CORDIC: Difference between revisions

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cordic=: {{alpha=. y

XY=. 1 0 assert. 0 <: alpha assert. 0.~~5p1~~ >: alpha

XY=. 1 0 assert. 0 <: alpha assert. 0.25p1 >: alpha

while. epsilon < alpha do.

k=. phin I. alpha

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}}

CORDIC -9

CORDIC=: {{

'octant angle'=. 8 0.25p1#:y

select. octant

case. 0 do. cordic angle

case. 1 do. |.cordic 0.25p1-angle

case. 2 do. _1 1*|.cordic angle

case. 3 do. _1 1* cordic 0.25p1-angle

case. 4 do. _1 _1* cordic angle

case. 5 do. _1 _1*|.cordic 0.25p1-angle

case. 6 do. 1 _1*|.cordic angle

case. 7 do. 1 _1* cordic 0.25p1-angle

end.

}}</syntaxhighlight>

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Task examples (cos is the left value in the result, argument is in radians):

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<syntaxhighlight lang=J> CORDIC -9

_0.92954 _0.420445

CORDIC 0

1 0

CORDIC 1.5

0.~~103588~~ 1.~~46074~~

0.070762 0.997844

CORDIC 6

0.~~405107~~ _1.~~39209~~</syntaxhighlight>

0.970161 _0.282323</syntaxhighlight>

⚫

Task examples (cos is the left value in the result, argument is in radians):

⚫

<syntaxhighlight lang=J>~~FIXME</syntaxhighlight>~~

=== Notes ===

CAUTION: At the time of this writing, the task description declares that the cordic algorithm is valid in the range 0 .. π/2. But it appears that the algorithm can only be valid in the range 0..π/4.

⚫

~~Here~~, we use three constants, two of which are lookup tables (<code>tent</code> gives us negative powers of ten as a lookup table):

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In this J implementation, we use three constants, two of which are lookup tables (<code>tent</code> gives us negative powers of ten as a lookup table):

<syntaxhighlight lang=J> epsilon

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<syntaxhighlight lang=J> {&phin

{ &0.785398163397448279 0.0996686524911620381 0.00999966668666523936 0.000999999666666867007 9.99999996666667089e_5 9.99999999966667302e_6 9.99999999999667283e_7 9.9999999999999744e_8 1.00000000000000085e_8 1.00000000000000089e_9 1.00000000000000107e_10 1....</syntaxhighlight>

That said, it's not clear that this algorithm can be more accurate than something near 2% for the general case.

Also: [[j:Vocabulary/SpecialCombinations#Preexecuting_verbs_with_.28.28_.29.29|double parenthesis around a noun phrase]] tells the interpreter that that expression is a constant which should be evaluated once, ahead of time.