From 4ae7952e2b3566d373c55c8e9740051ca37ed738 Mon Sep 17 00:00:00 2001 From: lewuathe Date: Wed, 6 Jan 2021 01:59:45 +0000 Subject: [PATCH] [mlir] Fix MathJax rendering in Affine doc MathJax is not properly imported in Affine doc. It causes the invalid rendering of math formulas in the Affine doc page. https://mlir.llvm.org/docs/Dialects/Affine/#affine-expressions Importing MathJax code from CDN resolved the rendering issue as follows. {F14942131} Reviewed By: ftynse Differential Revision: https://reviews.llvm.org/D94004 --- mlir/docs/Dialects/Affine.md | 16 ++++++++-------- 1 file changed, 8 insertions(+), 8 deletions(-) diff --git a/mlir/docs/Dialects/Affine.md b/mlir/docs/Dialects/Affine.md index cedbb01..1ce535a 100644 --- a/mlir/docs/Dialects/Affine.md +++ b/mlir/docs/Dialects/Affine.md @@ -124,19 +124,19 @@ one-dimensional affine expressions, with the entire list enclosed in parentheses. **Context:** An affine function, informally, is a linear function plus a -constant. More formally, a function f defined on a vector $$\vec{v} \in -\mathbb{Z}^n$$ is a multidimensional affine function of $$\vec{v}$$ if -$$f(\vec{v})$$ can be expressed in the form $$M \vec{v} + \vec{c}$$ where $$M$$ -is a constant matrix from $$\mathbb{Z}^{m \times n}$$ and $$\vec{c}$$ is a -constant vector from $$\mathbb{Z}$$. $$m$$ is the dimensionality of such an +constant. More formally, a function f defined on a vector $\vec{v} \in +\mathbb{Z}^n$ is a multidimensional affine function of $\vec{v}$ if +$f(\vec{v})$ can be expressed in the form $M \vec{v} + \vec{c}$ where $M$ +is a constant matrix from $\mathbb{Z}^{m \times n}$ and $\vec{c}$ is a +constant vector from $\mathbb{Z}$. $m$ is the dimensionality of such an affine function. MLIR further extends the definition of an affine function to allow 'floordiv', 'ceildiv', and 'mod' with respect to positive integer constants. Such extensions to affine functions have often been referred to as quasi-affine functions by the polyhedral compiler community. MLIR uses the term 'affine map' to refer to these multidimensional quasi-affine functions. As -examples, $$(i+j+1, j)$$, $$(i \mod 2, j+i)$$, $$(j, i/4, i \mod 4)$$, $$(2i+1, -j)$$ are two-dimensional affine functions of $$(i, j)$$, but $$(i \cdot j, -i^2)$$, $$(i \mod j, i/j)$$ are not affine functions of $$(i, j)$$. +examples, $(i+j+1, j)$, $(i \mod 2, j+i)$, $(j, i/4, i \mod 4)$, $(2i+1, +j)$ are two-dimensional affine functions of $(i, j)$, but $(i \cdot j, +i^2)$, $(i \mod j, i/j)$ are not affine functions of $(i, j)$. ### Affine Maps -- 2.7.4