Minkowski question-mark function: Difference between revisions
Content added Content deleted
m (J: make it easier to experiment with longer continued fractions (though it's not clear that this length should match for minkowski and its inverse)) |
m (J: remove some silliness, add a small but movtivating example) |
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node=. t (1-b)} node |
node=. t (1-b)} node |
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end. |
end. |
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(<.y)+B+/ .* |
(<.y)+B+/ .*2^-1+i.ITERCOUNT |
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}} |
}} |
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invmink=: {{ |
invmink=: {{ |
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f=. 1|y |
f=. 1|y |
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end. |
end. |
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f=. f*2 |
f=. f*2 |
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b=. 1 >`<@.cur f |
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cf=. cf, |
cf=. cf,(-.b)#cnt |
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cnt=. 1+b*cnt |
cnt=. 1+b*cnt |
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cur=. cur=b |
cur=. cur=b |
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3.53553 |
3.53553 |
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minkowski invmink (p:%%:)2 |
minkowski invmink (p:%%:)2 |
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3.53553 |
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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