Cedric,
Part of the issue is that different architectures will have different values for machine epsilon (1e-09 in your post). Machine epsilon is defined to be the largest float such that
0.0 + epsilon = 0.0
Its value varies according to your machine though - typically a machine with a much larger machine word size in its floating point processor will have a much smaller machine epsilon. (The following is an example of a Simple Lie, for an introduction to the Complicated Truth I suggest you get hold of a book on Numerical Computation, which is an important study in Computer Science).
Things are complicated further in that in any radix based number system there are very simple numbers that cannot be written exactly. In the decimal number system any fraction with a denominator relatively prime to the radix tends to be an infinitely repeating fraction. 1/3 or 3/7 are examples.
Computers use binary numbers inside. 1/10 is not expressible as a nonrecurring binary fraction, nor is 1/3, 3/10, 2/5 or 1/20.
Squeak does a good job of trying to promote numbers to ScaledDecimals, but they are much more expensive to calculate than IEEE floats or Integers.
If we repeat your examples using Fractions we get
1 - (2/10) - (5/100) - ( 3/10) - (1/10) -(1/10) = (1/4) true
because Fractions are exact - in fact the definition of equality for fractions is defined to be
( a/b ) = ( c/d ) if and only if ( a * d ) = (b * c)
which only uses Integer and BigNum arithmetic and allows arbitrary precision (unless the numbers are so big you run out of memory).
Your idea of redefining equality for floats is a very bad idea because (1) it assumes all hardware has the same value for machine epsilon and (2) will break 50 years worth of programs that do numerical computation.
The simplest rule is any attempt to test floats (or doubles, or IEEE decwords) for equality is a bug. If there's a decimal point in your calculations (or if there could be) then don't test for equality. This is taught to computing students at University in the first few weeks. Any work done by a Uni student who breaks this rule gets marked down very severely!
I commend you on discovering this on your own by the way - it shows an inquiring mind. It's not everyone who hits one of the key issues in Computer Science by themselves, and then thinks about it.
Yours,
John.
Hi,
I noticed in my image (damien last beta so 3.10 - windows XP and Vista) that I have a strange bug when soustracting floats successively. Here is how I reproduce it in a workspace:
1 - 0.2 -0.05 -0.3 = 0.45 "true" 1 - 0.2 -0.05 -0.3 -0.1= 0.35 "true" 1 - 0.2 -0.05 -0.3 -0.1 - 0.10= 0.25 "*****false*****" 1 - 0.2 -0.05 -0.3 -0.1 - 0.10= 0.24999999999999995 true
or again: 1 - 0.1 = 0.9 true 1 - 0.1 - 0.1 = 0.8 true 1 - 0.1 - 0.1 - 0.1 = 0.7 false
Can somebody explain that or is it a bug ? I don't know yet if it's specific to my image, so does other have the same behavior? I can force the rounding of the result but find it strange.
Cédrick
2008/2/17, danil osipchuk danil.osipchuk@gmail.com:
This is not even squeak specific. Decimal floats not always can be represented precisely in binary form:
http://en.wikipedia.org/wiki/Floating_point#Accuracy_problems
Hi Cédrick,
if you need to operate with exact precision just don't trustfloats. Use ScaledDecimals instead. In Squeak ScaledDecimals are implemented with the fraction so it's matematically stronger than floats. Use floats at presentation or user interface time and evade them at domain model.
cheers,Sebastian Sastre
uhm ok, good to know. Actually, it was just a test that failed so I was surprised.
I still find the result odd.
Seeing ScaledDecimal>>testConvertFromFloat, I'm wandering if it would be better to have Float>>= considering egality if the difference is less than 1.0e-9.
<primitive: 47> aNumber isNumber ifFalse: [^ false]. ^ (aNumber asFloat - self) abs < 1.0e-9
I would prefer having = working as I expect, even if it would be wrong for smaller values than 1.0e-9. For strict egality, == can be used.
Is it possible to disable a primitive call like here (it's optimized no ?) ?
Anyway, thanks for your answers.
Cédrick _______________________________________________ Beginners mailing list Beginners@lists.squeakfoundation.org http://lists.squeakfoundation.org/mailman/listinfo/beginners