'From Pharo1.0beta of 16 May 2008 [Latest update: #10411] on 11 August 2009 at 4:17:57 pm'!
Magnitude subclass: #Complex
	instanceVariableNames: 'real imaginary'
	classVariableNames: ''
	poolDictionaries: ''
	category: 'Kernel-Numbers'!

!Complex methodsFor: 'accessing' stamp: 'KenD 8/9/2009 10:03'!
imag
	"Convenience alias for #imaginary"
	^ imaginary! !

!Complex methodsFor: 'arithmetic' stamp: 'KenD 8/9/2009 14:52'!
< other
	"self < other if other's real-part is to the right or the real-parts are equal and the oher's imaginary part is larger"
	| otherCpx |
	otherCpx := other asComplex.
	^self real < otherCpx real
			or: [self real = otherCpx real  and: [self imag < otherCpx imag]]! !

!Complex methodsFor: 'arithmetic' stamp: 'KenD 8/10/2009 15:29'!
conjugate

	^ Complex real: real imaginary: (imaginary negated)! !

!Complex methodsFor: 'arithmetic' stamp: 'KenD 8/10/2009 15:22'!
inverse

	^(self / (self norm))! !

!Complex methodsFor: 'arithmetic' stamp: 'KenD 8/10/2009 15:32'!
norm

	^(self * (self conjugate))! !

!Complex methodsFor: 'converting' stamp: 'KenD 8/9/2009 19:13'!
adaptToPoint: rcvr andSend: selector
	"If I am involved in arithmetic with a Point, convert me to a Point."
	^ rcvr perform: selector with: (self asPoint)! !

!Complex methodsFor: 'converting' stamp: 'KenD 8/9/2009 14:49'!
asComplex
	^self! !

!Complex methodsFor: 'converting' stamp: 'KenD 8/9/2009 19:14'!
asPoint
	^real@imaginary! !

!Complex methodsFor: 'converting' stamp: 'KenD 8/10/2009 15:59'!
asString

   ((imaginary = 0) | (imaginary = nil))
	  ifTrue: [ ^ real ifNil: ['0'] ifNotNil: [real asString]]
	  ifFalse: [
		((real = 0) | (real = nil))
	  	ifTrue: [ ^ (imaginary asString), 'i']
	  	ifFalse: [ ^ '(' , (real asString) , ' + ' , (imaginary asString) , 'i)'].
	  ].! !

!Complex methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 19:16'!
angle
	"Answer my angle in radians"
	^ ((imaginary / real) arcTan)! !

!Complex methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 20:49'!
arcCos
	^(((Float pi)/2) - (self arcSin))! !

!Complex methodsFor: 'mathematical functions' stamp: 'KenD 8/10/2009 15:44'!
arcCosH
	| x y az az2 hairy |
	x := real asFloat.
	y := imaginary asFloat.
   az := (self abs).
	az2 := az squared.
   hairy := ((((az2 - 1) squared) + (4 * y * y)) sqrt).

	^Complex real: (1/2 * ((hairy + az2) arcCosH))
	    imaginary: (1/2 * (y signum) 
			* ((Float pi) - ((x signum) * ((hairy - az2) arcCos))))! !

!Complex methodsFor: 'mathematical functions' stamp: 'KenD 8/10/2009 15:44'!
arcSin
	| x y az az2 hairy |
	x := real.
	y := imaginary.
   az := (self abs).
	az2 := az squared.
   hairy := ((((az2 - 1) squared) + (4 * y * y)) sqrt).

	^Complex real: ((1/2) * (x signum) * ((hairy - az2) arcCos))
	   imaginary: ((1/2) * (y signum) * ((hairy + az2) arcCosH))! !

!Complex methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 19:39'!
arcSinH

	^(self + ((1 + (self squared)) sqrt)) ln! !

!Complex methodsFor: 'mathematical functions' stamp: 'KenD 8/10/2009 16:06'!
arcTan

	| x y |
	x := real.
	y := imaginary.
	^Complex real: (1/2 * 
					((x ~= 0) 
						ifTrue: [(2 * x) arcTan: (1 - ((self abs) squared))]
						ifFalse: [ 
							((y abs) > 1)
							ifTrue: [(Float pi) * (x signum)]
							ifFalse: [0].
						])
					)
	   imaginary: (1/2 * (((2 * y) / (1 + ((self abs) squared))) arcTanH)).! !

!Complex methodsFor: 'mathematical functions' stamp: 'KenD 8/10/2009 17:13'!
arcTanH
	| x y az2 |
	x := real.
	y := imaginary.
	az2 := (self abs) squared.

	^ Complex real: (1/2 * (((2 * x) / (1 + az2)) arcTanH))
	    imaginary: (1/2 * 
					((y ~= 0) 
					ifTrue: [(2 * y) arcTan: (1 - az2)]
					ifFalse: [
						((x abs) > 1)
						ifTrue: [((Float pi) negated) * (x signum)]
						ifFalse: [0]
					]))! !

!Complex methodsFor: 'mathematical functions' stamp: 'KenD 8/10/2009 15:50'!
cos
	"Answer receiver's cosine."
"	| x y |
	x := real.
	y := imaginary.
	^ Complex real: ((x cos) * (y cosH))
		imaginary: (((x sin) * (y sinH)) negated)"
	| iself |
	iself := 1 i * self.
	^ (iself exp + iself negated exp) / 2! !

!Complex methodsFor: 'mathematical functions' stamp: 'KenD 8/10/2009 16:10'!
cosH
	"Answer receiver's hyperbolic cosine."

	| x y |
	x := real asFloat.
	y := imaginary asFloat.
	^ Complex real: ((x cosH) * (y cos)) 
		imaginary: ((x sinH) * (y sin))
	"^ (self exp + self negated exp) / 2"! !

!Complex methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 19:22'!
cotH
        "Answer the hyperbolic cotangent of the receiver taken as an angle in radians."

        ^ ( (self exp) + ((self negated) exp) ) / ( (self exp) - ((self negated) exp) )! !

!Complex methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 19:23'!
cscH
        "Answer the hyperbolic cosecant of the receiver taken as an angle in radians."

        ^ 2 / ( (self exp) - ((self negated) exp) ) ! !

!Complex methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 16:40'!
exp
	"Answer the exponential of the receiver."
	| x y e2x |
	x := real.
	y := imaginary.
	e2x := x exp.
	^ (Complex real: (e2x * (y cos)) imaginary: (e2x * (y sin)))! !

!Complex methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 18:42'!
ln
" See Mantis bug-1815
	| x y |
	x := real.
	y := imaginary.
	^ (Complex real: ( 1/2 * ((((self abs) squared) asFloat) ln) )
	     imaginary: (y arcTan: x))"
	^ self abs ln + (1 i * self arg)! !

!Complex methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 19:17'!
magnitude
	"answer my magnitude (length from self as point to origin"
	^self abs! !

!Complex methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 19:23'!
secH
        "Answer the hyperbolic secant of the receiver taken as an angle in radians."

        ^ 2 / ( (self exp) + ((self negated) exp) ) ! !

!Complex methodsFor: 'mathematical functions' stamp: 'KenD 8/10/2009 15:11'!
sinH
	 "Answer the hyperbolic sine of the receiver taken as an angle in radians."

	"^ (self exp - self negated exp) / 2"
	| x y |
	x := real asFloat.
	y := imaginary asFloat.
	^ Complex real: ((x sinH) * (y cos))
		imaginary: ((x cosH) * (y sin))! !

!Complex methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 15:01'!
sqrt
	| az |
	az := self abs.
	^Complex real: (((az + real) / 2) sqrt) 
	   imaginary: ((imaginary signum) * (((az - real) / 2) sqrt))! !

!Complex methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 19:10'!
squared
	"Answer the receiver multipled by itself."
"	| x y |
	x := real.
	y := imaginary.
	^ Complex real: ((x + y) * (x - y))
	     imaginary: (2 * x * y)"
	^self * self! !

!Complex methodsFor: 'mathematical functions' stamp: 'KenD 8/10/2009 15:54'!
tan
	"Answer receivers tangent."
	| x2 y2 |
	x2 := (real * 2).
	y2 := (imaginary * 2).
	^Complex real: ((x2 sin) / ((x2 cos) + (y2 cosH)))
	   imaginary: ((y2 tanH) / (1 + ((x2 cos) / (y2 cosH))))
	"^ self sin / self cos"! !

!Complex methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 19:11'!
tanH
	| x2 y2 |
	x2 := (real * 2) asFloat.
	y2 := (imaginary * 2) asFloat.
	^ Complex real: ((x2 tanH) / (1 + ((y2 cos)/(x2 cosH))))
	    imaginary: ((y2 sin) / ((x2 cosH) + (y2 cos)))! !

!Complex methodsFor: 'printing' stamp: 'KenD 8/9/2009 16:17'!
printOn: aStream
	(real = 0)
	ifTrue: [
		imaginary printOn: aStream.
		aStream nextPut: $i]
	ifFalse: [
		aStream nextPut: $(.
		real printOn: aStream.
		(imaginary < 0)
			ifFalse:  [aStream nextPut: $+].
		imaginary printOn: aStream.
		aStream nextPut: $i.
		aStream nextPut: $) ]
! !

!Complex methodsFor: 'private' stamp: 'KenD 8/9/2009 16:21'!
signum
	"NB: signum(0) is 1 [required]"
	| za |
	za := self abs.
	(za = 0)
	ifTrue: [^ real signum]
	ifFalse: [^self / za]! !

!Complex methodsFor: 'truncation and rounding' stamp: 'KenD 8/9/2009 19:20'!
ceiling
	"distribute"
	^Complex real: (real ceiling) imaginary: (imaginary ceiling)! !

!Complex methodsFor: 'truncation and rounding' stamp: 'KenD 8/9/2009 19:20'!
floor
	"distribute"
	^Complex real: (real floor) imaginary: (imaginary floor)! !

!Complex methodsFor: 'truncation and rounding' stamp: 'KenD 8/9/2009 19:20'!
reduce
	"distribute"
	^Complex real: (real reduce) imaginary: (imaginary reduce)! !

!Complex methodsFor: 'truncation and rounding' stamp: 'KenD 8/9/2009 16:29'!
roundTo: quantum
	"distribute."

	^Complex real: (real roundTo: quantum) 
			  imaginary: (imaginary roundTo: quantum)! !

!Complex methodsFor: 'truncation and rounding' stamp: 'KenD 8/9/2009 16:35'!
roundUpTo: quantum
	"distribute."

	^Complex real: (real roundUpTo: quantum) 
			  imaginary: (imaginary roundUpTo: quantum)! !

!Complex methodsFor: 'truncation and rounding' stamp: 'KenD 8/9/2009 16:37'!
truncateTo: aNumber
	"distribute."

	^Complex real: (real truncateTo: aNumber) 
			  imaginary: (imaginary truncateTo: aNumber)! !

!Complex methodsFor: 'truncation and rounding' stamp: 'KenD 8/9/2009 16:36'!
truncated
	"distribute."

	^Complex real: (real truncated) 
			  imaginary: (imaginary truncated)! !


!Complex class methodsFor: 'deprecated' stamp: 'KenD 8/10/2009 15:20'!
quickCheck: aStream

"Expected Result
================================
Sample Complex usage:
 3.2i prints as: 3.2i
     a = ((1/2) + 2.1i)
     b = ((3/4) + 5.7i)
 a + b = ((5/4) + 7.8i)
 a - b = ((-1/4) + -3.6i)
 a * b = (-11.595 + 4.425i)
 a * 3 = (1.5 + 6.3i)
 3 * b = (2.25 + 17.1i)
 a / b = (0.373497 + -0.038575i)
 a / 3 = (0.166667 + 0.7i)
 3 / b = (0.0680735 + -0.517359i)
sin(a) = (1.98689 + 3.52951i)
cos(a) = (3.63698 + -1.92818i)
tan(a) = (0.0248288 + 0.983615i)
 ln(3) = 1.09861
ln(-3) = (1.09861 + 3.14159i)
 ln(a) = (0.769508 + 1.33705i)
exp(3) = 20.0855
exp(a) = (-0.832351 + 1.42319i)
conjugate(a) = ((1/2) + -2.1i)
  inverse(a) = (0.107296 + 0.450644i)
     norm(a) = 4.66
asin(sin(a)) = (0.5 + 2.1i)
acos(cos(a)) = (0.5 + 2.1i)
atan(tan(a)) = (0.5 + 2.1i)
  abs(a - b) = 3.60867
 norm(a - b) = 13.0225
     sinh(a) = (-0.263073 + 0.973377i)
     cosh(a) = (-0.569278 + 0.449814i)
     tanh(a) = (1.11624 + -0.827849i)
asinh(sinh(a)) = (-0.5 + 1.04159i)
acosh(cosh(a)) = (0.5 + 2.1i)
atanh(tanh(a)) = (0.5 + 2.1i)
"

	| a b |
	aStream cr.
	aStream show: 'Sample Complex usage:'.
 	aStream cr.
	aStream show: ' 3.2i prints as: ' , (3.2i asString).

	a := Complex real: 1/2 imaginary: 2.1 .
	b := Complex real: 3/4 imaginary: 5.7 .

	aStream cr.
	aStream show: '     a = ' , (a asString).
 	aStream cr.
	aStream show: '     b = ' , (b asString).
 	aStream cr.
	aStream show: ' a + b = ' , ((a + b) asString).
 	aStream cr.
	aStream show: ' a - b = ' , ((a - b) asString).
 	aStream cr.
	aStream show: ' a * b = ' , ((a * b) asString).
 	aStream cr.
	aStream show: ' a * 3 = ' , ((a * 3) asString).
 	aStream cr.
	aStream show: ' 3 * b = ' , ((3 * b) asString).
 	aStream cr.
	aStream show: ' a / b = ' , ((a / b) asString).
 	aStream cr.
	aStream show: ' a / 3 = ' , ((a / 3) asString).
 	aStream cr.
	aStream show: ' 3 / b = ' , ((3 / b) asString).

 	aStream cr.
	aStream show: 'sin(a) = ' , ((a sin) asString).
 	aStream cr.
	aStream show: 'cos(a) = ' , ((a cos) asString).
 	aStream cr.
	aStream show: 'tan(a) = ' , ((a tan) asString).

 	aStream cr.
	aStream show: ' ln(3) = ' , ((3 ln) asString).
 	aStream cr.
	aStream show: 'ln(-3) = ' , ((-3 ln) asString).
 	aStream cr.
	aStream show: ' ln(a) = ' , ((a ln) asString).
 	aStream cr.
	aStream show: 'exp(3) = ' , ((3 exp) asString).
 	aStream cr.
	aStream show: 'exp(a) = ' , ((a exp) asString).

 	aStream cr.
	aStream show: 'conjugate(a) = ' , ((a conjugate) asString).
 	aStream cr.
	aStream show: '  inverse(a) = ' , ((a inverse) asString).
 	aStream cr.
	aStream show: '     norm(a) = ' , ((a norm) asString).

 	aStream cr.
	aStream show: 'asin(sin(a)) = ' , (((a sin) arcSin) asString).
 	aStream cr.
	aStream show: 'acos(cos(a)) = ' , (((a cos) arcCos) asString).
 	aStream cr.
	aStream show: 'atan(tan(a)) = ' , (((a tan) arcTan) asString).

 	aStream cr.
	aStream show: '  abs(a - b) = ' , (((a - b) abs) asString).
 	aStream cr.
	aStream show: ' norm(a - b) = ' , (((a - b) norm) asString).

 	aStream cr.
	aStream show: '     sinh(a) = ' , ((a sinH) asString).
 	aStream cr.
	aStream show: '     cosh(a) = ' , ((a cosH) asString).
 	aStream cr.
	aStream show: '     tanh(a) = ' , ((a tanH) asString).
 	aStream cr.
	aStream show: 'asinh(sinh(a)) = ' , (((a sinH) arcSinH) asString).
 	aStream cr.
	aStream show: 'acosh(cosh(a)) = ' , (((a cosH) arcCosH) asString).
 	aStream cr.
	aStream show: 'atanh(tanh(a)) = ' , (((a tanH) arcTanH) asString).
	aStream cr.
	aStream show: ''
! !


!ComplexTest methodsFor: 'tests' stamp: 'KenD 8/11/2009 14:52'!
testCompare
   "Anything along either the real or imaginary number line should compare sanely"
	self assert: (-1i < 1i).
	self assert: (-1 asComplex < 1 asComplex).
	"Kinda silly if the following did not work"
	self assert: (1 + -1i) < (1 + 1i).! !

!ComplexTest methodsFor: 'tests' stamp: 'KenD 8/9/2009 14:54'!
testConversion
	"self run: #testConversion"
	"self debug: #testConversion"
	
	self assert: ((1 + 2i) + 1) =  (2 + 2 i).
	self assert: (1 + (1 + 2i)) =  (2 + 2 i).
	self assert: ((1 + 2i) + 1.0) =  (2.0 + 2 i).
	self assert: (1.0 + (1 + 2i)) =  (2.0 + 2 i).
	self assert: ((1 + 2i) + (2/3)) = ((5/3) + 2 i ).
	self assert: ((2/3) + (1 + 2i)) = ((5/3) + 2 i ).
	self assert: (1 + 0i) = 1 asComplex.! !

!ComplexTest methodsFor: 'tests' stamp: 'KenD 8/9/2009 19:27'!
testExpLn
	"self run: #testMath"

	| a epsilon |
	a := ((1/2) + 2.1i).
	epsilon := 0.00001.
	"Because of rounding, the following do not compare exactly."
 	self assert: ((3 ln)  roundTo: epsilon) = (1.09861 roundTo: epsilon).
 	self assert: ((-3 ln) roundTo: epsilon) = ((1.09861 + 3.14159i) roundTo: epsilon).
 	self assert: ((a ln)  roundTo: epsilon) = ((0.769508 + 1.33705i) roundTo: epsilon).
 	self assert: ((3 exp) roundTo: epsilon) = (20.08553692318767 roundTo: epsilon).
 	self assert: ((a exp) roundTo: epsilon) 
			= ((-0.832350511083887 + 1.423191643861584i) roundTo: epsilon).
! !

!ComplexTest methodsFor: 'tests' stamp: 'KenD 8/11/2009 13:56'!
testHyperbolicMath
	| a epsilon |
	a := ((1/2) + 2.1i).
	epsilon := 0.00001.
	"Because of rounding, the following do not compare exactly."
 	self assert: ((a sinH) roundTo: epsilon) = ((-0.263073 + 0.973377i) roundTo: epsilon).
 	self assert: ((a cosH) roundTo: epsilon) = ((-0.569278 + 0.449814i) roundTo: epsilon).
 	self assert: ((a tanH) roundTo: epsilon) = ((1.11624 + -0.827849i) roundTo: epsilon).
 	self assert: ((a sinH arcSinH) roundTo: epsilon)  "bogus, but same as Chez Scheme"
			= ((-0.5 + 1.041592653589793i) roundTo: epsilon).
 	self assert: ((a cosH arcCosH) roundTo: epsilon)  = a.
 	self assert: ((a tanH arcTanH) roundTo: epsilon) = a.
! !

!ComplexTest methodsFor: 'tests' stamp: 'KenD 8/9/2009 14:52'!
testLess
	self assert: ((1 negated asComplex) < (1 asComplex)).
	self assert: (((1 negated)i) < (1i)).! !

!ComplexTest methodsFor: 'tests' stamp: 'KenD 8/11/2009 14:51'!
testMath

	| a b epsilon |
	a := ((1/2) + 2.1i).
    b := ((3/4) + 5.7i).
	epsilon := 0.00001.
	"Because of rounding, the following do not compare exactly."
 	self assert: ((a + b) roundTo: epsilon) = (((5/4) + 7.8i) roundTo: epsilon).
 	self assert: ((a - b) roundTo: epsilon) = (((-1/4) + -3.6i) roundTo: epsilon).
 	self assert: ((a * b) roundTo: epsilon) = ((-11.595 + 4.425i) roundTo: epsilon).
 	self assert: ((a * 3) roundTo: epsilon) = ((1.5 + 6.3i) roundTo: epsilon).
 	self assert: ((3 * b) roundTo: epsilon) = ((2.25 + 17.1i) roundTo: epsilon).
 	self assert: ((a / b) roundTo: epsilon) 
			= ((0.3734967097798956 + -0.0385749943272067i) roundTo: epsilon).
 	self assert: ((a / 3) roundTo: epsilon) 
			= ((0.1666666666666666 + 0.7i) roundTo: epsilon).
 	self assert: ((3 / b) roundTo: epsilon)
			 = ((0.068073519400953 -0.517358747447243i) roundTo: epsilon).

! !

!ComplexTest methodsFor: 'tests' stamp: 'KenD 8/9/2009 16:22'!
testPrivate
	self assert: (0 signum = 1).
	self assert: (-3 signum = -1).
	self assert: (3 signum = 1).
	self assert: (2 asComplex signum) = 1 asComplex.
	self assert: (0+0i signum = 1).! !

!ComplexTest methodsFor: 'tests' stamp: 'KenD 8/9/2009 10:39'!
testSqrt
	self assert: (-4 sqrt) = (2.0i).! !

!ComplexTest methodsFor: 'tests' stamp: 'KenD 8/11/2009 14:16'!
testTrig
	| a epsilon |
	a := ((1/2) + 2.1i).
	epsilon := 0.00001.
	"Because of rounding, the following do not compare exactly."
 	self assert: ((a sin) roundTo: epsilon) 
			= ((1.986889573868458 + 3.529511343338503i) roundTo: epsilon).
 	self assert: ((a cos) roundTo: epsilon) 
			= ((3.63698 + -1.92818i) roundTo: epsilon).
 	self assert: ((a tan) roundTo: epsilon) = ((0.0248288 + 0.983615i) roundTo: epsilon).
 	self assert: ((a sin arcSin) roundTo: epsilon) = a.
 	self assert: ((a cos arcCos) roundTo: epsilon) = a.
 	self assert: ((a tan arcTan) roundTo: epsilon) = a.
   self assert: (-1 arcCos) = (Float pi).
	self assert: (Float pi) cos = -1.0.
	self assert: (Float pi / 2) sin = 1.0.
	self assert: (((Float pi / 4) tan) roundTo: epsilon) = 1.0.
	self assert: (1 arcCos) = 0.0.
	self assert: (1 arcSin) = ((Float pi) / 2).
	self assert: (1 arcTan) = ((Float pi) / 4).
	self assert: (-1 arcCos) = (Float pi).
	! !


!Number methodsFor: 'converting' stamp: 'KenD 8/9/2009 14:49'!
asComplex
	^Complex real: self imaginary: 0! !

!Number methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 19:29'!
log
	"Answer the base-10 log of the receiver."
 	(self < 0)
        ifTrue: [ ^ (self asComplex) log: 10 ]
        ifFalse: [ ^self asFloat log ].! !

!Number methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 20:58'!
sqrt
	"Answer the square root of the receiver."

	(self < 0)
	ifTrue: [^self asComplex sqrt]
	ifFalse: [^self asFloat sqrt]! !

!Number methodsFor: 'private' stamp: 'KenD 8/9/2009 15:03'!
signum
        "private For complex number implementation. NB: 0 signum -> 1"

        (self < 0)
                ifTrue: [ ^ -1 ]
                ifFalse: [ ^ 1 ].! !


!Float methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 19:47'!
arcCosH
        "answer hyperbolic arc cosine of self"

        (self >= 1)
                ifTrue: [ ^ (self * (1 + ((1 - (1 / (self * self))) sqrt))) ln]
                ifFalse: [
                        ((self abs) <= 1)
                        ifTrue: [ ^ (((1 - (self * self)) sqrt) arcTan: self)i ]
                        ifFalse: [ ^ Complex real: ((self negated) arcCosH) 
								  imaginary: (Float pi)].
                ].! !

!Float methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 19:47'!
arcSinH
        "answer hyperbolic arc sine of self"

        ^(1/2 * (self signum) * ((1 + (self squared * 2)) arcCosH))! !

!Float methodsFor: 'mathematical functions' stamp: 'KenD 8/10/2009 17:16'!
arcTan: denominator
	"Answer the angle in radians.
	 Optional. See Object documentation whatIsAPrimitive."

	| result |

	(self = 0.0) ifTrue: [ (denominator > 0.0) ifTrue: [ result := 0 ]
										    ifFalse: [ result := Pi ]
						]
			    ifFalse: [(denominator = 0.0)
					ifTrue: [ (self > 0.0) ifTrue: [ result := Halfpi ]
												ifFalse: [ result := Halfpi negated ]
							]
					ifFalse: [ (denominator > 0) ifTrue: [ result := (self / denominator) arcTan ]
								 ifFalse: [ result := ((self / denominator) arcTan) + Pi 
									"(self > 0) ifTrue: [result := ((self / denominator) arcTan) + Pi ]
															ifFalse: [result := ((self / denominator) arcTan) - Pi]"
											]
							].
						].
	
	^ result
! !

!Float methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 20:54'!
arcTanH
        "answer hyperbolic arc tangent of self"

        | az |
        az := self abs.
        (az < 1)
          ifTrue: [^ (1/2) * (((1 + self) / (1 - self)) ln)]
          ifFalse: [^ Complex real: ((1/self) arcTanH) 
                         imaginary: ((((Float pi)/2) * (self signum)) negated)].! !

!Float methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 19:48'!
cosH
        "Answer the hyperbolic cosine of the receiver taken as an angle in radians."

        ^ ( (self exp) + ((self negated) exp) ) / 2
! !

!Float methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 19:48'!
cotH
        "Answer the hyperbolic cotangent of the receiver taken as an angle in radians."

        ^ ( (self exp) + ((self negated) exp) ) / ( (self exp) - ((self negated) exp) ) ! !

!Float methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 19:48'!
cscH
        "Answer the hyperbolic cosecant of the receiver taken as an angle in radians."

        ^ 2 / ( (self exp) - ((self negated) exp) )! !

!Float methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 16:50'!
ln
        "Answer the natural logarithm of the receiver.
         PrimOp fails for complex case."

        (self <= 0.0)
                ifTrue: [^ self asComplex ln ]
                ifFalse: [^ self lnPrivate ].! !

!Float methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 19:49'!
secH
        "Answer the hyperbolic secant of the receiver taken as an angle in radians."

        ^ 2 / ( (self exp) + ((self negated) exp) )! !

!Float methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 19:49'!
sinH
        "Answer the hyperbolic sine of the receiver taken as an angle in radians."

        ^ ( (self exp) - ((self negated) exp) ) / 2! !

!Float methodsFor: 'mathematical functions' stamp: 'KenD 8/9/2009 21:23'!
tanH
        "Answer the hyperbolic tangent of the receiver taken as an angle in radians."

        ^ ( (self exp) - ((self negated) exp) ) / ( (self exp) + ((self negated) exp) ) ! !

!Float methodsFor: 'private' stamp: 'KenD 8/9/2009 16:50'!
lnPrivate
	"Answer the natural logarithm of the receiver.
	 Optional. See Object documentation whatIsAPrimitive."

	| expt n mant x div pow delta sum eps |

	"Taylor series"
	self <= 0.0 ifTrue: [self error: 'ln is only defined for x > 0.0'].

	"get a rough estimate from binary exponent"
	expt := self exponent.
	n := Ln2 * expt.
	mant := self timesTwoPower: 0 - expt.

	"compute fine correction from mantinssa in Taylor series"
	"mant is in the range [0..2]"
	"we unroll the loop to avoid use of abs"
	x := mant - 1.0.
	div := 1.0.
	pow := delta := sum := x.
	x := x negated.  "x <= 0"
	eps := Epsilon * (n abs + 1.0).
	[delta > eps] whileTrue: [
		"pass one: delta is positive"
		div := div + 1.0.
		pow := pow * x.
		delta := pow / div.
		sum := sum + delta.
		"pass two: delta is negative"
		div := div + 1.0.
		pow := pow * x.
		delta := pow / div.
		sum := sum + delta].

	^ n + sum

	"2.718284 ln 1.0"! !


!Point methodsFor: 'converting' stamp: 'KenD 8/10/2009 16:40'!
asComplex
	^Complex real: x imaginary: y! !


!Float reorganize!
('arithmetic' * + - / abs negated reciprocal)
('comparing' < <= = > >= closeTo: hash ~=)
('converting' adaptToComplex:andSend: adaptToFraction:andCompare: adaptToFraction:andSend: adaptToInteger:andCompare: adaptToInteger:andSend: asApproximateFraction asApproximateFractionAtOrder: asComplex asFloat asFraction asIEEE32BitWord asTrueFraction degreesToRadians isInf radiansToDegrees)
('copying' deepCopy shallowCopy veryDeepCopyWith:)
('mathematical functions' arcCos arcCosH arcSin arcSinH arcTan arcTan: arcTanH cos cosH cotH cscH degreeCos degreeSin exp floorLog: ln log reciprocalFloorLog: reciprocalLogBase2 safeArcCos secH sin sinH sqrt tan tanH timesTwoPower:)
('printing' absByteEncode:base: absPrintExactlyOn:base: absPrintOn:base: byteEncode:base: hex printOn:base: printPaddedWith:to: printShowingDecimalPlaces: storeOn:base:)
('testing' hasContentsInExplorer isFinite isFloat isInfinite isLiteral isNaN isPowerOfTwo isZero sign)
('truncation and round off' exponent fractionPart integerPart predecessor reduce rounded significand significandAsInteger successor truncated)
('private' absPrintOn:base:digitCount: lnPrivate)
!


!Number reorganize!
('arithmetic' * + - / // \\ abs arg negated quo: reciprocal rem:)
('comparing' closeTo:)
('converting' @ adaptToCollection:andSend: adaptToFloat:andCompare: adaptToFloat:andSend: adaptToFraction:andSend: adaptToInteger:andSend: adaptToPoint:andSend: adaptToString:andSend: asB3DVector3 asComplex asDuration asFloatD asFloatE asFloatQ asInteger asNumber asPoint asScaledDecimal asScaledDecimal: asSmallAngleDegrees asSmallPositiveDegrees day days degreesToRadians hour hours i milliSecond milliSeconds minute minutes nanoSecond nanoSeconds radiansToDegrees second seconds sign: week weeks)
('filter streaming' byteEncode:)
('intervals' to: to:by: to:by:do: to:do:)
('mathematical functions' arcCos arcSin arcTan arcTan: cos degreeCos degreeSin exp floorLog: interpolateTo:at: ln log log: raisedTo: raisedToInteger: sin sqrt squared tan)
('printing' defaultLabelForInspector isOrAreStringWith: printOn: printOn:base: printShowingDecimalPlaces: printString printStringBase: storeOn: storeOn:base: storeStringBase: stringForReadout)
('testing' basicType even isDivisibleBy: isInf isInfinite isNaN isNumber isZero negative odd positive sign strictlyPositive)
('truncation and round off' ceiling detentBy:atMultiplesOf:snap: floor fractionPart integerPart reduce roundTo: roundUpTo: rounded truncateTo: truncated)
('private' signum)
!


!Complex class reorganize!
('instance creation' abs:arg: new real:imaginary:)
('deprecated' quickCheck:)
!

Complex removeSelector: #cosh!
Complex removeSelector: #imag:!
Complex removeSelector: #quickCheck:!
Complex removeSelector: #sinh!
Complex removeSelector: #truncate!

!Complex reorganize!
('accessing' imag imaginary real)
('arithmetic' * + - / < abs arg conjugate divideFastAndSecureBy: divideSecureBy: inverse negated norm reciprocal)
('comparing' = hash)
('converting' adaptToCollection:andSend: adaptToFloat:andSend: adaptToFraction:andSend: adaptToInteger:andSend: adaptToPoint:andSend: asComplex asPoint asString)
('mathematical functions' angle arcCos arcCosH arcSin arcSinH arcTan arcTanH cos cosH cotH cscH exp ln log: magnitude secH sin sinH sqrt squared tan tanH)
('printing' printOn:)
('testing' isComplex isNumber isZero)
('private' imaginary: real: signum)
('truncation and rounding' ceiling floor reduce roundTo: roundUpTo: truncateTo: truncated)
!