[Pkg] The Trunk: Kernel-nice.645.mcz
commits at source.squeak.org
commits at source.squeak.org
Sat Oct 29 09:43:50 UTC 2011
Nicolas Cellier uploaded a new version of Kernel to project The Trunk:
http://source.squeak.org/trunk/Kernel-nice.645.mcz
==================== Summary ====================
Name: Kernel-nice.645
Author: nice
Time: 29 October 2011, 11:42:54.825 am
UUID: 6c7fe149-d362-481d-803f-eecbec00619c
Ancestors: Kernel-ael.643
Yet another version of #nthRoot: from Cuis
1) Receivers too big for Float arithmetic but without exact answer, and a better float than infinity is possible.
2) Besides, a small performance tweak: don't call 'selfAsFloat nthRoot: aPositiveInteger' if the result will be infinity, i.e. if the receiver is infinity.
=============== Diff against Kernel-ael.643 ===============
Item was changed:
----- Method: Integer>>nthRoot: (in category 'mathematical functions') -----
nthRoot: aPositiveInteger
+ "Answer the nth root of the receiver.
+ See #nthRootAlt: for an alternative implementation."
- "Answer the nth root of the receiver."
+ | selfAsFloat floatResult guess delta higher lower raised |
- | selfAsFloat floatResult guess raised higher lower delta |
selfAsFloat := self asFloat.
- floatResult := selfAsFloat nthRoot: aPositiveInteger.
+ "If we can't do Float arithmetic because we are too big, then look for an exact answer in exact arithmetic"
+ selfAsFloat isInfinite ifTrue: [
- "If we can't do Float arithmetic, then look for an exact answer in exact arithmetic"
- floatResult isInfinite ifTrue: [
guess := self nthRootTruncated: aPositiveInteger.
+ (guess raisedToInteger: aPositiveInteger) = self
+ ifTrue: [ ^ guess ].
+ "Nothing else can be done. No exact answer means answer must be a Float.
+ Answer the best we have."
+ ^guess asFloat ].
- (guess raisedToInteger: aPositiveInteger) = self ifTrue: [^guess].
- ^floatResult ].
+ floatResult := selfAsFloat nthRoot: aPositiveInteger.
guess := floatResult rounded.
"If got an exact answer, answer it."
raised := guess raisedToInteger: aPositiveInteger.
raised = self
ifTrue: [ ^ guess ].
"In this case, maybe it failed because we are such a big integer that the Float
method gets inexact, even if we are a whole square number.
+ Note 1(jmv): This algorithm is faster than #nthRootTruncated: for big n (aPositiveInteger)
+ but fails if self asFloat isInfinite.
+ Note 2(jmv): The algorithms I found for computing the nthRoot would havily use
- Note (jmv): The algorithms I found for computing the nthRoot would havily use
very large fractions. I wrote this one, that doesn't create fractions."
selfAsFloat abs >= (Float maxExactInteger asFloat raisedToInteger: aPositiveInteger)
ifTrue: [
raised > self
ifTrue: [
higher := guess.
delta := floatResult predecessor - floatResult.
[
floatResult := floatResult + delta.
lower := floatResult rounded.
(lower raisedToInteger: aPositiveInteger) > self ] whileTrue: [
delta := delta * 2.
higher := lower ] ]
ifFalse: [
lower := guess.
delta := floatResult successor - floatResult.
[
floatResult := floatResult + delta.
higher := floatResult rounded.
(higher raisedToInteger: aPositiveInteger) < self ] whileTrue: [
delta := delta * 2.
lower := higher ]].
[ higher - lower > 1 ] whileTrue: [
guess := lower + higher // 2.
raised := guess raisedToInteger: aPositiveInteger.
raised = self
ifTrue: [
^ guess ].
raised > self
ifTrue: [ higher := guess ]
ifFalse: [ lower := guess ]]].
"We need an approximate result"
^floatResult!
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