Le Vendredi 28 Avril 2006 20:08, nicolas cellier a écrit :
> However i still have the bellerophon algorithm (from tony's reference)
> failing with last bit incorrect in a few cases (i can check that with
> asTrueFraction for number greater than 1.0 timestwoPower: 53). So i do not
> release it yet.
>
> Nicolas

Subjects developped in this (too) long email are:
 - A) Float readFrom: now round exactly :)
 - B) my solution use a new ArbitraryPrecisionFloat class :(
 - C) this class can solve other asFloat problems :)
 - D) shouldn't the readFrom: fix better be moved to asFloat fix ?

A)----------------------------------------------------------------------------

OK, now i have the Float reading working, also for gradual underflow !

This of course solve Andreas' Numerics question: reading floating point 
constants,
i now have
(SqNumberParser on: '6.07710050630396597660e-11') nextNumber hex = 
'3DD0B4611A600000'.

B)----------------------------------------------------------------------------

The solution is not as light as i wanted, because i finally added an 
ArbitraryPrecisionFloat class to handle 64bits arithmetic involved in 
Bellerophon.
So i do not know if i should publish my solution at 
http://bugs.impara.de/view.php?id=3512, or rather in SM.
Unfortunately my SM account is blocked inactive...

It's funny how easy creating a new Number class was.
Of course, ArbitraryPrecisionFloat lacks a short literal form syntax, it does 
not implement usual mathematical functions (default is to convert to Float).
And it's not optimized at all (please don't compare to hardwired Float 
arithmetic...).
But it's more general than just reading Float. This is why i wanted to publish 
on SM.

C)----------------------------------------------------------------------------

This can potentially solve other asFloat incorrect rounding behaviour:

C.1) current implementation of LargeInteger>>asFloat.
will not round to nearest even Float when highBit > 53.

example:
 16r1FFFFFFFFFFFF081 asFloat hex

The ArbitraryPrecisionFloat implements IEEE rounding mode, so it can cure this 
one easily.

C.2) it is more difficult with Fraction>>asFloat
which does neither round to nearest even Float...

Bellerophon and ArbitraryPrecisionFloat together can fix the Fraction problem 
(conversion from decimal to binary representation is just a special case of 
these Large fractions).

I now know why i never succedeed in implementing my own Smalltalk Float 
reading in VW, despite of Integer infinite precision... I was over-trusting 
asFloat implementation that suffer the same problem...

D)----------------------------------------------------------------------------

So, maybe we should better move the fixes i wrote from Number>>readFrom: to 
LargeInteger and Fraction>>asFloat,
Then exactly rounded Float>>readFrom: will be a side effect...

Nicolas