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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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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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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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2448
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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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convArray := OrderedCollection new.
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convArray addAll:#(yourself asInteger asFloat asShortFloat asLongFloat).
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(Smalltalk at:#LargeFloat) notNil ifTrue:[
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convArray add:#asLargeFloat.
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].
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(Smalltalk at:#QDouble) notNil ifTrue:[
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convArray add:#asQDouble.
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].
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check := [:iv1 :iv2|
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convArray do:[:conv1 |
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v1 := (iv1 perform:conv1).
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self assert:( v1 = nil ) not.
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self assert:( nil = v1 ) not.
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self assert:( v1 ~= nil ).
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self assert:( nil ~= v1 ).
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convArray do:[:conv2 |
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v1b := (iv1 perform:conv2).
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self assert:( v1 = v1b ).
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self assert:( v1 <= v1b ).
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self assert:( v1 >= v1b ).
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v2 := (iv2 perform:conv2).
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|
|
325 |
|
|
|
326 |
self assert:( v1 < v2 ).
|
|
|
327 |
self assert:( v1 <= v2 ).
|
|
|
328 |
self assert:( v2 >= v1 ).
|
|
|
329 |
self assert:( v2 > v1 ).
|
|
|
330 |
]
|
|
|
331 |
].
|
|
|
332 |
].
|
|
|
333 |
|
|
|
334 |
check value:2 value:3.
|
|
|
335 |
check value:0 value:1.
|
|
|
336 |
check value:-1 value:0.
|
|
|
337 |
check value:-3 value:-2.
|
|
|
338 |
check value:-3 value:3.
|
|
|
339 |
|
|
|
340 |
check value:-30 value:1.
|
|
|
341 |
check value:-1 value:30.
|
|
|
342 |
|
|
|
343 |
"/ showing that float precision is limited...
|
|
|
344 |
|
|
|
345 |
"/ test fails when stc code, jit code works
|
|
|
346 |
false "(Helper
|
|
|
347 |
isStcCompiledMethod:#'test05_Comparing'
|
|
|
348 |
in:self)" ifTrue:[
|
|
|
349 |
"/ stc-compiled code handles not slightly differently
|
|
|
350 |
"/ listed compares will fail
|
|
|
351 |
'FloatTest >> test05_Comparing: test with 200000000000000000000 or similiar are skipped due would fail when stc code' infoPrintCR.
|
|
|
352 |
] ifFalse:[
|
|
|
353 |
self assert:( 200000000000000000000.0 = 200000000000000000001.0 ).
|
|
|
354 |
|
|
|
355 |
self assert:( 200000000000000000000.0 = 200000000000000000001 ).
|
|
|
356 |
self assert:( 200000000000000000000.0 = 200000000000000000000 ).
|
|
|
357 |
self assert:( 200000000000000000000.0 asLongFloat = 200000000000000000000 ).
|
|
|
358 |
|
|
|
359 |
self assert:( 200000000000000000000 = 200000000000000000000.0).
|
|
|
360 |
self assert:( 200000000000000000000 = 200000000000000000000.0 asLongFloat ).
|
|
|
361 |
|
|
|
362 |
self assert:( 200000000000000000000.0 < 200000100000000000000 ).
|
|
|
363 |
self assert:( 200000000000000000000.0 asLongFloat < 200000000000100000000 ).
|
|
|
364 |
self assert:( 200000000000000000000.0 asShortFloat < 200001000000000000000 ).
|
|
|
365 |
|
|
|
366 |
self assert:( 200000000000000000000 < 200001000000000000000.0).
|
|
|
367 |
self assert:( 200000000000000000000 < 200001000000000000000.0 asLongFloat ).
|
|
|
368 |
self assert:( 200000000000000000000 < 200001000000000000000.0 asShortFloat ).
|
|
|
369 |
|
|
|
370 |
self assert:( 200000000000000000000.0 <= 200000100000000000000 ).
|
|
|
371 |
self assert:( 200000000000000000000.0 <= 200000000000000000000 ).
|
|
|
372 |
self assert:( 200000000000000000000.0 asLongFloat <= 200000000000000000001 ).
|
|
|
373 |
self assert:( 200000000000000000000.0 asLongFloat <= 200000000000000000000 ).
|
|
|
374 |
|
|
|
375 |
self assert:( 200000000000000000000 <= 200001000000000000000.0).
|
|
|
376 |
self assert:( 200000000000000000000 <= 200000000000000000000.0).
|
|
|
377 |
self assert:( 200000000000000000000 <= 200001000000000000000.0 asLongFloat ).
|
|
|
378 |
self assert:( 200000000000000000000 <= 200000000000000000000.0 asLongFloat ).
|
|
|
379 |
].
|
|
|
380 |
|
|
|
381 |
self assert:( 2000000.0 asShortFloat = 2000000 ).
|
|
|
382 |
self assert:( 2000000 = 2000000.0 asShortFloat ).
|
|
|
383 |
|
|
|
384 |
self assert:( 2000000.0 asShortFloat <= 200000100000000000000 ).
|
|
|
385 |
self assert:( 2000000.0 asShortFloat <= 2000000 ).
|
|
|
386 |
|
|
|
387 |
self assert:( 2000000 <= 2000000.0 asShortFloat ).
|
|
|
388 |
self assert:( 2000000 <= 2000000.0 asShortFloat ).
|
|
|
389 |
|
|
|
390 |
"
|
|
|
391 |
self basicNew test05_Comparing
|
|
|
392 |
"
|
|
|
393 |
|
|
|
394 |
"Modified: / 06-05-2019 / 14:11:42 / Claus Gittinger"
|
|
|
395 |
!
|
|
|
396 |
|
|
|
397 |
test06_MiscMath
|
|
|
398 |
|epsilon|
|
|
|
399 |
|
|
|
400 |
epsilon := 0.000001.
|
|
|
401 |
|
|
|
402 |
#(
|
|
|
403 |
sqrt 0.5 0.707107
|
|
|
404 |
sqrt 4 2.0
|
|
|
405 |
exp 0.5 1.64872
|
|
|
406 |
ln 0.5 -0.693147
|
|
|
407 |
log10 0.5 -0.30103
|
|
|
408 |
|
|
|
409 |
sin 0.5 0.479426
|
|
|
410 |
cos 0.5 0.877583
|
|
|
411 |
tan 0.5 0.546302
|
|
|
412 |
arcSin 0.5 0.523599
|
|
|
413 |
arcCos 0.5 1.0472
|
|
|
414 |
arcTan 0.5 0.463648
|
|
|
415 |
sinh 0.5 0.521095
|
|
|
416 |
cosh 0.5 1.12763
|
|
|
417 |
tanh 0.5 0.462117
|
|
|
418 |
arcSinh 0.5 0.481212
|
|
|
419 |
arcCosh 1.5 1.24983
|
|
|
420 |
arcTanh 0.5 0.549306
|
|
|
421 |
|
|
|
422 |
sin 0.0 0.0
|
|
|
423 |
cos 0.0 1.0
|
|
|
424 |
tan 0.0 0.0
|
|
|
425 |
sinh 0.0 0.0
|
|
|
426 |
cosh 0.0 1.0
|
|
|
427 |
tanh 0.0 0.0
|
|
|
428 |
|
|
|
429 |
sin 1.0 0.841471
|
|
|
430 |
cos 1.0 0.540302
|
|
|
431 |
tan 1.0 1.55741
|
|
|
432 |
sinh 1.0 1.1752
|
|
|
433 |
cosh 1.0 1.54308
|
|
|
434 |
tanh 1.0 0.761594
|
|
|
435 |
|
|
|
436 |
sin 3.14159 0.0
|
|
|
437 |
cos 3.14159 -1.0
|
|
|
438 |
tan 3.14159 0.0
|
|
|
439 |
sinh 3.14159 11.5487
|
|
|
440 |
cosh 3.14159 11.5919
|
|
|
441 |
tanh 3.14159 0.996272
|
|
|
442 |
|
|
|
443 |
|
|
|
444 |
tan 0.785398 1.0 "pi/4 -> should be 1"
|
|
|
445 |
arcCos -1.0 3.14159 "should be pi"
|
|
|
446 |
arcSin 1.0 1.5708 "should be pi/2 (1.5708)"
|
|
|
447 |
arcTan 1.0 0.785398 "should be pi/4 (.785398)"
|
|
|
448 |
) inGroupsOf:3 do:[:op :x :expected|
|
|
|
449 |
|rslt rsltShortFloat rsltLongFloat rsltLargeFloat rsltQDouble|
|
|
|
450 |
|
|
|
451 |
rslt := x perform:op.
|
|
|
452 |
rsltShortFloat := x asShortFloat perform:op.
|
|
|
453 |
rsltLongFloat := x asLongFloat perform:op.
|
|
|
454 |
"/ rsltLargeFloat := arg asLargeFloat perform:op.
|
|
|
455 |
"/ rsltQDouble := x asQDouble perform:op.
|
|
|
456 |
|
|
|
457 |
self assert:(rslt class == Float).
|
|
|
458 |
"/ self assert:(rsltShortFloat class == Float). "/ ??? not a good test; some return a float
|
|
|
459 |
self assert:(rsltLongFloat class == LongFloat).
|
|
|
460 |
"/ self assert:(rsltQDouble class == QDouble).
|
|
|
461 |
|
|
|
462 |
self assert:( rslt - rsltShortFloat ) < epsilon.
|
|
|
463 |
self assert:( rslt - rsltLongFloat ) < epsilon.
|
|
|
464 |
"/ self assert:( rslt - rsltQDouble ) < epsilon.
|
|
|
465 |
"/ self assert:( rslt - rsltLargeFloat ) < epsilon.
|
|
|
466 |
self assert:( rslt - rslt asShortFloat ) < epsilon.
|
|
|
467 |
self assert:( rslt - rslt asLongFloat ) < epsilon.
|
|
|
468 |
"/ self assert:( rslt - rsltQDouble asFloat) < epsilon.
|
|
|
469 |
"/ self assert:( rslt - rslt asLargeFloat ) < epsilon.
|
|
|
470 |
].
|
|
|
471 |
|
|
|
472 |
self should:[ -2 arcSin ] raise:DomainError.
|
|
|
473 |
self should:[ -2 arcCos ] raise:DomainError.
|
|
|
474 |
self should:[ -1 arcTanh ] raise:DomainError.
|
|
|
475 |
|
|
|
476 |
#(
|
|
|
477 |
0.0
|
|
|
478 |
0.5
|
|
|
479 |
1.0
|
|
|
480 |
2.0
|
|
|
481 |
1.57079
|
|
|
482 |
) do:[:x |
|
|
|
483 |
self assert:( x sin arcSin - x < epsilon).
|
|
|
484 |
self assert:( x cos arcCos - x < epsilon).
|
|
|
485 |
self assert:( x tan arcTan - x < epsilon).
|
|
|
486 |
].
|
|
|
487 |
|
|
|
488 |
#(
|
|
|
489 |
-1.0
|
|
|
490 |
-0.5
|
|
|
491 |
0.0
|
|
|
492 |
0.5
|
|
|
493 |
1.0
|
|
|
494 |
) do:[:x |
|
|
|
495 |
self assert:( x arcSin sin - x < epsilon).
|
|
|
496 |
self assert:( x arcCos cos - x < epsilon).
|
|
|
497 |
self assert:( x arcTan tan - x < epsilon).
|
|
|
498 |
].
|
|
|
499 |
|
|
|
500 |
#(
|
|
|
501 |
0.0
|
|
|
502 |
0.5
|
|
|
503 |
1.0
|
|
|
504 |
2.0
|
|
|
505 |
10
|
|
|
506 |
) do:[:x |
|
|
|
507 |
self assert:( x cosh arcCosh - x < epsilon).
|
|
|
508 |
].
|
|
|
509 |
#(
|
|
|
510 |
-10
|
|
|
511 |
-2
|
|
|
512 |
-1
|
|
|
513 |
-0.5
|
|
|
514 |
0.0
|
|
|
515 |
0.5
|
|
|
516 |
1.0
|
|
|
517 |
2.0
|
|
|
518 |
10
|
|
|
519 |
) do:[:x |
|
|
|
520 |
self assert:( x sinh arcSinh - x < epsilon).
|
|
|
521 |
self assert:( x tanh arcTanh - x < epsilon).
|
|
|
522 |
].
|
|
|
523 |
|
|
|
524 |
|
|
|
525 |
#(
|
|
|
526 |
-0.99
|
|
|
527 |
-0.5
|
|
|
528 |
0.0
|
|
|
529 |
0.5
|
|
|
530 |
0.99
|
|
|
531 |
) do:[:x |
|
|
|
532 |
self assert:( x arcTanh - (( ( (1+x)/(1-x) ) ln ) / 2 ) ) < epsilon.
|
|
|
533 |
].
|
|
|
534 |
|
|
|
535 |
#(
|
|
|
536 |
-10
|
|
|
537 |
-5
|
|
|
538 |
-2.0
|
|
|
539 |
-1.0
|
|
|
540 |
0.0
|
|
|
541 |
1.0
|
|
|
542 |
2.0
|
|
|
543 |
10
|
|
|
544 |
) do:[:x |
|
|
|
545 |
self assert:( x arcSinh sinh - x < epsilon).
|
|
|
546 |
].
|
|
|
547 |
|
|
|
548 |
#(
|
|
|
549 |
1.0
|
|
|
550 |
2.0
|
|
|
551 |
10.0
|
|
|
552 |
) do:[:x |
|
|
|
553 |
self assert:( x arcCosh cosh - x < epsilon).
|
|
|
554 |
].
|
|
|
555 |
|
|
|
556 |
self assert:(2.0 raisedTo:2) = 4.0.
|
|
|
557 |
self assert:(2 raisedTo:2.0) = 4.0.
|
|
|
558 |
self assert:(2.0 raisedTo:2.0) = 4.0.
|
|
|
559 |
|
|
|
560 |
"
|
|
|
561 |
self basicNew test06_MiscMath
|
|
|
562 |
"
|
|
|
563 |
|
|
|
564 |
"Modified: / 02-07-2017 / 00:51:05 / cg"
|
|
|
565 |
!
|
|
|
566 |
|
|
|
567 |
test07_Truncation
|
|
|
568 |
|check|
|
|
|
569 |
|
|
|
570 |
check := [:num |
|
|
|
571 |
self assert:( num fractionPart + num truncated ) = num.
|
|
|
572 |
self assert:( num fractionPart + num truncated ) class == num class.
|
|
|
573 |
].
|
|
|
574 |
|
|
|
575 |
check value:1.6.
|
|
|
576 |
check value:-1.6.
|
|
|
577 |
|
|
|
578 |
check value:1.6 asShortFloat.
|
|
|
579 |
check value:-1.6 asShortFloat.
|
|
|
580 |
|
|
|
581 |
check value:1.6 asLongFloat.
|
|
|
582 |
check value:-1.6 asLongFloat.
|
|
|
583 |
|
|
|
584 |
|
|
|
585 |
self assert:( 1.6 ceiling ) = 2.
|
|
|
586 |
self assert:( 1.6 asShortFloat ceiling ) = 2.
|
|
|
587 |
self assert:( 1.6 asLongFloat ceiling ) = 2.
|
|
|
588 |
|
|
|
589 |
self assert:( 1.6 ceilingAsFloat ) = 2.0.
|
|
|
590 |
self assert:( 1.6 ceilingAsFloat ) class == Float.
|
|
|
591 |
self assert:( 1.6 asShortFloat ceilingAsFloat ) = 2.0 asShortFloat.
|
|
|
592 |
self assert:( 1.6 asShortFloat ceilingAsFloat ) class == ShortFloat.
|
|
|
593 |
self assert:( 1.6 asLongFloat ceilingAsFloat ) = 2.0 asLongFloat.
|
|
|
594 |
self assert:( 1.6 asLongFloat ceilingAsFloat ) class == LongFloat.
|
|
|
595 |
|
|
|
596 |
|
|
|
597 |
self assert:( 1.6 floor ) = 1.
|
|
|
598 |
self assert:( 1.6 asShortFloat floor ) = 1.
|
|
|
599 |
self assert:( 1.6 asLongFloat floor ) = 1.
|
|
|
600 |
|
|
|
601 |
self assert:( 1.6 floorAsFloat ) = 1.0.
|
|
|
602 |
self assert:( 1.6 floorAsFloat ) class == Float.
|
|
|
603 |
self assert:( 1.6 asShortFloat floorAsFloat ) = 1.0 asShortFloat.
|
|
|
604 |
self assert:( 1.6 asShortFloat floorAsFloat ) class == ShortFloat.
|
|
|
605 |
self assert:( 1.6 asLongFloat floorAsFloat ) = 1.0 asLongFloat.
|
|
|
606 |
self assert:( 1.6 asLongFloat floorAsFloat ) class == LongFloat.
|
|
|
607 |
|
|
|
608 |
self assert:( -1.6 floor ) = -2.
|
|
|
609 |
self assert:( -1.6 asShortFloat floor ) = -2.
|
|
|
610 |
self assert:( -1.6 asLongFloat floor ) = -2.
|
|
|
611 |
|
|
|
612 |
self assert:( -1.6 floorAsFloat ) = -2.0.
|
|
|
613 |
self assert:( -1.6 floorAsFloat ) class == Float.
|
|
|
614 |
self assert:( -1.6 asShortFloat floorAsFloat ) = -2.0 asShortFloat.
|
|
|
615 |
self assert:( -1.6 asShortFloat floorAsFloat ) class == ShortFloat.
|
|
|
616 |
self assert:( -1.6 asLongFloat floorAsFloat ) = -2.0 asLongFloat.
|
|
|
617 |
self assert:( -1.6 asLongFloat floorAsFloat ) class == LongFloat.
|
|
|
618 |
|
|
|
619 |
|
|
|
620 |
self assert:( 0.4 rounded ) class == SmallInteger.
|
|
|
621 |
self assert:( 0.4 rounded = 0 ).
|
|
|
622 |
self assert:( 0.5 rounded = 1 ).
|
|
|
623 |
self assert:( 0.6 rounded = 1 ).
|
|
|
624 |
self assert:( -0.4 rounded = 0 ).
|
|
|
625 |
self assert:( -0.5 rounded = -1 ).
|
|
|
626 |
self assert:( -0.6 rounded = -1 ).
|
|
|
627 |
|
|
|
628 |
self assert:( 0.4 roundedAsFloat ) class == Float.
|
|
|
629 |
self assert:( 0.4 roundedAsFloat = 0.0 ).
|
|
|
630 |
self assert:( 0.5 roundedAsFloat = 1.0 ).
|
|
|
631 |
self assert:( 0.6 roundedAsFloat = 1.0 ).
|
|
|
632 |
self assert:( -0.4 roundedAsFloat = 0 ).
|
|
|
633 |
self assert:( -0.5 roundedAsFloat = -1.0 ).
|
|
|
634 |
self assert:( -0.6 roundedAsFloat = -1.0 ).
|
|
|
635 |
|
|
|
636 |
self assert:( 0.4 asShortFloat rounded ) class == SmallInteger.
|
|
|
637 |
self assert:( 0.4 asShortFloat rounded = 0 ).
|
|
|
638 |
self assert:( 0.5 asShortFloat rounded = 1 ).
|
|
|
639 |
self assert:( 0.6 asShortFloat rounded = 1 ).
|
|
|
640 |
self assert:( -0.4 asShortFloat rounded = 0 ).
|
|
|
641 |
self assert:( -0.5 asShortFloat rounded = -1 ).
|
|
|
642 |
self assert:( -0.6 asShortFloat rounded = -1 ).
|
|
|
643 |
|
|
|
644 |
self assert:( 0.4 asShortFloat roundedAsFloat ) class == ShortFloat.
|
|
|
645 |
self assert:( 0.4 asShortFloat roundedAsFloat = 0.0 ).
|
|
|
646 |
self assert:( 0.5 asShortFloat roundedAsFloat = 1.0 ).
|
|
|
647 |
self assert:( 0.6 asShortFloat roundedAsFloat = 1.0 ).
|
|
|
648 |
self assert:( -0.4 asShortFloat roundedAsFloat = 0 ).
|
|
|
649 |
self assert:( -0.5 asShortFloat roundedAsFloat = -1.0 ).
|
|
|
650 |
self assert:( -0.6 asShortFloat roundedAsFloat = -1.0 ).
|
|
|
651 |
|
|
|
652 |
self assert:( 0.4 asLongFloat rounded ) class == SmallInteger.
|
|
|
653 |
self assert:( 0.4 asLongFloat rounded = 0 ).
|
|
|
654 |
self assert:( 0.5 asLongFloat rounded = 1 ).
|
|
|
655 |
self assert:( 0.6 asLongFloat rounded = 1 ).
|
|
|
656 |
self assert:( -0.4 asLongFloat rounded = 0 ).
|
|
|
657 |
self assert:( -0.5 asLongFloat rounded = -1 ).
|
|
|
658 |
self assert:( -0.6 asLongFloat rounded = -1 ).
|
|
|
659 |
|
|
|
660 |
self assert:( 0.4 asLongFloat roundedAsFloat ) class == LongFloat.
|
|
|
661 |
self assert:( 0.4 asLongFloat roundedAsFloat = 0.0 ).
|
|
|
662 |
self assert:( 0.5 asLongFloat roundedAsFloat = 1.0 ).
|
|
|
663 |
self assert:( 0.6 asLongFloat roundedAsFloat = 1.0 ).
|
|
|
664 |
self assert:( -0.4 asLongFloat roundedAsFloat = 0 ).
|
|
|
665 |
self assert:( -0.5 asLongFloat roundedAsFloat = -1.0 ).
|
|
|
666 |
self assert:( -0.6 asLongFloat roundedAsFloat = -1.0 ).
|
|
|
667 |
|
|
|
668 |
self assert:( 0.4 truncated ) class == SmallInteger.
|
|
|
669 |
self assert:( 0.4 truncated = 0 ).
|
|
|
670 |
self assert:( 0.5 truncated = 0 ).
|
|
|
671 |
self assert:( 0.6 truncated = 0 ).
|
|
|
672 |
self assert:( -0.4 truncated = 0 ).
|
|
|
673 |
self assert:( -0.5 truncated = 0 ).
|
|
|
674 |
self assert:( -0.6 truncated = 0 ).
|
|
|
675 |
|
|
|
676 |
self assert:( 0.4 truncatedAsFloat ) class == Float.
|
|
|
677 |
self assert:( 0.4 truncatedAsFloat = 0.0 ).
|
|
|
678 |
self assert:( 0.5 truncatedAsFloat = 0.0 ).
|
|
|
679 |
self assert:( 0.6 truncatedAsFloat = 0.0 ).
|
|
|
680 |
self assert:( -0.4 truncatedAsFloat = 0 ).
|
|
|
681 |
self assert:( -0.5 truncatedAsFloat = 0.0 ).
|
|
|
682 |
self assert:( -0.6 truncatedAsFloat = 0.0 ).
|
|
|
683 |
|
|
|
684 |
self assert:( 0.4 asShortFloat truncated ) class == SmallInteger.
|
|
|
685 |
self assert:( 0.4 asShortFloat truncated = 0 ).
|
|
|
686 |
self assert:( 0.5 asShortFloat truncated = 0 ).
|
|
|
687 |
self assert:( 0.6 asShortFloat truncated = 0 ).
|
|
|
688 |
self assert:( -0.4 asShortFloat truncated = 0 ).
|
|
|
689 |
self assert:( -0.5 asShortFloat truncated = 0 ).
|
|
|
690 |
self assert:( -0.6 asShortFloat truncated = 0 ).
|
|
|
691 |
|
|
|
692 |
self assert:( 0.4 asShortFloat truncatedAsFloat ) class == ShortFloat.
|
|
|
693 |
self assert:( 0.4 asShortFloat truncatedAsFloat = 0.0 ).
|
|
|
694 |
self assert:( 0.5 asShortFloat truncatedAsFloat = 0.0 ).
|
|
|
695 |
self assert:( 0.6 asShortFloat truncatedAsFloat = 0.0 ).
|
|
|
696 |
self assert:( -0.4 asShortFloat truncatedAsFloat = 0 ).
|
|
|
697 |
self assert:( -0.5 asShortFloat truncatedAsFloat = 0.0 ).
|
|
|
698 |
self assert:( -0.6 asShortFloat truncatedAsFloat = 0.0 ).
|
|
|
699 |
|
|
|
700 |
self assert:( 0.4 asLongFloat truncated ) class == SmallInteger.
|
|
|
701 |
self assert:( 0.4 asLongFloat truncated = 0 ).
|
|
|
702 |
self assert:( 0.5 asLongFloat truncated = 0 ).
|
|
|
703 |
self assert:( 0.6 asLongFloat truncated = 0 ).
|
|
|
704 |
self assert:( -0.4 asLongFloat truncated = 0 ).
|
|
|
705 |
self assert:( -0.5 asLongFloat truncated = 0 ).
|
|
|
706 |
self assert:( -0.6 asLongFloat truncated = 0 ).
|
|
|
707 |
|
|
|
708 |
self assert:( 0.4 asLongFloat truncatedAsFloat ) class == LongFloat.
|
|
|
709 |
self assert:( 0.4 asLongFloat truncatedAsFloat = 0.0 ).
|
|
|
710 |
self assert:( 0.5 asLongFloat truncatedAsFloat = 0.0 ).
|
|
|
711 |
self assert:( 0.6 asLongFloat truncatedAsFloat = 0.0 ).
|
|
|
712 |
self assert:( -0.4 asLongFloat truncatedAsFloat = 0 ).
|
|
|
713 |
self assert:( -0.5 asLongFloat truncatedAsFloat = 0.0 ).
|
|
|
714 |
self assert:( -0.6 asLongFloat truncatedAsFloat = 0.0 ).
|
|
|
715 |
|
|
|
716 |
"
|
|
|
717 |
self basicNew test07_Truncation
|
|
|
718 |
"
|
|
|
719 |
!
|
|
|
720 |
|
|
|
721 |
test08_Representation
|
|
|
722 |
|noQuadFloats noOctaFloats|
|
|
|
723 |
|
|
|
724 |
noQuadFloats := UnimplementedFunctionalityError catch:[1.0 asQuadFloat].
|
|
|
725 |
noOctaFloats := UnimplementedFunctionalityError catch:[1.0 asOctaFloat].
|
|
|
726 |
|
|
|
727 |
self assert: (Float unity class == Float).
|
|
|
728 |
self assert: (ShortFloat unity class == ShortFloat).
|
|
|
729 |
self assert: (LongFloat unity class == LongFloat).
|
|
|
730 |
|
|
|
731 |
self assert: (Float unity = 1.0).
|
|
|
732 |
self assert: (ShortFloat unity = 1.0).
|
|
|
733 |
self assert: (LongFloat unity = 1.0).
|
|
|
734 |
|
|
|
735 |
self assert: (Float zero class == Float).
|
|
|
736 |
self assert: (ShortFloat zero class == ShortFloat).
|
|
|
737 |
self assert: (LongFloat zero class == LongFloat).
|
|
|
738 |
|
|
|
739 |
self assert: (Float zero = 0.0).
|
|
|
740 |
self assert: (ShortFloat zero = 0.0).
|
|
|
741 |
self assert: (LongFloat zero = 0.0).
|
|
|
742 |
|
|
|
743 |
self assert:( LongFloat unity = 1 asLongFloat ).
|
|
|
744 |
self assert:( ShortFloat unity = 1 asShortFloat ).
|
|
|
745 |
self assert:( Float unity = 1 asFloat ).
|
|
|
746 |
|
|
|
747 |
self assert:( 0.0 exponent = 0 ).
|
|
|
748 |
self assert:( 1.0 exponent = 1 ).
|
|
|
749 |
self assert:( 2.0 exponent = 2 ).
|
|
|
750 |
self assert:( 3.0 exponent = 2 ).
|
|
|
751 |
self assert:( 4.0 exponent = 3 ).
|
|
|
752 |
self assert:( 0.5 exponent = 0 ).
|
|
|
753 |
self assert:( 0.4 exponent = -1 ).
|
|
|
754 |
self assert:( 0.25 exponent = -1 ).
|
|
|
755 |
self assert:( 0.125 exponent = -2 ).
|
|
|
756 |
self assert:( 0.00000011111 exponent = -23 ).
|
|
|
757 |
|
|
|
758 |
self assert:( 0.0 asShortFloat exponent = 0 ).
|
|
|
759 |
self assert:( 1.0 asShortFloat exponent = 1 ).
|
|
|
760 |
self assert:( 2.0 asShortFloat exponent = 2 ).
|
|
|
761 |
self assert:( 3.0 asShortFloat exponent = 2 ).
|
|
|
762 |
self assert:( 4.0 asShortFloat exponent = 3 ).
|
|
|
763 |
self assert:( 0.5 asShortFloat exponent = 0 ).
|
|
|
764 |
self assert:( 0.4 asShortFloat exponent = -1 ).
|
|
|
765 |
self assert:( 0.25 asShortFloat exponent = -1 ).
|
|
|
766 |
self assert:( 0.125 asShortFloat exponent = -2 ).
|
|
|
767 |
self assert:( 0.00000011111 asShortFloat exponent = -23 ).
|
|
|
768 |
|
|
|
769 |
self assert:( 0.0 asLongFloat exponent = 0 ).
|
|
|
770 |
self assert:( 1.0 asLongFloat exponent = 1 ).
|
|
|
771 |
self assert:( 2.0 asLongFloat exponent = 2 ).
|
|
|
772 |
self assert:( 3.0 asLongFloat exponent = 2 ).
|
|
|
773 |
self assert:( 4.0 asLongFloat exponent = 3 ).
|
|
|
774 |
self assert:( 0.5 asLongFloat exponent = 0 ).
|
|
|
775 |
self assert:( 0.4 asLongFloat exponent = -1 ).
|
|
|
776 |
self assert:( 0.25 asLongFloat exponent = -1 ).
|
|
|
777 |
self assert:( 0.125 asLongFloat exponent = -2 ).
|
|
|
778 |
self assert:( 0.00000011111 asLongFloat exponent = -23 ).
|
|
|
779 |
|
|
|
780 |
#( 1.0 1
|
|
|
781 |
2.0 2
|
|
|
782 |
3.0 3
|
|
|
783 |
4.0 4
|
|
|
784 |
12345.0 12345
|
|
|
785 |
0.0 0
|
|
|
786 |
-1.0 -1
|
|
|
787 |
-2.0 -2
|
|
|
788 |
-3.0 -3
|
|
|
789 |
-4.0 -4
|
|
|
790 |
-12345.0 -12345
|
|
|
791 |
) pairWiseDo:[:f :i |
|
|
|
792 |
self assert:( f exponent = i exponent ).
|
|
|
793 |
self assert:( f mantissa = i mantissa ).
|
|
|
794 |
self assert:( f mantissa * (2 raisedTo:f exponent))= f.
|
|
|
795 |
self assert:( i mantissa * (2 raisedTo:i exponent)) = i.
|
|
|
796 |
|
|
|
797 |
self assert:( f exponent = f asShortFloat exponent ).
|
|
|
798 |
self assert:( f exponent = f asLongFloat exponent ).
|
|
|
799 |
self assert:( f exponent = f asQDouble exponent ).
|
|
|
800 |
self assert:( f asShortFloat mantissa * (2 raisedTo:f asShortFloat exponent))= f.
|
|
|
801 |
self assert:( f asLongFloat mantissa * (2 raisedTo:f asLongFloat exponent))= f.
|
|
|
802 |
self assert:( f asQDouble mantissa * (2 raisedTo:f asQDouble exponent))= f.
|
|
|
803 |
|
|
|
804 |
noQuadFloats ifFalse:[
|
|
|
805 |
self assert:( f exponent = f asQuadFloat exponent ).
|
|
|
806 |
self assert:( f asQuadFloat mantissa * (2 raisedTo:f asQuadFloat exponent))= f.
|
|
|
807 |
].
|
|
|
808 |
noOctaFloats ifFalse:[
|
|
|
809 |
self assert:( f exponent = f asOctaFloat exponent ).
|
|
|
810 |
self assert:( f asOctaFloat mantissa * (2 raisedTo:f asOctaFloat exponent))= f.
|
|
|
811 |
].
|
|
|
812 |
].
|
|
|
813 |
"
|
|
|
814 |
self basicNew test08_Representation
|
|
|
815 |
"
|
|
|
816 |
|
|
|
817 |
"Modified: / 02-08-2011 / 18:34:39 / cg"
|
|
|
818 |
!
|
|
|
819 |
|
|
|
820 |
test09_ComplexRoots
|
|
|
821 |
|rslt|
|
|
|
822 |
|
|
|
823 |
self should:[ -4 sqrt ] raise:ImaginaryResultError.
|
|
|
824 |
|
|
|
825 |
rslt := Complex trapImaginary:[ -4 sqrt ].
|
|
|
826 |
self assert:(rslt = 2 i).
|
|
|
827 |
|
|
|
828 |
rslt := nil.
|
|
|
829 |
Complex trapImaginary:[ rslt := -4 sqrt ].
|
|
|
830 |
self assert:(rslt = 2 i).
|
|
|
831 |
|
|
|
832 |
self shouldnt:[ rslt := -8 cbrt ] raise:ImaginaryResultError.
|
|
|
833 |
self assert:(rslt = -2).
|
|
|
834 |
|
|
|
835 |
"
|
|
|
836 |
self basicNew test09_ComplexRoots
|
|
|
837 |
"
|
|
|
838 |
|
|
|
839 |
"Created: / 03-07-2017 / 13:51:54 / cg"
|
|
|
840 |
!
|
|
|
841 |
|
|
|
842 |
test_11a_pi
|
|
|
843 |
"/ Machin's Formula for Pi pi / 4 = 4 arctan(1/5) - arctan(1/239)
|
|
|
844 |
|
|
|
845 |
| at1_5 at1_239 pi_4 pi err|
|
|
|
846 |
|
|
|
847 |
at1_5 := (1.0 / 5) arcTan.
|
|
|
848 |
at1_239 := (1.0 / 239) arcTan.
|
|
|
849 |
pi_4 := (at1_5 * 4) - at1_239.
|
|
|
850 |
pi := pi_4 * 4.
|
|
|
851 |
err := Float pi - pi.
|
|
|
852 |
self assert:(err < (8 * Float epsilon)).
|
|
|
853 |
!
|
|
|
854 |
|
|
|
855 |
test_11b_pi
|
|
|
856 |
"/ Salamin-Brent Quadratic Formula for Pi
|
|
|
857 |
|
|
|
858 |
| max_iter a b s m a_new b_new p_old pi err|
|
|
|
859 |
|
|
|
860 |
max_iter := 6.
|
|
|
861 |
|
|
|
862 |
a := 1.0 asFloat.
|
|
|
863 |
b := 0.5 asFloat sqrt.
|
|
|
864 |
s := 0.5 asFloat.
|
|
|
865 |
m := 1.0 asFloat.
|
|
|
866 |
|
|
|
867 |
pi := 2.0 asFloat * a squared / s.
|
|
|
868 |
1 to:max_iter do:[:i |
|
|
|
869 |
m := m * 2.
|
|
|
870 |
a_new := 0.5 * (a+b).
|
|
|
871 |
b_new := a * b.
|
|
|
872 |
s := s - (m * (a_new squared - b_new)).
|
|
|
873 |
a := a_new.
|
|
|
874 |
b := b_new sqrt.
|
|
|
875 |
p_old := pi.
|
|
|
876 |
pi := 2 * a squared / s.
|
|
|
877 |
].
|
|
|
878 |
|
|
|
879 |
err := Float pi - pi.
|
|
|
880 |
self assert:(err < (8 * Float epsilon)).
|
|
|
881 |
!
|
|
|
882 |
|
|
|
883 |
test_12_e
|
|
|
884 |
"/ Taylor for e
|
|
|
885 |
|
|
|
886 |
| e t n i err|
|
|
|
887 |
|
|
|
888 |
e := 2.0.
|
|
|
889 |
t := 1.0.
|
|
|
890 |
n := 1.0.
|
|
|
891 |
i := 0.
|
|
|
892 |
|
|
|
893 |
[t > Float epsilon] whileTrue:[
|
|
|
894 |
i := i + 1.
|
|
|
895 |
n := n + 1.0.
|
|
|
896 |
t := t / n.
|
|
|
897 |
e := e + t.
|
|
|
898 |
].
|
|
|
899 |
|
|
|
900 |
err := Float e - e.
|
|
|
901 |
self assert:(err < (8 * Float epsilon)).
|
|
|
902 |
! !
|
|
|
903 |
|
|
|
904 |
!IEEEFloatTest class methodsFor:'documentation'!
|
|
|
905 |
|
|
|
906 |
version_CVS
|
|
|
907 |
^ '$Header$'
|
|
|
908 |
! !
|
|
|
909 |
|