Minkowski question-mark function: Difference between revisions
Content added Content deleted
m (J: remove some silliness, add a small but movtivating example) |
(J: trivia) |
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f=. 1|y |
f=. 1|y |
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node=. *i.2 2 NB. node of Stern-Brocot tree |
node=. *i.2 2 NB. node of Stern-Brocot tree |
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B=.'' |
B=. '' |
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for.i.ITERCOUNT do. |
for. i.ITERCOUNT do. |
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B=.B, b=. f>:%/t=. +/node |
B=. B, b=. f>:%/t=. +/node |
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node=. t (1-b)} node |
node=. t (1-b)} node |
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end. |
end. |
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| Line 486: | Line 486: | ||
cf=. i.0 |
cf=. i.0 |
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cur=. 0 NB. 1 if generating "top" side of cf |
cur=. 0 NB. 1 if generating "top" side of cf |
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cnt=. 1 NB. bits |
cnt=. 1 NB. "bits" (proposed continued fraction element) |
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for.i.ITERCOUNT do. |
for. i.ITERCOUNT do. |
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if. f=<. f do. |
if. f=<. f do. |
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cf=. cf,%cnt break. |
cf=. cf,%cnt break. |
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| Line 500: | Line 500: | ||
(+%)/(<.y),cf |
(+%)/(<.y),cf |
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}}</lang> |
}}</lang> |
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Task examples: |
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<lang J> minkowski 0.5*1+%:5 |
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1.66667 |
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((%:13)-7)%6 |
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_0.565741 |
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invmink _5%9 |
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_0.565741 |
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(p:%%:)2 |
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3.53553 |
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invmink minkowski (p:%%:)2 |
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3.53553 |
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minkowski invmink (p:%%:)2 |
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3.53553 |
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*:invmink 1.4 NB. square of inverse minkowski of 1.4 |
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2</lang> |
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That said, note that this algorithm introduces significant numeric instability for √7 divided by 3: |
That said, note that this algorithm introduces significant numeric instability for √7 divided by 3: |
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