The Trunk: Kernel-nice.841.mcz

Nicolas Cellier uploaded a new version of Kernel to project The Trunk:
http://source.squeak.org/trunk/Kernel-nice.841.mcz

==================== Summary ====================

Name: Kernel-nice.841
Author: nice
Time: 13 March 2014, 2:58:18.732 am
UUID: e651c760-2924-469e-874b-deafb85737a0
Ancestors: Kernel-nice.840

Provide a somehow slower, but correct version of Integer>>#nthRoot: w.r.t. exactness

=============== Diff against Kernel-nice.840 ===============

Item was changed:
  ----- Method: Integer>>nthRoot: (in category 'mathematical functions') -----
  nthRoot: aPositiveInteger
  "Answer the nth root of the receiver.
+ Answer an Integer if root is exactly this Integer, else answer the Float nearest the exact root."
- See #nthRootAlt: for an alternative implementation."
 
+ | guess p |
- | selfAsFloat floatResult guess delta higher lower raised |
- selfAsFloat := self asFloat.
 
+ guess := self nthRootRounded: aPositiveInteger.
+ (guess raisedTo: aPositiveInteger) = self
- "If we can't do Float arithmetic because we are too big, then look for an exact answer in exact arithmetic"
- selfAsFloat 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 ].
-
- floatResult := selfAsFloat nthRoot: aPositiveInteger.
- guess := floatResult rounded.
-
- "If got an exact answer, answer it."
- raised := guess raisedToInteger: aPositiveInteger.
- raised = self
  ifTrue: [ ^ guess ].
 
+ p := Float precision - guess highBitOfMagnitude.
+ p < 0 ifTrue: [ ^ guess asFloat ].
- "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
- 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 ]]].
 
+ guess := self << (p * aPositiveInteger) nthRootRounded: aPositiveInteger.
+ ^(guess / (1 << p)) asFloat!
- "We need an approximate result"
- ^floatResult!

Item was added:
+ ----- Method: Integer>>nthRootRounded: (in category 'mathematical functions') -----
+ nthRootRounded: aPositiveInteger
+ "Answer the integer nearest the nth root of the receiver."
+ | guess |
+ self = 0 ifTrue: [^0].
+ self negative
+ ifTrue:
+ [aPositiveInteger even ifTrue: [ ArithmeticError signal: 'Negative numbers don''t have even roots.' ].
+ ^(self negated nthRootRounded: aPositiveInteger) negated].
+ guess := self nthRootTruncated: aPositiveInteger.
+ ^self * 2 > ((guess + 1 raisedTo: aPositiveInteger) + (guess raisedTo: aPositiveInteger))
+ ifTrue: [guess + 1]
+ ifFalse: [guess]!