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o. Improved

initial writing: 2002-11-13 last updated: 2004-10-26

The dyad o. circle function has been made more efficient in time and space on real arguments with real results. For example:

   x=: 0.001*_500+?1e5$1000
   y=: (*x)+x+0=x
   z=: |y

   ts=: 6!:2 , 7!:2@]  NB. time and space
   ts 'expression'

Expression		J 5.02		J 5.01		Ratio
_7 o. x		0.0262740   1.04922e6		0.228579   5.24358e6		8.70   5.00
_6 o. z		0.0317026   1.04922e6		0.301152   5.24358e6		9.50   5.00
_5 o. x		0.0333802   1.04922e6		0.275311   5.24358e6		8.25   5.00
_4 o. y		0.0187753   1.04922e6		0.226301   5.24358e6		12.05   5.00
_3 o. x		0.0348033   1.04922e6		0.292260   5.24358e6		8.40   5.00
_2 o. x		0.0566949   1.04922e6		0.182072   5.24358e6		3.21   5.00
_1 o. x		0.0558347   1.04922e6		0.163727   5.24358e6		2.93   5.00
0 o. x		0.0129550   1.04922e6		0.169990   5.24358e6		13.12   5.00
1 o. x		0.0248325   1.04922e6		0.140806   5.24358e6		5.67   5.00
2 o. x		0.0261544   1.04922e6		0.139136   5.24358e6		5.32   5.00
3 o. x		0.0322787   1.04922e6		0.207790   5.24358e6		6.44   5.00
4 o. x		0.0129360   1.04922e6		0.182361   5.24358e6		14.10   5.00
5 o. x		0.0851955   1.04922e6		0.305229   5.24358e6		3.58   5.00
6 o. x		0.0877715   1.04922e6		0.298816   5.24358e6		3.40   5.00
7 o. x		0.0955809   1.04922e6		0.519837   5.24358e6		5.44   5.00

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