[PATCH] Complex package
Locked
 
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I noticed that GST does not have complex numbers. This adds them, as
well as adding hyperbolic functions. Paolo 2007-07-17 Paolo Bonzini <[hidden email]> * kernel/Number.st: Add hyperbolic functions. * packages/complex/Complex.st: New. * packages/complex/complextests.st: New. --- orig/configure.ac +++ mod/configure.ac @@ -246,6 +246,7 @@ GST_PACKAGE([BloxTK], [blox/tk], [gst_cv_tcltk_libs], [Makefile], [blox-tk.la]) GST_PACKAGE([Browser], [browser]) +GST_PACKAGE([Complex], [complex]) GST_PACKAGE([Continuations], [continuations]) GST_PACKAGE([DebugTools], [debug]) GST_PACKAGE([DB], [db]) --- orig/kernel/Number.st +++ mod/kernel/Number.st @@ -345,9 +345,7 @@ retryDivisionCoercing: aNumber exception if aNumber is zero" aNumber = 0 ifTrue: [ self zeroDivide ]. - ^self negative == aNumber negative - ifTrue: [ self rem: aNumber ] - ifFalse: [ (self rem: aNumber) + aNumber ] + ^self - ((self // aNumber) * aNumber) ! quo: aNumber @@ -586,12 +584,12 @@ arcTan: x ^self generality < x generality ifTrue: [ x generality < 0.0e generality - ifTrue: [ FloatD pi * self sign / -2 ] - ifFalse: [ x class pi * self sign / -2 ]] + ifTrue: [ FloatD pi * self sign / 2 ] + ifFalse: [ x class pi * self sign / 2 ]] ifFalse: [ self generality < 0.0e generality - ifTrue: [ FloatD pi * self sign / -2 ] - ifFalse: [ self class pi * self sign / -2 ]]]. + ifTrue: [ FloatD pi * self sign / 2 ] + ifFalse: [ self class pi * self sign / 2 ]]]. result := (self / x) arcTan. ^x < 0 @@ -602,6 +600,33 @@ arcTan: x ifTrue: [ result - result class pi ] ] ! +cosh + "Answer the hyperbolic cosine of the receiver." + ^(self exp + self negated exp) / 2! + +sinh + "Answer the hyperbolic sine of the receiver." + ^(self exp - self negated exp) / 2! + +tanh + "Answer the hyperbolic tangent of the receiver." + | ep en | + ep := self exp. + en := self negated exp. + ^(ep - en) / (ep + en)! + +arcCosh + "Answer the hyperbolic arc-cosine of the receiver." + ^(self + (self squared - 1) sqrt) ln! + +arcSinh + "Answer the hyperbolic arc-sine of the receiver." + ^(self + (self squared + 1) sqrt) ln! + +arcTanh + "Answer the hyperbolic arc-tangent of the receiver." + ^((1 + self) / (1 - self)) ln / 2! + sqrt "Answer the square root of the receiver" ^self asFloatD sqrt * added files --- /dev/null 2007-07-18 00:40:21.000000000 +0300 +++ mod/packages/complex/Complex.st @@ -0,0 +1,459 @@ +"====================================================================== +| +| Complex number declarations +| +| + ======================================================================" + + +"====================================================================== +| +| Copyright 2007 Free Software Foundation, Inc. +| Written by Paolo Bonzini +| +| This file is part of the GNU Smalltalk class library. +| +| The GNU Smalltalk class library is free software; you can redistribute it +| and/or modify it under the terms of the GNU Lesser General Public License +| as published by the Free Software Foundation; either version 2.1, or (at +| your option) any later version. +| +| The GNU Smalltalk class library is distributed in the hope that it will be +| useful, but WITHOUT ANY WARRANTY; without even the implied warranty of +| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser +| General Public License for more details. +| +| You should have received a copy of the GNU Lesser General Public License +| along with the GNU Smalltalk class library; see the file COPYING.LIB. +| If not, write to the Free Software Foundation, 59 Temple Place - Suite +| 330, Boston, MA 02110-1301, USA. +| + ======================================================================" + +Number subclass: #Complex + instanceVariableNames: 're im' + classVariableNames: 'Zero One I' + poolDictionaries: '' + category: 'Examples-Useful'! + +Complex comment: 'I provide complex numbers, with full interoperability +with other kinds of numbers. Complex numbers can be created from imaginary +numbers, which in turn are created with `Complex i'' or the #i method +(e.g. `3 i''). Alternatively, they can be created from polar numbers.'! + +!Complex class methodsFor: 'instance creation'! + +initialize + "Initialize some common complex numbers." + Zero := Complex basicNew setReal: 0 imaginary: 0. + One := Complex basicNew setReal: 1 imaginary: 0. + I := Complex real: 0 imaginary: 1! + +i + "Return the imaginary unit, -1 sqrt." + ^I! + +new + self shouldNotImplement! + +rho: dist theta: angle + "Return a complex number whose absolute value is dist and whose + argument is angle." + ^Complex + realResult: dist * angle cos + imaginary: dist * angle sin! + +realResult: re imaginary: im + "Private - Return a new complex number knowing that re and im have the + same generality." + im = 0 ifTrue: [ ^re ]. + ^self basicNew setReal: re imaginary: im! + +real: re imaginary: im + "Return a complex number with the given real and imaginary parts." + im = 0 ifTrue: [ ^re ]. + re isComplex ifTrue: [ ^re + im i ]. + im isComplex ifTrue: [ ^re + im i ]. + + re generality = im generality + ifTrue: [ ^self basicNew setReal: re imaginary: im ]. + + ^re generality < im generality + ifTrue: [ ^self basicNew setReal: (im coerce: re) imaginary: im ] + ifFalse: [ ^self basicNew setReal: re imaginary: (re coerce: im) ]! ! + +!Complex methodsFor: 'math'! + ++ z + "Sum the receiver with the (real or complex) number z." + ^Complex + realResult: self real + z real + imaginary: self imaginary + z imaginary! + +- z + "Subtract the (real or complex) number z from the receiver." + ^Complex + realResult: self real - z real + imaginary: self imaginary - z imaginary! + +* z + "Multiply the receiver by the (real or complex) number z." + z isComplex ifFalse: [ + ^Complex + realResult: self real * z + imaginary: self imaginary * z ]. + ^Complex + realResult: (self real * z real) - (self imaginary * z imaginary) + imaginary: (self real * z imaginary) + (self imaginary * z real)! + +/ z + "Divide the receiver by the (real or complex) number z." + z isComplex ifFalse: [ + ^Complex + realResult: self real / z + imaginary: self imaginary / z ]. + ^self * z reciprocal! + +reciprocal + "Return the reciprocal of the receiver." + | absSquared | + absSquared := self absSquared. + ^Complex + realResult: self real / absSquared + imaginary: self imaginary negated / absSquared! + +abs + "Return the absolute value of the receiver." + ^(self real squared + self imaginary squared) sqrt! + +absSquared + "Return the squared absolute value of the receiver." + ^(self real squared + self imaginary squared)! + +conjugate + "Return the complex conjugate of the receiver." + ^Complex + realResult: self real + imaginary: self imaginary negated! + +!Complex methodsFor: 'transcendental functions'! + +exp + "Return e raised to the receiver." + | expRe | + expRe := self real exp. + ^Complex + realResult: expRe * self imaginary cos + imaginary: expRe * self imaginary sin! + +sqrt + "Return the square root of the receiver. Can be improved!" + | abs | + self imaginary < 0 ifTrue: [ ^self conjugate sqrt conjugate ]. + abs := self abs. + ^Complex + realResult: ((abs + self real) / 2) sqrt + imaginary: ((abs - self real) / 2) sqrt! + +sin + "Return the sine of the receiver." + | sinhIm | + sinhIm := self imaginary sinh. + ^Complex + realResult: self real sin * (sinhIm squared + 1) sqrt + imaginary: self real cos * sinhIm! + +cos + "Return the cosine of the receiver." + | sinhIm | + sinhIm := self imaginary sinh. + ^Complex + realResult: self real cos * (sinhIm squared + 1) sqrt + imaginary: self real sin negated * sinhIm! + +sinh + "Return the hyperbolic sine of the receiver." + | sinhRe | + sinhRe := self real sinh. + ^Complex + realResult: sinhRe * self imaginary cos + imaginary: (sinhRe squared + 1) sqrt * self imaginary sin! + +cosh + "Return the hyperbolic cosine of the receiver." + | sinhRe | + sinhRe := self real sinh. + ^Complex + realResult: (sinhRe squared + 1) sqrt * self imaginary cos + imaginary: sinhRe * self imaginary sin! + +arg + "Return the argument of the receiver." + ^self imaginary arcTan: self real! + +arcTan + "Return the arc-tangent of the receiver." + | z | + z := ((Complex i + self) / (Complex i - self) asFloat) ln. + ^Complex real: 0 imaginary: z / 2! + +arcTan: aNumber + "Return the arc-tangent of aNumber divided by the receiver." + | z | + z := ((aNumber i + self) / (aNumber i - self) asFloat) ln. + ^Complex real: 0 imaginary: z / 2! + +ln + "Return the natural logarithm of the receiver." + ^Complex + realResult: self absSquared ln / 2 + imaginary: self arg! + +log + "Return the base-10 logarithm of the receiver." + | ln | + ln := self ln. + ^ln / ln real class ln10! + +tanh + "Return the hyperbolic tangent of the receiver." + ^self sinh / self cosh! + +tan + "Return the tangent of the receiver." + ^self sin / self cos! ! + +!Complex methodsFor: 'comparing'! + +< aNumber + ^self abs < aNumber abs! + +<= aNumber + ^self abs <= aNumber abs! + +>= aNumber + ^self abs >= aNumber abs! + +> aNumber + ^self abs > aNumber abs! + += aNumber + aNumber isNumber ifFalse: [ ^false ]. + ^self real = aNumber real and: [ self imaginary = aNumber imaginary ]! + +~= aNumber + aNumber isNumber ifFalse: [ ^true ]. + ^self real ~= aNumber real or: [ self imaginary ~= aNumber imaginary ]! + +hash + ^self real hash bitXor: self imaginary hash! + +!Complex methodsFor: 'converting'! + +asFloat + ^Complex + real: self real asFloat + imaginary: self imaginary asFloat! + +asFloatD + ^Complex + real: self real asFloatD + imaginary: self imaginary asFloatD! + +asFloatE + ^Complex + real: self real asFloatE + imaginary: self imaginary asFloatE! + +asFloatQ + ^Complex + real: self real asFloatQ + imaginary: self imaginary asFloatQ! + +asFraction + ^Complex + real: self real asFraction + imaginary: self imaginary asFraction! + +asExactFraction + ^Complex + real: self real asExactFraction + imaginary: self imaginary asExactFraction! + +floor + ^Complex + real: self real floor + imaginary: self imaginary floor! + +ceiling + ^Complex + real: self real ceiling + imaginary: self imaginary ceiling! + +truncated + ^Complex + real: self real truncated + imaginary: self imaginary truncated! + +rounded + ^Complex + real: self real rounded + imaginary: self imaginary rounded! ! + +!Complex methodsFor: 'printing'! + +printOn: aStream + aStream + nextPut: $(; + print: self real; + nextPut: $+; + print: self imaginary; + nextPut: $i; + nextPut: $)! + +storeOn: aStream + aStream + nextPut: $(; + store: self real; + nextPut: $+; + store: self imaginary; + nextPutAll: ' i)'! + +!Complex methodsFor: 'creation/coercion'! + +isComplex + ^true! + +zero + ^Zero! + +one + ^One! + +generality + ^re generality + 1000! + +real + ^re! + +imaginary + ^im! + +coerce: aNumber + aNumber isComplex + ifFalse: [ ^Complex basicNew setReal: aNumber imaginary: aNumber zero ]. + + ^Complex basicNew + setReal: (re coerce: aNumber real) + imaginary: (re coerce: aNumber imaginary)! + +setReal: real imaginary: imag + re := real. + im := imag! + +i + "Return the receiver multiplied by the imaginary unit." + ^Complex real: self imaginary negated imaginary: self real! + +!Number methodsFor: 'accessing'! + +real + "Return the real part of the receiver." + ^self +! + +imaginary + "Return the imaginary part of the receiver, which is zero." + ^self zero +! + +conjugate + "Return the receiver, which is the same as its conjugate." + ^self +! + +isComplex + ^false! + +absSquared + "Return the square of the receiver, which is also the squared absolute + value for real numbers." + ^self squared +! + +raisedTo: aNumber + "Return the receiver, raised to aNumber. This may answer a complex number + if the receiver is negative." + | log theta | + aNumber isComplex ifFalse: [ + ^Complex + rho: (self absSquared raisedTo: aNumber / 2) + theta: (self arg * aNumber) ]. + log := self abs ln. + theta := self arg. + ^Complex + rho: ((aNumber real * log) - (aNumber imaginary * theta)) exp + theta: (aNumber real * theta) + (aNumber imaginary * log)! + +arg + "Return the argument of the receiver." + ^self >= 0 ifTrue: [ 0.0d ] ifFalse: [ FloatD pi ] +! + +i + "Return the receiver multiplied by the imaginary unit." + ^Complex real: self zero imaginary: self +! ! + +!Float methodsFor: 'private'! + +primLn + "Answer the natural logarithm of the receiver" + <primitive: VMpr_Float_ln> + self primitiveFailed +! + +primSqrt + "Answer the square root of the receiver" + <primitive: VMpr_Float_sqrt> + self primitiveFailed +! + +!Float methodsFor: 'transcendental functions'! + +arg + "Return the argument of the receiver." + ^self >= 0 ifTrue: [ self zero ] ifFalse: [ self class pi ] +! + +ln + "Answer the natural logarithm of the receiver" + self >= 0 ifTrue: [ ^self primLn ]. + ^Complex real: self negated primLn imaginary: self class pi +! + +sqrt + "Answer the square root of the receiver" + self >= 0 ifTrue: [ ^self primSqrt ]. + ^Complex real: 0 imaginary: self negated primSqrt +! ! + +!Number methodsFor: 'transcendental functions'! + +arcCos + "Return the arc-cosine of the receiver." + | z | + z := (Complex real: self imaginary: ((1 - self squared) sqrt)) ln. + ^Complex real: 0 imaginary: z negated! + +arcSin + "Return the arc-sine of the receiver." + | z | + z := (Complex real: ((1 - self squared) sqrt) imaginary: self) ln. + ^Complex real: 0 imaginary: z negated! ! + +Float methodDictionary + removeKey: #arcSin; + removeKey: #arcCos! + +Complex initialize! --- /dev/null +++ mod/packages/complex/complextests.st @@ -0,0 +1,339 @@ +"====================================================================== +| +| Complex numbers test suite +| +| + ======================================================================" + + +"====================================================================== +| +| Copyright 2007 Free Software Foundation, Inc. +| Written by Paolo Bonzini +| +| This file is part of the GNU Smalltalk class library. +| +| The GNU Smalltalk class library is free software; you can redistribute it +| and/or modify it under the terms of the GNU Lesser General Public License +| as published by the Free Software Foundation; either version 2.1, or (at +| your option) any later version. +| +| The GNU Smalltalk class library is distributed in the hope that it will be +| useful, but WITHOUT ANY WARRANTY; without even the implied warranty of +| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser +| General Public License for more details. +| +| You should have received a copy of the GNU Lesser General Public License +| along with the GNU Smalltalk class library; see the file COPYING.LIB. +| If not, write to the Free Software Foundation, 59 Temple Place - Suite +| 330, Boston, MA 02110-1301, USA. +| + ======================================================================" + +PackageLoader fileInPackage: #Complex! +PackageLoader fileInPackage: #SUnit! + +TestCase subclass: #ComplexTest + instanceVariableNames: '' + classVariableNames: '' + poolDictionaries: '' + category: 'Examples-Useful'! + +!ComplexTest methodsFor: 'asserting'! + +assert: x closeTo: y + self assert: (x closeTo: y) +! ! + +!ComplexTest methodsFor: 'unit tests'! + +testI + self assert: Complex i real == 0. + self assert: Complex i imaginary == 1. + self assert: Complex i == Complex i. + self assert: 1 i real == 0. + self assert: 1 i imaginary == 1. + self assert: Complex i i == -1! + +testPolar + self assert: (Complex rho: 1 theta: 0) = 1. + self assert: (Complex rho: 1 theta: FloatD pi / 2) closeTo: Complex i. + self assert: (Complex rho: 1 theta: FloatD pi) closeTo: -1. + self assert: (Complex rho: 2 theta: 0) = 2! + +testCartesion + self assert: (Complex real: 1 imaginary: 0) == 1. + self assert: (Complex real: Complex i imaginary: 0) = Complex i. + self assert: (Complex real: 0 imaginary: Complex i) == -1. + self assert: (Complex real: 1 imaginary: Complex i) == 0. + self assert: (Complex real: 1 imaginary: 1) real == 1. + self assert: (Complex real: 1 imaginary: 1) imaginary == 1. + self assert: (Complex real: 1 imaginary: 1.0) real isFloat. + self assert: (Complex real: 1.0 imaginary: 1) imaginary isFloat! + +testPlus + self assert: (1 + 2 i) real == 1. + self assert: (1 + 2 i) imaginary == 2. + self assert: 0.5 i + (1 + 2 i) = (1 + 2.5 i). + self assert: 0.5 + (1 + 2 i) = (1.5 + 2 i). + self assert: (3 + 4 i) + (1 + 2 i) = (4 + 6 i)! + +testMinus + self assert: (1 - 2 i) real == 1. + self assert: (1 - 2 i) imaginary == -2. + self assert: 0.5 i - (1 + 2 i) = (-1 + -1.5 i). + self assert: 0.5 - (1 + 2 i) = (-0.5 + -2 i). + self assert: (3 + 4 i) - (1 + 3 i) = (2 + 1 i). + self assert: (1 + 2.0 i) - (1 + 2 i) = 0. + self assert: (1.0 + 2 i) - (1 + 2 i) = 0! + +testMultiply + self assert: Complex i * Complex i = -1. + self assert: Complex i * 1 = Complex i. + self assert: Complex i * 0.5 = 0.5 i. + self assert: (3 + 4 i) * (1 + 2 i) = (-5 + 10 i)! + +testDivide + self assert: Complex i / Complex i == 1. + self assert: Complex i / 1 = Complex i. + self assert: Complex i / 0.5 = 2 i. + self assert: ((3 + 4 i) / (1 + 2 i)) = ((22 - 4 i) / 10). + self assert: ((3 + 4 i) / (1 + 2 i)) real * 10 == 22. + self assert: ((3 + 4 i) / (1 + 2 i)) imaginary * 10 == -4! + +testReciprocal + self assert: Complex i reciprocal real == 0. + self assert: Complex i reciprocal imaginary == -1. + self assert: (1 + 2 i) reciprocal real * 5 == 1. + self assert: (1 + 2 i) reciprocal imaginary * 5 == -2! + +testAbs + self assert: (3 + 4 i) abs = 5. + self assert: (3 - 4 i) abs = 5. + self assert: (-3 + 4 i) abs = 5. + self assert: (-3 - 4 i) abs = 5! + +testAbsSquared + self assert: (3 + 4 i) absSquared == 25. + self assert: (3 - 4 i) absSquared == 25. + self assert: (-3 + 4 i) absSquared == 25. + self assert: (-3 - 4 i) absSquared == 25! + +testConjugate + self assert: Complex i * Complex i conjugate == 1. + self assert: (3 + 4 i) conjugate = (3 - 4 i). + self assert: 3 conjugate == 3! + +testExp + self assert: (FloatD pi negated i) exp closeTo: -1. + self assert: (FloatD pi i) exp closeTo: -1. + self assert: (FloatD pi i / 2) exp closeTo: Complex i. + self assert: (1 + FloatD pi i) exp closeTo: 1 exp negated! + +testSin + self assert: 1 i sin imaginary = 1 sinh. + self assert: (FloatD pi + 1 i) sin imaginary = -1 sinh. + self assert: (FloatD pi / 2 + 1 i) sin real = 1 cosh! + +testCos + self assert: 1 i cos = 1 cosh! + +testSinh + self assert: FloatD pi i sinh closeTo: 0! + +testCosh + self assert: FloatD pi i cosh closeTo: -1! + +testArcCos + self assert: 1 cosh arcCos real closeTo: 0. + self assert: 1 cosh arcCos imaginary closeTo: 1! + +testArcSin + self assert: 1 cosh arcSin imaginary closeTo: -1. + self assert: 1 cosh arcSin real closeTo: FloatD pi / 2! + +testArcTan + self assert: 1 tanh i arcTan real closeTo: 0. + self assert: 1 tanh i arcTan imaginary closeTo: 1. + self assert: (Complex i arcTan: 1 tanh reciprocal) real closeTo: 0. + self assert: (Complex i arcTan: 1 tanh reciprocal) imaginary closeTo: 1! + +testArg + self assert: -1 arg closeTo: FloatD pi. + self assert: Complex i arg closeTo: (FloatD pi / 2). + self assert: (1 + 1 i) arg closeTo: (FloatD pi / 4)! + +testSqrt + self assert: -1 sqrt isComplex. + self deny: 1 sqrt isComplex. + self assert: -1 sqrt = Complex i. + self assert: Complex i sqrt real = Complex i sqrt imaginary. + self assert: (3 + 4 i) sqrt = (2+1i)! + +testLn + self assert: -1 ln isComplex. + self deny: 1 ln isComplex. + self assert: -1 ln imaginary closeTo: FloatD pi. + self assert: (1 + 1 i) ln real * 2 closeTo: 2 ln. + self assert: (1 + 1 i) ln imaginary closeTo: (FloatD pi / 4)! + +testLog + "Return the base-10 logarithm of the receiver." + self assert: (1 + 1 i) log real * 2 = 2 log! + +testTanh + "Return the hyperbolic tangent of the receiver." + self assert: Complex i tanh closeTo: 1 tan i! + +testTan + "Return the tangent of the receiver." + self assert: Complex i tan closeTo: 1 tanh i! + +testLess + self deny: (1 + 1 i) < 1. + self deny: (1 + 1 i) < -1. + self deny: (3 + 4 i) < 5. + self deny: (3 + 4 i) < -5. + self deny: (3 + 4 i) < (4 + 3 i). + self deny: (3 + 4 i) < (4 - 3 i). + self deny: (3 - 4 i) < (4 + 3 i). + self deny: (3 - 4 i) < (4 - 3 i). + self assert: (1 + 1 i) < 10. + self assert: (1 + 1 i) < -10! + +testLessEqual + self deny: (1 + 1 i) <= 1. + self deny: (1 + 1 i) <= -1. + self assert: (3 + 4 i) <= 5. + self assert: (3 + 4 i) <= -5. + self assert: (3 + 4 i) <= (4 + 3 i). + self assert: (3 + 4 i) <= (4 - 3 i). + self assert: (3 - 4 i) <= (4 + 3 i). + self assert: (3 - 4 i) <= (4 - 3 i). + self assert: (1 + 1 i) <= 10. + self assert: (1 + 1 i) <= -10! + +testGreaterEqual + self assert: (1 + 1 i) >= 1. + self assert: (1 + 1 i) >= -1. + self assert: (3 + 4 i) >= 5. + self assert: (3 + 4 i) >= -5. + self assert: (3 + 4 i) >= (4 + 3 i). + self assert: (3 + 4 i) >= (4 - 3 i). + self assert: (3 - 4 i) >= (4 + 3 i). + self assert: (3 - 4 i) >= (4 - 3 i). + self deny: (1 + 1 i) >= 10. + self deny: (1 + 1 i) >= -10! + +testGreater + self assert: (1 + 1 i) > 1. + self assert: (1 + 1 i) > -1. + self deny: (3 + 4 i) > 5. + self deny: (3 + 4 i) > -5. + self deny: (3 + 4 i) > (4 + 3 i). + self deny: (3 + 4 i) > (4 - 3 i). + self deny: (3 - 4 i) > (4 + 3 i). + self deny: (3 - 4 i) > (4 - 3 i). + self deny: (1 + 1 i) > 10. + self deny: (1 + 1 i) > -10! + +testEqual + self assert: (3 + 4 i) = (3 + 4 i). + self assert: (3 + 4 i) = (3.0 + 4.0 i). + self deny: (3 + 4 i) = 5. + self deny: (3 + 4 i) = -5. + self deny: (3 + 4 i) = (4 + 3 i). + self deny: (3 + 4 i) = (4 - 3 i). + self deny: (3 - 4 i) = (4 + 3 i). + self deny: (3 - 4 i) = (4 - 3 i)! + +testNotEqual + self deny: (3 + 4 i) ~= (3 + 4 i). + self deny: (3 + 4 i) ~= (3.0 + 4.0 i). + self assert: (3 + 4 i) ~= 5. + self assert: (3 + 4 i) ~= -5. + self assert: (3 + 4 i) ~= (4 + 3 i). + self assert: (3 + 4 i) ~= (4 - 3 i). + self assert: (3 - 4 i) ~= (4 + 3 i). + self assert: (3 - 4 i) ~= (4 - 3 i)! + +testHash + self assert: (3 + 4 i) hash = (3 + 4 i) hash. + self assert: (3 + 4 i) hash = (3.0 + 4.0 i) hash! + +testAsFloat + self assert: (3 + 4 i) asFloat real isFloat. + self assert: (3 + 4 i) asFloat imaginary isFloat! + +testAsFloatD + self assert: (3 + 4 i) asFloatD real isFloat. + self assert: (3 + 4 i) asFloatD imaginary isFloat! + +testAsFloatE + self assert: (3 + 4 i) asFloatE real isFloat. + self assert: (3 + 4 i) asFloatE imaginary isFloat! + +testAsFloatQ + self assert: (3 + 4 i) asFloatQ real isFloat. + self assert: (3 + 4 i) asFloatQ imaginary isFloat! + +testAsFraction + self deny: (3.0 + 4 i) asFraction real isFloat. + self deny: (3.0 + 4 i) asFraction imaginary isFloat! + +testAsExactFraction + self deny: (3.0 + 4 i) asFraction real isFloat. + self deny: (3.0 + 4 i) asFraction imaginary isFloat! + +testFloor + self assert: (3.5 + 4.5 i) floor real == 3. + self assert: (3.5 + 4.5 i) floor imaginary == 4. + self assert: (-2.5 - 3.5 i) floor real == -3. + self assert: (-2.5 - 3.5 i) floor imaginary == -4! + +testCeiling + self assert: (2.5 + 3.5 i) ceiling real == 3. + self assert: (2.5 + 3.5 i) ceiling imaginary == 4. + self assert: (-3.5 - 4.5 i) ceiling real == -3. + self assert: (-3.5 - 4.5 i) ceiling imaginary == -4! + +testTruncated + self assert: (3.5 + 4.5 i) truncated real == 3. + self assert: (3.5 + 4.5 i) truncated imaginary == 4. + self assert: (-3.5 - 4.5 i) truncated real == -3. + self assert: (-3.5 - 4.5 i) truncated imaginary == -4! + +testRounded + self assert: (3.25 + 3.75 i) rounded real == 3. + self assert: (3.25 + 3.75 i) rounded imaginary == 4. + self assert: (-3.25 - 3.75 i) rounded real == -3. + self assert: (-3.25 - 3.75 i) rounded imaginary == -4! + +testIsComplex + self assert: Complex i isComplex. + self deny: (Complex real: 5 imaginary: 0) isComplex. + self deny: 5 isComplex! + +testZero + self assert: Complex i zero = 0. + self assert: 0 = Complex i zero! + +testOne + self assert: Complex i one = 1. + self assert: 1 = Complex i one! + +testReal + self assert: 5 real == 5. + self assert: 5.0 real = 5.0. + self assert: Complex i real = 0. + self assert: Complex i one real = 1! + +testImaginary + self assert: 5 imaginary == 0. + self assert: 5.0 imaginary = 0. + self assert: Complex i imaginary = 1. + self assert: Complex i one imaginary = 0! + +testRaisedTo + self assert: (Complex i raisedTo: Complex i) closeTo: (Float pi / -2) exp. + self assert: (1 raisedTo: Complex i) = 1! ! _______________________________________________ help-smalltalk mailing list [hidden email] http://lists.gnu.org/mailman/listinfo/help-smalltalk |
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