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+/ .* Improved

initial writing: 2006-03-28 last updated: 2006-03-31

The dyad x +/ .* y has been made more efficient in the following circumstances:

• x is Boolean, or
• y is Boolean, or
• *./1=}.$y , in particular if y is a vector

(There is no change if both x and y are Boolean.) The amount of improvement depends on the size of the arguments and on the number of 1s in a Boolean argument. The following benchmarks demonstrate the improvement:

ts=: 6!:2 , 7!:2@]  NB. time and space
ts 'x +/ .* y'

x		y		J 6.01				J 5.04				Ratio
2e4 ?@$ 2		2e4 100 ?@$ 0		0.00407861		2112		0.00656611		264384		1.61		125.18
5 2e4 ?@$ 2		2e4 100 ?@$ 0		0.02057971		5184		0.03784747		1053888		1.84		203.30
0=2e4 ?@$ 10		2e4 100 ?@$ 0		0.00102496		2112		0.00197282		264384		1.92		125.18
0=5 2e4 ?@$ 10		2e4 100 ?@$ 0		0.00518482		5184		0.01039583		1053888		2.01		203.30
100 2e4 ?@$ 0		2e4 ?@$ 2		0.01304037		2112		0.04706877		264384		3.61		125.18
100 2e4 ?@$ 0		2e4 5?@$ 2		0.08213707		5184		0.15116245		1053888		1.84		203.30
100 2e4 ?@$ 0		0=2e4 ?@$ 10		0.00993831		2112		0.03910959		264384		3.94		125.18
100 2e4 ?@$ 0		0=2e4 5?@$ 10		0.04794872		5184		0.09891527		1053888		2.06		203.30
100 2e4 ?@$ 0		2e4 ?@$ 0		0.00667827		2112		0.03896374		2240		5.83		1.06
j./2 100 2e4 ?@$ 0		j./2 2e4 ?@$ 0		0.02276409		3136		0.04351965		3264		1.91		1.04
2e5 ?@$ 0		2e5 ?@$ 0		0.00138537		1152		0.00445404		1280		3.22		1.11
2e6 ?@$ 0		2e6 ?@$ 0		0.01210311		1152		0.04429559		1280		3.66		1.11
j./2 2e5 ?@$ 0		j./2 2e5 ?@$ 0		0.00293892		1152		0.00473435		1280		1.61		1.11
j./2 2e6 ?@$ 0		j./2 2e6 ?@$ 0		0.02595096		1152		0.04706550		1280		1.81		1.11

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