hg/stx-libbasic: comparison LargeFloat.st

equal deleted inserted replaced

-:b649e176c1a1
+:6f761d2b4f20
 "Created: / 10-10-2017 / 15:50:01 / cg"
 !
 naiveRaisedToInteger: n
-	"Very naive algorithm: use full precision.
+"Very naive algorithm: use full precision.
-	Use only for small n"
+Use only for small n"
-	| m e |
+| m e |
-	m _ mantissa raisedToInteger: n.
+m := mantissa raisedToInteger: n.
-	e _ biasedExponent * n.
+e := biasedExponent * n.
-	^(m asLargeFloatPrecision: precision) timesTwoPower: e
+^(m asLargeFloatPrecision: precision) timesTwoPower: e
+"Modified (comment): / 28-05-2019 / 17:43:40 / Claus Gittinger"
 !
 negated
 mantissa = 0 ifTrue:[
 biasedExponent = 0 ifTrue:[ ^ self ].
 		exponent: 0
 		precision: precision
 !
 pi
-	"answer the value of pi rounded to precision.
+"answer the value of pi rounded to precision.
-	Note: use the Brent-Salamin Arithmetic Geometric Mean algorithm"
+Note: use the Brent-Salamin Arithmetic Geometric Mean algorithm"
-	| a b c k pi oldpi oldExpo expo |
+| a b c k pi oldpi oldExpo expo |
-	a _ self one asLargeFloatPrecision: precision + 16.
+a := self one asLargeFloatPrecision: precision + 16.
-	b _ (a timesTwoPower: 1) sqrt reciprocal.
+b := (a timesTwoPower: 1) sqrt reciprocal.
-	c _ a timesTwoPower: -1.
+c := a timesTwoPower: -1.
-	k _ 1.
+k := 1.
-	oldpi _ Float pi.
+oldpi := Float pi.
-	oldExpo _ 2.
+oldExpo := 2.
-	[| am gm a2 |
+[| am gm a2 |
-	am _ a + b timesTwoPower: -1.
+am := a + b timesTwoPower: -1.
-	gm _ (a * b) sqrt.
+gm := (a * b) sqrt.
-	a _ am.
+a := am.
-	b _ gm.
+b := gm.
-	a2 _ a squared.
+a2 := a squared.
-	c inPlaceSubtract: (a2 - b squared timesTwoPower: k).
+c inPlaceSubtract: (a2 - b squared timesTwoPower: k).
-	pi _ (a2 timesTwoPower: 1) / c.
+pi := (a2 timesTwoPower: 1) / c.
-	expo _ (oldpi - pi) exponent.
+expo := (oldpi - pi) exponent.
-	expo isZero or: [expo > oldExpo or: [expo < (-1 - precision)]]]
+expo isZero or: [expo > oldExpo or: [expo < (-1 - precision)]]]
-			whileFalse:
+whileFalse:
-				[oldpi _ pi.
+[oldpi := pi.
-				oldExpo _ expo.
+oldExpo := expo.
-				k _ k + 1].
+k := k + 1].
-	^pi asLargeFloatPrecision: precision
+^pi asLargeFloatPrecision: precision
+"Modified (comment): / 28-05-2019 / 17:43:46 / Claus Gittinger"
 !
 piDoublePrecision
 	^ (self class mantissa: 0 exponent: 0 precision: precision + 1 * 2) pi
 !
 ! !
 !LargeFloat methodsFor:'initialization'!
 setPrecisionTo: n
-precision _ n.
+precision := n.
 self roundToPrecision
 "Modified: / 28-05-2019 / 11:22:21 / Claus Gittinger"
+"Modified (format): / 28-05-2019 / 17:45:16 / Claus Gittinger"
 ! !
 !LargeFloat methodsFor:'mathematical functions'!
 agm: aNumber
-	"Answer the arithmetic geometric mean of self and aNumber"
+"Answer the arithmetic geometric mean of self and aNumber"
-	| a b am gm |
+| a b am gm |
-	a _ self.
+a := self.
-	b _ aNumber.
+b := aNumber.
-	[am _ a + b timesTwoPower: -1.	"am is arithmetic mean"
+[am := a + b timesTwoPower: -1.  "am is arithmetic mean"
-	gm _ (a * b) sqrt.	"gm is geometric mean"
+gm := (a * b) sqrt.      "gm is geometric mean"
-	a = am or: [b = gm]]
+a = am or: [b = gm]]
-			whileFalse:
+whileFalse:
-				[a _ am.
+[a := am.
-				b _ gm].
+b := gm].
-	^am
+^am
+"Modified (format): / 28-05-2019 / 17:42:34 / Claus Gittinger"
 !
 arCosh
-	"Evaluate the area hyperbolic cosine of the receiver."
+"Evaluate the area hyperbolic cosine of the receiver."
-	| arCosh x one y two |
+| arCosh x one y two |
-	x _ self asLargeFloatPrecision: 16 + precision.
+x := self asLargeFloatPrecision: 16 + precision.
-	one _ x one.
+one := x one.
-	x < one ifTrue: [DomainError signal: 'cannot compute arCosh of a number less than 1'].
+x < one ifTrue: [DomainError signal: 'cannot compute arCosh of a number less than 1'].
-	x = one ifTrue: [^self zero].
+x = one ifTrue: [^self zero].
-	y _ x - one.
+y := x - one.
-	y < one
+y < one
-		ifTrue:
+ifTrue:
-			[y exponent * -4 >= precision
+[y exponent * -4 >= precision
-				ifTrue: [arCosh _ (y powerExpansionArCoshp1Precision: y precision) * (y timesTwoPower: 1) sqrt]
+ifTrue: [arCosh := (y powerExpansionArCoshp1Precision: y precision) * (y timesTwoPower: 1) sqrt]
-				ifFalse:
+ifFalse:
-					[two _ one timesTwoPower: 1.
+[two := one timesTwoPower: 1.
-					arCosh _ ((y * (y + two)) sqrt + y + one) ln]]
+arCosh := ((y * (y + two)) sqrt + y + one) ln]]
-		ifFalse: [arCosh _ ((x squared - one) sqrt + x) ln].
+ifFalse: [arCosh := ((x squared - one) sqrt + x) ln].
-	^arCosh asLargeFloatPrecision: precision
+^arCosh asLargeFloatPrecision: precision
+"Modified (format): / 28-05-2019 / 17:42:40 / Claus Gittinger"
 !
 arSinh
-	"Evaluate the area hyperbolic sine of the receiver."
+"Evaluate the area hyperbolic sine of the receiver."
-	| arSinh x one |
+| arSinh x one |
-	self isZero ifTrue: [^self].
+self isZero ifTrue: [^self].
-	self exponent negated > precision ifTrue: [^self].
+self exponent negated > precision ifTrue: [^self].
-	x _ self asLargeFloatPrecision: 16 + precision.
+x := self asLargeFloatPrecision: 16 + precision.
-	x inPlaceAbs.
+x inPlaceAbs.
-	self exponent * -4 >= precision
+self exponent * -4 >= precision
-		ifTrue: [arSinh _ x powerExpansionArSinhPrecision: x precision]
+ifTrue: [arSinh := x powerExpansionArSinhPrecision: x precision]
-		ifFalse:
+ifFalse:
-			[one _ x one.
+[one := x one.
-			arSinh _ ((x squared + one) sqrt + x) ln].
+arSinh := ((x squared + one) sqrt + x) ln].
-	self negative ifTrue: [arSinh inPlaceNegated].
+self negative ifTrue: [arSinh inPlaceNegated].
-	^arSinh asLargeFloatPrecision: precision
+^arSinh asLargeFloatPrecision: precision
+"Modified (format): / 28-05-2019 / 17:42:45 / Claus Gittinger"
 !
 arTanh
-	"Evaluate the area hyperbolic tangent of the receiver."
+"Evaluate the area hyperbolic tangent of the receiver."
-	| arTanh x one |
+| arTanh x one |
-	self isZero ifTrue: [^self].
+self isZero ifTrue: [^self].
-	x _ self asLargeFloatPrecision: 16 + precision.
+x := self asLargeFloatPrecision: 16 + precision.
-	x inPlaceAbs.
+x inPlaceAbs.
-	one _ x one.
+one := x one.
-	x >= one ifTrue: [DomainError signal: 'cannot evaluate arTanh of number of magnitude >= 1'].
+x >= one ifTrue: [DomainError signal: 'cannot evaluate arTanh of number of magnitude >= 1'].
-	self exponent * -4 >= precision
+self exponent * -4 >= precision
-		ifTrue: [arTanh _ x powerExpansionArTanhPrecision: x precision]
+ifTrue: [arTanh := x powerExpansionArTanhPrecision: x precision]
-		ifFalse:
+ifFalse:
-			[arTanh _ ((one + x) / (one - x)) ln.
+[arTanh := ((one + x) / (one - x)) ln.
-			arTanh inPlaceTimesTwoPower: -1].
+arTanh inPlaceTimesTwoPower: -1].
-	self negative ifTrue: [arTanh inPlaceNegated].
+self negative ifTrue: [arTanh inPlaceNegated].
-	^arTanh asLargeFloatPrecision: precision
+^arTanh asLargeFloatPrecision: precision
+"Modified (format): / 28-05-2019 / 17:42:49 / Claus Gittinger"
 !
 arcCos
 "Evaluate the arc cosine of the receiver."
 "Modified (format): / 28-05-2019 / 16:17:10 / Claus Gittinger"
 !
 exp
-	"Answer the exponential of the receiver."
+"Answer the exponential of the receiver."
-	| ln2 x q r ri res n maxIter p one two |
+| ln2 x q r ri res n maxIter p one two |
-	one _ self one.
+one := self one.
-	two _ one timesTwoPower: 1.
+two := one timesTwoPower: 1.
-	"Use following decomposition:
+"Use following decomposition:
-		x exp = (2 ln * q + r) exp.
+x exp = (2 ln * q + r) exp.
-		x exp = (2**q * r exp)"
+x exp = (2**q * r exp)"
-	ln2 _ two ln.
+ln2 := two ln.
-	x _ self / ln2.
+x := self / ln2.
-	q _ x truncated.
+q := x truncated.
-	r _ (x - q) * ln2.
+r := (x - q) * ln2.
-	"now compute r exp by power series expansion
+"now compute r exp by power series expansion
-	we compute (r/(2**p)) exp ** (2**p) in order to have faster convergence"
+we compute (r/(2**p)) exp ** (2**p) in order to have faster convergence"
-	p _ 10 min: precision // 2.
+p := 10 min: precision // 2.
-	r _ r timesTwoPower: p negated.
+r := r timesTwoPower: p negated.
-	ri _ one asLargeFloatPrecision: precision + 16.
+ri := one asLargeFloatPrecision: precision + 16.
-	res _ ri copy.
+res := ri copy.
-	n _ 0.
+n := 0.
-	maxIter _ 1 + ((precision + 16) / p) ceiling.
+maxIter := 1 + ((precision + 16) / p) ceiling.
-	[n <= maxIter] whileTrue:
+[n <= maxIter] whileTrue:
-			[n _ n + 1.
+[n := n + 1.
-			ri inPlaceMultiplyBy: r / n.
+ri inPlaceMultiplyBy: r / n.
-			res inPlaceAdd: ri].
+res inPlaceAdd: ri].
-	p timesRepeat: [res inPlaceMultiplyBy: res].
+p timesRepeat: [res inPlaceMultiplyBy: res].
-	res inPlaceTimesTwoPower: q.
+res inPlaceTimesTwoPower: q.
-	"now use a Newton iteration to refine the result
+"now use a Newton iteration to refine the result
-	res = res * (self - res ln + 1)"
+res = res * (self - res ln + 1)"
-	[| oldres delta |
+[| oldres delta |
-	oldres _ res.
+oldres := res.
-	res _ res asLargeFloatPrecision: res precision + 32.
+res := res asLargeFloatPrecision: res precision + 32.
-	res inPlaceMultiplyBy: self - res ln + 1.
+res inPlaceMultiplyBy: self - res ln + 1.
-	delta _ (res - oldres) exponent.
+delta := (res - oldres) exponent.
-	delta = 0 or: [delta <= (res exponent - precision - 8)]]
+delta = 0 or: [delta <= (res exponent - precision - 8)]]
-			whileFalse.
+whileFalse.
-	^res asLargeFloatPrecision: precision
+^res asLargeFloatPrecision: precision
+"Modified (comment): / 28-05-2019 / 17:43:06 / Claus Gittinger"
 !
 ln
-	"Answer the neperian logarithm of the receiver."
+"Answer the neperian logarithm of the receiver."
-	| x4 one two p res selfHighRes prec e |
+| x4 one two p res selfHighRes prec e |
-	self <= self zero ifTrue: [DomainError signal: 'ln is only defined for x > 0.0'].
+self <= self zero ifTrue: [DomainError signal: 'ln is only defined for x > 0.0'].
-	one _ self one.
+one := self one.
-	self = one ifTrue: [^self zero].
+self = one ifTrue: [^self zero].
-	two _ one timesTwoPower: 1.
+two := one timesTwoPower: 1.
-	"Use Salamin algorithm (approximation is good if x is big enough)
+"Use Salamin algorithm (approximation is good if x is big enough)
-		x ln = Pi  / (2 * (1 agm: 4/x) ).
+x ln = Pi  / (2 * (1 agm: 4/x) ).
-	If x not big enough, compute (x timesTwoPower: p) ln - (2 ln * p)
+If x not big enough, compute (x timesTwoPower: p) ln - (2 ln * p)
-	if x is close to 1, better use a power expansion"
+if x is close to 1, better use a power expansion"
-	prec _ precision + 16.
+prec := precision + 16.
-	e _ self exponent.
+e := self exponent.
-	e < 0 ifTrue: [e _ -1 - e].
+e < 0 ifTrue: [e := -1 - e].
-	e > prec
+e > prec
-		ifTrue: [p _ 0]
+ifTrue: [p := 0]
-		ifFalse:
+ifFalse:
-			[p _ prec - e.
+[p := prec - e.
-			prec _ prec + p highBit].
+prec := prec + p highBit].
-	selfHighRes _ self asLargeFloatPrecision: prec.
+selfHighRes := self asLargeFloatPrecision: prec.
-	(selfHighRes - one) exponent * -4 >= precision ifTrue: [^(selfHighRes powerExpansionLnPrecision: prec) asLargeFloatPrecision: precision].
+(selfHighRes - one) exponent * -4 >= precision ifTrue: [^(selfHighRes powerExpansionLnPrecision: prec) asLargeFloatPrecision: precision].
-	self < one ifTrue: [selfHighRes inPlaceReciprocal].	"Use ln(1/x) => - ln(x)"
+self < one ifTrue: [selfHighRes inPlaceReciprocal].     "Use ln(1/x) => - ln(x)"
-	x4 _ (4 asLargeFloatPrecision: prec)
+x4 := (4 asLargeFloatPrecision: prec)
-				inPlaceDivideBy: selfHighRes;
+inPlaceDivideBy: selfHighRes;
-				inPlaceTimesTwoPower: p negated.
+inPlaceTimesTwoPower: p negated.
-	res _ selfHighRes pi / (one agm: x4) timesTwoPower: -1.
+res := selfHighRes pi / (one agm: x4) timesTwoPower: -1.
-	res _ selfHighRes = two
+res := selfHighRes = two
-		ifTrue: [res / (p + 1)]
+ifTrue: [res / (p + 1)]
-		ifFalse: [p = 0 ifTrue: [res] ifFalse: [res - ((two asLargeFloatPrecision: prec) ln * p)]].
+ifFalse: [p = 0 ifTrue: [res] ifFalse: [res - ((two asLargeFloatPrecision: prec) ln * p)]].
-	self < one ifTrue: [res inPlaceNegated].
+self < one ifTrue: [res inPlaceNegated].
-	^res asLargeFloatPrecision: precision
+^res asLargeFloatPrecision: precision
+"Modified (comment): / 28-05-2019 / 17:43:30 / Claus Gittinger"
 !
 sin
 "Evaluate the sine of the receiver"
 "Modified (format): / 28-05-2019 / 16:18:20 / Claus Gittinger"
 !
 sincos
-	"Evaluate the sine and cosine of the receiver"
+"Evaluate the sine and cosine of the receiver"
-	| pi halfPi quarterPi x sincos sinneg cosneg |
+| pi halfPi quarterPi x sincos sinneg cosneg |
-	x _ self moduloNegPiToPi.
+x := self moduloNegPiToPi.
-	sinneg _ x negative.
+sinneg := x negative.
-	x inPlaceAbs.
+x inPlaceAbs.
-	pi _ self piDoublePrecision.
+pi := self piDoublePrecision.
-	halfPi _ pi timesTwoPower: -1.
+halfPi := pi timesTwoPower: -1.
-	(cosneg _ x > halfPi) ifTrue: [x inPlaceSubtract: pi; inPlaceNegated].
+(cosneg := x > halfPi) ifTrue: [x inPlaceSubtract: pi; inPlaceNegated].
-	quarterPi _ halfPi timesTwoPower: -1.
+quarterPi := halfPi timesTwoPower: -1.
-	x > quarterPi
+x > quarterPi
-		ifTrue:
+ifTrue:
-			[x inPlaceSubtract: halfPi; inPlaceNegated.
+[x inPlaceSubtract: halfPi; inPlaceNegated.
-			sincos _ (self sincos: x) reversed]
+sincos := (self sincos: x) reversed]
-		ifFalse:
+ifFalse:
-			[sincos _ self sincos: x].
+[sincos := self sincos: x].
-	sinneg ifTrue: [sincos first inPlaceNegated].
+sinneg ifTrue: [sincos first inPlaceNegated].
-	cosneg ifTrue: [sincos last inPlaceNegated].
+cosneg ifTrue: [sincos last inPlaceNegated].
-	^sincos collect: [:e| e asLargeFloatPrecision: precision]
+^sincos collect: [:e| e asLargeFloatPrecision: precision]
+"Modified (format): / 28-05-2019 / 17:45:28 / Claus Gittinger"
 !
 sinh
 | e x |
 self isZero ifTrue: [^self].
 ifTrue:
 [^ DomainError signal: 'sqrt undefined for number less than zero.'].
 self isZero ifTrue: [^self].
 "use additional bits"
-decimalPlaces _ precision + 16.
+decimalPlaces := precision + 16.
-n _ self asLargeFloatPrecision: decimalPlaces.
+n := self asLargeFloatPrecision: decimalPlaces.
 "constants"
-one _ n one.
+one := n one.
 "normalize n"
-norm _ n exponent quo: 2.
+norm := n exponent quo: 2.
-n _ n timesTwoPower: norm * -2.
+n := n timesTwoPower: norm * -2.
 "Initial guess for sqrt(1/n)"
-previousGuess _ self class
+previousGuess := self class
 mantissa: 3
 exponent: -2 - (n exponent quo: 2)
 precision: decimalPlaces.
-guess _ previousGuess copy.
+guess := previousGuess copy.
-"use iterations x(k+1) _ x*( 1 +  (1-x*x*n)/2) to guess sqrt(1/n)"
+"use iterations x(k+1) := x*( 1 +  (1-x*x*n)/2) to guess sqrt(1/n)"
 [guess inPlaceMultiplyNoRoundBy: guess.
 guess inPlaceMultiplyBy: n.
 guess inPlaceNegated.
 guess inPlaceAddNoRound: one.
 "stop when no evolution of precision + 12 first bits"
-stopIteration _ guess isZero or: [guess exponent < (decimalPlaces - 4) negated].
+stopIteration := guess isZero or: [guess exponent < (decimalPlaces - 4) negated].
 guess inPlaceTimesTwoPower: -1.
 guess inPlaceAddNoRound: one.
 guess inPlaceMultiplyNoRoundBy: previousGuess.
 guess negative ifTrue: [guess inPlaceNegated].
 guess inPlaceMultiplyBy: n.
 guess inPlaceTimesTwoPower: norm.
 ^guess asLargeFloatPrecision: precision
 "Modified: / 28-05-2019 / 11:22:33 / Claus Gittinger"
+"Modified (comment): / 28-05-2019 / 17:45:39 / Claus Gittinger"
 !
 tan
 "Evaluate the tangent of the receiver"
 ! !
 !LargeFloat methodsFor:'private'!
 cos: x
-	"Evaluate the cosine of x by recursive cos(2x) formula and power series expansion.
+"Evaluate the cosine of x by recursive cos(2x) formula and power series expansion.
-	Note that it is better to use this method with x <= pi/4."
+Note that it is better to use this method with x <= pi/4."
-	| one cos fraction power |
+| one cos fraction power |
-	x isZero ifTrue: [^x one].
+x isZero ifTrue: [^x one].
-	power _ ((precision bitShift: -1) + x exponent max: 0) highBit.
+power := ((precision bitShift: -1) + x exponent max: 0) highBit.
-	fraction _ x timesTwoPower: power negated.
+fraction := x timesTwoPower: power negated.
-	cos _ fraction powerExpansionCosPrecision: precision + (1 bitShift: 1 + power).
+cos := fraction powerExpansionCosPrecision: precision + (1 bitShift: 1 + power).
-	one _ x one.
+one := x one.
-	power timesRepeat:
+power timesRepeat:
-		["Evaluate cos(2x)=2 cos(x)^2-1"
+["Evaluate cos(2x)=2 cos(x)^2-1"
-		cos inPlaceMultiplyBy: cos; inPlaceTimesTwoPower: 1; inPlaceSubtract: one].
+cos inPlaceMultiplyBy: cos; inPlaceTimesTwoPower: 1; inPlaceSubtract: one].
-	^cos
+^cos
+"Modified (comment): / 28-05-2019 / 17:42:54 / Claus Gittinger"
 !
 digitCompare: b
-	"both are positive or negative.
+"both are positive or negative.
-	answer +1 if i am of greater magnitude, -1 if i am of smaller magnitude, 0 if equal magnitude"
+answer +1 if i am of greater magnitude, -1 if i am of smaller magnitude, 0 if equal magnitude"
-	| compare |
+| compare |
-	self isZero
+self isZero
-		ifTrue: [b isZero
+ifTrue: [b isZero
-				ifTrue: [^ 0]
+ifTrue: [^ 0]
-				ifFalse: [^ -1]].
+ifFalse: [^ -1]].
-	b isZero
+b isZero
-		ifTrue: [^ 1].
+ifTrue: [^ 1].
-	compare _ (self exponent - b exponent) sign.
+compare := (self exponent - b exponent) sign.
-	^ compare = 0
+^ compare = 0
-		ifTrue: [(self abs - b abs) sign]
+ifTrue: [(self abs - b abs) sign]
-		ifFalse: [compare]
+ifFalse: [compare]
+"Modified (comment): / 28-05-2019 / 17:42:59 / Claus Gittinger"
 !
 inPlaceAbs
-	mantissa _ mantissa abs
+mantissa := mantissa abs
+"Modified (format): / 28-05-2019 / 17:43:09 / Claus Gittinger"
 !
 inPlaceAdd: b
 | delta |
 b isZero ifTrue: [^self roundToPrecision].
 self isZero ifTrue:[
-mantissa _ b mantissa.
+mantissa := b mantissa.
-biasedExponent _ b biasedExponent
+biasedExponent := b biasedExponent
 ] ifFalse:[
 biasedExponent = b biasedExponent ifTrue: [
-mantissa _ mantissa + b mantissa
+mantissa := mantissa + b mantissa
 ] ifFalse:[
 "check for early truncation. beware, keep 2 bits for rounding"
-delta _ biasedExponent - b biasedExponent.
+delta := biasedExponent - b biasedExponent.
 delta - 2 > (precision max: self precisionInMantissa) ifFalse:[
 delta negated - 2 > (precision max: b precisionInMantissa) ifTrue:[
-mantissa _ b mantissa.
+mantissa := b mantissa.
-biasedExponent _ b exponent
+biasedExponent := b exponent
 ] ifFalse:[
-delta _ biasedExponent - b exponent.
+delta := biasedExponent - b exponent.
 delta > 0 ifTrue:[
-mantissa _ (self shift: mantissa by: delta) + b mantissa.
+mantissa := (self shift: mantissa by: delta) + b mantissa.
-biasedExponent _ biasedExponent - delta
+biasedExponent := biasedExponent - delta
 ] ifFalse: [
-mantissa _ mantissa + (self shift: b mantissa by: delta negated)
+mantissa := mantissa + (self shift: b mantissa by: delta negated)
 ]
 ]
 ]
 ]
 ].
 self roundToPrecision
 "Created: / 26-05-2019 / 03:44:50 / Claus Gittinger"
 "Modified: / 28-05-2019 / 08:49:15 / Claus Gittinger"
+"Modified (format): / 28-05-2019 / 17:43:15 / Claus Gittinger"
 !
 inPlaceAddNoRound: b
 | delta |
 inPlaceSubtract: b
 | delta |
 b isZero ifTrue: [^self roundToPrecision].
 self isZero
 ifTrue:
-[mantissa _ b mantissa negated.
+[mantissa := b mantissa negated.
-biasedExponent _ b biasedExponent]
+biasedExponent := b biasedExponent]
 ifFalse:
 [biasedExponent = b biasedExponent
-ifTrue: [mantissa _ mantissa - b mantissa]
+ifTrue: [mantissa := mantissa - b mantissa]
 ifFalse:
 ["check for early truncation. beware, keep 2 bits for rounding"
-delta _ biasedExponent - b biasedExponent.
+delta := biasedExponent - b biasedExponent.
 delta - 2 > (precision max: self precisionInMantissa)
 ifFalse:
 [delta negated - 2 > (precision max: b precisionInMantissa)
 ifTrue:
-[mantissa _ b mantissa negated.
+[mantissa := b mantissa negated.
-biasedExponent _ b biasedExponent]
+biasedExponent := b biasedExponent]
 ifFalse:
-[delta _ biasedExponent - b biasedExponent.
+[delta := biasedExponent - b biasedExponent.
 delta >= 0
 ifTrue:
-[mantissa _ (self shift: mantissa by: delta) - b mantissa.
+[mantissa := (self shift: mantissa by: delta) - b mantissa.
-biasedExponent _ biasedExponent - delta]
+biasedExponent := biasedExponent - delta]
-ifFalse: [mantissa _ mantissa - (self shift: b mantissa by: delta negated)]]]]].
+ifFalse: [mantissa := mantissa - (self shift: b mantissa by: delta negated)]]]]].
 self roundToPrecision
 "Modified: / 28-05-2019 / 08:48:46 / Claus Gittinger"
+"Modified (format): / 28-05-2019 / 17:43:21 / Claus Gittinger"
 !
 inPlaceSubtractNoRound: b
 | delta |
 b isZero ifTrue: [^self].
 "Modified (format): / 28-05-2019 / 16:17:47 / Claus Gittinger"
 !
 inPlaceTimesTwoPower: n
-	self isZero
+self isZero
-		ifFalse: [biasedExponent _ biasedExponent + n]
+ifFalse: [biasedExponent := biasedExponent + n]
+"Modified (format): / 28-05-2019 / 17:43:24 / Claus Gittinger"
 !
 mantissa:mantissaArg exponent:exponentArg
 "set instance variables.
 Notice, that the float's value is m * 2^e"
 "Modified (comment): / 17-07-2017 / 14:50:10 / cg"
 "Modified: / 28-05-2019 / 11:19:14 / Claus Gittinger"
 !
 moduloNegPiToPi
-	"answer a copy of the receiver modulo 2*pi, with doubled precision"
+"answer a copy of the receiver modulo 2*pi, with doubled precision"
-	| x pi twoPi quo |
+| x pi twoPi quo |
-	x _ (self asLargeFloatPrecision: precision * 2).
+x := (self asLargeFloatPrecision: precision * 2).
-	self negative ifTrue: [x inPlaceNegated].
+self negative ifTrue: [x inPlaceNegated].
-	pi _ x pi.
+pi := x pi.
-	twoPi _ pi timesTwoPower: 1.
+twoPi := pi timesTwoPower: 1.
-	x > pi ifTrue:
+x > pi ifTrue:
-		[quo _ x + pi quo: twoPi.
+[quo := x + pi quo: twoPi.
-		quo highBitOfMagnitude > precision ifTrue:
+quo highBitOfMagnitude > precision ifTrue:
-			[x _ (self abs asLargeFloatPrecision: precision + quo highBitOfMagnitude).
+[x := (self abs asLargeFloatPrecision: precision + quo highBitOfMagnitude).
-			pi _ x pi.
+pi := x pi.
-			twoPi _ pi timesTwoPower: 1.
+twoPi := pi timesTwoPower: 1.
-			quo _ x + pi quo: twoPi].
+quo := x + pi quo: twoPi].
-		x inPlaceSubtract: twoPi * quo.
+x inPlaceSubtract: twoPi * quo.
-		self negative ifTrue: [x inPlaceNegated]].
+self negative ifTrue: [x inPlaceNegated]].
-	^x asLargeFloatPrecision: precision * 2
+^x asLargeFloatPrecision: precision * 2
+"Modified (format): / 28-05-2019 / 17:43:36 / Claus Gittinger"
 !
 normalize
 "adjust m & e such that m is the smallest possible
 (i.e. has no least significant zero bit).
 "Modified (comment): / 26-05-2019 / 03:34:00 / Claus Gittinger"
 !
 powerExpansionArCoshp1Precision: precBits
-	"Evaluate arcosh(x+1)/sqrt(2*x) for the receiver x by power series expansion.
+"Evaluate arcosh(x+1)/sqrt(2*x) for the receiver x by power series expansion.
-	The algorithm is interesting when the receiver is close to zero"
+The algorithm is interesting when the receiver is close to zero"
-	| one two count count2 sum term term1 term2 |
+| one two count count2 sum term term1 term2 |
-	one _ self one.
+one := self one.
-	two _ one timesTwoPower: 1.
+two := one timesTwoPower: 1.
-	count _ one copy.
+count := one copy.
-	count2 _ one copy.
+count2 := one copy.
-	sum _ one copy.
+sum := one copy.
-	term1 _ one copy.
+term1 := one copy.
-	term2 _ one copy.
+term2 := one copy.
-	[term1 inPlaceMultiplyBy: self.
+[term1 inPlaceMultiplyBy: self.
-	term1 inPlaceNegated.
+term1 inPlaceNegated.
-	term2 inPlaceMultiplyBy: count2.
+term2 inPlaceMultiplyBy: count2.
-	term2 inPlaceMultiplyBy: count2.
+term2 inPlaceMultiplyBy: count2.
-	term2 inPlaceDivideBy: count.
+term2 inPlaceDivideBy: count.
-	count inPlaceAdd: one.
+count inPlaceAdd: one.
-	count2 inPlaceAdd: two.
+count2 inPlaceAdd: two.
-	term2 inPlaceDivideBy: count2.
+term2 inPlaceDivideBy: count2.
-	term2 inPlaceTimesTwoPower: -2.
+term2 inPlaceTimesTwoPower: -2.
-	term _ term1 * term2.
+term := term1 * term2.
-	sum inPlaceAdd: term.
+sum inPlaceAdd: term.
-	term exponent + precBits < sum exponent] whileFalse.
+term exponent + precBits < sum exponent] whileFalse.
-	^sum
+^sum
+"Modified (comment): / 28-05-2019 / 17:43:51 / Claus Gittinger"
 !
 powerExpansionArSinhPrecision: precBits
-	"Evaluate the area hypebolic sine of the receiver by power series expansion.
+"Evaluate the area hypebolic sine of the receiver by power series expansion.
-	The algorithm is interesting when the receiver is close to zero"
+The algorithm is interesting when the receiver is close to zero"
-	| one x2 two count sum term |
+| one x2 two count sum term |
-	one _ self one.
+one := self one.
-	two _ one timesTwoPower: 1.
+two := one timesTwoPower: 1.
-	count _ one copy.
+count := one copy.
-	sum _ one copy.
+sum := one copy.
-	term _ one copy.
+term := one copy.
-	x2 _ self squared.
+x2 := self squared.
-	[term inPlaceMultiplyBy: x2.
+[term inPlaceMultiplyBy: x2.
-	term inPlaceMultiplyBy: count.
+term inPlaceMultiplyBy: count.
-	term inPlaceDivideBy: count + one.
+term inPlaceDivideBy: count + one.
-	term inPlaceNegated.
+term inPlaceNegated.
-	count inPlaceAdd: two.
+count inPlaceAdd: two.
-	sum inPlaceAdd: term / count.
+sum inPlaceAdd: term / count.
-	term exponent + precBits < sum exponent] whileFalse.
+term exponent + precBits < sum exponent] whileFalse.
-	sum inPlaceMultiplyBy: self.
+sum inPlaceMultiplyBy: self.
-	^sum
+^sum
+"Modified (comment): / 28-05-2019 / 17:43:57 / Claus Gittinger"
 !
 powerExpansionArTanhPrecision: precBits
-	"Evaluate the area hyperbolic tangent of the receiver by power series expansion.
+"Evaluate the area hyperbolic tangent of the receiver by power series expansion.
-	arTanh (x) = x (1 + x^2/3 + x^4/5 + ... ) for -1 < x < 1
+arTanh (x) = x (1 + x^2/3 + x^4/5 + ... ) for -1 < x < 1
-	The algorithm is interesting when the receiver is close to zero"
+The algorithm is interesting when the receiver is close to zero"
-	| one x2 two count sum term |
+| one x2 two count sum term |
-	one _ self one.
+one := self one.
-	two _ one timesTwoPower: 1.
+two := one timesTwoPower: 1.
-	count _ one copy.
+count := one copy.
-	sum _ one copy.
+sum := one copy.
-	term _ one copy.
+term := one copy.
-	x2 _ self squared.
+x2 := self squared.
-	[term inPlaceMultiplyBy: x2.
+[term inPlaceMultiplyBy: x2.
-	count inPlaceAdd: two.
+count inPlaceAdd: two.
-	sum inPlaceAdd: term / count.
+sum inPlaceAdd: term / count.
-	term exponent + precBits < sum exponent] whileFalse.
+term exponent + precBits < sum exponent] whileFalse.
-	sum inPlaceMultiplyBy: self.
+sum inPlaceMultiplyBy: self.
-	^sum
+^sum
+"Modified (comment): / 28-05-2019 / 17:44:04 / Claus Gittinger"
 !
 powerExpansionArcSinPrecision: precBits
-	"Evaluate the arc sine of the receiver by power series expansion.
+"Evaluate the arc sine of the receiver by power series expansion.
-	The algorithm is interesting when the receiver is close to zero"
+The algorithm is interesting when the receiver is close to zero"
-	| one x2 two count sum term |
+| one x2 two count sum term |
-	one _ self one.
+one := self one.
-	two _ one timesTwoPower: 1.
+two := one timesTwoPower: 1.
-	count _ one copy.
+count := one copy.
-	sum _ one copy.
+sum := one copy.
-	term _ one copy.
+term := one copy.
-	x2 _ self squared.
+x2 := self squared.
-	[term inPlaceMultiplyBy: x2.
+[term inPlaceMultiplyBy: x2.
-	term inPlaceMultiplyBy: count.
+term inPlaceMultiplyBy: count.
-	term inPlaceDivideBy: count + one.
+term inPlaceDivideBy: count + one.
-	count inPlaceAdd: two.
+count inPlaceAdd: two.
-	sum inPlaceAdd: term / count.
+sum inPlaceAdd: term / count.
-	term exponent + precBits < sum exponent] whileFalse.
+term exponent + precBits < sum exponent] whileFalse.
-	sum inPlaceMultiplyBy: self.
+sum inPlaceMultiplyBy: self.
-	^sum
+^sum
+"Modified (comment): / 28-05-2019 / 17:44:09 / Claus Gittinger"
 !
 powerExpansionArcTanPrecision: precBits
-	"Evaluate the arc tangent of the receiver by power series expansion.
+"Evaluate the arc tangent of the receiver by power series expansion.
-	arcTan (x) = x (1 - x^2/3 + x^4/5 - ... ) for -1 < x < 1
+arcTan (x) = x (1 - x^2/3 + x^4/5 - ... ) for -1 < x < 1
-	The algorithm is interesting when the receiver is close to zero"
+The algorithm is interesting when the receiver is close to zero"
-	| count one sum term two x2 |
+| count one sum term two x2 |
-	one _ self one.
+one := self one.
-	two _ one timesTwoPower: 1.
+two := one timesTwoPower: 1.
-	count _ one copy.
+count := one copy.
-	sum _ one copy.
+sum := one copy.
-	term _ one copy.
+term := one copy.
-	x2 _ self squared.
+x2 := self squared.
-	[term inPlaceMultiplyBy: x2.
+[term inPlaceMultiplyBy: x2.
-	term inPlaceNegated.
+term inPlaceNegated.
-	count inPlaceAdd: two.
+count inPlaceAdd: two.
-	sum inPlaceAdd: term / count.
+sum inPlaceAdd: term / count.
-	term exponent + precBits < sum exponent] whileFalse.
+term exponent + precBits < sum exponent] whileFalse.
-	sum inPlaceMultiplyBy: self.
+sum inPlaceMultiplyBy: self.
-	^sum
+^sum
+"Modified (comment): / 28-05-2019 / 17:44:15 / Claus Gittinger"
 !
 powerExpansionCosPrecision: precBits
-	"Evaluate the cosine of the receiver by power series expansion.
+"Evaluate the cosine of the receiver by power series expansion.
-	The algorithm is interesting when the receiver is close to zero"
+The algorithm is interesting when the receiver is close to zero"
-	| count one sum term two x2 |
+| count one sum term two x2 |
-	one _ self one.
+one := self one.
-	two _ one timesTwoPower: 1.
+two := one timesTwoPower: 1.
-	count _ one copy.
+count := one copy.
-	sum _ one copy.
+sum := one copy.
-	term _ one copy.
+term := one copy.
-	x2 _ self squared.
+x2 := self squared.
-	[term inPlaceMultiplyBy: x2.
+[term inPlaceMultiplyBy: x2.
-	term inPlaceDivideBy: count * (count + one).
+term inPlaceDivideBy: count * (count + one).
-	term inPlaceNegated.
+term inPlaceNegated.
-	count inPlaceAdd: two.
+count inPlaceAdd: two.
-	sum inPlaceAdd: term.
+sum inPlaceAdd: term.
-	term exponent + precBits < sum exponent] whileFalse.
+term exponent + precBits < sum exponent] whileFalse.
-	^sum
+^sum
+"Modified (comment): / 28-05-2019 / 17:44:25 / Claus Gittinger"
 !
 powerExpansionCoshPrecision: precBits
-	"Evaluate the hyperbolic cosine of the receiver by power series expansion.
+"Evaluate the hyperbolic cosine of the receiver by power series expansion.
-	The algorithm is interesting when the receiver is close to zero"
+The algorithm is interesting when the receiver is close to zero"
-	| count one sum term two x2 |
+| count one sum term two x2 |
-	one _ self one.
+one := self one.
-	two _ one timesTwoPower: 1.
+two := one timesTwoPower: 1.
-	count _ one copy.
+count := one copy.
-	sum _ one copy.
+sum := one copy.
-	term _ one copy.
+term := one copy.
-	x2 _ self squared.
+x2 := self squared.
-	[term inPlaceMultiplyBy: x2.
+[term inPlaceMultiplyBy: x2.
-	term inPlaceDivideBy: count * (count + one).
+term inPlaceDivideBy: count * (count + one).
-	count inPlaceAdd: two.
+count inPlaceAdd: two.
-	sum inPlaceAdd: term.
+sum inPlaceAdd: term.
-	term exponent + precBits < sum exponent] whileFalse.
+term exponent + precBits < sum exponent] whileFalse.
-	^sum
+^sum
+"Modified (comment): / 28-05-2019 / 17:44:30 / Claus Gittinger"
 !
 powerExpansionLnPrecision: precBits
-	"Evaluate the neperian logarithm of the receiver by power series expansion.
+"Evaluate the neperian logarithm of the receiver by power series expansion.
-	For quadratic convergence, use:
+For quadratic convergence, use:
-	ln ((1+y)/(1-y)) = 2 y (1 + y^2/3 + y^4/5 + ... ) = 2 ar tanh( y )
+ln ((1+y)/(1-y)) = 2 y (1 + y^2/3 + y^4/5 + ... ) = 2 ar tanh( y )
-	(1+y)/(1-y) = self => y = (self-1)/(self+1)
+(1+y)/(1-y) = self => y = (self-1)/(self+1)
-	This algorithm is interesting when the receiver is close to 1"
+This algorithm is interesting when the receiver is close to 1"
-	| one |
+| one |
-	one _ self one.
+one := self one.
-	^((self - one)/(self + one) powerExpansionArTanhPrecision: precBits) timesTwoPower: 1
+^((self - one)/(self + one) powerExpansionArTanhPrecision: precBits) timesTwoPower: 1
+"Modified (comment): / 28-05-2019 / 17:44:38 / Claus Gittinger"
 !
 powerExpansionSinCosPrecision: precBits
-	"Evaluate the sine and cosine of the receiver by power series expansion.
+"Evaluate the sine and cosine of the receiver by power series expansion.
-	The algorithm is interesting when the receiver is close to zero"
+The algorithm is interesting when the receiver is close to zero"
-	| count one sin cos term |
+| count one sin cos term |
-	one _ self one.
+one := self one.
-	count _ one copy.
+count := one copy.
-	cos _ one copy.
+cos := one copy.
-	sin _ self copy.
+sin := self copy.
-	term _ self copy.
+term := self copy.
-	[count inPlaceAdd: one.
+[count inPlaceAdd: one.
-	term
+term
-		inPlaceMultiplyBy: self;
+inPlaceMultiplyBy: self;
-		inPlaceDivideBy: count;
+inPlaceDivideBy: count;
-		inPlaceNegated.
+inPlaceNegated.
-	cos inPlaceAdd: term.
+cos inPlaceAdd: term.
-	count inPlaceAdd: one.
+count inPlaceAdd: one.
-	term
+term
-		inPlaceMultiplyBy: self;
+inPlaceMultiplyBy: self;
-		inPlaceDivideBy: count.
+inPlaceDivideBy: count.
-	sin inPlaceAdd: term.
+sin inPlaceAdd: term.
-	term exponent + precBits < sin exponent] whileFalse.
+term exponent + precBits < sin exponent] whileFalse.
-	^Array with: sin with: cos
+^Array with: sin with: cos
+"Modified (comment): / 28-05-2019 / 17:44:43 / Claus Gittinger"
 !
 powerExpansionSinPrecision: precBits
-	"Evaluate the sine of the receiver by power series expansion.
+"Evaluate the sine of the receiver by power series expansion.
-	The algorithm is interesting when the receiver is close to zero"
+The algorithm is interesting when the receiver is close to zero"
-	| count one sum term two x2 |
+| count one sum term two x2 |
-	one _ self one.
+one := self one.
-	two _ one timesTwoPower: 1.
+two := one timesTwoPower: 1.
-	count _ two copy.
+count := two copy.
-	sum _ self copy.
+sum := self copy.
-	term _ self copy.
+term := self copy.
-	x2 _ self squared.
+x2 := self squared.
-	[term inPlaceMultiplyBy: x2.
+[term inPlaceMultiplyBy: x2.
-	term inPlaceDivideBy: count * (count + one).
+term inPlaceDivideBy: count * (count + one).
-	term inPlaceNegated.
+term inPlaceNegated.
-	count inPlaceAdd: two.
+count inPlaceAdd: two.
-	sum inPlaceAdd: term.
+sum inPlaceAdd: term.
-	term exponent + precBits < sum exponent] whileFalse.
+term exponent + precBits < sum exponent] whileFalse.
-	^sum
+^sum
+"Modified (comment): / 28-05-2019 / 17:44:50 / Claus Gittinger"
 !
 powerExpansionSinhPrecision: precBits
-	"Evaluate the hyperbolic sine of the receiver by power series expansion.
+"Evaluate the hyperbolic sine of the receiver by power series expansion.
-	The algorithm is interesting when the receiver is close to zero"
+The algorithm is interesting when the receiver is close to zero"
-	| count one sum term two x2 |
+| count one sum term two x2 |
-	one _ self one.
+one := self one.
-	two _ one timesTwoPower: 1.
+two := one timesTwoPower: 1.
-	count _ two copy.
+count := two copy.
-	sum _ self copy.
+sum := self copy.
-	term _ self copy.
+term := self copy.
-	x2 _ self squared.
+x2 := self squared.
-	[term inPlaceMultiplyBy: x2.
+[term inPlaceMultiplyBy: x2.
-	term inPlaceDivideBy: count * (count + one).
+term inPlaceDivideBy: count * (count + one).
-	count inPlaceAdd: two.
+count inPlaceAdd: two.
-	sum inPlaceAdd: term.
+sum inPlaceAdd: term.
-	term exponent + precBits < sum exponent] whileFalse.
+term exponent + precBits < sum exponent] whileFalse.
-	^sum
+^sum
+"Modified (comment): / 28-05-2019 / 17:44:56 / Claus Gittinger"
 !
 powerExpansionTanPrecision: precBits
-	"Evaluate the tangent of the receiver by power series expansion.
+"Evaluate the tangent of the receiver by power series expansion.
-	The algorithm is interesting when the receiver is close to zero"
+The algorithm is interesting when the receiver is close to zero"
-	| count one sum term pow two x2 seidel |
+| count one sum term pow two x2 seidel |
-	one _ self one.
+one := self one.
-	two _ one timesTwoPower: 1.
+two := one timesTwoPower: 1.
-	count _ two copy.
+count := two copy.
-	sum _ one copy.
+sum := one copy.
-	pow _ one copy.
+pow := one copy.
-	x2 _ self squared.
+x2 := self squared.
-	seidel _ OrderedCollection new: 256.
+seidel := OrderedCollection new: 256.
-	seidel add: 1.
+seidel add: 1.
-	[pow inPlaceMultiplyBy: x2.
+[pow inPlaceMultiplyBy: x2.
-	pow inPlaceDivideBy: count * (count + one).
+pow inPlaceDivideBy: count * (count + one).
-	count inPlaceAdd: two.
+count inPlaceAdd: two.
-	2 to: seidel size do: [:i | seidel at: i put: (seidel at: i-1) + (seidel at: i)].
+2 to: seidel size do: [:i | seidel at: i put: (seidel at: i-1) + (seidel at: i)].
-	seidel addLast: seidel last.
+seidel addLast: seidel last.
-	seidel size to: 2 by: -1 do: [:i | seidel at: i - 1 put: (seidel at: i-1) + (seidel at: i)].
+seidel size to: 2 by: -1 do: [:i | seidel at: i - 1 put: (seidel at: i-1) + (seidel at: i)].
-	seidel addFirst: seidel first.
+seidel addFirst: seidel first.
-	term _ pow * seidel first.
+term := pow * seidel first.
-	sum inPlaceAdd: term.
+sum inPlaceAdd: term.
-	term exponent + precBits < sum exponent] whileFalse.
+term exponent + precBits < sum exponent] whileFalse.
-	sum inPlaceMultiplyBy: self.
+sum inPlaceMultiplyBy: self.
-	^sum
+^sum
+"Modified (comment): / 28-05-2019 / 17:45:02 / Claus Gittinger"
 !
 powerExpansionTanhPrecision: precBits
-	"Evaluate the hyperbolic tangent of the receiver by power series expansion.
+"Evaluate the hyperbolic tangent of the receiver by power series expansion.
-	The algorithm is interesting when the receiver is close to zero"
+The algorithm is interesting when the receiver is close to zero"
-	| count one sum term pow two x2 seidel |
+| count one sum term pow two x2 seidel |
-	one _ self one.
+one := self one.
-	two _ one timesTwoPower: 1.
+two := one timesTwoPower: 1.
-	count _ two copy.
+count := two copy.
-	sum _ one copy.
+sum := one copy.
-	pow _ one copy.
+pow := one copy.
-	x2 _ self squared.
+x2 := self squared.
-	seidel _ OrderedCollection new: 256.
+seidel := OrderedCollection new: 256.
-	seidel add: 1.
+seidel add: 1.
-	[pow inPlaceMultiplyBy: x2.
+[pow inPlaceMultiplyBy: x2.
-	pow inPlaceDivideBy: count * (count + one).
+pow inPlaceDivideBy: count * (count + one).
-	pow inPlaceNegated.
+pow inPlaceNegated.
-	count inPlaceAdd: two.
+count inPlaceAdd: two.
-	2 to: seidel size do: [:i | seidel at: i put: (seidel at: i-1) + (seidel at: i)].
+2 to: seidel size do: [:i | seidel at: i put: (seidel at: i-1) + (seidel at: i)].
-	seidel addLast: seidel last.
+seidel addLast: seidel last.
-	seidel size to: 2 by: -1 do: [:i | seidel at: i - 1 put: (seidel at: i-1) + (seidel at: i)].
+seidel size to: 2 by: -1 do: [:i | seidel at: i - 1 put: (seidel at: i-1) + (seidel at: i)].
-	seidel addFirst: seidel first.
+seidel addFirst: seidel first.
-	term _ pow * seidel first.
+term := pow * seidel first.
-	sum inPlaceAdd: term.
+sum inPlaceAdd: term.
-	term exponent + precBits < sum exponent] whileFalse.
+term exponent + precBits < sum exponent] whileFalse.
-	sum inPlaceMultiplyBy: self.
+sum inPlaceMultiplyBy: self.
-	^sum
+^sum
+"Modified (comment): / 28-05-2019 / 17:45:07 / Claus Gittinger"
 !
 precision:precisionArg
 "set instance variables.
 Notice, that the float's value is m * 2^e"
 "Created: / 26-05-2019 / 03:45:02 / Claus Gittinger"
 !
 reduce
-	"remove trailing zero bits from mantissa so that we can do arithmetic on smaller integer
+"remove trailing zero bits from mantissa so that we can do arithmetic on smaller integer
-	(that will un-normalize self)"
+(that will un-normalize self)"
-	| trailing |
+| trailing |
-	trailing _ mantissa abs lowBit - 1.
+trailing := mantissa abs lowBit - 1.
-	trailing > 0
+trailing > 0
-		ifFalse: [ ^ self ].
+ifFalse: [ ^ self ].
-	mantissa _ self shift: mantissa by: trailing negated.
+mantissa := self shift: mantissa by: trailing negated.
-	biasedExponent _ biasedExponent + trailing
+biasedExponent := biasedExponent + trailing
+"Modified (comment): / 28-05-2019 / 17:45:13 / Claus Gittinger"
 !
 roundToPrecision
 "destructive inplace round
 apply algorithm round to nearest even used by IEEE arithmetic"
 "Created: / 26-05-2019 / 03:22:12 / Claus Gittinger"
 !
 sin: x
-	"Evaluate the sine of x by sin(5x) formula and power series expansion."
+"Evaluate the sine of x by sin(5x) formula and power series expansion."
-	| sin sin2 sin4 fifth five |
+| sin sin2 sin4 fifth five |
-	x isZero ifTrue: [^x zero].
+x isZero ifTrue: [^x zero].
-	five _ 5 asLargeFloatPrecision: x precision.
+five := 5 asLargeFloatPrecision: x precision.
-	fifth _ x / five.
+fifth := x / five.
-	sin _ fifth powerExpansionSinPrecision: precision + 8.
+sin := fifth powerExpansionSinPrecision: precision + 8.
-	sin2 _ sin squared.
+sin2 := sin squared.
-	sin2 inPlaceTimesTwoPower: 2.
+sin2 inPlaceTimesTwoPower: 2.
-	sin4 _ sin2 squared.
+sin4 := sin2 squared.
-	sin2 inPlaceMultiplyBy: five.
+sin2 inPlaceMultiplyBy: five.
-	^sin4
+^sin4
-		inPlaceSubtract: sin2;
+inPlaceSubtract: sin2;
-		inPlaceAdd: five;
+inPlaceAdd: five;
-		inPlaceMultiplyBy: sin;
+inPlaceMultiplyBy: sin;
-		yourself
+yourself
+"Modified (format): / 28-05-2019 / 17:45:21 / Claus Gittinger"
 !
 sincos: x
-	"Evaluate the sine and cosine of x by recursive sin(2x) and cos(2x) formula and power series expansion.
+"Evaluate the sine and cosine of x by recursive sin(2x) and cos(2x) formula and power series expansion.
-	Note that it is better to use this method with x <= pi/4."
+Note that it is better to use this method with x <= pi/4."
-	| one sin cos sincos fraction power |
+| one sin cos sincos fraction power |
-	x isZero ifTrue: [^Array with: x zero with: x one].
+x isZero ifTrue: [^Array with: x zero with: x one].
-	power _ ((precision bitShift: -1) + x exponent max: 0) highBit.
+power := ((precision bitShift: -1) + x exponent max: 0) highBit.
-	fraction _ x timesTwoPower: power negated.
+fraction := x timesTwoPower: power negated.
-	sincos _ fraction powerExpansionSinCosPrecision: precision + (1 bitShift: 1 + power).
+sincos := fraction powerExpansionSinCosPrecision: precision + (1 bitShift: 1 + power).
-	sin _ sincos first.
+sin := sincos first.
-	cos _ sincos last.
+cos := sincos last.
-	one _ x one.
+one := x one.
-	power timesRepeat:
+power timesRepeat:
-		["Evaluate sin(2x)=2 sin(x) cos(x)"
+["Evaluate sin(2x)=2 sin(x) cos(x)"
-		sin inPlaceMultiplyBy: cos; inPlaceTimesTwoPower: 1.
+sin inPlaceMultiplyBy: cos; inPlaceTimesTwoPower: 1.
-		"Evaluate cos(2x)=2 cos(x)^2-1"
+"Evaluate cos(2x)=2 cos(x)^2-1"
-		cos inPlaceMultiplyBy: cos; inPlaceTimesTwoPower: 1; inPlaceSubtract: one].
+cos inPlaceMultiplyBy: cos; inPlaceTimesTwoPower: 1; inPlaceSubtract: one].
-	^sincos
+^sincos
+"Modified (comment): / 28-05-2019 / 17:45:33 / Claus Gittinger"
 ! !
 !LargeFloat methodsFor:'queries'!
 epsilon

changeset 24220	6f761d2b4f20
parent 24218	7c7369cb0189
child 24257	3d3652e1f81c