zec
/
halo2
mirror of https://github.com/zcash/halo2.git
1
0
Fork 0
Code Issues Projects Releases Wiki Activity

Merge pull request #164 from daira/book-decomposition 

[book] decomposition.md: avoid introducing `m` when we already have `range`
This commit is contained in:
str4d 2021-07-27 17:10:50 +01:00 committed by GitHub
parent ee878ddc57 b2e25b5ac3
commit a273307661
No known key found for this signature in database
GPG Key ID: 4AEE18F83AFDEB23
1 changed files with 1 additions and 1 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

2
book/src/design/circuit/gadgets/decomposition.md
View File

@ -73,4 +73,4 @@ $$q_\mathit{lookup} \cdot \left(q_\mathit{running} \cdot (z_i - 2^K \cdot z_{i+1
where $z_i$ and $\textsf{word}$ are the same cell (but distinguished here for clarity of usage).
## Short range decomposition
For a short range (for instance, $[0, m)$ where $m \leq 8$), we can range-constrain each word using a degree-$m$ polynomial constraint instead of a lookup: $$\texttt{range\_check(word, range)} = \texttt{word} \cdot (1 - \texttt{word}) \cdots (\texttt{range} - 1 - \texttt{word}).$$
For a short range (for instance, $[0, \texttt{range})$ where $\texttt{range} \leq 8$), we can range-constrain each word using a degree-$\texttt{range}$ polynomial constraint instead of a lookup: $$\texttt{range\_check(word, range)} = \texttt{word} \cdot (1 - \texttt{word}) \cdots (\texttt{range} - 1 - \texttt{word}).$$