From b2e25b5ac3705020d9ae622a3a825658d0d1b0f0 Mon Sep 17 00:00:00 2001 From: Daira Hopwood Date: Tue, 27 Jul 2021 17:06:36 +0100 Subject: [PATCH] [book] decomposition.md: avoid introducing `m` when we already have `range`. Signed-off-by: Daira Hopwood --- book/src/design/circuit/gadgets/decomposition.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/book/src/design/circuit/gadgets/decomposition.md b/book/src/design/circuit/gadgets/decomposition.md index 84de73bf..5b8eddac 100644 --- a/book/src/design/circuit/gadgets/decomposition.md +++ b/book/src/design/circuit/gadgets/decomposition.md @@ -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}).$$