Comparing floating point numbers

Discussion in 'C++' started by nw, Apr 30, 2007.

  1. nw

    nw Guest

    Hi,

    I'd like to compare 2 floating point numbers within a given error. I'd
    rather not use a absolute error but one related to the number of
    values that can be represented between the two floats. I've been
    reading: http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm
    where the following function is provided to do this:

    bool AlmostEqual2sComplement(float A, float B, int maxUlps) {
    // Make sure maxUlps is non-negative and small enough that the
    // default NAN won't compare as equal to anything.
    assert(maxUlps > 0 && maxUlps < 4 * 1024 * 1024);
    int aInt = *(int*)&A;
    // Make aInt lexicographically ordered as a twos-complement int
    if (aInt < 0)
    aInt = 0x80000000 - aInt;
    // Make bInt lexicographically ordered as a twos-complement int
    int bInt = *(int*)&B;
    if (bInt < 0)
    bInt = 0x80000000 - bInt;
    int intDiff = abs(aInt - bInt);
    if (intDiff <= maxUlps)
    return true;
    return false;
    }

    However, as the article states, this relies on a number of compiler
    specific features, such as the size of int (and I guess float). It
    also relies on the floats using IEEE representation (I guess all
    compilers use this, but is it in the standard?).

    So my question is this. Is there a good compiler independent method
    for comparing floating point numbers with a relative error?
    nw, Apr 30, 2007
    #1
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  2. nw wrote:
    > I'd like to compare 2 floating point numbers within a given error. [...]
    >
    > However, as the article states, this relies on a number of compiler
    > specific features, such as the size of int (and I guess float). It
    > also relies on the floats using IEEE representation (I guess all
    > compilers use this, but is it in the standard?).


    Right.

    > So my question is this. Is there a good compiler independent method
    > for comparing floating point numbers with a relative error?


    double a, b;
    ...
    if ( fabs(a-b) < myepsilon * max(fabs(a),fabs(b)) )
    // they are "equal"

    Pick myepsilon as you deem fit. That's your "relative error".

    V
    --
    Please remove capital 'A's when replying by e-mail
    I do not respond to top-posted replies, please don't ask
    Victor Bazarov, Apr 30, 2007
    #2
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  3. nw

    nw Guest

    > double a, b;
    > ...
    > if ( fabs(a-b) < myepsilon * max(fabs(a),fabs(b)) )
    > // they are "equal"
    >
    > Pick myepsilon as you deem fit. That's your "relative error".


    ok, if I'm reading this correctly this will mean that large numbers
    are allowed a bigger distance than smaller ones? This isn't exactly
    what I want. The function I previously posted allows me to say "are
    these two numbers with the X nearest possible floating point values"
    is it possible to do that in a compiler independent way?
    nw, Apr 30, 2007
    #3
  4. nw wrote:
    >> double a, b;
    >> ...
    >> if ( fabs(a-b) < myepsilon * max(fabs(a),fabs(b)) )
    >> // they are "equal"
    >>
    >> Pick myepsilon as you deem fit. That's your "relative error".

    >
    > ok, if I'm reading this correctly this will mean that large numbers
    > are allowed a bigger distance than smaller ones?


    Bigger absolute distance, but the same relative distance.

    > This isn't exactly
    > what I want.


    But that's what "relative" means.

    > The function I previously posted allows me to say "are
    > these two numbers with the X nearest possible floating point values"


    Huh? Please re-read the statement inside double quotes and try
    expressing it in mathematical notation.

    > is it possible to do that in a compiler independent way?


    As soon as I know what exactly (or relatively) it is you want, I'll
    try to help.

    V
    --
    Please remove capital 'A's when replying by e-mail
    I do not respond to top-posted replies, please don't ask
    Victor Bazarov, Apr 30, 2007
    #4
  5. In message <f14re1$a8u$>, Victor Bazarov
    <> writes
    >nw wrote:
    >>> double a, b;
    >>> ...
    >>> if ( fabs(a-b) < myepsilon * max(fabs(a),fabs(b)) )
    >>> // they are "equal"
    >>>
    >>> Pick myepsilon as you deem fit. That's your "relative error".

    >>
    >> ok, if I'm reading this correctly this will mean that large numbers
    >> are allowed a bigger distance than smaller ones?

    >
    >Bigger absolute distance, but the same relative distance.
    >
    >> This isn't exactly
    >> what I want.

    >
    >But that's what "relative" means.
    >
    >> The function I previously posted allows me to say "are
    >> these two numbers with the X nearest possible floating point values"

    >
    >Huh? Please re-read the statement inside double quotes and try
    >expressing it in mathematical notation.
    >
    >> is it possible to do that in a compiler independent way?

    >
    >As soon as I know what exactly (or relatively) it is you want, I'll
    >try to help.


    I think you need to read the cited article to find out what this is
    about. This isn't really a "relative error", it's asking the question
    "is the number of representable floating-point values between given A
    and B less than N?"

    --
    Richard Herring
    Richard Herring, Apr 30, 2007
    #5
  6. nw

    nw Guest

    > I think you need to read the cited article to find out what this is
    > about. This isn't really a "relative error", it's asking the question
    > "is the number of representable floating-point values between given A
    > and B less than N?"


    Yes what he said. :)

    Sorry, the question wasn't defined as clearly as it could have been.
    So is there any compiler independent method for this? Or is it perhaps
    not even a particularly good idea?
    nw, Apr 30, 2007
    #6
  7. Richard Herring wrote:
    > [...]
    > I think you need to read the cited article to find out what this is
    > about. This isn't really a "relative error", it's asking the question
    > "is the number of representable floating-point values between given A
    > and B less than N?"


    Right. My fault for not reading the article, and I think we can call
    it "relative error" after all. Each of the "next representable FP
    number" from a certain value differs from it on a relative basis (the
    exponent plays the part of the scaling factor).

    To the OP:

    It can be done, but only if the platform does have the integral type
    large enough to represent the floating point representation, and that
    the FP representation and the integral representation share the same
    base (2). The information is available through 'std::numeric_limits'
    specialisations, take a look.

    V
    --
    Please remove capital 'A's when replying by e-mail
    I do not respond to top-posted replies, please don't ask
    Victor Bazarov, Apr 30, 2007
    #7
  8. nw wrote:
    >> I think you need to read the cited article to find out what this is
    >> about. This isn't really a "relative error", it's asking the question
    >> "is the number of representable floating-point values between given A
    >> and B less than N?"

    >
    > Yes what he said. :)
    >
    > Sorry, the question wasn't defined as clearly as it could have been.
    > So is there any compiler independent method for this? Or is it perhaps
    > not even a particularly good idea?


    Since there is no requirement that FP values are represented in the same
    base as integral values, the answer is most likely "no".

    V
    --
    Please remove capital 'A's when replying by e-mail
    I do not respond to top-posted replies, please don't ask
    Victor Bazarov, Apr 30, 2007
    #8
  9. nw

    P.J. Plauger Guest

    "nw" <> wrote in message
    news:...

    >> I think you need to read the cited article to find out what this is
    >> about. This isn't really a "relative error", it's asking the question
    >> "is the number of representable floating-point values between given A
    >> and B less than N?"

    >
    > Yes what he said. :)
    >
    > Sorry, the question wasn't defined as clearly as it could have been.
    > So is there any compiler independent method for this? Or is it perhaps
    > not even a particularly good idea?


    You need the C99 function nexttoward, which does almost exactly what
    you want. It'll be a part of the next C++ Standard, but right now it's
    relatively rare. See our Compleat Library, available at our web site.

    P.J. Plauger
    Dinkumware, Ltd.
    http://www.dinkumware.com
    P.J. Plauger, Apr 30, 2007
    #9
  10. nw

    nw Guest

    > You need the C99 function nexttoward, which does almost exactly what
    > you want. It'll be a part of the next C++ Standard, but right now it's
    > relatively rare. See our Compleat Library, available at our web site.


    Yep that does sound like what I want. I guess I'll just have to test
    within absolute limits for now and patiently await the new C standard.

    Thanks for your help!
    nw, Apr 30, 2007
    #10
  11. P.J. Plauger wrote:
    > "nw" <> wrote in message
    > news:...
    >
    >>> I think you need to read the cited article to find out what this is
    >>> about. This isn't really a "relative error", it's asking the
    >>> question "is the number of representable floating-point values
    >>> between given A and B less than N?"

    >>
    >> Yes what he said. :)
    >>
    >> Sorry, the question wasn't defined as clearly as it could have been.
    >> So is there any compiler independent method for this? Or is it
    >> perhaps not even a particularly good idea?

    >
    > You need the C99 function nexttoward, which does almost exactly what
    > you want. It'll be a part of the next C++ Standard, but right now it's
    > relatively rare. See our Compleat Library, available at our web site.


    There is also nextafter which is almost the same but maybe slightly more
    appropriate since it takes parameters of the same type instead of
    having the second parameter always as a long double for reasons
    probably only numerical analysts know.

    They are also included with recent GNU libc versions that are used on
    most Linux systems.

    --
    Markus
    Markus Schoder, Apr 30, 2007
    #11
  12. nw

    James Kanze Guest

    On Apr 30, 3:15 pm, "Victor Bazarov" <> wrote:
    > nw wrote:
    > > I'd like to compare 2 floating point numbers within a given error. [...]


    > > However, as the article states, this relies on a number of compiler
    > > specific features, such as the size of int (and I guess float). It
    > > also relies on the floats using IEEE representation (I guess all
    > > compilers use this, but is it in the standard?).


    > Right.


    Which standard. IEEE representation is a standard, but it's not
    required in C++, and is far from universal.

    --
    James Kanze (Gabi Software) email:
    Conseils en informatique orientée objet/
    Beratung in objektorientierter Datenverarbeitung
    9 place Sémard, 78210 St.-Cyr-l'École, France, +33 (0)1 30 23 00 34
    James Kanze, May 1, 2007
    #12
  13. James Kanze wrote:
    > On Apr 30, 3:15 pm, "Victor Bazarov" <> wrote:
    >> nw wrote:
    >>> I'd like to compare 2 floating point numbers within a given error.
    >>> [...]

    >
    >>> However, as the article states, this relies on a number of compiler
    >>> specific features, such as the size of int (and I guess float). It
    >>> also relies on the floats using IEEE representation (I guess all
    >>> compilers use this, but is it in the standard?).

    >
    >> Right.

    >
    > Which standard. IEEE representation is a standard, but it's not
    > required in C++, and is far from universal.


    Yes. Are you agreeing or disagreeing with my saying "right"?

    V
    --
    Please remove capital 'A's when replying by e-mail
    I do not respond to top-posted replies, please don't ask
    Victor Bazarov, May 1, 2007
    #13
  14. nw

    James Kanze Guest

    On May 1, 3:29 pm, "Victor Bazarov" <> wrote:
    > James Kanze wrote:
    > > On Apr 30, 3:15 pm, "Victor Bazarov" <> wrote:
    > >> nw wrote:
    > >>> I'd like to compare 2 floating point numbers within a given error.
    > >>> [...]


    > >>> However, as the article states, this relies on a number of compiler
    > >>> specific features, such as the size of int (and I guess float). It
    > >>> also relies on the floats using IEEE representation (I guess all
    > >>> compilers use this, but is it in the standard?).


    > >> Right.


    > > Which standard. IEEE representation is a standard, but it's not
    > > required in C++, and is far from universal.


    > Yes. Are you agreeing or disagreeing with my saying "right"?


    It depends on what you meant by "right". The way I read it was:

    >> I guess all compilers use IEEE representation, but is it in
    >> the standard?


    > Right [meaning yes, it is in the standard].


    However, I don't find "right" very idiomatic for responding to
    this kind of question, so maybe you meant for it to apply to
    something else.

    --
    James Kanze (GABI Software) email:
    Conseils en informatique orientée objet/
    Beratung in objektorientierter Datenverarbeitung
    9 place Sémard, 78210 St.-Cyr-l'École, France, +33 (0)1 30 23 00 34
    James Kanze, May 2, 2007
    #14
  15. James Kanze wrote:
    > On May 1, 3:29 pm, "Victor Bazarov" <> wrote:
    >> James Kanze wrote:
    >>> On Apr 30, 3:15 pm, "Victor Bazarov" <>
    >>> wrote:
    >>>> nw wrote:
    >>>>> I'd like to compare 2 floating point numbers within a given error.
    >>>>> [...]

    >
    >>>>> However, as the article states, this relies on a number of
    >>>>> compiler specific features, such as the size of int (and I guess
    >>>>> float). It also relies on the floats using IEEE representation (I
    >>>>> guess all compilers use this, but is it in the standard?).

    >
    >>>> Right.

    >
    >>> Which standard. IEEE representation is a standard, but it's not
    >>> required in C++, and is far from universal.

    >
    >> Yes. Are you agreeing or disagreeing with my saying "right"?

    >
    > It depends on what you meant by "right".


    It is meant as a confirmation response. What else could I mean?

    > The way I read it was:
    >
    >>> I guess all compilers use IEEE representation, but is it in
    >>> the standard?

    >
    >> Right [meaning yes, it is in the standard].

    >
    > However, I don't find "right" very idiomatic for responding to
    > this kind of question, so maybe you meant for it to apply to
    > something else.


    Good, you're doubting yourself. That's the first step to finding
    the common ground.

    I responded to the whole paragraph. Chiefly, it means I responded
    to "this relies" and "It also relies". If I were to answer the
    the "is it in the standard?" question, I'd use the word "standard"
    in my reply somehow.

    V
    --
    Please remove capital 'A's when replying by e-mail
    I do not respond to top-posted replies, please don't ask
    Victor Bazarov, May 2, 2007
    #15
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