UTF-8 String Indexing Strategies

This article was discussed on Hacker News.

When designing or, in some cases, implementing a programming language with built-in support for Unicode strings, an important decision must be made about how to represent or encode those strings in memory. Not all representations are equal, and there are trade-offs between different choices.

One issue to consider is that strings typically feature random access indexing of code points with a time complexity resembling constant time (O(1)). However, not all string representations actually support this well. Strings using variable length encoding, such as UTF-8 or UTF-16, have O(n) time complexity indexing, ignoring special cases (discussed below). The most obvious choice to achieve O(1) time complexity — an array of 32-bit values, as in UCS-4 — makes very inefficient use of memory, especially with typical strings.

Despite this, UTF-8 is still chosen in a number of programming languages, or at least in their implementations. In this article I’ll discuss three examples — Emacs Lisp, Julia, and Go — and how each takes a slightly different approach.

Emacs Lisp

Emacs Lisp has two different types of strings that generally can be used interchangeably: unibyte and multibyte. In fact, the difference between them is so subtle that I bet that most people writing Emacs Lisp don’t even realize there are two kinds of strings.

Emacs Lisp uses UTF-8 internally to encode all “multibyte” strings and buffers. To fully support arbitrary sequences of bytes in the files being edited, Emacs uses its own extension of Unicode to precisely and unambiguously represent raw bytes intermixed with text. Any arbitrary sequence of bytes can be decoded into Emacs’ internal representation, then losslessly re-encoded back into the exact same sequence of bytes.

Unibyte strings and buffers are really just byte-strings. In practice, they’re essentially ISO/IEC 8859-1, a.k.a. Latin-1. It’s a Unicode string where all code points are below 256. Emacs prefers the smallest and simplest string representation when possible, similar to CPython 3.3+.

(multibyte-string-p "hello")
;; => nil

(multibyte-string-p "π ≈ 3.14")
;; => t

Emacs Lisp strings are mutable, and therein lies the kicker: As soon as you insert a code point above 255, Emacs quietly converts the string to multibyte.

(defvar fish "fish")

(multibyte-string-p fish)
;; => nil

(setf (aref fish 2) ?ŝ
      (aref fish 3) ?o)

fish
;; => "fiŝo"

(multibyte-string-p fish)
;; => t

Constant time indexing into unibyte strings is straightforward, and Emacs does the obvious thing when indexing into unibyte strings. It helps that most strings in Emacs are probably unibyte, even when the user isn’t working in English.

Most buffers are multibyte, even if those buffers are generally just ASCII. Since Emacs uses gap buffers it generally doesn’t matter: Nearly all accesses are tightly clustered around the point, so O(n) indexing doesn’t often matter.

That leaves multibyte strings. Consider these idioms for iterating across a string in Emacs Lisp:

(dotimes (i (length string))
  (let ((c (aref string i)))
    ...))

(cl-loop for c being the elements of string
         ...)

The latter expands into essentially the same as the former: An incrementing index that uses aref to index to that code point. So is iterating over a multibyte string — a common operation — an O(n^2) operation?

The good news is that, at least in this case, no! It’s essentially just as efficient as iterating over a unibyte string. Before going over why, consider this little puzzle. Here’s a little string comparison function that compares two strings a code point at a time, returning their first difference:

(defun compare (string-a string-b)
  (cl-loop for a being the elements of string-a
           for b being the elements of string-b
           unless (eql a b)
           return (cons a b)))

Let’s examine benchmarks with some long strings (100,000 code points):

(benchmark-run
    (let ((a (make-string 100000 0))
          (b (make-string 100000 0)))
      (compare a b)))
;; => (0.012568031 0 0.0)

With using two, zeroed unibyte strings it takes 13ms. How about changing the last code point in one of them to 256, converting it to a multibyte string:

(benchmark-run
    (let ((a (make-string 100000 0))
          (b (make-string 100000 0)))
      (setf (aref a (1- (length a))) 256)
      (compare a b)))
;; => (0.012680513 0 0.0)

Same running time, so that multibyte string cost nothing more to iterate across. Let’s try making them both multibyte:

(benchmark-run
    (let ((a (make-string 100000 0))
          (b (make-string 100000 0)))
      (setf (aref a (1- (length a))) 256
            (aref b (1- (length b))) 256)
      (compare a b)))
;; => (2.327959762 0 0.0)

That took 2.3 seconds: about 2000x longer to run! Iterating over two multibyte strings concurrently seems to have broken an optimization. Can you reason about what’s happened?

To avoid the O(n) cost on this common indexing operating, Emacs keeps a “bookmark” for the last indexing location into a multibyte string. If the next access is nearby, it can starting looking from this bookmark, forwards or backwards. Like a gap buffer, this gives a big advantage to clustered accesses, including iteration.

However, this string bookmark is global, one per Emacs instance, not once per string. In the last benchmark, the two multibyte strings are constantly fighting over a single string bookmark, and indexing in comparison function is reduced to O(n^2) time complexity.

So, Emacs pretends it has constant time access into its UTF-8 text data, but it’s only faking it with some simple optimizations. This usually works out just fine.

Julia

Another approach is to not pretend at all, and to make this limitation of UTF-8 explicit in the interface. Julia took this approach, and it was one of my complaints about the language. I don’t think this is necessarily a bad choice, but I do still think it’s inappropriate considering Julia’s target audience (i.e. Matlab users).

Julia strings are explicitly byte strings containing valid UTF-8 data. All indexing occurs on bytes, which is trivially constant time, and always decodes the multibyte code point starting at that byte. But it is an error to index to a byte that doesn’t begin a code point. That error is also trivially checked in constant time.

s = "π"

s[1]
# => 'π'

s[2]
# ERROR: UnicodeError: invalid character index
#  in getindex at ./strings/basic.jl:37

Slices are still over bytes, but they “round up” to the end of the current code point:

s[1:1]
# => "π"

Iterating over a string requires helper functions which keep an internal “bookmark” so that each access is constant time:

for i in eachindex(string)
    c = string[i]
    # ...
end

So Julia doesn’t pretend, it makes the problem explicit.

Go

Go is very similar to Julia, but takes an even more explicit view of strings. All strings are byte strings and there are no restrictions on their contents. Conventionally strings contain UTF-8 encoded text, but this is not strictly required. There’s a unicode/utf8 package for working with strings containing UTF-8 data.

Beyond convention, the range clause also assumes the string contains UTF-8 data, and it’s not an error if it does not. Bytes not containing valid UTF-8 data appear as a REPLACEMENT CHARACTER (U+FFFD).

func main() {
    s := \xff"
    for _, r := range s {
        fmt.Printf("U+%04x\n", r)
    }
}

// U+03c0
// U+fffd

A further case of the language favoring UTF-8 is that casting a string to []rune decodes strings into code points, like UCS-4, again using REPLACEMENT CHARACTER:

func main() {
    s := \xff"
    r := []rune(s)
    fmt.Printf("U+%04x\n", r[0])
    fmt.Printf("U+%04x\n", r[1])
}

// U+03c0
// U+fffd

So, like Julia, there’s no pretending, and the programmer explicitly must consider the problem.

Preferences

All-in-all I probably prefer how Julia and Go are explicit with UTF-8’s limitations, rather than Emacs Lisp’s attempt to cover it up with an internal optimization. Since the abstraction is leaky, it may as well be made explicit.

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Chris Wellons