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# public scooby /gybe_ls

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1. index_notes
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 ... ... `@@ -0,0 +1,65 @@` 1 `+So...` 2 `+` 3 `+An indexed structure is simply trees mapping into tuples. That's not too hard, and we can probably work out a clustered arrangement.` 4 `+` 5 `+But.` 6 `+` 7 `+Some values can be negative.` 8 `+` 9 `+How can we create a reasonably efficient index that handles both negative and positive values?` 10 `+` 11 `+How do indexes affect our basic operations?` 12 `+` 13 `+Let's take the first one.` 14 `+` 15 `+Assuming a universal comparator, we'd like to arrange values of the attribute Foo as an ordering.` 16 `+` 17 `+Say foo has the values a, b, c, !0, !b, !cd` 18 `+` 19 `+Our ordering would be:` 20 `+` 21 `+? !0, !b, !cd` 26 `+a -> a, !0, !b, !cd` 27 `+a !0, !b, !cd` 28 `+b -> b, !0, !cd` 29 `+b !0, !b, !cd` 30 `+c -> c, !0, !b` 31 `+c !0, !b, !cd` 32 `+d -> !0, !b` 33 `+d !0, !b, !cd` 34 `+` 35 `+It simply makes sense to have two mappings, one for positive and one for negative.` 36 `+` 37 `+Not sure what the negative mapping needs to do.` 38 `+` 39 `+If I want to find everything between b and d:` 40 `+` 41 `+b, !0, !cd` 42 `+!0, !b, !cd` 43 `+c, !0, !b` 44 `+!0, !b, !cd` 45 `+!0, !b` 46 `+` 47 `+So the negative mapping is an exclusion map.` 48 `+` 49 `+We know that in the interstices all infinite values apply. So it's really a positive map of which ones can be removed.` 50 `+` 51 `+b -> !b` 52 `+c -> !cd` 53 `+d -> !cd` 54 `+` 55 `+But we need a set of all negatives to start with, so they need to be ordered.` 56 `+` 57 `+Say a, b, c, d = 2, 4, 6, 8.` 58 `+U = !0 = 1, 2, 3, 4, 5, 6, 7, 8, 9` 59 `+!b = 1, 2, 3, 5, 6, 7, 8, 9` 60 `+!cd = 1, 2, 3, 4, 5, 7, 9` 61 `+` 62 `+Ordering, therefore, would be !0 (since it always has a lesser value),` 63 `+then !cd, then !b.` 64 `+` 65 `+But for simplicity, we can probably just order them like lists of positives.`

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