Array Predicates - Revision history

WikiSysop at 01:16, 20 February 2011

2011-02-20T01:16:00Z

← Older revision		Revision as of 21:16, 19 February 2011
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	This clever idea of Bob Bernecky's [http://www.snakeisland.com/predicat.pdf] provides a performance improvement for certain expressions by marking certain arrays with special properties. For example, the property of being a Permutation Vector [http://mathworld.wolfram.com/Permutation.html] is invariant (is still a Permutation Vector, albeit a different one) under various APL primitives such as rotate/reversal (<apll>L⌽PV</apll> and <apll>⌽PV</apll>) and grade up/down (<apll>⍋PV</apll> and <apll>⍒PV</apll>).		This clever idea of Bob Bernecky's [http://www.snakeisland.com/predicat.pdf] provides a performance improvement for certain expressions by marking certain arrays with special properties. For example, the property of being a Permutation Vector [http://mathworld.wolfram.com/Permutation.html] is invariant (is still a Permutation Vector, albeit a different one) under various APL primitives such as rotate/reversal (<apll>L⌽PV</apll> and <apll>⌽PV</apll>) and grade up/down (<apll>⍋PV</apll> and <apll>⍒PV</apll>).

	Bernecky has defined several array predicate properties, ~~one~~ of which ~~has~~ been implemented in ~~NARS~~ so far.		Bernecky has defined several array predicate properties, two of which have been implemented in NARS2000 so far.

	== Permutation Vectors ==		== Permutation Vectors ==
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	<p>In the common expression <apll>⍋⍋R</apll>, the right hand grade sets the bit and the left hand grade reads it and uses a linear algorithm to produce the result.</p>		<p>In the common expression <apll>⍋⍋R</apll>, the right hand grade sets the bit and the left hand grade reads it and uses a linear algorithm to produce the result.</p>

			== All 2s ==

			<p>Mostly for the Representation primitive (<apll>L⊤R</apll>), if the left argument is all 2s and the right argument is integer, the result can be represented as Boolean.</p>

WikiSysop at 20:41, 21 September 2010

2010-09-21T20:41:50Z

← Older revision		Revision as of 16:41, 21 September 2010
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	== Permutation Vectors ==		== Permutation Vectors ==

	<p>In this case, index generator (<apll>⍳S</apll>) produces a Permutation Vector, as do the grade primitives (<apll>⍋V</apll> and <apll>⍒V</apll>), as well as deal (<apll>L?R</apll>) when the left and right arguments are the same — the results of these primitives are marked internally as Permutation Vectors. Subsequent use of such arrays maintains that property when operated on by rotate/reversal (<apll>L⌽PV</apll> and <apll>⌽PV</apll>) ~~and grade up/down~~. Moreover, the two grade (<apll>⍋PV</apll> and <apll>⍒PV</apll>) and the index of (<apll>PV⍳R</apll>) and membership (<apll>L∊PV</apll>) primitives use a much faster (linear) algorithm than they would normally, given that the ~~appropriate~~ argument is a Permutation Vector.</p>		<p>In this case, index generator (<apll>⍳S</apll>) produces a Permutation Vector, as do the grade primitives (<apll>⍋V</apll> and <apll>⍒V</apll>), as well as deal (<apll>L?R</apll>) when the left and right arguments are the same — the results of these primitives are marked internally as Permutation Vectors. Subsequent use of such arrays maintains that property when operated on by rotate/reversal (<apll>L⌽PV</apll> and <apll>⌽PV</apll>). Moreover, the two grade (<apll>⍋PV</apll> and <apll>⍒PV</apll>) and the index of (<apll>PV⍳R</apll>) and membership (<apll>L∊PV</apll>) primitives use a much faster (linear) algorithm than they would normally, given that the lookup argument is a Permutation Vector.</p>

	<p>In summary,</p>		<p>In summary,</p>

	<p>Set ~~The~~ bit: <apll>⍳S</apll>, <apll>⍋V</apll>, <apll>⍒V</apll>, and <apll>R?R</apll>.</p>		<p>Set the bit in the result: <apll>⍳S</apll>, <apll>⍋V</apll>, <apll>⍒V</apll>, and <apll>R?R</apll>.</p>

	<p>Pass on the bit: ~~<apll>⍋V</apll>, <apll>⍒V</apll>,~~ <apll>L⌽PV</apll>, and <apll>⌽PV</apll>.</p>		<p>Pass on the bit: <apll>L⌽PV</apll> and <apll>⌽PV</apll>.</p>

	<p>Read and take advantage of the bit: <apll>⍋V</apll>, <apll>⍒V</apll>, <apll>PV⍳R</apll>, and <apll>L∊PV</apll>.</p>		<p>Read and take advantage of the bit: <apll>⍋PV</apll>, <apll>⍒PV</apll>, <apll>PV⍳R</apll>, and <apll>L∊PV</apll>.</p>

			== Example ==

			<p>In the common expression <apll>⍋⍋R</apll>, the right hand grade sets the bit and the left hand grade reads it and uses a linear algorithm to produce the result.</p>

WikiSysop: /* Permutation Vectors */

2010-09-21T18:46:18Z

Permutation Vectors

← Older revision		Revision as of 14:46, 21 September 2010
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	== Permutation Vectors ==		== Permutation Vectors ==

	In this case, index generator (<apll>⍳R</apll>) produces a Permutation Vector, as do the grade primitives (<apll>⍋V</apll> and <apll>⍒V</apll>), as well as deal (<apll>L?R</apll>) when the left and right arguments are the same — the results of these primitives are marked internally as Permutation Vectors. Subsequent use of such arrays maintains that property when operated on by rotate/reversal and grade up/down. Moreover, the two grade (<apll>⍋PV</apll> and <apll>⍒PV</apll>) and the index of (<apll>PV⍳R</apll>) and membership (<apll>L∊PV</apll>) primitives use a much faster (linear) algorithm than they would normally, given that the appropriate argument is a Permutation Vector.		<p>In this case, index generator (<apll>⍳S</apll>) produces a Permutation Vector, as do the grade primitives (<apll>⍋V</apll> and <apll>⍒V</apll>), as well as deal (<apll>L?R</apll>) when the left and right arguments are the same — the results of these primitives are marked internally as Permutation Vectors. Subsequent use of such arrays maintains that property when operated on by rotate/reversal (<apll>L⌽PV</apll> and <apll>⌽PV</apll>) and grade up/down. Moreover, the two grade (<apll>⍋PV</apll> and <apll>⍒PV</apll>) and the index of (<apll>PV⍳R</apll>) and membership (<apll>L∊PV</apll>) primitives use a much faster (linear) algorithm than they would normally, given that the appropriate argument is a Permutation Vector.</p>

			<p>In summary,</p>

			<p>Set The bit: <apll>⍳S</apll>, <apll>⍋V</apll>, <apll>⍒V</apll>, and <apll>R?R</apll>.</p>

			<p>Pass on the bit: <apll>⍋V</apll>, <apll>⍒V</apll>, <apll>L⌽PV</apll>, and <apll>⌽PV</apll>.</p>

			<p>Read and take advantage of the bit: <apll>⍋V</apll>, <apll>⍒V</apll>, <apll>PV⍳R</apll>, and <apll>L∊PV</apll>.</p>

WikiSysop: /* Permutation Vectors */

2009-05-26T15:48:01Z

Permutation Vectors

← Older revision		Revision as of 11:48, 26 May 2009
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	== Permutation Vectors ==		== Permutation Vectors ==

	In this case, index generator (<apll>⍳R</apll>) produces a Permutation Vector, as ~~does~~ deal (<apll>L?R</apll>) when the left and right arguments are the same — the results of these primitives are marked internally as Permutation Vectors. Subsequent use of such arrays maintains that property when operated on by rotate/reversal and grade up/down. Moreover, the two grade (<apll>⍋PV</apll> and <apll>⍒PV</apll>) and the index of (<apll>PV⍳R</apll>) and membership (<apll>L∊PV</apll>) primitives use a much faster (linear) algorithm than they would normally, given that the appropriate argument is a Permutation Vector.		In this case, index generator (<apll>⍳R</apll>) produces a Permutation Vector, as do the grade primitives (<apll>⍋V</apll> and <apll>⍒V</apll>), as well as deal (<apll>L?R</apll>) when the left and right arguments are the same — the results of these primitives are marked internally as Permutation Vectors. Subsequent use of such arrays maintains that property when operated on by rotate/reversal and grade up/down. Moreover, the two grade (<apll>⍋PV</apll> and <apll>⍒PV</apll>) and the index of (<apll>PV⍳R</apll>) and membership (<apll>L∊PV</apll>) primitives use a much faster (linear) algorithm than they would normally, given that the appropriate argument is a Permutation Vector.

Sudleyplace: /* Permutation Vectors */

2008-11-22T19:09:18Z

Permutation Vectors

← Older revision		Revision as of 15:09, 22 November 2008
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	== Permutation Vectors ==		== Permutation Vectors ==

	In this case, index generator (<apll>⍳R</apll>) produces a Permutation Vector, as does deal (<apll>L?R</apll>) when the left and right arguments are the same — the results of these primitives are marked internally as Permutation Vectors. Subsequent use of such arrays maintains that property when operated on by rotate/reversal and grade up/down. Moreover, the two grade (<apll>⍋PV</apll> and <apll>⍒PV</apll>) and the index of (<apll>PV⍳R</apll>) primitives use a much faster (linear) algorithm than they would normally, given that the appropriate argument is a Permutation Vector.		In this case, index generator (<apll>⍳R</apll>) produces a Permutation Vector, as does deal (<apll>L?R</apll>) when the left and right arguments are the same — the results of these primitives are marked internally as Permutation Vectors. Subsequent use of such arrays maintains that property when operated on by rotate/reversal and grade up/down. Moreover, the two grade (<apll>⍋PV</apll> and <apll>⍒PV</apll>) and the index of (<apll>PV⍳R</apll>) and membership (<apll>L∊PV</apll>) primitives use a much faster (linear) algorithm than they would normally, given that the appropriate argument is a Permutation Vector.

Sudleyplace at 19:51, 18 August 2008

2008-08-18T19:51:16Z

← Older revision		Revision as of 15:51, 18 August 2008
Line 1:		Line 1:
	This clever idea of Bob Bernecky's [http://www.snakeisland.com/predicat.pdf] provides a performance improvement for certain expressions by marking certain arrays with special properties. For example, a ~~permutation vector~~ [http://mathworld.wolfram.com/Permutation.html] ~~has the property that it~~ is invariant under various APL primitives such as rotate/reversal (<apll>~~L⌽R~~</apll> and <apll>⌽R</apll>) and grade up/down (<apll>⍋R</apll> and <apll>⍒R</apll>).		This clever idea of Bob Bernecky's [http://www.snakeisland.com/predicat.pdf] provides a performance improvement for certain expressions by marking certain arrays with special properties. For example, the property of being a Permutation Vector [http://mathworld.wolfram.com/Permutation.html] is invariant (is still a Permutation Vector, albeit a different one) under various APL primitives such as rotate/reversal (<apll>L⌽PV</apll> and <apll>⌽PV</apll>) and grade up/down (<apll>⍋PV</apll> and <apll>⍒PV</apll>).

	Bernecky has defined several array predicate properties, one of which has been implemented in NARS so far.		Bernecky has defined several array predicate properties, one of which has been implemented in NARS so far.
Line 5:		Line 5:
	== Permutation Vectors ==		== Permutation Vectors ==

	In this case, index generator (<apll>⍳R</apll>) produces a Permutation Vector, as does deal (<apll>L?R</apll>) when the left and right arguments are the same — the results of these primitives are marked internally as Permutation Vectors. Subsequent use of such arrays maintains that property when operated on by rotate/reversal and grade up/down. Moreover, the two grade (<apll>⍋PV</apll> and <apll>⍒PV</apll>) and the index of (<apll>PV⍳R</apll>) primitives use a much faster (linear) algorithm than they would normally ~~use when~~ the appropriate argument is a Permutation Vector.		In this case, index generator (<apll>⍳R</apll>) produces a Permutation Vector, as does deal (<apll>L?R</apll>) when the left and right arguments are the same — the results of these primitives are marked internally as Permutation Vectors. Subsequent use of such arrays maintains that property when operated on by rotate/reversal and grade up/down. Moreover, the two grade (<apll>⍋PV</apll> and <apll>⍒PV</apll>) and the index of (<apll>PV⍳R</apll>) primitives use a much faster (linear) algorithm than they would normally, given that the appropriate argument is a Permutation Vector.

Sudleyplace: /* Permutation Vectors */

2008-08-18T19:43:24Z

Permutation Vectors

← Older revision		Revision as of 15:43, 18 August 2008
Line 5:		Line 5:
	== Permutation Vectors ==		== Permutation Vectors ==

	In this case, index generator (<apll>⍳R</apll>) produces a Permutation Vector, as does deal (L<apll>?</apll>R) when the left and right arguments are the same — the results of these primitives are marked internally as Permutation Vectors. ~~Further~~ use of such arrays maintains that property when operated on by rotate/reversal and grade up/down. Moreover, ~~both~~ the grade and index of (<apll>~~L⍳R~~</apll>) primitives use a much faster (linear) algorithm than they would normally use.		In this case, index generator (<apll>⍳R</apll>) produces a Permutation Vector, as does deal (<apll>L?R</apll>) when the left and right arguments are the same — the results of these primitives are marked internally as Permutation Vectors. Subsequent use of such arrays maintains that property when operated on by rotate/reversal and grade up/down. Moreover, the two grade (<apll>⍋PV</apll> and <apll>⍒PV</apll>) and the index of (<apll>PV⍳R</apll>) primitives use a much faster (linear) algorithm than they would normally use when the appropriate argument is a Permutation Vector.

Sudleyplace at 04:59, 18 August 2008

2008-08-18T04:59:36Z

← Older revision		Revision as of 00:59, 18 August 2008
Line 1:		Line 1:
	This clever idea of Bob Bernecky's [http://www.snakeisland.com/predicat.pdf] provides a performance improvement for certain expressions by marking certain arrays with special properties. For example, a permutation vector [http://mathworld.wolfram.com/Permutation.html] has the property that it is invariant under various APL primitives such as rotate/reversal (<apll>⌽</apll>) and grade up/down (<apll>~~⍋ ⍒~~</apll>).		This clever idea of Bob Bernecky's [http://www.snakeisland.com/predicat.pdf] provides a performance improvement for certain expressions by marking certain arrays with special properties. For example, a permutation vector [http://mathworld.wolfram.com/Permutation.html] has the property that it is invariant under various APL primitives such as rotate/reversal (<apll>L⌽R</apll> and <apll>⌽R</apll>) and grade up/down (<apll>⍋R</apll> and <apll>⍒R</apll>).

	Bernecky has defined several array predicate properties, one of which has been implemented in NARS so far~~: permutation vectors~~.		Bernecky has defined several array predicate properties, one of which has been implemented in NARS so far.

	In this case, ~~monadic iota~~ (<apll>~~{iota}~~</apll>) produces a ~~permutation vector~~, as does deal (<apll>?</apll>) when the left and right arguments are the same~~, and~~ are marked internally as ~~such~~. Further use of such arrays ~~maintain~~ that property when operated on by rotate/reversal and grade up/down. Moreover, the grade ~~primitive uses~~ a much faster (linear) algorithm than it would normally use.		== Permutation Vectors ==

			In this case, index generator (<apll>⍳R</apll>) produces a Permutation Vector, as does deal (L<apll>?</apll>R) when the left and right arguments are the same — the results of these primitives are marked internally as Permutation Vectors. Further use of such arrays maintains that property when operated on by rotate/reversal and grade up/down. Moreover, both the grade and index of (<apll>L⍳R</apll>) primitives use a much faster (linear) algorithm than they would normally use.

Sudleyplace: New page: This clever idea of Bob Bernecky's [http://www.snakeisland.com/predicat.pdf] provides a performance improvement for certain expressions by marking certain arrays with special properties. ...

2008-08-17T16:57:27Z

New page: This clever idea of Bob Bernecky's [http://www.snakeisland.com/predicat.pdf] provides a performance improvement for certain expressions by marking certain arrays with special properties. ...

New page

This clever idea of Bob Bernecky's [http://www.snakeisland.com/predicat.pdf] provides a performance improvement for certain expressions by marking certain arrays with special properties. For example, a permutation vector [http://mathworld.wolfram.com/Permutation.html] has the property that it is invariant under various APL primitives such as rotate/reversal (<apll>⌽</apll>) and grade up/down (<apll>⍋ ⍒</apll>).

Bernecky has defined several array predicate properties, one of which has been implemented in NARS so far: permutation vectors.

In this case, monadic iota (<apll>{iota}</apll>) produces a permutation vector, as does deal (<apll>?</apll>) when the left and right arguments are the same, and are marked internally as such. Further use of such arrays maintain that property when operated on by rotate/reversal and grade up/down. Moreover, the grade primitive uses a much faster (linear) algorithm than it would normally use.