Python -- floating point arithmetic

[david mainzer]

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Hash: SHA384

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@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 += 0.1
....
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
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[bart.c]

... sum += 0.1
...

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?

I think the main problem is, as sum gets bigger, the less significant bits
of the 0.1 representation fall off the end (enough to make it effectively
just under 0.1 you're adding instead of just over).

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

Try "google ieee floating point". The problems aren't specific to Python.

 

[bart.c]

... sum += 0.1
...

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?

I think the main problem is, as sum gets bigger, the less significant bits
of the 0.1 representation fall off the end (enough to make it effectively
just under 0.1 you're adding instead of just over).

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

Try "google ieee floating point". The problems aren't specific to Python.