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https://github.com/mmcloughlin/mathfmt

Document mathematical Go code beautifully
https://github.com/mmcloughlin/mathfmt

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Document mathematical Go code beautifully

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# mathfmt



Document mathematical Go code beautifully.



* Write mathematical formulae in a [LaTeX](https://en.wikipedia.org/wiki/LaTeX)-ish syntax

* Super/subscripts formatted with Unicode characters: `2^32` becomes `2³²` and `x_{i+1}` becomes `xᵢ₊₁`

* Comprehensive [symbol library](symbols.md): `\zeta(s) = \sum 1/n^{s}` becomes `ζ(s) = ∑ 1/nˢ`



Inspired by [Filippo Valsorda](https://filippo.io/)'s [literate Go

implementation of

Poly1305](https://blog.filippo.io/a-literate-go-implementation-of-poly1305/), which can be [reproduced using `mathfmt`](testdata/poly1305.in).



## Usage



Install `mathfmt` with:



```

go get -u github.com/mmcloughlin/mathfmt

```



Apply to files just like you would with `gofmt`.



```

mathfmt -w file.go

```



## Example



Here's our variance function in Go, documented with LaTeX-ish equations in comments.



[embedmd]:# (testdata/stats.in go /\/\/ Variance/ /^}/)

```go

// Variance computes the population variance of the population x_{i} of size N.

// Specifically, it computes \sigma^2 where

//

//		\sigma^2 = \sum (x_{i} - \mu)^2 / N

//

// See also: https://en.wikipedia.org/wiki/Variance.

func Variance(X []float64) float64 {

	// Compute the average \mu.

	mu := Mean(X)



	// Compute the sum \sum (x_{i} - \mu)^2.

	ss := 0.0

	for _, x := range X {

		ss += (x - mu) * (x - mu) // (x_{i} - \mu)^2

	}



	// Final divide by N to produce \sigma^2.

	return ss / float64(len(X))

}

```



Run it through `mathfmt` and voila!



[embedmd]:# (testdata/stats.golden go /\/\/ Variance/ /^}/)

```go

// Variance computes the population variance of the population xᵢ of size N.

// Specifically, it computes σ² where

//

//	σ² = ∑ (xᵢ - μ)² / N

//

// See also: https://en.wikipedia.org/wiki/Variance.

func Variance(X []float64) float64 {

	// Compute the average μ.

	mu := Mean(X)



	// Compute the sum ∑ (xᵢ - μ)².

	ss := 0.0

	for _, x := range X {

		ss += (x - mu) * (x - mu) // (xᵢ - μ)²

	}



	// Final divide by N to produce σ².

	return ss / float64(len(X))

}

```



## Syntax



First a warning: `mathfmt` does not have a rigorous grammar, it's a

combination of string replacement and regular expressions that appears to

work most of time. However you may run into some [thorny edge

cases](https://github.com/mmcloughlin/mathfmt/issues/9).



### Source



`mathfmt` only works on Go source code. _Every_ comment in the

file is processed, both single- and multi-line.



### Symbols



`mathfmt` recognizes a [huge symbol table](symbols.md) that is

almost entirely borrowed from LaTeX packages. Every symbol macro in comment

text will be replaced with its corresponding Unicode character. In addition

to LaTeX symbol macros, `mathfmt` supports a [limited set of

"aliases"](symbols.md#aliases) for character combinations commonly used to

represent mathematical symbols.



### Super/subscripts



Like LaTeX, superscripts use the `^` character and subscripts use `_`. If the

super/subscript consists entirely of digits, then no braces are required: for

example `2^128` or `x_13`. Otherwise braces must be used to surround the

super/subscript, for example `2^{i}` or `x_{i+j}`.



Note that Unicode support for super/subscripts is limited, and in particular

does not support the full alphabet. Therefore, if there is not a

corresponding super/subscript character available for any character in braces

`{...}`, `mathfmt` will not perform any substition at all. For example there

is no superscript `q`, so `mathfmt` will not be able to process `2^{q}`, and

likewise with `x_{K}`.



## Credits



Thank you to Günter Milde for the exhaustive [`unimathsymbols`

database](http://milde.users.sourceforge.net/LUCR/Math/) of Unicode symbols

and corresponding LaTeX math mode commands.



## License



`mathfmt` is available under the [BSD 3-Clause License](LICENSE).