Math errors in python

Discussion in 'Python' started by Radioactive Man, Sep 18, 2004.

  1. 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

    20.399999999999999
    >>> 1.1 - 0.2

    0.90000000000000013


    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]

    [0.012999999999999999, 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?
    Radioactive Man, Sep 18, 2004
    #1
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  2. Radioactive Man

    DogWalker Guest

    Have a look at the FAQ (before the response to your message builds).

    ----- Original Message -----
    From: Radioactive Man
    Newsgroups: comp.lang.python
    To:
    Sent: Saturday, September 18, 2004 9:50 AM
    Subject: Math errors in python


    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

    20.399999999999999
    >>> 1.1 - 0.2

    0.90000000000000013


    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]

    [0.012999999999999999, 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?
    --
    http://mail.python.org/mailman/listinfo/python-list
    DogWalker, Sep 18, 2004
    #2
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  3. Radioactive Man

    Tim Peters Guest

    [Radioactive Man]
    > 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

    > 20.399999999999999


    ....

    Please read the Tutorial appendix on floating-point issues:

    http://docs.python.org/tut/node15.html
    Tim Peters, Sep 18, 2004
    #3
  4. Radioactive Man

    Gary Herron Guest

    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

    >
    > 20.399999999999999



    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/general.html#why-are-floating-point-calculations-so-inaccurate


    Gary Herron
    Gary Herron, Sep 18, 2004
    #4
  5. Jeremy Bowers, Sep 18, 2004
    #5
  6. Radioactive Man

    Peter Otten Guest

    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":

    >>> from decimal import *
    >>> Decimal("12.10") + Decimal("8.30")

    Decimal("20.40")
    >>> Decimal("1.1") - Decimal("0.2")

    Decimal("0.9")
    >>> Decimal("130.0")-Decimal("129.0") == Decimal("1.0")

    True
    >>> a, b, c = map(Decimal, "0.013 0.0129 0.0001".split())
    >>> a, b, c

    (Decimal("0.013"), Decimal("0.0129"), Decimal("0.0001"))
    >>> (a-b) == c

    True


    Peter
    Peter Otten, Sep 18, 2004
    #6
  7. Hi !

    Many languages, yes.
    All languages, no.

    Few languages can use the DCB possibilities of the processors.

    @-salutations
    --
    Michel Claveau
    =?iso-8859-1?Q?Michel_Claveau_-_abstraction_m=E9ta, Sep 18, 2004
    #7
  8. On Sat, 18 Sep 2004 20:54:42 +0200, Michel Claveau - abstraction
    méta-galactique non triviale en fuite perpétuelle.
    <> declaimed the
    following in comp.lang.python:

    >
    > Few languages can use the DCB possibilities of the processors.
    >

    Uhmm... Data Control Block?

    Did you mean BCD -- binary coded decimal. Which is a form of
    decimal arithmetic, and not native binary floating point.

    Considering how often the question about strange floating point
    output comes up, I come to the conclusion that CS courses no longer
    teach the basics of representation... (Try reading the Ada Reference
    Manual regarding the differences between float and fixed, neither of
    which imply decimal.)

    Or find a copy of "Real Computing Made Real"
    http://www.amazon.com/exec/obidos/tg/detail/-/0691036632/104-1507668-6795157?v=glance

    --
    > ============================================================== <
    > | Wulfraed Dennis Lee Bieber KD6MOG <
    > | Bestiaria Support Staff <
    > ============================================================== <
    > Home Page: <http://www.dm.net/~wulfraed/> <
    > Overflow Page: <http://wlfraed.home.netcom.com/> <
    Dennis Lee Bieber, Sep 18, 2004
    #8
  9. Hi !

    BCD (english) ==> DCB (french)


    And Alcyane-basic run, in 1976, with floating-based-DCB-arithmétique, on the
    8080, before than IEEE normalize the floating-arithmétique-pow(256)-based
    (and longer before Ada).

    And DCB is native in all Intel processors.

    And before, when i use Fortran on mini-computer, there was no this problem.
    But, then it's very much easy to work with pow(256), And the anscendant
    compatibility become... Hélas.


    *sorry for my bad english*


    Michel Claveau
    =?iso-8859-1?Q?Michel_Claveau_-_abstraction_m=E9ta, Sep 18, 2004
    #9
  10. On Sat, 18 Sep 2004 22:58:13 +0200, Michel Claveau - abstraction
    méta-galactique non triviale en fuite perpétuelle.
    <> declaimed the
    following in comp.lang.python:

    >
    > And before, when i use Fortran on mini-computer, there was no this problem.


    It may have been there, but you never saw it in print <G>

    When I took classes in the 70s, we were taught never to rely
    upon comparing two floating point numbers for equality. Instead, we were
    told to compare for the difference between the two numbers being less
    than some epsilon, with the epsilon defined as the smallest difference
    that could be considered equal for the numbers being compared (if the
    input is only good for 5 significant figures, the epsilon should not be
    down into 7 significant)

    a = 5.234
    b = 5.235
    epsilon = 0.0005
    if abs(a - b) < epsilon then
    equal

    --
    > ============================================================== <
    > | Wulfraed Dennis Lee Bieber KD6MOG <
    > | Bestiaria Support Staff <
    > ============================================================== <
    > Home Page: <http://www.dm.net/~wulfraed/> <
    > Overflow Page: <http://wlfraed.home.netcom.com/> <
    Dennis Lee Bieber, Sep 18, 2004
    #10
  11. Radioactive Man

    Dan Bishop Guest

    Gary Herron <> wrote in message news:<>...
    > 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

    > >
    > > 20.399999999999999

    >
    >
    > It's not a bug, it's a feature of binary arithmetic on ALL coumputers
    > in ALL languages.


    Actually, it's a feature of limited-precision floating-point in ANY
    base, not just binary. This includes base-10. (I'm sure you've seen
    BCD calculators that give 1/3*3=0.99999999.)
    Dan Bishop, Sep 19, 2004
    #11
  12. Radioactive Man

    Chris S. Guest

    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

    >>
    >>20.399999999999999

    >
    >
    >
    > 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/general.html#why-are-floating-point-calculations-so-inaccurate


    That's nonsense. My 7-year old TI-83 performs that calculation just
    fine, and you're telling me, in this day and age, that Python running on
    a modern 32-bit processor can't even compute simple decimals accurately?
    Don't defend bad code.
    Chris S., Sep 19, 2004
    #12
  13. Radioactive Man

    Chris S. Guest

    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.
    Chris S., Sep 19, 2004
    #13
  14. Radioactive Man

    Chris S. Guest

    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/general.html#why-are-floating-point-calculations-so-inaccurate
    >


    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., Sep 19, 2004
    #14
  15. Radioactive Man

    Peter Otten Guest

    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
    Peter Otten, Sep 19, 2004
    #15
  16. Radioactive Man

    Gary Herron Guest

    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/general.html#why-are-floating-point-calcula
    > >tions-so-inaccurate

    >
    > 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, Sep 19, 2004
    #16
  17. Radioactive Man

    Chris S. Guest

    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
    grade-school. 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.
    Chris S., Sep 19, 2004
    #17
  18. Radioactive Man

    Chris S. Guest

    Peter Otten wrote:

    > 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.


    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?
    Chris S., Sep 19, 2004
    #18
  19. Radioactive Man

    Paul Rubin Guest

    Peter Otten <> 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?
    Paul Rubin, Sep 19, 2004
    #19
  20. 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 ?

    --
    Richard
    Richard Townsend, Sep 19, 2004
    #20
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