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chore: aligns the Ignore Max Namespace description with the implementation #199

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May 18, 2023
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chore: aligns the Ignore Max Namespace description with the implementation #199

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afef9af
updates Ignore Max Namespace logic to match the implementation
staheri14 May 18, 2023
a5be247
fixes markdownlint issues
staheri14 May 18, 2023
375e9ee
Merge branch 'master' into update-ignore-max-namespace-description
staheri14 May 18, 2023
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12 changes: 7 additions & 5 deletions docs/nmt-lib.md
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Expand Up @@ -45,12 +45,14 @@ idSize := tree.NamespaceSize() // outputs 1
### Ignore Max Namespace

If the NMT is configured with `IgnoreMaxNamespace` set to true (the flag is explained [here](#nmt-initialization-and-configuration)), then the calculation of the namespace ID range of non-leaf nodes in the [namespace hash function](./spec/nmt.md#namespaced-hash) will change slightly.
That is, when determining the upper limit of the namespace ID range for a tree node, the maximum possible namespace `maxPossibleNamespace` should not be taken into account.
(In the preceding code example with the ID size of `1` byte, the value of `maxPossibleNamespace` is $2^8-1 = 0xFF$.)
That is, if the right child of a node is entirely filled with leaves with the maximum possible namespace `maxPossibleNamespace`, i.e., its minimum and maximum namespace are equal to the `maxPossibleNamespace`, then the right child is excluded from the calculation of the namespace ID range of the parent node, and the parent node inherits the namespace range of the left child.
In the preceding code example with the ID size of `1` byte, the value of `maxPossibleNamespace` is $2^8-1 = 0xFF$.
Concretely, consider a node `n` with children `l` and `r`. If `r.minNs` and `r.maxNs` are both equal to `maxPossibleNamespace` (indicating that it represents the root of a subtree whose leaves all have the namespace ID of `maxPossibleNamespace`), then the namespace ID range of `n` is set to the namespace range of `l`, i.e., `n.MinNs = l.MinNs` and `n.MaxNs = l.MaxNs`.
Otherwise, the namespace ID range of `n` is set as normal i.e., `n.minNs = min(l.minNs, r.minNs)` and `n.maxNs = max(l.maxNs, r.maxNs)`.

Concretely, for a node `n` with children `l` and `r`, the namespace ID is the largest namespace value from `l` and `r` smaller than `maxPossibleNamespace`, if such a namespace ID exists.
Otherwise, if all candidate values are equal to `maxPossibleNamespace`, the namespace ID of `n` is set to `maxPossibleNamespace`.
Precisely, if a set `C` $= \bigl \lbrace$ `ns` $\in \lbrace$`l.minNs`, `l.maxNs`, `r.minNs`, `r.maxNs` $\rbrace:$ `ns` $<$ `maxPossibleNamespace` $\bigr \rbrace$ is not empty, `n.maxNs = max(C)`. If `C` is empty, `n.maxNs = maxPossibleNamespace`.
Note that the `IgnoreMaxNamespace` flag is Celestia-specific and is motivated by the fact that half of the data items in the NMT are associated with reserved namespace IDs (i.e., the highest possible value within the ID size) and do not need to be queried using their namespace IDs.

[//]: # (Precisely, if a set `C` $= \bigl \lbrace$ `ns` $\in \lbrace$`l.minNs`, `l.maxNs`, `r.minNs`, `r.maxNs` $\rbrace:$ `ns` $<$ `maxPossibleNamespace` $\bigr \rbrace$ is not empty, `n.maxNs = max&#40;C&#41;`. If `C` is empty, `n.maxNs = maxPossibleNamespace`.)

## Add Leaves

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