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README.md

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If it's useful in academic work, you can cite it with this DOI: [![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.5047409.svg)](https://doi.org/10.5281/zenodo.5047409)
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<details><summary><b>Notation</b></summary>
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## Notation
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<details>
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Index notation for some simple functions:
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```
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</details>
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<details><summary><b>Fast & slow</b></summary>
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## Fast & Slow
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<details>
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When used with LoopVectorization, on straightforward matrix multiplication of real numbers,
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`@tullio` tends to be about as fast as OpenBLAS. Depending on the size, and on your computer.
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```
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</details>
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## Gradients & GPU
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<details><summary><b>Derivatives & GPU</b></summary>
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```julia
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</details>
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<details><summary><b>Larger expressions</b></summary>
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## Larger Expressions
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<details>
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The expression need not be just one line, for example:
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```
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</details>
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<details><summary><b>Options</b></summary>
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## Keyword Options
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<details>
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The default setting is:
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```@tullio threads=true fastmath=true avx=true tensor=true cuda=256 grad=Base verbose=false A[i,j] := ...```
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* `Tullio.@einsum` is a variant with a few changes, to allow the running of Einsum.jl's tests.
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</details>
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<details><summary><b>Internals</b></summary>
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## How it Works
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<details>
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The following three macros all end up calling the same functions as does `C = A * B`:
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Scalar reductions, such as `@tullio s := A[i,j] * log(B[j,i])`, are slightly different in that the `act!` function simply returns the sum, i.e. the variable `acc` above.
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</details>
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<details><summary><b>Elsewhere</b></summary>
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## Elsewhere
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Back-end friends & relatives:
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