# [Pkg] The Trunk: Kernel-nice.573.mcz

commits at source.squeak.org commits at source.squeak.org
Sun Apr 24 20:49:13 UTC 2011

```Nicolas Cellier uploaded a new version of Kernel to project The Trunk:
http://source.squeak.org/trunk/Kernel-nice.573.mcz

==================== Summary ====================

Name: Kernel-nice.573
Author: nice
Time: 24 April 2011, 10:48:34.956 pm
UUID: 6467b07b-fb80-8c41-8f33-91c673a57e88
Ancestors: Kernel-nice.572

Arrange arCosh to answer a positive real part.
Arrange arcCos + arcSin to answer halfPi.
Implement sinh cosh without intermediate Complex creation.

=============== Diff against Kernel-nice.572 ===============

Item was changed:
----- Method: Complex>>arCosh (in category 'mathematical functions') -----
arCosh
"Answer receiver's area hyperbolic cosine.
+ 	That is the inverse function of cosh.
+ 	Some possible implementations:
- 	That is the inverse function of cosh."
-
- 	"Some possible implementation:
-
^imaginary > 0
ifTrue: [(self + (self * self - 1) sqrt) ln]
+ 		ifFalse: [(self + (self * self - 1) sqrt) ln negated]
+ 	^self arcCos i
+ 	This implementation provides an answer with a positive real part.
+ 	It also avoids creating intermediate Complex."
+
+ 	| x y tmp sh2x shx delta ch2x chx |
+ 	imaginary = 0 ifTrue: [real abs > 1
+ 			ifTrue:
+ 				[y := real < 0
+ 					ifTrue: [Float pi]
+ 					ifFalse: .
+ 				x := real abs arCosh.
+ 				^self class real: x imaginary: y]
+ 			ifFalse: [^self class real: 0 imaginary: real arcCos]].
+ 	tmp := self squaredNorm - 1 / 2.
+ 	delta := tmp squared + imaginary squared.
+ 	sh2x := tmp + delta sqrt.
+ 	shx := sh2x sqrt.
+ 	ch2x := 1 + sh2x.
+ 	chx := ch2x sqrt.
+ 	x := shx arSinh.
+ 	y := imaginary copySignTo: (real / chx) arcCos.
+ 	^self class real: x imaginary: y!
- 		ifFalse: [(self + (self * self - 1) sqrt) ln negated]"
-
- 	^self arcCos i negated!

Item was changed:
----- Method: Complex>>arcCos (in category 'mathematical functions') -----
arcCos
"Answer the arc cosine of the receiver.
This is the inverse function of cos."

| x y tmp sh2y shy delta ch2y chy |
imaginary = 0 ifTrue: [real abs > 1
ifTrue:
[x := real < 0
ifTrue: [Float pi]
ifFalse: .
+ 				y := real copySignTo: real abs arCosh.
- 				y := real abs arCosh.
^self class real: x imaginary: y]
ifFalse: [^self class real: real arcCos imaginary: 0]].
tmp := self squaredNorm - 1 / 2.
delta := tmp squared + imaginary squared.
sh2y := tmp + delta sqrt.
shy := sh2y sqrt.
ch2y := 1 + sh2y.
chy := ch2y sqrt.
y := imaginary copySignTo: shy arSinh.
x := (real / chy) arcCos.
^self class real: x imaginary: y negated!

Item was changed:
----- Method: Complex>>arcSin (in category 'mathematical functions') -----
arcSin
"Answer the arc sine of the receiver.
This is the inverse function of sin."

| x y tmp delta sh2y shy ch2y chy |
imaginary = 0
ifTrue:
[real abs > 1
ifTrue:
[x := Float pi / 2 * real sign.
+ 					y := (real copySignTo: real abs arCosh) negated.
- 					y := real abs arCosh * real sign.
^self class real: x imaginary: y]
ifFalse: [^self class real: real arcSin imaginary: 0]].
tmp := (self squaredNorm - 1) / 2.
delta := tmp squared + imaginary squared.
sh2y := tmp + delta sqrt.
shy := sh2y sqrt.
ch2y := 1 + sh2y.
chy := ch2y sqrt.
y := imaginary copySignTo: shy arSinh.
x := (real / chy) arcSin.
^self class real: x imaginary: y!

Item was changed:
----- Method: Complex>>cosh (in category 'mathematical functions') -----
cosh
+ 	"Answer receiver's hyperbolic cosine.
+ 	Hyperbolic cosine is defined by same power serie expansion as for real numbers, that is in term of exponential:
+ 	^ (self exp + self negated exp) / 2.
+ 	This implementation avoids creating intermediate objects."
+
+ 	^self class
+ 		real: real cosh * imaginary cos
+ 		imaginary: real sinh * imaginary sin!
- 	"Answer receiver's hyperbolic cosine."
-
- 	^ (self exp + self negated exp) / 2!

Item was changed:
----- Method: Complex>>sinh (in category 'mathematical functions') -----
sinh
+ 	"Answer receiver's hyperbolic sine.
+ 	Hyperbolic sine is defined by same power serie expansion as for real numbers, that is in term of exponential:
+ 	^ (self exp - self negated exp) / 2.
+ 	This implementation avoids creating intermediate objects."
+
+ 	^self class
+ 		real: real sinh * imaginary cos
+ 		imaginary: real cosh * imaginary sin!
- 	"Answer receiver's hyperbolic sine."
-
- 	^ (self exp - self negated exp) / 2!

```

More information about the Packages mailing list