Fwd: asApproximateFraction[AtOrder:]

> 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

> asApproximateFraction
> "Answer a Fraction approximating the receiver. This conversion uses the
> continued fraction method to approximate a floating point number."
>
> ^self asApproximateFractionToEpsilon: self abs / 1.0e6
>
> …Seems to work well:
>
>
> | them |
> them := (1 to: 6) collect: [:po10| (1 / ((10 raisedTo: po10) * 3))
> asFloat].
> them collect: [:fraction| fraction asApproximateFractionToEpsilon:
> fraction
> / 1.0e6] {(1/30) . (1/300) . (1/3000) . (1/30000) . (1/300000) .
> (1/3000000)}
>
> | them |
> them := (1 to: 6) collect: [:po10| (1 / ((10 raisedTo: po10) / 3))
> asFloat].
> them collect: [:fraction| fraction asApproximateFractionToEpsilon:
> fraction
> / 1.0e6]
>  {(3/10) . (3/100) . (3/1000) . (3/10000) . (3/100000) . (3/1000000)}
>
> Float classPool associations
> select: [:assoc| assoc value isFloat and: [assoc value isFinite and:
> [assoc
> value fractionPart ~= 0]]]
> thenCollect: [:assoc|
> assoc key -> (assoc value asApproximateFractionToEpsilon: assoc value /
> 1.0e6)] {#Ln2->(1143/1649) . #Halfpi->(355/226) . #ThreePi->(1065/113) .
> #RadiansPerDegree->(71/4068) . #Epsilon->(1/1000000000000) .
> #MaxValLn->(16325/23) . #Ln10->(624/271) . #Pi->(355/113) .
> #Sqrt2->(1393/985) . #Twopi->(710/113) . #E->(1264/465)}
>
>
> So I'm for
>
> asApproximateFraction
>        "Answer a Fraction approximating the receiver. This conversion uses
> the
>        continued fraction method to approximate a floating point number."
>
>        ^self asApproximateFractionToEpsilon: (self / 1e6) abs
>
> talking in numerical analysis ignorance...
>
> --
> _,,,^..^,,,_
> best, Eliot