Thank you Nicolas!

I moved my two packages from inbox to treated.

Dave

> Hi all,
> I couldn't resist, and posted a version to the trunk ;)
> We can have both (un)limited number of iterations and limited precision
> (it
> is limited by Float ulp / 2 anyway...).
> I kept the default to 10 decimal places, but we can reduce it to 6 if we
> want to...
>
>
> 2018-04-26 5:03 GMT+02:00 David T. Lewis <lewis at mail.msen.com>:
>
>> On Wed, Apr 25, 2018 at 06:32:51PM -0700, Eliot Miranda wrote:
>> > On Mon, Apr 23, 2018 at 8:06 PM, David T. Lewis <lewis at mail.msen.com>
>> wrote:
>> >
>> > > Hi Eliot,
>> > >
>> > > I think that the confusing behavior is is related to the
>> interpretation of
>> > > single
>> > > precision floats in the VM when represented as double precision
>> Float
>> in
>> > > Squeak.
>> > >
>> > > How about implementing #asApproximateFractionFloatPrecision: to
>> specify
>> > > the
>> > > assumed accuracy of the float when derived from single precision,
>> but
>> > > represented
>> > > in the image as a double precision Squeak float?
>> > >
>> >
>> > Thanks, David.  This looks good to me.  But I'm no expert here.  If I
>> were
>> > to put this into trunk I would modify asApproximateFraction: to
>> > send asApproximateFractionAtOrder:floatPrecision: directly.
>> >
>>
>> Oops, emails crossed in the ether. I just committed a small but
>> important
>> fix
>> to the inbox, and I missed your suggestion.
>>
>> Should this go to trunk? If so I will add your change when merging.
>>
>> Dave
>>
>> >
>> > > Thus:
>> > >
>> > >   (FloatArray new: 1) at: 1 put: 1/3; at: 1 ==> 0.3333333432674408
>> "single
>> > > precision float cast from FloatArray to Squeak double precision"
>> > >
>> > >   0.3333333432674408 asApproximateFraction ==> (11184811/33554432)
>> "bad,
>> > > original default implementation assumes float double precision"
>> > >
>> > >   0.3333333432674408 asApproximateFractionFloatPrecision: 5 ==>
>> (1/3)
>> > > "better, limit precision when cast from single precision to double"
>> > >
>> > > An implementation is in the inbox in Kernel-dtl.1165.
>> > >
>> > > Note, orignal author for these methods has initials 'st' is, which
>> > > according to
>> > > SqueakMap is Samuel Tardieu (sam at rfc1149.net, home page
>> > > https://rfc1149.net/sam.html).
>> > > Even for those of us not who may not be interested in numerical
>> methods, I
>> > > must
>> > > highly recommend his references to rfc1149.
>> > >
>> > > Dave
>> > >
>> > >
>> > > On Mon, Apr 23, 2018 at 01:23:03PM -0700, Eliot Miranda wrote:
>> > > > Hi All,
>> > > >
>> > > >     asApproximateFraction isn't that useful.  It is based on
>> > > > asApproximateFractionAtOrder:, which gives you the best fraction
>> it
>> can
>> > > > find up to order.  e.g.
>> > > >
>> > > > testContinuedFractions
>> > > > self assert: (Float pi asApproximateFractionAtOrder: 1) = (22/7).
>> > > > self assert: (Float pi asApproximateFractionAtOrder: 3) =
>> (355/113)
>> > > > Here's 32-bit Float 1/3:
>> > > >
>> > > > ((FloatArray new: 1) at: 1 put: 1/3; at: 1) 0.3333333432674408
>> > > >
>> > > > ((FloatArray new: 1) at: 1 put: 1/3; at: 1) asApproximateFraction
>> > > > (11184811/33554432)
>> > > >
>> > > > That's not what I expected :-).  The problem is that
>> > > > asApproximateFractionAtOrder: is great if you know the number
>> you're
>> > > > dealing with, but if you don't then it'll give you too much
>> information.
>> > > >
>> > > > [This value comes up in the vm parameters system report page,
>> where
>> 1/3
>> > > is
>> > > > the ratio of growth to heap size above which a full GC is
>> performed,
>> i.e.
>> > > > by default every time a scavenge causes the heap grows by 1/3 from
>> the
>> > > last
>> > > > time a full GC was performed, the system will do a full GC.  It
>> would be
>> > > > great to report this as 1/3, not 0.33333298563957214, which is
>> what's
>> > > > emerging from the C code in the VM].
>> > > >
>> > > > Let's get a feeling for orders; they're effectively negative
>> powers
>> of
>> > > 10:
>> > > >
>> > > > (1 to: 20) collect: [:order| | f |
>> > > > { order. (f := Float pi asApproximateFractionAtOrder: order). f
>> asFloat.
>> > > (f
>> > > > asFloat - Float pi) abs}]
>> > > > {{1 . (22/7) . 3.142857142857143 . 0.0012644892673496777}.
>> > > >  {2 . (333/106) . 3.141509433962264 . 8.32196275291075e-5}.
>> > > >  {3 . (355/113) . 3.1415929203539825 . 2.667641894049666e-7}.
>> > > >  {4 . (103993/33102) . 3.1415926530119025 .
>> 5.778906242426274e-10}.
>> > > >  {5 . (104348/33215) . 3.141592653921421 .
>> 3.3162805834763276e-10}.
>> > > >  {6 . (208341/66317) . 3.1415926534674368 .
>> 1.2235634727630895e-10}.
>> > > >  {7 . (312689/99532) . 3.1415926536189365 .
>> 2.914335439641036e-11}.
>> > > >  {8 . (833719/265381) . 3.141592653581078 .
>> 8.715250743307479e-12}.
>> > > >  {9 . (1146408/364913) . 3.141592653591404 .
>> 1.6107115641261771e-12}.
>> > > >  {10 . (4272943/1360120) . 3.141592653589389 .
>> 4.04121180963557e-13}.
>> > > >  {11 . (5419351/1725033) . 3.1415926535898153 .
>> 2.220446049250313e-14}.
>> > > >  {12 . (80143857/25510582) . 3.1415926535897927 .
>> 4.440892098500626e-16}.
>> > > >  {13 . (245850922/78256779) . 3.141592653589793 . 0.0}.
>> > > >  {14 . (817696623/260280919) . 3.141592653589793 . 0.0}.
>> > > >  {15 . (19052873251/6064717916) . 3.141592653589793 . 0.0}.
>> > > >  {16 . (19870569874/6324998835) . 3.141592653589793 . 0.0}.
>> > > >  {17 . (19870569874/6324998835) . 3.141592653589793 . 0.0}.
>> > > >  {18 . (19870569874/6324998835) . 3.141592653589793 . 0.0}.
>> > > >  {19 . (19870569874/6324998835) . 3.141592653589793 . 0.0}.
>> > > >  {20 . (19870569874/6324998835) . 3.141592653589793 . 0.0}}
>> > > >
>> > > >
>> > > > More useful would be something like:
>> > > >
>> > > > asApproximateFractionToEpsilon: epsilon
>> > > > "Answer a Fraction approximating the receiver. This conversion
>> uses
>> the
>> > > > continued fraction method to approximate a floating point number."
>> > > >
>> > > > 1 to: 12 do:
>> > > > [:order| | fraction |
>> > > > fraction := self asApproximateFractionAtOrder: order.
>> > > > (fraction - self) abs <= epsilon ifTrue:
>> > > > [^fraction]].
>> > > > ^ self asApproximateFractionAtOrder: 0
>> > > >
>> > > > and then instead of
>> > > >
>> > > > asApproximateFraction
>> > > > "Answer a Fraction approximating the receiver. This conversion
>> uses
>> the
>> > > > continued fraction method to approximate a floating point number."
>> > > >
>> > > > ^ self asApproximateFractionAtOrder: 0
>> > > >
>> > > > one could have
>> > > >
>> > > > asApproximateFraction
>> > > > "Answer a Fraction approximating the receiver. This conversion
>> uses
>> the
>> > > > continued fraction method to approximate a floating point number."
>> > > >
>> > > > ^self asApproximateFractionToEpsilon: 1e-6
>> > > >
>> > > > And hence
>> > > >
>> > > > { 0.0. 0.333. 0.5. 1.0. Float pi . ((FloatArray new: 1) at: 1 put:
>> 1/3;
>> > > at:
>> > > > 1) } collect:
>> > > >     [:n| n asApproximateFractionToEpsilon: 1e-6]
>> > > > {0 . (333/1000) . (1/2) . 1 . (355/113) . (1/3)}
>> > > >
>> > > > Votes for or against changing asApproximateFraction to use
>> > > > asApproximateFractionToEpsilon:? (asApproximateFraction has no
>> senders
>> > > into
>> > > > base image)
>> > > >
>> > > > Suggestions for a selector that would use self
>> > > > asApproximateFractionToEpsilon: 1e-6 (less clumsy than e.g.
>> > > > asUsefulApproximateFraction).
>> > > >
>> > > > _,,,^..^,,,_
>> > > > best, Eliot
>> > >
>> > > >
>> > >
>> > >
>> > >
>> >
>> >
>> > --
>> > _,,,^..^,,,_
>> > best, Eliot
>>
>> >
>>
>>
>>
>
>