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Moved 4 packages from PolyMath
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‎.project‎

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{
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'srcDirectory' : 'src'
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}

‎src/.properties‎

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{
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#format : #tonel
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}

‎src/Math-Core/ArrayedCollection.extension.st‎

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Extension { #name : #ArrayedCollection }
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{ #category : #'*Math-Core' }
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ArrayedCollection >> addWithVector: aVector [
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"Answers the sum of the receiver with aVector."
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| answer n |
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answer := self class new: self size.
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n := 0.
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self with: aVector do:
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[ :a :b |
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n := n + 1.
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answer at: n put: ( a + b).
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].
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^ answer
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]

‎src/Math-Core/Number.extension.st‎

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Extension { #name : #Number }
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{ #category : #'*Math-Core' }
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Number >> addWithRegularMatrix: aMatrix [
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"Adds itself to every row of the matrix"
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^ PMMatrix rows: (aMatrix rowsCollect: [ :row | row + self ])
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]
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{ #category : #'*Math-Core' }
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Number >> addWithVector: aVector [
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"Adds itself to each element of the vector"
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^ aVector collect: [ :each | each + self ]
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]

‎src/Math-Core/PMFloatingPointMachine.class.st‎

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"
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A `PMFloatingPointMachine` represents the numerical precision of this system.
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##Instance Variables
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- `defaultNumericalPrecision` The relative numerical precision that can be expected for a general numerical computation. One should consider to numbers a and b equal if the relative difference between them is less than the default machine precision,
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- `largestExponentArgument` Natural logarithm of largest number,
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- `largestNumber` The largest positive number that can be represented in the machine,
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- `machinePrecision` $r^{-(n+1)}$, with the largest n such that $(1 + r^{-n}) - 1$ != 0,
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- `negativeMachinePrecision` $r^{-(n+1)}$, with the largest n such that $(1 - r^{-n}) - 1$ != 0,
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- `radix` The radix of the floating point representation. This is often 2,
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- `smallNumber` A number that can be added to some value without noticeably changing the result of the computation,
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- `smallestNumber` The smallest positive number different from 0.
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This class is detailed in Object Oriented Implementation of Numerical Methods, Section 1.4.1 and 1.4.2.
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"
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Class {
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#name : #PMFloatingPointMachine,
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#superclass : #Object,
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#instVars : [
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'defaultNumericalPrecision',
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'radix',
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'machinePrecision',
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'negativeMachinePrecision',
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'smallestNumber',
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'largestNumber',
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'smallNumber',
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'largestExponentArgument'
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],
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#classVars : [
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'UniqueInstance'
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],
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#category : #'Math-Core'
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}
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{ #category : #'instance creation' }
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PMFloatingPointMachine class >> new [
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UniqueInstance ifNil: [ UniqueInstance := super new ].
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^ UniqueInstance
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]
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{ #category : #accessing }
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PMFloatingPointMachine class >> reset [
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UniqueInstance := nil
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]
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{ #category : #information }
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PMFloatingPointMachine >> computeLargestNumber [
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| one floatingRadix fullMantissaNumber |
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one := 1.0.
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floatingRadix := self radix asFloat.
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fullMantissaNumber := one - ( floatingRadix * self negativeMachinePrecision).
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largestNumber := fullMantissaNumber.
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[ [ fullMantissaNumber := fullMantissaNumber * floatingRadix.
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fullMantissaNumber isInfinite ifTrue: [^nil].
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largestNumber := fullMantissaNumber.
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true] whileTrue: [ ].
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] on: Error do: [ :signal | signal return: nil]
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]
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{ #category : #information }
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PMFloatingPointMachine >> computeMachinePrecision [
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| one zero inverseRadix tmp |
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one := 1.0.
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zero := 0.0.
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inverseRadix := one / self radix asFloat.
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machinePrecision := one.
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[ tmp := one + machinePrecision.
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tmp - one = zero]
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whileFalse:[ machinePrecision := machinePrecision * inverseRadix]
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]
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{ #category : #information }
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PMFloatingPointMachine >> computeNegativeMachinePrecision [
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| one zero floatingRadix inverseRadix tmp |
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one := 1.0.
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zero := 0.0.
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floatingRadix := self radix asFloat.
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inverseRadix := one / floatingRadix.
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negativeMachinePrecision := one.
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[ tmp := one - negativeMachinePrecision.
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tmp - one = zero]
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whileFalse:[ negativeMachinePrecision := negativeMachinePrecision * inverseRadix]
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]
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{ #category : #information }
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PMFloatingPointMachine >> computeRadix [
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| one zero a b tmp1 tmp2|
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one := 1.0.
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zero := 0.0.
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a := one.
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[ a := a + a.
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tmp1 := a + one.
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tmp2 := tmp1 - a.
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tmp2 - one = zero] whileTrue:[].
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b := one.
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[ b := b + b.
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tmp1 := a + b.
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radix := ( tmp1 - a) truncated.
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radix = 0 ] whileTrue: []
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]
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{ #category : #information }
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PMFloatingPointMachine >> computeSmallestNumber [
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| one floatingRadix inverseRadix fullMantissaNumber |
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one := 1 asFloat.
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floatingRadix := self radix asFloat.
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inverseRadix := one / floatingRadix.
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fullMantissaNumber := one - (floatingRadix * self negativeMachinePrecision).
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smallestNumber := fullMantissaNumber.
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[[fullMantissaNumber := fullMantissaNumber * inverseRadix.
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fullMantissaNumber = 0.0 ifTrue: [Error signal ].
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smallestNumber := fullMantissaNumber.
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true]
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whileTrue: []]
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on: Error do: [:signal | signal return: nil]
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]
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{ #category : #information }
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PMFloatingPointMachine >> defaultNumericalPrecision [
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defaultNumericalPrecision isNil
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ifTrue: [ defaultNumericalPrecision := self machinePrecision sqrt].
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^defaultNumericalPrecision
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]
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{ #category : #information }
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PMFloatingPointMachine >> largestExponentArgument [
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largestExponentArgument isNil
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ifTrue: [ largestExponentArgument := self largestNumber ln].
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^largestExponentArgument
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]
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{ #category : #information }
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PMFloatingPointMachine >> largestNumber [
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largestNumber isNil
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ifTrue: [ self computeLargestNumber].
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^largestNumber
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]
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{ #category : #information }
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PMFloatingPointMachine >> machinePrecision [
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machinePrecision isNil
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ifTrue: [ self computeMachinePrecision].
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^machinePrecision
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]
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{ #category : #information }
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PMFloatingPointMachine >> negativeMachinePrecision [
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negativeMachinePrecision isNil
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ifTrue: [ self computeNegativeMachinePrecision].
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^negativeMachinePrecision
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]
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{ #category : #information }
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PMFloatingPointMachine >> radix [
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radix isNil
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ifTrue: [ self computeRadix].
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^radix
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]
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{ #category : #display }
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PMFloatingPointMachine >> showParameters [
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Transcript cr; cr;
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nextPutAll: 'Floating-point machine parameters'; cr;
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nextPutAll: '---------------------------------';cr;
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nextPutAll: 'Radix: '.
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self radix printOn: Transcript.
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Transcript cr; nextPutAll: 'Machine precision: '.
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self machinePrecision printOn: Transcript.
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Transcript cr; nextPutAll: 'Negative machine precision: '.
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self negativeMachinePrecision printOn: Transcript.
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Transcript cr; nextPutAll: 'Smallest number: '.
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self smallestNumber printOn: Transcript.
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Transcript cr; nextPutAll: 'Largest number: '.
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self largestNumber printOn: Transcript.
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Transcript flush
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]
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{ #category : #information }
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PMFloatingPointMachine >> smallNumber [
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smallNumber isNil
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ifTrue: [ smallNumber := self smallestNumber sqrt].
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^smallNumber
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]
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{ #category : #information }
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PMFloatingPointMachine >> smallestNumber [
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smallestNumber isNil
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ifTrue: [ self computeSmallestNumber].
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^smallestNumber
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]

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