Nicolas Cellier uploaded a new version of Kernel to project The Trunk:
http://source.squeak.org/trunk/Kernel-nice.510.mcz

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

Name: Kernel-nice.510
Author: nice
Time: 31 October 2010, 10:25:03.794 pm
UUID: 80b9fa44-3abc-4414-adae-10f3f03b0420
Ancestors: Kernel-ul.509

Provide an implementation of #degreeCos and #degreeSin such that results are exact for any multiple of 90.

Care is also taken to evaluate the sine between -90° and 90°, this will avoid #degreesToRadians and i386 FPU sine fonction to accumulate round off errors due to approximate representation of pi.
We can thus evaluate 240 degreeCos with at most 1 ulp error. It's not perfect, but better than previous implementation.

For cosine, we know that:
	cosd(x)=cosd(abs(x))
	cosd(x)=sind(90-x)
thus the trick is to evaluate:
	cosd(x)=sind(90-abs(x)) after appropriate modulo in [-180,180[
This way, we are sure to evaluate the sine between -90° and 90°
The #degreesToRadians and #sin are used rather than #degreeSin to avoid cycles.

For sine, it would be necessary to evaluate either
sind(x) if abs(x) <=90
or sind(180-x) if abs(x) >= 90
A possible implementation would be:
	| x |
	x := 90 + self \\ 360 - 90.
	x >= 180 ifTrue: [x := 180 - x].
	^x degreesToRadians sin
We prefer evaluating cosd(90-x) thus providing a branch free implementation.

=============== Diff against Kernel-ul.509 ===============

Item was changed:
  ----- Method: Float>>degreeCos (in category 'mathematical functions') -----
  degreeCos
+ 	"Take care of exceptional values"
+ 	
+ 	self isFinite ifTrue: [^super degreeCos].
+ 	^self radiansToDegrees cos!
- 	"Answer the cosine of the receiver taken as an angle in degrees."
- 
- 	^ self degreesToRadians cos!

Item was changed:
  ----- Method: Float>>degreeSin (in category 'mathematical functions') -----
  degreeSin
+ 	"Take care of exceptional values"
+ 	
+ 	self isFinite ifTrue: [^super degreeSin].
+ 	^self radiansToDegrees sin!
- 	"Answer the sine of the receiver taken as an angle in degrees."
- 
- 	^ self degreesToRadians sin!

Item was changed:
  ----- Method: Number>>degreeCos (in category 'mathematical functions') -----
  degreeCos
  	"Answer the cosine of the receiver taken as an angle in degrees."
  	
+ 	^ (90 - (180 + self \\ 360 - 180) abs) degreesToRadians sin!
- 	^ (90 + self) degreeSin!

Item was changed:
  ----- Method: Number>>degreeSin (in category 'mathematical functions') -----
  degreeSin
  	"Answer the sine of the receiver taken as an angle in degrees."
  	
+ 	^(90 - self) degreeCos!
- 	^ self asFloat degreesToRadians sin!