[squeak-dev] The Inbox: Kernel-dtl.1166.mcz
Nicolas Cellier
nicolas.cellier.aka.nice at gmail.com
Thu Apr 26 07:45:48 UTC 2018
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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