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+ on Sparse Arguments Improved

initial writing: 2001-08-02 last updated: 2004-10-26

The dyad + (and other atomic functions such as - * ) on sparse arguments are now more efficient in time and space. For example:

   s=: 13 17 19
   x=: ?.1600$1e6
   i=: ?.(1600,#s)$s
   
   p=: (800{.x) (<"1 ]800{.i)}1$.s
   q=: (800}.x) (<"1 ]800}.i)}1$.s

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

Expression	J 5.01				J 4.06				Ratio
p + q	0.000450895		33792		0.001660546		153856		3.68		4.55
p - q	0.000447822		33792		0.001658311		153856		3.70		4.55
p * q	0.000249473		5248		0.000749537		52608		3.00		10.02
p % q	0.000645613		33792		0.001753016		153856		2.72		4.55
p = q	0.000742552		19456		0.001741841		127232		2.35		6.54
p ~:q	0.000748978		19456		0.001632051		127232		2.18		6.54
p < q	0.000670756		19456		0.001730108		136448		2.58		7.01

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