>> 
<< 
Usr 
Pri 
JfC 
LJ 
Phr 
Dic 
Rel 
Voc 
!: 
Help 
Release
| 
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 | 
>> 
<< 
Usr 
Pri 
JfC 
LJ 
Phr 
Dic 
Rel 
Voc 
!: 
Help 
Release