I would just like to say that I really enjoy reading your math related
changes. I usually learn something new - but always get a enjoy the
opportunity to think about these things in a different light.

Thanks,
cbc

On Aug 13, 2017 3:03 PM, <commits at source.squeak.org> wrote:

> Nicolas Cellier uploaded a new version of Kernel to project The Trunk:
> http://source.squeak.org/trunk/Kernel-nice.1111.mcz
>
> ==================== Summary ====================
>
> Name: Kernel-nice.1111
> Author: nice
> Time: 14 August 2017, 12:02:46.695166 am
> UUID: 280f8152-036b-48e1-b3f3-038fa2611ea7
> Ancestors: Kernel-tpr.1110
>
> Avoid costly and useless LargeInteger arithmetics when evaluating:
> (2009/2000) raisedTo: (3958333/100000)
>
> These large integer operations were helping to find the nearest Float
> approximation to the #nthRoot: but
> 1) they do not scale when the radical increases,
> 2) we then spoil the accuracy by raising the root to an Integer power
> naively and inacurately.
>
> Instead, if the result is inexact, fall back to a ln/exp formulation which
> is a few ulp off but at least fast.
>
> =============== Diff against Kernel-tpr.1110 ===============
>
> Item was changed:
>   ----- Method: Fraction>>nthRoot: (in category 'mathematical functions')
> -----
>   nthRoot: aPositiveInteger
>         "Answer the nth root of the receiver."
>
> +       | guess |
> +       guess := (numerator nthRootTruncated: aPositiveInteger) /
> (denominator nthRootTruncated: aPositiveInteger).
> +       (guess raisedTo: aPositiveInteger) = self ifTrue: [^guess].
> +       "There is no exact nth root, so answer a Float approximation"
> +       ^(self abs ln / aPositiveInteger) exp * self sign!
> -       | d n |
> -       n := numerator nthRoot: aPositiveInteger.
> -       d := denominator nthRoot: aPositiveInteger.
> -       "The #sqrt method in integer will only answer a Float if there's
> no exact square root.
> -       So, we need a float anyway."
> -       (n isInfinite or: [ d isInfinite ]) ifTrue: [
> -               ^self asFloat nthRoot: aPositiveInteger ].
> -       ^n / d!
>
> Item was added:
> + ----- Method: Fraction>>raisedToFraction: (in category 'mathematical
> functions') -----
> + raisedToFraction: aFraction
> +       | root |
> +       root := (self numerator nthRootTruncated: aFraction denominator) /
> (self denominator nthRootTruncated: aFraction denominator).
> +       (root raisedToInteger: aFraction denominator) = self ifTrue:
> [^root raisedToInteger: aFraction numerator].
> +       ^super raisedToFraction: aFraction!
>
> Item was added:
> + ----- Method: Integer>>raisedToFraction: (in category 'mathematical
> functions') -----
> + raisedToFraction: aFraction
> +       | root |
> +       root := self nthRootTruncated: aFraction denominator.
> +       (root raisedToInteger: aFraction denominator) = self ifTrue:
> [^root raisedToInteger: aFraction numerator].
> +       ^super raisedToFraction: aFraction!
>
> Item was changed:
>   ----- Method: Number>>raisedTo: (in category 'mathematical functions')
> -----
>   raisedTo: aNumber
>         "Answer the receiver raised to aNumber."
>
>         aNumber isInteger ifTrue: [
>                 "Do the special case of integer power"
>                 ^ self raisedToInteger: aNumber].
>         aNumber isFraction ifTrue: [
>                 "Special case for fraction power"
> +               ^ self raisedToFraction: aNumber].
> -               ^ (self nthRoot: aNumber denominator) raisedToInteger:
> aNumber numerator ].
>         self negative ifTrue: [
>                 ^ ArithmeticError signal: 'Negative numbers can''t be
> raised to float powers.' ].
>         aNumber isZero ifTrue: [^ self class one].      "Special case of
> exponent=0"
>         1 = aNumber ifTrue: [^ self].   "Special case of exponent=1"
>         self isZero ifTrue: [                           "Special case of
> self = 0"
>                 aNumber negative
>                         ifTrue: [^ (ZeroDivide dividend: 1) signal]
>                         ifFalse: [^ self]].
>         ^ (aNumber * self ln) exp               "Otherwise use logarithms"!
>
> Item was added:
> + ----- Method: Number>>raisedToFraction: (in category 'mathematical
> functions') -----
> + raisedToFraction: aFraction
> +       self isZero
> +               ifTrue:
> +                       [aFraction negative ifTrue: [^ (ZeroDivide
> dividend: 1) signal].
> +                       ^self].
> +       self negative ifFalse: [^(self ln * aFraction) exp].
> +       aFraction denominator even
> +               ifTrue: [^ ArithmeticError signal: 'nth root only defined
> for positive Integer n.'].
> +       ^(self negated ln * aFraction) exp negated!
>
> Item was added:
> + ----- Method: ScaledDecimal>>raisedToFraction: (in category
> 'mathematical functions') -----
> + raisedToFraction: aFraction
> +       | result |
> +       result := self asFraction raisedToFraction: aFraction.
> +       ^result isFloat
> +               ifTrue: [result]
> +               ifFalse: [result asScaledDecimal: scale]!
>
>
>
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