2013/3/26 Louis LaBrunda Lou@keystone-software.com:
On Tue, 26 Mar 2013 18:59:12 +0100, Nicolas Cellier nicolas.cellier.aka.nice@gmail.com wrote:
2013/3/26 Louis LaBrunda Lou@keystone-software.com:
On Tue, 26 Mar 2013 18:32:31 +0100, Stéphane Rollandin lecteur@zogotounga.net wrote:
Example (0.995 round: 2) -> 1.00 though 0.995 < (995/1000) so it should round to 0.99.
.. and I just noticed that
0.995 printShowingDecimalPlaces: 2 ==> '1.00'Do we have a method returning the correct value ?
That looks right to me, because 0.995 was rounded up.
Lou
No it's not, because 0.995 < 0.995s3 so it should be rounded down. In a recent trunk image, print is OK: (0.995 printShowingDecimalPlaces: 2) -> '0.99'
In VA Smalltalk:
0.995 = 0.995s3 => true 0.995 < 0.995s3 => false
This is a default st80 behavior which converts minimumGenerality number to maximumGenerality. Maybe some of these conventions are hardwired in VM, I don't know, but in other dialects it's handled at image side.
The idea was this one: if you perform an operation between an inexact value and an exact value, the result is inexact. So Float + * / - Integer,Fraction,ScaledDecimal will result into a Float. Thus Float got a higher generality.
The idea behind Squeak change is that every Float has an exact value (asTrueFraction). Since we have only two possible answers true/false for comparison, and no maybe or dontKnow, it makes sense to compare the exact value. This reduces the number of paradoxal equalities
| a b c | a := 1 << Float precision. b := a + 1. c := a asFloat. { c = b. c = a. a = b. }
In VW and VA, the first two are true, the last is false, which suggests that = is not an equivalence relation. In Squeak, only the second one is true.
Same with inequalities, we expect (a < b) & (a = c) ==> (c < b) etc... This is still true in Squeak, not in VA/VW/st80. I think gst and Dolphin and maybe stx adopted Squeak behavior (to be confirmed).
I think in VA Smalltalk there is some VM magic going on that makes the above work the way it does. The #= and #< of Float are implemented in a primitive. I guess when converting the '0.995' string to a float a little is lost and that would make it less than 0.995s3 but there is a lot of code floating around (sorry about the puns) to make floats look better. In that case I would think people would want (0.995 printShowingDecimalPlaces: 2) to show '1.00' and not '0.99'.
No, people should not rely on such behavior with Floats, because sooner than later they will be bitten. We cannot cheat very long with this kind of assumptions. My POV is that it is better to educate about false expectations with Float, and that's the main benefit of (1/10) ~= 0.1.
I would add that such print policy is not the behaviour of every other language I know of.
printf( "%.2f",0.995) -> 0.99
Because libm are carefully written nowdays and other languages libraries are either built over libm or much more careful than Smalltalk were (that mostly means more recent).
Anyway, we should try not to use floats without a very, very good reason. Like we have to send them outside of Smalltalk or we really need the speed or decimals and fractions take up too much memory. But then we must live with their inaccuracies and display mess.
Good advice, let's put those expectations on decimal fractions (ScaledDecimal/FixedPoint) or general Fraction.
I have an untested theory that fractions can be close in speed to floats because divisions (that are expensive) can be pushed to the end of a computation because with fractions they are multiplies.
Lou
Why not, but huge numerators and denominators are not cheap compared to Float operations. OK reducing the fraction is the expensive part, but how does the cost grow versus the length of operands?
Also some geometric operations are not even possible on Q (hypot) so you might soon need AlgebraicNumber. And Smalltalk is also about graphics and geometry.
Nicolas
Louis LaBrunda Keystone Software Corp. SkypeMe callto://PhotonDemon mailto:Lou@Keystone-Software.com http://www.Keystone-Software.com