[Tutor] Rounding a float to n significant digits

[Dick Moores]

At 11:19 PM 11/27/2006, Dick Moores wrote:
>I just dug this Tim Smith creation out of the Tutor archive.
>
>def round_to_n(x, n):
>         """
>         Rounds float x to n significant digits, in scientific notation.
>         Written by Tim Peters. See his Tutor list post of 7/3/04 at
>         http://mail.python.org/pipermail/tutor/2004-July/030324.html
>         """
>         if n < 1:
>                 raise ValueError("number of significant digits must be >= 1")
>         return "%.*e" % (n-1, x)
>
>Thought others might find it of use.
>
>Dick Moores

I've run into the limitation on the size of an int that can be 
converted to a float. Out of curiosity I've tried to close in on what 
that limit is:
 >>> round_to_n(2*10**308,4)
Traceback (most recent call last):
   File "E:\Program Files\Wing IDE Personal 
2.1\src\debug\server\_sandbox.py", line 1, in <module>
     # Used internally for debug sandbox under external interpreter
   File "e:\Python25\Lib\site-packages\mine\mycalc.py", line 35, in round_to_n
     return "%.*e" % (n-1, x)
TypeError: float argument required
 >>> round_to_n(1.75*10**308,4)
'1.750e+308'
 >>> round_to_n(1.2*10**308,4)
'1.200e+308'
 >>> round_to_n(1.87*10**308,4)
'1.#IOe+000'
 >>> round_to_n(1.81*10**308,4)
'1.#IOe+000'
 >>> round_to_n(1.78*10**308,4)
'1.780e+308'

So I've run across the curious '1.#IOe+000'. What is that? And what 
is the exact limit? I suppose it's some power of 2? But 2**1023 is 
too low; 2**1024 is too high; so is 2**1024-1.

Dick Moores