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SKILL arithmetic comparisons

sri125

 SKILL is notorious for the way it stores numbers in memory. e.g variable w, which

should be 0.4 gets stored as 0.3999999999999 or something like that.

 

So when you use it in 'if-else' loop like:

if( w == 0.4 then 

    block good;

else

   block bad;

 )

 

You will end up in block bad unless you do something like

 

abs( w - 0.4 ) < 0.000001 

or something like above.

 

Is there an elegant way to handle this in SKILL ?

 

thanks

 

 

 

  • There is nothing "notorious" or special with the way that SKILL stores floating point numbers compared to other programming languages.  A floating point number is typically stored in an IEEE (754) format which is comprised of a sign, an exponent and a mantissa (or significand).  Most decimal numbers do not have an exact representation in the binary floating-point storage format used in single-precision and double-precision data types.  So in order to be able to test for equality in a reliable fashion, the best thing is to subtract one number from the other and test the remainder against a small number, exactly as you have shown.  The small number could be a fraction of the input number so that the test works equally well for large values and smaller values.

    Sorry, that's just how things are for floating point number comparison, I'm not sure if there is any better way?

    Regards,

    Lawrence.

  • As Lawrence says, you get exactly the same kind of rounding errors in C and all languages using IEEE floating point numbers. In fact whenever this comes up with someone saying this is a bug in SKILL, I show a C program with the same behaviour.

    The trick is to write a function to do floating point "equality" checks. If you know the magnitude of the numbers, you can use a fixed size "epsilon" as in your example.

    Or you can do something like:

    procedure(myCompare(a b @key (reltol 1e-6) (abstol 1e-12))
    let((tol)
    tol=reltol*max(abs(a) abs(b))+abstol
    abs(a-b) < tol
    )
    )

    This has both a relative and absolute tolerance in the comparison.

    Regards,

    Andrew

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