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2443
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"{ Package: 'stx:goodies/regression' }"
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"{ NameSpace: RegressionTests }"
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TestCase subclass:#IEEEFloatTest
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instanceVariableNames:''
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classVariableNames:''
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poolDictionaries:''
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category:'tests-Regression-Numbers'
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!
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!IEEEFloatTest class methodsFor:'helpers'!
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actualPrecisionOf:aFloatClass
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"get the actual number of valid bits in the mantissa.
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This does a real test (i.e. does not believe the compiled-in ifdefs)"
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|one x count|
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one := aFloatClass unity. "/ 1.0 in this class
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x := one.
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count := 0.
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[one + x > one] whileTrue:[
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x := x / 2.
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count := count + 1.
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].
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^ count
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"
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self actualPrecisionOf:ShortFloat
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self actualPrecisionOf:Float
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self actualPrecisionOf:LongFloat
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"
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! !
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!IEEEFloatTest methodsFor:'tests'!
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test00_Precision
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"computed precision vs. assumed precision."
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"/ verify IEEE values
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2458
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self assert:((IEEEFloat fromFloat:1.0) radix == 2).
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2443
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self assert:((IEEEFloat fromFloat:1.0) emin == 1.0 emin).
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self assert:((IEEEFloat fromFloat:1.0) emax == 1.0 emax).
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self assert:((IEEEFloat fromFloat:1.0) eBias == 1.0 eBias).
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self assert:((IEEEFloat fromFloat:1.0 asShortFloat) emin == 1.0 asShortFloat emin).
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self assert:((IEEEFloat fromFloat:1.0 asShortFloat) emax == 1.0 asShortFloat emax).
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self assert:((IEEEFloat fromFloat:1.0 asShortFloat) eBias == 1.0 asShortFloat eBias).
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self assert:((IEEEFloat fromFloat:1.0 asLongFloat) emin == 1.0 asLongFloat emin).
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self assert:((IEEEFloat fromFloat:1.0 asLongFloat) emax == 1.0 asLongFloat emax).
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self assert:((IEEEFloat fromFloat:1.0 asLongFloat) eBias == 1.0 asLongFloat eBias).
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"
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self basicNew test00_Precision
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"
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!
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test01_Nan
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"NaN in all avaliable formats."
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|shouldBeNaN|
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shouldBeNaN := 0.0 asIEEEFloat uncheckedDivide: 0.0 asIEEEFloat.
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self assert:( shouldBeNaN isNaN ).
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self assert:( shouldBeNaN isFinite not ).
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"/ but these are:
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self assert:( shouldBeNaN + 1 ) isNaN.
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self assert:( shouldBeNaN + 1.0 ) isNaN.
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self assert:( shouldBeNaN + 1.0 asShortFloat ) isNaN.
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self assert:( shouldBeNaN + 1.0 asLongFloat ) isNaN.
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self assert:( shouldBeNaN - 1 ) isNaN.
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self assert:( shouldBeNaN - 1.0 ) isNaN.
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self assert:( shouldBeNaN - 1.0 asShortFloat ) isNaN.
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self assert:( shouldBeNaN - 1.0 asLongFloat ) isNaN.
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self assert:( shouldBeNaN * 1 ) isNaN.
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self assert:( shouldBeNaN * 1.0 ) isNaN.
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self assert:( shouldBeNaN * 1.0 asShortFloat ) isNaN.
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self assert:( shouldBeNaN * 1.0 asLongFloat ) isNaN.
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self assert:( shouldBeNaN * 2 ) isNaN.
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self assert:( shouldBeNaN * 2.0 ) isNaN.
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self assert:( shouldBeNaN * 2.0 asShortFloat ) isNaN.
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self assert:( shouldBeNaN * 2.0 asLongFloat ) isNaN.
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self assert:( shouldBeNaN / 1 ) isNaN.
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self assert:( shouldBeNaN / 1.0 ) isNaN.
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self assert:( shouldBeNaN / 1.0 asShortFloat ) isNaN.
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self assert:( shouldBeNaN / 1.0 asLongFloat ) isNaN.
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"
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self basicNew test01_Nan
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"
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"Modified: / 20-06-2017 / 14:00:08 / cg"
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!
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test02_Inf
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"Infinity in all avaliable formats."
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|check posInf negInf|
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check :=
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[:v1 :v2 |
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posInf := v1 uncheckedDivide: v2.
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self assert:( posInf isMemberOf:v1 class ).
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self assert:( posInf isNaN not ).
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self assert:( posInf isFinite not ).
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self assert:( posInf isInfinite ).
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self assert:( posInf positive ).
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self assert:( posInf negative not ).
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self assert:( posInf isNegativeInfinity not).
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self assert:( posInf isPositiveInfinity ).
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negInf := v1 negated uncheckedDivide: v2.
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self assert:( negInf isMemberOf:v1 class ).
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self assert:( negInf isNaN not ).
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self assert:( negInf isFinite not ).
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self assert:( negInf isInfinite ).
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self assert:( negInf positive not).
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self assert:( negInf negative ).
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self assert:( negInf isNegativeInfinity ).
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self assert:( negInf isPositiveInfinity not ).
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self assert:( negInf + negInf = negInf).
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self assert:( posInf + posInf = posInf).
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self assert:( negInf + posInf) isNaN.
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self assert:( posInf + negInf) isNaN.
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self assert:( negInf - posInf = negInf).
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self assert:( negInf - negInf) isNaN.
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self assert:( posInf - negInf = posInf).
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self assert:( posInf - posInf) isNaN.
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self assert:( posInf + v1) = posInf.
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self assert:( posInf - v1) = posInf.
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self assert:( negInf + v1) = negInf.
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self assert:( negInf - v1) = negInf.
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].
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check value: 1.0 value: 0.0.
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check value: 1.0 asShortFloat value: 0.0 asShortFloat.
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check value: 1.0 asLongFloat value: 0.0 asLongFloat.
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"/ these are not guaranteed to work with uncheckedDivide...
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"/ check value: 1.0 value: 0.0 asShortFloat.
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"/ check value: 1.0 value: 0.0 asLongFloat.
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"/
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"/ check value: 1.0 asShortFloat value: 0.0.
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"/ check value: 1.0 asShortFloat value: 0.0 asLongFloat.
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"/
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"/ check value: 1.0 asLongFloat value: 0.0 asShortFloat.
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"/ check value: 1.0 asLongFloat value: 0.0.
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{ Float . ShortFloat . LongFloat }
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do:[:cls |
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posInf := cls infinity.
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self assert:( posInf isInfinite ).
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self assert:( posInf isFinite not ).
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self assert:( posInf > 0 ).
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self assert:( posInf >= 0 ).
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self assert:( posInf < 0 ) not.
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self assert:( posInf <= 0 ) not.
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negInf := cls negativeInfinity.
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self assert:( negInf isInfinite ).
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self assert:( negInf isFinite not ).
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self assert:( negInf < 0 ).
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self assert:( negInf <= 0 ).
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self assert:( negInf > 0 ) not.
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self assert:( negInf >= 0 ) not.
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self assert:(posInf isNaN not).
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self assert:(posInf isFinite not).
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self assert:(posInf isInfinite).
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self assert:(negInf isNaN not).
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self assert:(negInf isFinite not).
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self assert:(negInf isInfinite).
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self assert:(posInf negated = negInf).
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self assert:(negInf negated = posInf).
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].
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"
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self basicNew test02_Inf
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"
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"Modified: / 20-06-2017 / 14:03:08 / cg"
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"Modified: / 10-06-2019 / 23:45:05 / Claus Gittinger"
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!
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test03_Conversion
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self assert:( 1.0 asTrueFraction == 1 ).
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self assert:( 2.0 asTrueFraction == 2 ).
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self assert:( 4.0 asTrueFraction == 4 ).
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self assert:( 8.0 asTrueFraction == 8 ).
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self assert:( 16.0 asTrueFraction == 16 ).
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self assert:( 1048576.0 asTrueFraction == 1048576 ).
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self assert:( 0.5 asTrueFraction = (1/2) ).
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self assert:( 0.25 asTrueFraction = (1/4) ).
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self assert:( 0.125 asTrueFraction = (1/8) ).
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self assert:( 1.0 asShortFloat asTrueFraction == 1 ).
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self assert:( 2.0 asShortFloat asTrueFraction == 2 ).
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self assert:( 4.0 asShortFloat asTrueFraction == 4 ).
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self assert:( 8.0 asShortFloat asTrueFraction == 8 ).
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self assert:( 16.0 asShortFloat asTrueFraction == 16 ).
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self assert:( 1048576.0 asShortFloat asTrueFraction == 1048576 ).
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self assert:( 0.5 asShortFloat asTrueFraction = (1/2) ).
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self assert:( 0.25 asShortFloat asTrueFraction = (1/4) ).
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self assert:( 0.125 asShortFloat asTrueFraction = (1/8) ).
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self assert:( 1.0 asLongFloat asTrueFraction == 1 ).
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self assert:( 2.0 asLongFloat asTrueFraction == 2 ).
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self assert:( 4.0 asLongFloat asTrueFraction == 4 ).
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self assert:( 8.0 asLongFloat asTrueFraction == 8 ).
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self assert:( 16.0 asLongFloat asTrueFraction == 16 ).
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self assert:( 1048576.0 asLongFloat asTrueFraction == 1048576 ).
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self assert:( 0.5 asLongFloat asTrueFraction = (1/2) ).
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self assert:( 0.25 asLongFloat asTrueFraction = (1/4) ).
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self assert:( 0.125 asLongFloat asTrueFraction = (1/8) ).
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self assert: ((5/9) asFloat - 0.555555555555) abs < 0.0000000001.
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self assert: ((5/9) asLongFloat - 0.555555555555) abs < 0.0000000001.
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self assert: ((Fraction basicNew setNumerator:500000000000 denominator:900000000000)
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asLongFloat - 0.555555555555) abs < 0.000000000001.
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self assert: ((Fraction basicNew setNumerator:500000000001 denominator:900000000000)
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asLongFloat - 0.555555555555) abs >= 0.000000000001.
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"/ under windows, a longFloat has only 10bytes with 64 bits precision
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OperatingSystem isMSWINDOWSlike ifFalse:[
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self assert: (8901234567890123456 asLongFloat asInteger = 8901234567890123456).
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self assert: (-8901234567890123456 asLongFloat asInteger = -8901234567890123456).
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].
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self assert: (89012345678901234567 asLongFloat = 89012345678901234567).
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self assert: (-89012345678901234567 asLongFloat = -89012345678901234567).
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self assert: (89012345678901234567 negated asLongFloat = -89012345678901234567).
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self assert: ((89012345678901234567 / 123456789123456789) asLongFloat - (89012345678901234567 asLongFloat / 123456789123456789 asLongFloat) ) abs < 0.000000000001.
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self assert: ((-89012345678901234567 / 123456789123456789) asLongFloat - (-89012345678901234567 asLongFloat / 123456789123456789 asLongFloat)) abs < 0.000000000001.
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"
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self basicNew test03_Conversion
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"
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"Modified: / 09-08-2011 / 21:01:57 / cg"
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!
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test04_Arithmetic
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self assert:( 1.0 asIEEEFloat + 1.0) class == IEEEFloat.
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self assert:( 1.0 asIEEEFloat + 1.0 asIEEEFloat) class == IEEEFloat.
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self assert:( 1.0 asIEEEFloat + 1.0 asShortFloat) class == IEEEFloat.
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self assert:( 1.0 asIEEEFloat + 1.0 asLongFloat) class == IEEEFloat.
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2448
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"/ self assert:( 1.0 asIEEEFloat + 1) class == IEEEFloat.
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2443
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self assert:( 1.0 asIEEEFloat - 1.0 ) isZero. "/ class == IEEEFloat.
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self assert:( 1.0 asIEEEFloat - 1.0 asIEEEFloat) isZero. "/ class == IEEEFloat.
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self assert:( 1.0 asIEEEFloat - 1.0 asShortFloat) isZero. "/ class == IEEEFloat.
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self assert:( 1.0 asIEEEFloat - 1.0 asLongFloat) isZero. "/ class == IEEEFloat.
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"/ self assert:( 1.0 asIEEEFloat - 1) class == IEEEFloat.
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self assert:( 1.0 asIEEEFloat * 1.0 ) class == IEEEFloat.
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self assert:( 1.0 asIEEEFloat * 1.0 asIEEEFloat) class == IEEEFloat.
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self assert:( 1.0 asIEEEFloat * 1.0 asShortFloat) class == IEEEFloat.
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self assert:( 1.0 asIEEEFloat * 1.0 asLongFloat) class == IEEEFloat.
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2448
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"/ self assert:( 1.0 asIEEEFloat * 1) class == IEEEFloat.
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2443
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self assert:( 1.0 asIEEEFloat / 1.0 ) class == IEEEFloat.
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self assert:( 1.0 asIEEEFloat / 1.0 asIEEEFloat) class == IEEEFloat.
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self assert:( 1.0 asIEEEFloat / 1.0 asShortFloat) class == IEEEFloat.
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self assert:( 1.0 asIEEEFloat / 1.0 asLongFloat) class == IEEEFloat.
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2448
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"/ self assert:( 1.0 asIEEEFloat / 1) class == IEEEFloat.
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2443
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2451
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"/ self assert:( 5.0 asIEEEFloat rem: 2.0 ) class == IEEEFloat.
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"/ self assert:( 1.0 asIEEEFloat rem: 2.0 asIEEEFloat) class == IEEEFloat.
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"/ self assert:( 5.0 asIEEEFloat rem: 2.0 asShortFloat) class == IEEEFloat.
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"/ self assert:( 5.0 asIEEEFloat rem: 2.0 asLongFloat) class == IEEEFloat.
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"/ "/ self assert:( 5.0 asIEEEFloat rem: 2) class == IEEEFloat.
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2443
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"
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self basicNew test04_Arithmetic
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"
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!
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test05_Comparing
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|convArray check v1 v2 v1b|
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self assert:( 0.0 = -0.0).
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self assert:( 0.0 asIEEEFloat = -0.0 asIEEEFloat).
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self assert:( 0.0 asIEEEFloat = 0.0).
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self assert:( 0.0 asIEEEFloat = -0.0).
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self assert:( -0.0 asIEEEFloat = 0.0).
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self assert:( -0.0 asIEEEFloat = -0.0).
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self assert:( 1.0 asIEEEFloat = 1.0).
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self assert:( 1.0 asIEEEFloat = 1.0 asIEEEFloat).
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self assert:( 1.0 asIEEEFloat = 1.0 asShortFloat).
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"/ fails currently
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"/ self assert:( 1.0 asIEEEFloat = 1.0 asLongFloat).
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2443
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convArray := OrderedCollection new.
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2451
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convArray addAll:#(asInteger asFloat asShortFloat asLongFloat).
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2443
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(Smalltalk at:#LargeFloat) notNil ifTrue:[
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convArray add:#asLargeFloat.
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319 |
].
|
|
|
320 |
(Smalltalk at:#QDouble) notNil ifTrue:[
|
|
|
321 |
convArray add:#asQDouble.
|
|
|
322 |
].
|
|
|
323 |
|
|
|
324 |
check := [:iv1 :iv2|
|
|
|
325 |
convArray do:[:conv1 |
|
|
|
326 |
v1 := (iv1 perform:conv1).
|
|
|
327 |
|
|
|
328 |
self assert:( v1 = nil ) not.
|
|
|
329 |
self assert:( nil = v1 ) not.
|
|
|
330 |
self assert:( v1 ~= nil ).
|
|
|
331 |
self assert:( nil ~= v1 ).
|
|
|
332 |
|
|
|
333 |
convArray do:[:conv2 |
|
|
|
334 |
v1b := (iv1 perform:conv2).
|
|
|
335 |
|
|
|
336 |
self assert:( v1 = v1b ).
|
|
|
337 |
self assert:( v1 <= v1b ).
|
|
|
338 |
self assert:( v1 >= v1b ).
|
|
|
339 |
|
|
|
340 |
v2 := (iv2 perform:conv2).
|
|
|
341 |
|
|
|
342 |
self assert:( v1 < v2 ).
|
|
|
343 |
self assert:( v1 <= v2 ).
|
|
|
344 |
self assert:( v2 >= v1 ).
|
|
|
345 |
self assert:( v2 > v1 ).
|
|
|
346 |
]
|
|
|
347 |
].
|
|
|
348 |
].
|
|
|
349 |
|
|
2451
|
350 |
check value:2.0 asIEEEFloat value:3.
|
|
|
351 |
check value:0.0 asIEEEFloat value:1.
|
|
|
352 |
check value:-1.0 asIEEEFloat value:0.
|
|
|
353 |
check value:-3.0 asIEEEFloat value:-2.
|
|
|
354 |
check value:-3.0 asIEEEFloat value:3.
|
|
2443
|
355 |
|
|
2451
|
356 |
check value:-30.0 asIEEEFloat value:1.
|
|
|
357 |
check value:-1.0 asIEEEFloat value:30.
|
|
2443
|
358 |
|
|
2451
|
359 |
|
|
2459
|
360 |
self assert:( 2000000.0 asIEEEFloat = 2000000.0 ).
|
|
|
361 |
self assert:( (IEEEFloat fromInteger:2000000) = 2000000.0 asIEEEFloat ).
|
|
2451
|
362 |
self assert:( 2000000.0 asIEEEFloat = 2000000 ).
|
|
|
363 |
self assert:( 2000000 = 2000000.0 asIEEEFloat ).
|
|
2443
|
364 |
|
|
2451
|
365 |
self assert:( 2000000.0 asIEEEFloat <= 200000100000000000000 ).
|
|
|
366 |
self assert:( 2000000.0 asIEEEFloat <= 2000000 ).
|
|
2443
|
367 |
|
|
2451
|
368 |
self assert:( 2000000 <= 2000000.0 asIEEEFloat ).
|
|
|
369 |
self assert:( 2000000 <= 2000000.0 asIEEEFloat ).
|
|
2443
|
370 |
|
|
|
371 |
"
|
|
|
372 |
self basicNew test05_Comparing
|
|
|
373 |
"
|
|
|
374 |
|
|
|
375 |
"Modified: / 06-05-2019 / 14:11:42 / Claus Gittinger"
|
|
|
376 |
!
|
|
|
377 |
|
|
|
378 |
test06_MiscMath
|
|
|
379 |
|epsilon|
|
|
|
380 |
|
|
|
381 |
epsilon := 0.000001.
|
|
|
382 |
|
|
|
383 |
#(
|
|
|
384 |
sqrt 0.5 0.707107
|
|
|
385 |
sqrt 4 2.0
|
|
|
386 |
exp 0.5 1.64872
|
|
|
387 |
ln 0.5 -0.693147
|
|
|
388 |
log10 0.5 -0.30103
|
|
|
389 |
|
|
|
390 |
sin 0.5 0.479426
|
|
|
391 |
cos 0.5 0.877583
|
|
|
392 |
tan 0.5 0.546302
|
|
|
393 |
arcSin 0.5 0.523599
|
|
|
394 |
arcCos 0.5 1.0472
|
|
|
395 |
arcTan 0.5 0.463648
|
|
|
396 |
sinh 0.5 0.521095
|
|
|
397 |
cosh 0.5 1.12763
|
|
|
398 |
tanh 0.5 0.462117
|
|
|
399 |
arcSinh 0.5 0.481212
|
|
|
400 |
arcCosh 1.5 1.24983
|
|
|
401 |
arcTanh 0.5 0.549306
|
|
|
402 |
|
|
|
403 |
sin 0.0 0.0
|
|
|
404 |
cos 0.0 1.0
|
|
|
405 |
tan 0.0 0.0
|
|
|
406 |
sinh 0.0 0.0
|
|
|
407 |
cosh 0.0 1.0
|
|
|
408 |
tanh 0.0 0.0
|
|
|
409 |
|
|
|
410 |
sin 1.0 0.841471
|
|
|
411 |
cos 1.0 0.540302
|
|
|
412 |
tan 1.0 1.55741
|
|
|
413 |
sinh 1.0 1.1752
|
|
|
414 |
cosh 1.0 1.54308
|
|
|
415 |
tanh 1.0 0.761594
|
|
|
416 |
|
|
|
417 |
sin 3.14159 0.0
|
|
|
418 |
cos 3.14159 -1.0
|
|
|
419 |
tan 3.14159 0.0
|
|
|
420 |
sinh 3.14159 11.5487
|
|
|
421 |
cosh 3.14159 11.5919
|
|
|
422 |
tanh 3.14159 0.996272
|
|
|
423 |
|
|
|
424 |
|
|
|
425 |
tan 0.785398 1.0 "pi/4 -> should be 1"
|
|
|
426 |
arcCos -1.0 3.14159 "should be pi"
|
|
|
427 |
arcSin 1.0 1.5708 "should be pi/2 (1.5708)"
|
|
|
428 |
arcTan 1.0 0.785398 "should be pi/4 (.785398)"
|
|
|
429 |
) inGroupsOf:3 do:[:op :x :expected|
|
|
|
430 |
|rslt rsltShortFloat rsltLongFloat rsltLargeFloat rsltQDouble|
|
|
|
431 |
|
|
|
432 |
rslt := x perform:op.
|
|
|
433 |
rsltShortFloat := x asShortFloat perform:op.
|
|
|
434 |
rsltLongFloat := x asLongFloat perform:op.
|
|
|
435 |
"/ rsltLargeFloat := arg asLargeFloat perform:op.
|
|
|
436 |
"/ rsltQDouble := x asQDouble perform:op.
|
|
|
437 |
|
|
|
438 |
self assert:(rslt class == Float).
|
|
|
439 |
"/ self assert:(rsltShortFloat class == Float). "/ ??? not a good test; some return a float
|
|
|
440 |
self assert:(rsltLongFloat class == LongFloat).
|
|
|
441 |
"/ self assert:(rsltQDouble class == QDouble).
|
|
|
442 |
|
|
|
443 |
self assert:( rslt - rsltShortFloat ) < epsilon.
|
|
|
444 |
self assert:( rslt - rsltLongFloat ) < epsilon.
|
|
|
445 |
"/ self assert:( rslt - rsltQDouble ) < epsilon.
|
|
|
446 |
"/ self assert:( rslt - rsltLargeFloat ) < epsilon.
|
|
|
447 |
self assert:( rslt - rslt asShortFloat ) < epsilon.
|
|
|
448 |
self assert:( rslt - rslt asLongFloat ) < epsilon.
|
|
|
449 |
"/ self assert:( rslt - rsltQDouble asFloat) < epsilon.
|
|
|
450 |
"/ self assert:( rslt - rslt asLargeFloat ) < epsilon.
|
|
|
451 |
].
|
|
|
452 |
|
|
|
453 |
self should:[ -2 arcSin ] raise:DomainError.
|
|
|
454 |
self should:[ -2 arcCos ] raise:DomainError.
|
|
|
455 |
self should:[ -1 arcTanh ] raise:DomainError.
|
|
|
456 |
|
|
|
457 |
#(
|
|
|
458 |
0.0
|
|
|
459 |
0.5
|
|
|
460 |
1.0
|
|
|
461 |
2.0
|
|
|
462 |
1.57079
|
|
|
463 |
) do:[:x |
|
|
|
464 |
self assert:( x sin arcSin - x < epsilon).
|
|
|
465 |
self assert:( x cos arcCos - x < epsilon).
|
|
|
466 |
self assert:( x tan arcTan - x < epsilon).
|
|
|
467 |
].
|
|
|
468 |
|
|
|
469 |
#(
|
|
|
470 |
-1.0
|
|
|
471 |
-0.5
|
|
|
472 |
0.0
|
|
|
473 |
0.5
|
|
|
474 |
1.0
|
|
|
475 |
) do:[:x |
|
|
|
476 |
self assert:( x arcSin sin - x < epsilon).
|
|
|
477 |
self assert:( x arcCos cos - x < epsilon).
|
|
|
478 |
self assert:( x arcTan tan - x < epsilon).
|
|
|
479 |
].
|
|
|
480 |
|
|
|
481 |
#(
|
|
|
482 |
0.0
|
|
|
483 |
0.5
|
|
|
484 |
1.0
|
|
|
485 |
2.0
|
|
|
486 |
10
|
|
|
487 |
) do:[:x |
|
|
|
488 |
self assert:( x cosh arcCosh - x < epsilon).
|
|
|
489 |
].
|
|
|
490 |
#(
|
|
|
491 |
-10
|
|
|
492 |
-2
|
|
|
493 |
-1
|
|
|
494 |
-0.5
|
|
|
495 |
0.0
|
|
|
496 |
0.5
|
|
|
497 |
1.0
|
|
|
498 |
2.0
|
|
|
499 |
10
|
|
|
500 |
) do:[:x |
|
|
|
501 |
self assert:( x sinh arcSinh - x < epsilon).
|
|
|
502 |
self assert:( x tanh arcTanh - x < epsilon).
|
|
|
503 |
].
|
|
|
504 |
|
|
|
505 |
|
|
|
506 |
#(
|
|
|
507 |
-0.99
|
|
|
508 |
-0.5
|
|
|
509 |
0.0
|
|
|
510 |
0.5
|
|
|
511 |
0.99
|
|
|
512 |
) do:[:x |
|
|
|
513 |
self assert:( x arcTanh - (( ( (1+x)/(1-x) ) ln ) / 2 ) ) < epsilon.
|
|
|
514 |
].
|
|
|
515 |
|
|
|
516 |
#(
|
|
|
517 |
-10
|
|
|
518 |
-5
|
|
|
519 |
-2.0
|
|
|
520 |
-1.0
|
|
|
521 |
0.0
|
|
|
522 |
1.0
|
|
|
523 |
2.0
|
|
|
524 |
10
|
|
|
525 |
) do:[:x |
|
|
|
526 |
self assert:( x arcSinh sinh - x < epsilon).
|
|
|
527 |
].
|
|
|
528 |
|
|
|
529 |
#(
|
|
|
530 |
1.0
|
|
|
531 |
2.0
|
|
|
532 |
10.0
|
|
|
533 |
) do:[:x |
|
|
|
534 |
self assert:( x arcCosh cosh - x < epsilon).
|
|
|
535 |
].
|
|
|
536 |
|
|
|
537 |
self assert:(2.0 raisedTo:2) = 4.0.
|
|
|
538 |
self assert:(2 raisedTo:2.0) = 4.0.
|
|
|
539 |
self assert:(2.0 raisedTo:2.0) = 4.0.
|
|
|
540 |
|
|
|
541 |
"
|
|
|
542 |
self basicNew test06_MiscMath
|
|
|
543 |
"
|
|
|
544 |
|
|
|
545 |
"Modified: / 02-07-2017 / 00:51:05 / cg"
|
|
|
546 |
!
|
|
|
547 |
|
|
|
548 |
test07_Truncation
|
|
2462
|
549 |
|t check|
|
|
|
550 |
|
|
|
551 |
t := 0.0 asIEEEFloat coerce:0.
|
|
|
552 |
self assert:(t isZero).
|
|
|
553 |
self assert:(t = 0.0 asIEEEFloat).
|
|
|
554 |
self assert:(t = 0.0).
|
|
|
555 |
|
|
2443
|
556 |
|
|
|
557 |
check := [:num |
|
|
2459
|
558 |
|nIEEE|
|
|
|
559 |
|
|
|
560 |
nIEEE := num asIEEEFloat.
|
|
|
561 |
self assert:( nIEEE fractionPart ) = num fractionPart asIEEEFloat.
|
|
|
562 |
nIEEE truncatedAsFloat.
|
|
|
563 |
self assert:( nIEEE truncatedAsFloat ) = num truncatedAsFloat asIEEEFloat.
|
|
|
564 |
self assert:( nIEEE truncated ) = num truncated.
|
|
|
565 |
self assert:( nIEEE fractionPart + nIEEE truncated ) = nIEEE.
|
|
|
566 |
self assert:( nIEEE fractionPart + nIEEE truncated ) class == nIEEE class.
|
|
|
567 |
self assert:( nIEEE fractionPart ) = num fractionPart.
|
|
|
568 |
self assert:( nIEEE truncated ) = num truncated.
|
|
2443
|
569 |
].
|
|
|
570 |
|
|
2459
|
571 |
check value:0.0 .
|
|
|
572 |
check value:0.6 .
|
|
|
573 |
check value:-0.6 .
|
|
|
574 |
check value:1.6 .
|
|
|
575 |
check value:-1.6 .
|
|
|
576 |
check value:1e20 .
|
|
|
577 |
check value:-1e20 .
|
|
|
578 |
check value:1e-20 .
|
|
|
579 |
check value:-1e-20 .
|
|
2443
|
580 |
|
|
2458
|
581 |
self assert:( 1.6 asIEEEFloat ceiling ) = 2.
|
|
|
582 |
self assert:( 1.6 asIEEEFloat ceilingAsFloat ) = 2.0.
|
|
2443
|
583 |
|
|
2458
|
584 |
self assert:( 1.6 asIEEEFloat floor ) = 1.
|
|
|
585 |
self assert:( 1.6 asIEEEFloat floorAsFloat ) = 1.0.
|
|
2443
|
586 |
|
|
2458
|
587 |
self assert:( -1.6 asIEEEFloat floor ) = -2.
|
|
|
588 |
self assert:( -1.6 asIEEEFloat floorAsFloat ) = -2.0.
|
|
2443
|
589 |
|
|
2458
|
590 |
self assert:( 0.4 asIEEEFloat rounded ) class == SmallInteger.
|
|
|
591 |
self assert:( 0.4 asIEEEFloat rounded = 0 ).
|
|
|
592 |
self assert:( 0.5 asIEEEFloat rounded = 1 ).
|
|
|
593 |
self assert:( 0.6 asIEEEFloat rounded = 1 ).
|
|
|
594 |
self assert:( -0.4 asIEEEFloat rounded = 0 ).
|
|
|
595 |
self assert:( -0.5 asIEEEFloat rounded = -1 ).
|
|
|
596 |
self assert:( -0.6 asIEEEFloat rounded = -1 ).
|
|
2443
|
597 |
|
|
2458
|
598 |
self assert:( 0.4 asIEEEFloat roundedAsFloat ) class == Float.
|
|
|
599 |
self assert:( 0.4 asIEEEFloat roundedAsFloat = 0.0 ).
|
|
|
600 |
self assert:( 0.5 asIEEEFloat roundedAsFloat = 1.0 ).
|
|
|
601 |
self assert:( 0.6 asIEEEFloat roundedAsFloat = 1.0 ).
|
|
|
602 |
self assert:( -0.4 asIEEEFloat roundedAsFloat = 0 ).
|
|
|
603 |
self assert:( -0.5 asIEEEFloat roundedAsFloat = -1.0 ).
|
|
|
604 |
self assert:( -0.6 asIEEEFloat roundedAsFloat = -1.0 ).
|
|
2443
|
605 |
|
|
2458
|
606 |
self assert:( 0.4 asIEEEFloat truncated ) class == SmallInteger.
|
|
|
607 |
self assert:( 0.4 asIEEEFloat truncated = 0 ).
|
|
|
608 |
self assert:( 0.5 asIEEEFloat truncated = 0 ).
|
|
|
609 |
self assert:( 0.6 asIEEEFloat truncated = 0 ).
|
|
|
610 |
self assert:( -0.4 asIEEEFloat truncated = 0 ).
|
|
|
611 |
self assert:( -0.5 asIEEEFloat truncated = 0 ).
|
|
|
612 |
self assert:( -0.6 asIEEEFloat truncated = 0 ).
|
|
2443
|
613 |
|
|
2458
|
614 |
self assert:( 0.4 asIEEEFloat truncatedAsFloat ) class == Float.
|
|
|
615 |
self assert:( 0.4 asIEEEFloat truncatedAsFloat = 0.0 ).
|
|
|
616 |
self assert:( 0.5 asIEEEFloat truncatedAsFloat = 0.0 ).
|
|
|
617 |
self assert:( 0.6 asIEEEFloat truncatedAsFloat = 0.0 ).
|
|
|
618 |
self assert:( -0.4 asIEEEFloat truncatedAsFloat = 0 ).
|
|
|
619 |
self assert:( -0.5 asIEEEFloat truncatedAsFloat = 0.0 ).
|
|
|
620 |
self assert:( -0.6 asIEEEFloat truncatedAsFloat = 0.0 ).
|
|
2443
|
621 |
|
|
|
622 |
"
|
|
|
623 |
self basicNew test07_Truncation
|
|
|
624 |
"
|
|
|
625 |
!
|
|
|
626 |
|
|
|
627 |
test08_Representation
|
|
|
628 |
|noQuadFloats noOctaFloats|
|
|
|
629 |
|
|
|
630 |
noQuadFloats := UnimplementedFunctionalityError catch:[1.0 asQuadFloat].
|
|
|
631 |
noOctaFloats := UnimplementedFunctionalityError catch:[1.0 asOctaFloat].
|
|
|
632 |
|
|
2451
|
633 |
self assert:( 1.0 asShortFloat exponentBits = 1.0 asShortFloat asIEEEFloat exponentBits).
|
|
|
634 |
self assert:( 1.0 exponentBits = 1.0 asIEEEFloat exponentBits ).
|
|
2443
|
635 |
|
|
2451
|
636 |
self assert:( 0.0 exponent = 0.0 asIEEEFloat exponent ).
|
|
|
637 |
self assert:( 1.0 exponent = 1.0 asIEEEFloat exponent ).
|
|
|
638 |
self assert:( 2.0 exponent = 2.0 asIEEEFloat exponent ).
|
|
|
639 |
self assert:( 3.0 exponent = 3.0 asIEEEFloat exponent ).
|
|
|
640 |
self assert:( 4.0 exponent = 4.0 asIEEEFloat exponent ).
|
|
|
641 |
self assert:( 0.5 exponent = 0.5 asIEEEFloat exponent ).
|
|
|
642 |
self assert:( 0.4 exponent = 0.4 asIEEEFloat exponent ).
|
|
|
643 |
self assert:( 0.25 exponent = 0.25asIEEEFloat exponent ).
|
|
|
644 |
self assert:( 0.125 exponent = 0.125 asIEEEFloat exponent ).
|
|
|
645 |
self assert:( 0.00000011111 exponent = 0.00000011111 asIEEEFloat exponent).
|
|
2443
|
646 |
|
|
2451
|
647 |
self assert:( 0.0 asShortFloat exponent = 0.0 asShortFloat asIEEEFloat exponent ).
|
|
|
648 |
self assert:( 1.0 asShortFloat exponent = 1.0 asShortFloat asIEEEFloat exponent ).
|
|
|
649 |
self assert:( 2.0 asShortFloat exponent = 2.0 asShortFloat asIEEEFloat exponent ).
|
|
|
650 |
self assert:( 3.0 asShortFloat exponent = 3.0 asShortFloat asIEEEFloat exponent ).
|
|
|
651 |
self assert:( 4.0 asShortFloat exponent = 4.0 asShortFloat asIEEEFloat exponent ).
|
|
|
652 |
self assert:( 0.5 asShortFloat exponent = 0.5 asShortFloat asIEEEFloat exponent ).
|
|
|
653 |
self assert:( 0.4 asShortFloat exponent = 0.4 asShortFloat asIEEEFloat exponent ).
|
|
|
654 |
self assert:( 0.25 asShortFloat exponent = 0.25 asShortFloat asIEEEFloat exponent ).
|
|
|
655 |
self assert:( 0.125 asShortFloat exponent = 0.125 asShortFloat asIEEEFloat exponent ).
|
|
|
656 |
self assert:( 0.00000011111 asShortFloat exponent = 0.00000011111 asIEEEFloat asShortFloat exponent ).
|
|
2443
|
657 |
|
|
2451
|
658 |
#( 1.0
|
|
|
659 |
2.0
|
|
|
660 |
3.0
|
|
|
661 |
4.0
|
|
|
662 |
12345.0
|
|
|
663 |
0.0
|
|
|
664 |
-1.0
|
|
|
665 |
-2.0
|
|
|
666 |
-3.0
|
|
|
667 |
-4.0
|
|
|
668 |
-12345.0
|
|
|
669 |
) do:[:f |
|
|
|
670 |
self assert:( f exponent = f asIEEEFloat exponent ).
|
|
|
671 |
self assert:( f mantissaBits = f asIEEEFloat mantissaBits ).
|
|
|
672 |
self assert:( f mantissa = f asIEEEFloat mantissa ).
|
|
|
673 |
self assert:( f mantissa * (2 raisedTo:f exponent)) = f.
|
|
|
674 |
self assert:( f asIEEEFloat mantissa * (2 raisedTo:f asIEEEFloat exponent)) = f asIEEEFloat.
|
|
2443
|
675 |
|
|
2451
|
676 |
self assert:( f asShortFloat exponent = f asShortFloat asIEEEFloat exponent ).
|
|
|
677 |
self assert:( f asShortFloat mantissaBits = f asShortFloat asIEEEFloat mantissaBits ).
|
|
|
678 |
self assert:( f asShortFloat mantissa = f asShortFloat asIEEEFloat mantissa ).
|
|
|
679 |
self assert:( f asShortFloat mantissa * (2 raisedTo:f asShortFloat exponent)) = f asShortFloat.
|
|
|
680 |
self assert:( f asShortFloat asIEEEFloat mantissa * (2 raisedTo:f asShortFloat asIEEEFloat exponent)) = f asShortFloat asIEEEFloat.
|
|
2443
|
681 |
|
|
|
682 |
noQuadFloats ifFalse:[
|
|
|
683 |
].
|
|
|
684 |
noOctaFloats ifFalse:[
|
|
|
685 |
].
|
|
|
686 |
].
|
|
|
687 |
"
|
|
|
688 |
self basicNew test08_Representation
|
|
|
689 |
"
|
|
|
690 |
|
|
|
691 |
"Modified: / 02-08-2011 / 18:34:39 / cg"
|
|
|
692 |
!
|
|
|
693 |
|
|
|
694 |
test09_ComplexRoots
|
|
|
695 |
|rslt|
|
|
|
696 |
|
|
|
697 |
self should:[ -4 sqrt ] raise:ImaginaryResultError.
|
|
|
698 |
|
|
|
699 |
rslt := Complex trapImaginary:[ -4 sqrt ].
|
|
|
700 |
self assert:(rslt = 2 i).
|
|
|
701 |
|
|
|
702 |
rslt := nil.
|
|
|
703 |
Complex trapImaginary:[ rslt := -4 sqrt ].
|
|
|
704 |
self assert:(rslt = 2 i).
|
|
|
705 |
|
|
|
706 |
self shouldnt:[ rslt := -8 cbrt ] raise:ImaginaryResultError.
|
|
|
707 |
self assert:(rslt = -2).
|
|
|
708 |
|
|
|
709 |
"
|
|
|
710 |
self basicNew test09_ComplexRoots
|
|
|
711 |
"
|
|
|
712 |
|
|
|
713 |
"Created: / 03-07-2017 / 13:51:54 / cg"
|
|
|
714 |
!
|
|
|
715 |
|
|
|
716 |
test_11a_pi
|
|
|
717 |
"/ Machin's Formula for Pi pi / 4 = 4 arctan(1/5) - arctan(1/239)
|
|
|
718 |
|
|
|
719 |
| at1_5 at1_239 pi_4 pi err|
|
|
|
720 |
|
|
|
721 |
at1_5 := (1.0 / 5) arcTan.
|
|
|
722 |
at1_239 := (1.0 / 239) arcTan.
|
|
|
723 |
pi_4 := (at1_5 * 4) - at1_239.
|
|
|
724 |
pi := pi_4 * 4.
|
|
|
725 |
err := Float pi - pi.
|
|
|
726 |
self assert:(err < (8 * Float epsilon)).
|
|
|
727 |
!
|
|
|
728 |
|
|
|
729 |
test_11b_pi
|
|
|
730 |
"/ Salamin-Brent Quadratic Formula for Pi
|
|
|
731 |
|
|
|
732 |
| max_iter a b s m a_new b_new p_old pi err|
|
|
|
733 |
|
|
|
734 |
max_iter := 6.
|
|
|
735 |
|
|
|
736 |
a := 1.0 asFloat.
|
|
|
737 |
b := 0.5 asFloat sqrt.
|
|
|
738 |
s := 0.5 asFloat.
|
|
|
739 |
m := 1.0 asFloat.
|
|
|
740 |
|
|
|
741 |
pi := 2.0 asFloat * a squared / s.
|
|
|
742 |
1 to:max_iter do:[:i |
|
|
|
743 |
m := m * 2.
|
|
|
744 |
a_new := 0.5 * (a+b).
|
|
|
745 |
b_new := a * b.
|
|
|
746 |
s := s - (m * (a_new squared - b_new)).
|
|
|
747 |
a := a_new.
|
|
|
748 |
b := b_new sqrt.
|
|
|
749 |
p_old := pi.
|
|
|
750 |
pi := 2 * a squared / s.
|
|
|
751 |
].
|
|
|
752 |
|
|
|
753 |
err := Float pi - pi.
|
|
|
754 |
self assert:(err < (8 * Float epsilon)).
|
|
|
755 |
!
|
|
|
756 |
|
|
|
757 |
test_12_e
|
|
|
758 |
"/ Taylor for e
|
|
|
759 |
|
|
|
760 |
| e t n i err|
|
|
|
761 |
|
|
|
762 |
e := 2.0.
|
|
|
763 |
t := 1.0.
|
|
|
764 |
n := 1.0.
|
|
|
765 |
i := 0.
|
|
|
766 |
|
|
|
767 |
[t > Float epsilon] whileTrue:[
|
|
|
768 |
i := i + 1.
|
|
|
769 |
n := n + 1.0.
|
|
|
770 |
t := t / n.
|
|
|
771 |
e := e + t.
|
|
|
772 |
].
|
|
|
773 |
|
|
|
774 |
err := Float e - e.
|
|
|
775 |
self assert:(err < (8 * Float epsilon)).
|
|
|
776 |
! !
|
|
|
777 |
|
|
|
778 |
!IEEEFloatTest class methodsFor:'documentation'!
|
|
|
779 |
|
|
|
780 |
version_CVS
|
|
|
781 |
^ '$Header$'
|
|
|
782 |
! !
|
|
|
783 |
|