[squeak-dev] The Inbox: Kernel-dtl.1166.mcz
Nicolas Cellier
nicolas.cellier.aka.nice at gmail.com
Thu Apr 26 07:53:07 UTC 2018
Also note that in base 2, we know the unit of least precision
So we could stop the loop when precision reaches half ulp, or
bitLimit := 1 - self ulp exponent.
[frac = 0 and: [denom1 highBit > bitLimit or: [...]] whileFalse: [...]
2018-04-26 9:45 GMT+02:00 Nicolas Cellier <
nicolas.cellier.aka.nice at gmail.com>:
> Here is the version that i use in VW (SYSBUG-FloatConversion in cincom
> public store)
>
> asApproximateFraction
> "Answer a Rational number--Integer or Fraction--representing the
> receiver.
> This conversion uses the continued fraction method to approximate
> a floating point number."
>
> | num1 denom1 num2 denom2 int frac newD temp limit |
> num1 := self asFraction. "use exact arithmetic"
> frac := num1 fractionPart. "The fractional part of self"
> int := num1 truncated. "The integer part of self"
> num1 := int. "The first of two alternating numerators"
> denom1 := 1. "The first of two alternating denominators"
> num2 := 1. "The second numerator"
> denom2 := 0. "The second denominator--will update"
> limit := self class precision + 7 // 8 + 1.
> [frac = 0 or: [denom1 digitLength > limit or: [(self coerce: (Fraction
> numerator: num1 denominator: denom1)) = self]]]
> whileFalse:
> ["repeat while the fractional part is not zero"
> newD := frac reciprocal. "Take reciprocal of the
> fractional part"
> int := newD truncated. "get the integer part of this"
> frac := newD fractionPart. "and save the fractional part
> for next time"
> temp := num2. "Get old numerator and save it"
> num2 := num1. "Set second numerator to first"
> num1 := num1 * int + temp. "Update first numerator"
> temp := denom2. "Get old denominator and save
> it"
> denom2 := denom1. "Set second denominator to first"
> denom1 := int * denom1 + temp. "Update first
> denominator"].
> "If fractional part is zero, return the first ratio"
> denom1 = 1
> ifTrue: ["Am i really an Integer?"
> ^num1"Yes, return Integer result"]
> ifFalse: ["Otherwise return Fraction result"
> ^Fraction numerator: num1 denominator: denom1]
>
> Note that I use self asFraction (asTrueFraction) and then perform all
> operations in Integer arithmetic.
> #digitLength is the number of bytes like in Squeak.
>
> For user-defined controlled precision like aimed by Eliot, we could use
> #decimalDigitLength and seed it by default with something like
> #decimalPrecision in Squeak.
> #decimalPrecision does not exist yet but could be (self class precision *
> 2 ln / 10 ln) rounded - or simply 15 or 16.
> Note that it's an absolute precision, not a relative precision which is
> used.
>
> Also note that we could rewrite the iteration like this:
> num1 := num2 + ((num2 := num1) * int).
> den1 := den2 + ((den2 := den1) * int).
>
> 2018-04-26 4:48 GMT+02:00 <commits at source.squeak.org>:
>
>> David T. Lewis uploaded a new version of Kernel to project The Inbox:
>> http://source.squeak.org/inbox/Kernel-dtl.1166.mcz
>>
>> ==================== Summary ====================
>>
>> Name: Kernel-dtl.1166
>> Author: dtl
>> Time: 25 April 2018, 10:48:38.572237 pm
>> UUID: 43d80609-fbc5-40a1-9d49-37d2c4f0b306
>> Ancestors: Kernel-dtl.1165
>>
>> In calculation of asApproximateFraction, the digit count for
>> floatPrecision should be
>> an integer, so do not convert it with asFlloat.
>>
>> Allows the following to be resolved without infinite loop on comparison
>> to Float infinity:
>> ((FloatArray new: 1) at: 1 put: 1 / 3; at: 1)
>> asApproximateFractionFloatPrecision: 10000
>>
>> =============== Diff against Kernel-dtl.1165 ===============
>>
>> Item was changed:
>> ----- Method: Float>>asApproximateFractionAtOrder:floatPrecision: (in
>> category 'converting') -----
>> asApproximateFractionAtOrder: maxOrder floatPrecision: decimalPlaces
>> "Answer a Fraction approximating the receiver. This conversion
>> uses the
>> continued fraction method to approximate a floating point number.
>> If maxOrder
>> is zero, use maximum order. Assume that I am a float with
>> decimalPlaces of
>> meaningful accuracy, regardless of the precision of my internal
>> representation."
>>
>> | num1 denom1 num2 denom2 int frac newD temp order floatPrecision
>> |
>> num1 := self asInteger. "The first of two alternating numerators"
>> denom1 := 1. "The first of two alternating
>> denominators"
>> num2 := 1. "The second numerator"
>> denom2 := 0. "The second denominator--will update"
>> int := num1. "The integer part of self"
>> frac := self fractionPart. "The fractional part of
>> self"
>> order := maxOrder = 0 ifTrue: [-1] ifFalse: [maxOrder].
>> + floatPrecision := 10 raisedTo: decimalPlaces.
>> - floatPrecision := (10 raisedTo: decimalPlaces) asFloat.
>> [frac = 0 or: [order = 0] ]
>> whileFalse:
>> ["repeat while the fractional part is not zero
>> and max order is not reached"
>> order := order - 1.
>> newD := 1.0 / frac. "Take
>> reciprocal of the fractional part"
>> int := newD asInteger. "get the integer
>> part of this"
>> frac := newD fractionPart. "and save the
>> fractional part for next time"
>> temp := num2. "Get old
>> numerator and save it"
>> num2 := num1. "Set
>> second numerator to first"
>> num1 := num1 * int + temp. "Update first
>> numerator"
>> temp := denom2. "Get old
>> denominator and save it"
>> denom2 := denom1. "Set
>> second denominator to first"
>> denom1 := int * denom1 + temp. "Update
>> first denominator"
>> floatPrecision < denom1
>> ifTrue:
>> ["Is ratio past float precision?
>> If so, pick which
>> of the two ratios to use"
>> num2 = 0.0
>> ifTrue: ["Is second
>> denominator 0?"
>> ^
>> Fraction numerator: num1 denominator: denom1].
>> ^ Fraction numerator: num2
>> denominator: denom2]].
>> "If fractional part is zero, return the first ratio"
>> denom1 = 1
>> ifTrue: ["Am I really an Integer?"
>> ^ num1 "Yes, return Integer result"]
>> ifFalse: ["Otherwise return Fraction result"
>> ^ Fraction numerator: num1 denominator:
>> denom1]!
>>
>>
>>
>
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