In python 2.3 (IDLE 1.0.3) running under windows 95, I get the
following types of errors whenever I do simple arithmetic:
1st example: 12.10 + 8.30
20.399999999999 999 1.1  0.2
0.9000000000000 0013
2nd example(no errors here): bool(130.0  129.0 == 1.0)
True
3rd example: a = 0.013 b = 0.0129 c = 0.0001 [a, b, c]
[0.0129999999999 99999, 0.0129, 0.0001] bool((a  b) == c)
False
This sort of error is no big deal in most cases, but I'm sure it could
become a problem under certain conditions, particularly the 3rd
example, where I'm using truth testing. The same results occur in all
cases whether I define variables a, b, and c, or enter the values
directly into the bool statement. Also, it doesn't make a difference
whether "a = 0.013" or "a = 0.0130".
I haven't checked this under windows 2000 or XP, but I expect the same
thing would happen. Any suggestions for a way to fix this sort of
error?
Jul 18 '05
89 5066
Gary Herron <gh*****@island training.com> wrote in message news:<ma******* *************** *************** *@python.org>.. . On Saturday 18 September 2004 09:50 am, Radioactive Man wrote: In python 2.3 (IDLE 1.0.3) running under windows 95, I get the following types of errors whenever I do simple arithmetic:
1st example:>> 12.10 + 8.30
20.399999999999 999
It's not a bug, it's a feature of binary arithmetic on ALL coumputers in ALL languages.
Actually, it's a feature of limitedprecision floatingpoint in ANY
base, not just binary. This includes base10. (I'm sure you've seen
BCD calculators that give 1/3*3=0.99999999. )
Gary Herron wrote: On Saturday 18 September 2004 09:50 am, Radioactive Man wrote:
In python 2.3 (IDLE 1.0.3) running under windows 95, I get the following types of errors whenever I do simple arithmetic:
1st example:
>12.10 + 8.30
20.3999999999 99999 It's not a bug, it's a feature of binary arithmetic on ALL coumputers in ALL languages. (But perhaps Python is the first time it has not been hidden from you.)
See the Python FAQ entry 1.4.2:
http://www.python.org/doc/faq/genera...soinaccurate
That's nonsense. My 7year old TI83 performs that calculation just
fine, and you're telling me, in this day and age, that Python running on
a modern 32bit processor can't even compute simple decimals accurately?
Don't defend bad code.
Peter Otten wrote: Radioactive Man wrote:
thing would happen. Any suggestions for a way to fix this sort of error?
Starting with Python 2.4 there will be the 'decimal' module supporting "arithmetic the way you know it":
Great, why fix what's broken when we can introduce a new module with an
inconvenient API.
Jeremy Bowers wrote: On Sat, 18 Sep 2004 16:50:16 +0000, Radioactive Man wrote:
In python 2.3 (IDLE 1.0.3) running under windows 95, I get the following types of errors whenever I do simple arithmetic:
Specifically (building on DogWalker's reply), http://www.python.org/doc/faq/genera...soinaccurate
Perhaps there's a simple explanation for this, but why do we go to the
trouble of computing fractions when our hardware can't handle the
result? If the decimal value of 1/3 is can't be represented in binary,
then don't. We should use an internal representation that stores the
numerator and denominator as separate integers.
Chris S. wrote: Starting with Python 2.4 there will be the 'decimal' module supporting "arithmetic the way you know it":
Great, why fix what's broken when we can introduce a new module with an inconvenient API.
1. It ain't broken.
2. What fraction of the numbers in your programs are constants?
Peter
On Sunday 19 September 2004 12:18 am, Chris S. wrote: Jeremy Bowers wrote: On Sat, 18 Sep 2004 16:50:16 +0000, Radioactive Man wrote:In python 2.3 (IDLE 1.0.3) running under windows 95, I get the following types of errors whenever I do simple arithmetic:
Specifically (building on DogWalker's reply), http://www.python.org/doc/faq/genera...pointcalcula tionssoinaccurate
Perhaps there's a simple explanation for this, but why do we go to the trouble of computing fractions when our hardware can't handle the result? If the decimal value of 1/3 is can't be represented in binary, then don't. We should use an internal representation that stores the numerator and denominator as separate integers.
That's called rational arithmetic, and I'm sure you can find a package
that implements it for you. However what would you propose for
irrational numbers like sqrt(2) and transcendental numbers like PI?
While I'd love to compute with all those numbers in infinite
precision, we're all stuck with FINITE sized computers, and hence with
the inaccuracies of finite representations of numbers.
Dr. Gary Herron
Gary Herron wrote: That's called rational arithmetic, and I'm sure you can find a package that implements it for you. However what would you propose for irrational numbers like sqrt(2) and transcendental numbers like PI?
Sqrt is a fair criticism, but Pi equals 22/7, exactly the form this
arithmetic is meant for. Any decimal can be represented by a fraction,
yet not all fractions can be represented by decimals. My point is that
such simple accuracy should be supported out of the box.
While I'd love to compute with all those numbers in infinite precision, we're all stuck with FINITE sized computers, and hence with the inaccuracies of finite representations of numbers.
So are our brains, yet we somehow manage to compute 12.10 + 8.30
correctly using nothing more than simple skills developed in
gradeschool. You could theoretically compute an infinitely long
equation by simply operating on single digits, yet Python, with all of
its resources, can't overcome this hurtle?
However, I understand Python's limitation in this regard. This
inaccuracy stems from the traditional C mindset, which typically
dismisses any approach not directly supported in hardware. As the FAQ
states, this problem is due to the "underlying C platform". I just find
it funny how a $20 calculator can be more accurate than Python running
on a $1000 Intel machine.
Peter Otten wrote: Chris S. wrote:
Starting with Python 2.4 there will be the 'decimal' module supporting "arithmeti c the way you know it":
Great, why fix what's broken when we can introduce a new module with an inconvenien t API.
1. It ain't broken.
Call it what you will, it doesn't produce the correct result. From where
I come from, that's either bad or broken.
2. What fraction of the numbers in your programs are constants?
What?
Peter Otten <__*******@web. de> writes: Starting with Python 2.4 there will be the 'decimal' module supporting "arithmetic the way you know it":
from decimal import * Decimal("12.10" ) + Decimal("8.30")
I haven't tried 2.4 yet. After
a = Decimal("1") / Decimal("3")
b = a * Decimal("3")
print b
What happens? Is that arithmetic as the way I know it?
On Sun, 19 Sep 2004 08:00:03 GMT, Chris S. wrote: Sqrt is a fair criticism, but Pi equals 22/7, exactly the form this arithmetic is meant for. Any decimal can be represented by a fraction, yet not all fractions can be represented by decimals. My point is that such simple accuracy should be supported out of the box.
Do you really think Pi equals 22/7 ? import math print math.pi
3.14159265359 print 22.0/7.0
3.14285714286
What do you get on your $20 calculator ?

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