Re: The smallest and largest values of numeric types
Michael Hoffman [EMAIL PROTECTED] wrote: 20859248300531693115643211913059311997417115606882000504639505780471641693377296 50765802242049L Of course performance decreases for longer longs. I once made a thing that tried to find the limit of longs and stopped when I had two or three screenfulls of numbers. I came to the conclusion that for integer arithmetic like this, the limit is either your memory size, or some other number that is so big that in practice you don't have to worry about it.. - Hendrik -- http://mail.python.org/mailman/listinfo/python-list
Re: The smallest and largest values of numeric types
On Wed, 18 Apr 2007 07:15:11 +0200, Hendrik van Rooyen wrote: I once made a thing that tried to find the limit of longs and stopped when I had two or three screenfulls of numbers. You should find that converting longs to strings (say, for printing them) is *very* slow. E.g. the following code big = 10L**100 # one google, a big number while True: print big # so we can see the last value before it fails big *= 10 will run terribly slow and should be written as: big = 10L**100 # one google, a big number try: while True: big *= 10 except: # don't know what exception will be raised, so catch ANYTHING print len(str(big))-1 # the number of digits only does the slow conversion to string once, instead of every time around the loop. However, once your machine starts paging, it will still slow down a lot. I came to the conclusion that for integer arithmetic like this, the limit is either your memory size, or some other number that is so big that in practice you don't have to worry about it.. Yes, longs are limited only by the amount of memory accessible. -- Steven D'Aprano -- http://mail.python.org/mailman/listinfo/python-list
Re: The smallest and largest values of numeric types
On Apr 18, 3:09�am, Steven D'Aprano [EMAIL PROTECTED] wrote: On Wed, 18 Apr 2007 07:15:11 +0200, Hendrik van Rooyen wrote: I once made a thing that tried to find the limit of longs and stopped when I had two or three screenfulls of numbers. You should find that converting longs to strings (say, for printing them) is *very* slow. E.g. the following code big = 10L**100 # one google, a big number while True: � � print big # so we can see the last value before it fails � � big *= 10 will run terribly slow and should be written as: big = 10L**100 # one google, a big number try: � � while True: � � � � big *= 10 except: # don't know what exception will be raised, so catch ANYTHING � � print len(str(big))-1 # the number of digits only does the slow conversion to string once, instead of every time around the loop. However, once your machine starts paging, it will still slow down a lot. I came to the conclusion that for integer arithmetic like this, the limit is either your memory size, or some other number that is so big that in practice you don't have to worry about it.. Yes, longs are limited only by the amount of memory accessible. But there may be other limitations even if you have the memory. For example, this test is limited to generation 10 because tne 11th generation produces outrageous exponent error. Here, every 9th 1st generation, starting from the fifth is a second generation, every 9th sencond, starting from the fifth, is a 3rd generation, every 9th 3rd gen, starting from the 5th is a 4th gen, etc. Closed form: Type12MH(k,i) Find ith, kth Generation Type [1,2] Mersenne Hailstone using the closed form equation 2**(6*((i-1)*9**(k-1)+(9**(k-1)-1)/2+1)-1)-1 2**5-1 generation: 1 2**29-1 generation: 2 2**245-1 generation: 3 2**2189-1 generation: 4 2**19685-1 generation: 5 2**177149-1 generation: 6 2**1594325-1 generation: 7 2**14348909-1 generation: 8 2**129140165-1 generation: 9 2**1162261469-1 generation:10 1.797 seconds There is never a number too large to worry about. -- Steven D'Aprano -- http://mail.python.org/mailman/listinfo/python-list
The smallest and largest values of numeric types
Hi! How can I determine the smallest and largest values of numeric types (for example int) possible in my system? I think there exists a function for this task but I don't know it. -- http://mail.python.org/mailman/listinfo/python-list
Re: The smallest and largest values of numeric types
In article [EMAIL PROTECTED], [EMAIL PROTECTED] wrote: Hi! How can I determine the smallest and largest values of numeric types (for example int) possible in my system? I think there exists a function for this task but I don't know it. There is or was a module called kinds which was an implementation of PEP 0242. I have it and it gives the values you are looking for (and more). But I don't know where I got it. I think it was once distributed with Macpython on MacPython.org, but I'm not sure. I've searched for it, but nothing shows up except my own questions about it from many years ago and they have no clues. Does anyone know where this package is? Or what might replace it. It is very useful. -- http://mail.python.org/mailman/listinfo/python-list
Re: The smallest and largest values of numeric types
On Apr 17, 7:12 am, [EMAIL PROTECTED] wrote: How can I determine the smallest and largest values of numeric types (for example int) possible in my system? I think there exists a function for this task but I don't know it. This should work for ints: import sys print sys.maxint For floats, just try until it fails. This is from http://projects.amor.org/geniusql/browser/trunk/geniusql/adapters.py#l41 # Determine max binary digits for float on this system. Crude but effective. maxfloat_digits = 2 while True: L = (2 ** (maxfloat_digits + 1)) - 1 if int(float(L)) != L: break maxfloat_digits += 1 Note this will get you the number of binary digits, which is not a simple matter to translate to maximum and minimum values, since floats are inexact numerics. IEEE 754 floats are stored with one bit for the sign, some bits for the exponent (which is biased) and some for the significand. See http://babbage.cs.qc.edu/IEEE-754/32bit.html for a visual example of how it works. Robert Brewer System Architect Amor Ministries [EMAIL PROTECTED] -- http://mail.python.org/mailman/listinfo/python-list
Re: The smallest and largest values of numeric types
Lou Pecora wrote: In article [EMAIL PROTECTED], [EMAIL PROTECTED] wrote: Hi! How can I determine the smallest and largest values of numeric types (for example int) possible in my system? I think there exists a function for this task but I don't know it. There is or was a module called kinds which was an implementation of PEP 0242. I have it and it gives the values you are looking for (and more). But I don't know where I got it. I think it was once distributed with Macpython on MacPython.org, but I'm not sure. I've searched for it, but nothing shows up except my own questions about it from many years ago and they have no clues. I'm surprised they also didn't turn up my replies to those questions. Does anyone know where this package is? Or what might replace it. It is very useful. It used to be distributed with Numeric. http://numpy.cvs.sourceforge.net/numpy/kinds/ numpy exposes the same information for floating point types with its finfo class. Nothing particular for ints. -- Robert Kern I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth. -- Umberto Eco -- http://mail.python.org/mailman/listinfo/python-list
Re: The smallest and largest values of numeric types
Thank you for your answers. Seems like the limits of numeric values aren't considered as important in Python as in C ;) -- http://mail.python.org/mailman/listinfo/python-list
Re: The smallest and largest values of numeric types
fumanchu wrote: On Apr 17, 7:12 am, [EMAIL PROTECTED] wrote: How can I determine the smallest and largest values of numeric types (for example int) possible in my system? I think there exists a function for this task but I don't know it. This should work for ints: import sys print sys.maxint One should note that ints bigger than sys.maxint are possible almost seamlessly since Python will use longs for these numbers: Python 2.5 (r25:51908, Mar 13 2007, 08:13:14) [GCC 3.4.4 (cygming special, gdc 0.12, using dmd 0.125)] on cygwin Type help, copyright, credits or license for more information. import sys sys.maxint 2147483647 sys.maxint+1 2147483648L sys.maxint*2 4294967294L sys.maxint**10 2085924830053169311564321191305931199741711560688200050463950578047164169337729650765802242049L Of course performance decreases for longer longs. -- Michael Hoffman -- http://mail.python.org/mailman/listinfo/python-list
Re: The smallest and largest values of numeric types
On Apr 17, 11:37 am, [EMAIL PROTECTED] wrote: Thank you for your answers. Seems like the limits of numeric values aren't considered as important in Python as in C ;) Sure, they're important, we just don't want to notice them. That's why conversion to longs is automatic, so that number size limits don't cause problems and your problems are solved rather than throw exceptions or produce invalid results. -- http://mail.python.org/mailman/listinfo/python-list
