math.log(n, base) + 1e-10), '%s %s' % (n, base)
    """
    count = 0
    while n >= base:
        count += 1
        n //= base
    return count

def sci_notation(n, prec=3):
    """
    Represent n in scientific notation, with the specified precision.

    >>> sci_notation(1234 * 10**1000)
    '1.234e+1003'
    >>> sci_notation(10**1000 // 2, prec=1)
    '5.0e+999'
    """
    base = 10
    exponent = ilog(n, base)
    mantissa = n / base**exponent
    return '{0:.{1}f}e{2:+d}'.format(mantissa, prec, exponent)