Python -- floating point arithmetic

[david mainzer]

Dear Python-User,


today i create some slides about floating point arithmetic. I used an
example from

http://docs.python.org/tutorial/floatingpoint.html

so i start the python shell on my linux machine:

dm at maxwell $ python
Python 2.6.5 (release26-maint, May 25 2010, 12:37:06)
[GCC 4.3.4] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> >>> sum = 0.0
>>> >>> for i in range(10):
...     sum += 0.1
...
>>> >>> sum
0.99999999999999989
>>> >>>
But thats looks a little bit wrong for me ... i must be a number greater
then 1.0 because 0.1 = 0.100000000000000005551115123125782702118158340454101562500000000000
in python ... if i print it.

So i create an example program:

sum = 0.0
n = 10
d = 1.0 / n
print "%.60f" % ( d )
for i in range(n):
    print "%.60f" % ( sum )
    sum += d

print sum
print "%.60f" % ( sum )


-------- RESULTs ------
0.100000000000000005551115123125782702118158340454101562500000
0.000000000000000000000000000000000000000000000000000000000000
0.100000000000000005551115123125782702118158340454101562500000
0.200000000000000011102230246251565404236316680908203125000000
0.300000000000000044408920985006261616945266723632812500000000
0.400000000000000022204460492503130808472633361816406250000000
0.500000000000000000000000000000000000000000000000000000000000
0.599999999999999977795539507496869191527366638183593750000000
0.699999999999999955591079014993738383054733276367187500000000
0.799999999999999933386618522490607574582099914550781250000000
0.899999999999999911182158029987476766109466552734375000000000
1.0
0.999999999999999888977697537484345957636833190917968750000000

and the jump from 0.50000000000000*** to 0.59999999* looks wrong
for me ... do i a mistake or is there something wrong in the
representation of the floating points in python?

my next question, why could i run

print "%.66f" % ( sum )

but not

print "%.67f" % ( sum )

can anybody tell me how python internal represent a float number??


Best and many thanks in advanced,
David