2011/10/29  <commits at source.squeak.org>:
> Nicolas Cellier uploaded a new version of Kernel to project The Trunk:
> http://source.squeak.org/trunk/Kernel-nice.646.mcz
>
> ==================== Summary ====================
>
> Name: Kernel-nice.646
> Author: nice
> Time: 29 October 2011, 3:25:43.994 pm
> UUID: cd46101c-40a4-49fd-b358-a8d0c555810f
> Ancestors: Kernel-nice.645
>
> There might be a best inexact square root approximation than Float infinity to some LargePositiveInteger in the range (1<<54-1<<970 to: 1<<54-1<<1994)
>

I mean a better approximation...
But it should effectively be the best.

> =============== Diff against Kernel-nice.645 ===============
>
> Item was changed:
>  ----- Method: Integer>>sqrt (in category 'mathematical functions') -----
>  sqrt
>        "Answer the square root of the receiver."
>
>        | selfAsFloat floatResult guess |
>        selfAsFloat := self asFloat.
>        floatResult := selfAsFloat sqrt.
>
>        floatResult isInfinite ifFalse: [
>                guess := floatResult truncated.
>
>                "If got an exact answer, answer it. Otherwise answer float approximate answer."
>                guess squared = self
>                        ifTrue: [ ^ guess ]].
>
>        "In this case, maybe it failed because we are such a big integer that the Float method becomes
>        inexact, even if we are a whole square number. So, try the slower but more general method"
>        selfAsFloat >= Float maxExactInteger asFloat squared
>                ifTrue: [
>                        guess := self sqrtFloor.
>                        guess squared = self ifTrue: [
> +                               ^guess ].
> +
> +                       "Nothing else can be done. No exact answer means answer must be a Float.
> +                       Answer the best we have which is the rounded sqrt."
> +                       guess := (self * 4) sqrtFloor.
> +                       ^(guess // 2 + (guess \\ 2)) asFloat].
> -                               ^guess ]].
>
>        "We need an approximate result"
>        ^floatResult!
>
> Item was changed:
>  ----- Method: LargePositiveInteger>>sqrt (in category 'mathematical functions') -----
>  sqrt
>        "If we know for sure no exact solution exists, then just answer the cheap float approximation without wasting time."
> +       | selfAsFloat |
> +       self mightBeASquare
> +               ifFalse:
> +                       [selfAsFloat := self asFloat.
> +                       selfAsFloat isFinite ifTrue: [^self asFloat sqrt ]].
> -       self mightBeASquare ifFalse: [
> -               ^self asFloat sqrt ].
>
> +       "If some exact solution might exist, or self asFloat isInfinite, call potentially expensive super"
> -       "If some exact solution might exist,  call potentially expensive super"
>        ^super sqrt!
>
>
>