Document mathematical Go code beautifully.

• Write mathematical formulae in a LaTeX-ish syntax
• Super/subscripts formatted with Unicode characters: 2^32 becomes 2³² and x_{i+1} becomes xᵢ₊₁
• Comprehensive symbol library: \zeta(s) = \sum 1/n^{s} becomes ζ(s) = ∑ 1/nˢ

Inspired by Filippo Valsorda's literate Go implementation of Poly1305, which can be reproduced using mathfmt.

Install mathfmt with:

go get -u github.com/mmcloughlin/mathfmt

Apply to files just like you would with gofmt.

mathfmt -w file.go

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

// 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!

// 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))
}

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.

mathfmt only works on Go source code. Every comment in the file is processed, both single- and multi-line.

mathfmt recognizes a huge symbol table 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" for character combinations commonly used to represent mathematical symbols.

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}.

Thank you to Günter Milde for the exhaustive unimathsymbols database of Unicode symbols and corresponding LaTeX math mode commands.

mathfmt is available under the BSD 3-Clause License.