The Trunk: Kernel-cwp.844.mcz

Colin Putney uploaded a new version of Kernel to project The Trunk:
http://source.squeak.org/trunk/Kernel-cwp.844.mcz

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

Name: Kernel-cwp.844
Author: cwp
Time: 22 March 2014, 7:57:39.797 pm
UUID: f4f1b55b-db99-4fae-9a9b-3fcdcc0a6716
Ancestors: Kernel-cwp.840, Kernel-nice.843

merge

=============== Diff against Kernel-cwp.840 ===============

Item was changed:
  ----- Method: Float>>absPrintOn:base:digitCount: (in category 'printing') -----
  absPrintOn: aStream base: base digitCount: digitCount
  "Print me in the given base, using digitCount significant figures."
 
  | fuzz x exp q fBase scale logScale xi |
  self isInfinite ifTrue: [^ aStream nextPutAll: 'Inf'].
  fBase := base asFloat.
  "x is myself normalized to [1.0, fBase), exp is my exponent"
+ exp := self floorLog: fBase.
- exp :=
- self < 1.0
- ifTrue: [self reciprocalFloorLog: fBase]
- ifFalse: [self floorLog: fBase].
  scale := 1.0.
  logScale := 0.
  [(x := fBase raisedTo: (exp + logScale)) = 0]
  whileTrue:
  [scale := scale * fBase.
  logScale := logScale + 1].
  x := self * scale / x.
  fuzz := fBase raisedTo: 1 - digitCount.
  "round the last digit to be printed"
  x := 0.5 * fuzz + x.
  x >= fBase
  ifTrue:
  ["check if rounding has unnormalized x"
  x := x / fBase.
  exp := exp + 1].
  (exp < 6 and: [exp > -4])
  ifTrue:
  ["decimal notation"
  q := 0.
  exp < 0 ifTrue: [1 to: 1 - exp do: [:i | aStream nextPut: ('0.0000'
  at: i)]]]
  ifFalse:
  ["scientific notation"
  q := exp.
  exp := 0].
  [x >= fuzz]
  whileTrue:
  ["use fuzz to track significance"
  xi := x asInteger.
  aStream nextPut: (Character digitValue: xi).
  x := x - xi asFloat * fBase.
  fuzz := fuzz * fBase.
  exp := exp - 1.
  exp = -1 ifTrue: [aStream nextPut: $.]].
  [exp >= -1]
  whileTrue:
  [aStream nextPut: $0.
  exp := exp - 1.
  exp = -1 ifTrue: [aStream nextPut: $.]].
  q ~= 0
  ifTrue:
  [aStream nextPut: $e.
  q printOn: aStream]!

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]!

Item was removed:
- ----- Method: LargePositiveInteger>>sqrtFloor (in category 'mathematical functions') -----
- sqrtFloor
- "Return the integer part of the square root of self"
-
- | powerOfTwo |
- (powerOfTwo := self lowBit - 1 // 2) > 1
- ifFalse: [^super sqrtFloor].
- ^(self bitShift: -2 * powerOfTwo) sqrtFloor bitShift: powerOfTwo!

Item was changed:
  ----- Method: ScaledDecimal>>integerPart (in category 'truncation and round off') -----
  integerPart
+ "Answer the integer part of the receiver."
- "Answer the fractional part of the receiver."
  ^ ScaledDecimal newFromNumber: fraction integerPart scale: scale!