writing about things, sometimes.

Parsing UTF-8

Written by Omar Polo on 11 January 2021 while listening to Metropolis Pt. 2 scenes From a Memory” by Dream Theater.

In one of the recent posts, the one were I was discussing the IRI implementation in gmid, I said that I wasn’t happy with the UTF-8 parser.

Since then, I improved the valid_multibyte_utf8 function at least two times, and I’m happy with the current result, but I thought to document here the various “generations” of that function.

The purpose of valid_multibyte_utf8 is to tell if a string starts with a valid UTF-8 encoded UNICODE character, and advance the pointer past that glyph. We’re interested only in U+80 and up, because of the characters in the ASCII range we’ve already taken care of.

UTF-8 is a multibyte character encoding for UNICODE text. Multibyte means that a single UNICODE codepoint can occupy more than one byte; in fact, UTF-8 is also variable-length: a codepoint can span between one and four bytes.

UTF-8 is also a nice encoding, easy to parse but, as with everything that is related to UNICODE, with subtle and annoying details.

The UNICODE codepoints are encoded as follows:

  • U+0000 - U+007F: one byte, compatible with ASCII
  • U+0080 - U+07FF: two bytes
  • U+0800 - U+D7FF and U+E0000 - U+FFFF: three bytes
  • U+10000 – U+10FFFF: four bytes

Byte-wise, every UTF-8 character starts with either a 0 or with the bit patter 11XXXXXX. Byte starting with 11 are called UTF-8 “start bytes”, and are followed by up to three byte that starts with 10XXXXXX, called “continuation bytes”.

one byte:       0.......
two bytes:      110..... 10......
three bytes:    1110.... 10...... 10......
four bytes:     11110... 10...... 10...... 10......

A first, quick implementation in C of a UTF-8 parser could look something like this:

#define CONT_BYTE(b) ((b & 0xC0) == 0x80)

valid_multibyte_utf8(struct parser *p)
	/* p->uri is our string */
	uint8_t s = *p->uri;

	if ((s & 0x80) == 0)
		/* return 1 here to accept ASCII */
		return 0;

	/* 2 bytes seq */
	if ((s & 0xE0) == 0xC0)
		return CONT_BYTE(*(++p->uri));

	/* 3 bytes seq */
	if ((s & 0xF0) == 0xE0)
		return CONT_BYTE(*(++p->uri))
			&& CONT_BYTE(*(++p->uri));

	/* 4 bytes seq */
	if ((s & 0xF8) == 0xF0)
		return CONT_BYTE(*(++p->uri))
			&& CONT_BYTE(*(++p->uri))
			&& CONT_BYTE(*(++p->uri));

	return 0;

This reads nice, and seems pretty straightforward. It checks the first byte, and then the appropriate number of continuation bytes. It won’t overflow if a codepoint is truncated due to the short-circuit nature of the logical and in C.

But it isn’t UNICODE compliant.

This parser will happily accept byte sequence that looks like UTF-8 but aren’t valid. In particular, everything in the range U+D800 - U+DFFF and U+110000 - U+1FFFFF DO NOT contain valid UNICODE codepoints. But this parser will accept them.

An easy “upgrade” could be something like this, that inverts the logic of the ifs and checks that the codepoint we parse is in the correct range:

valid_multibyte_utf8(struct parser *p)
	uint32_t c;
	uint8_t s;

	c = 0;
	s = *p->uri;

	if ((s & 0xE0) == 0xC0) {
		if (!CONT_BYTE(p->uri[1]))
			return 0;
		c = ((s & 0x1F) << 6) | (p->uri[1] & 0x3F);
		p->uri += 1;
	} else if ((s & 0xF0) == 0xE0) {
		if (!CONT_BYTE(p->uri[1]) ||
			return 0;
		c = (s & 0x0F) << 12
			| ((p->uri[1] & 0x3F) << 6)
			| ((p->uri[2] & 0x3F));
		p->uri += 2;
	} else if ((s & 0xF8) == 0xF0) {
		if (!CONT_BYTE(p->uri[1]) ||
		    !CONT_BYTE(p->uri[2]) ||
			return 0;
		c = (s & 0x07) << 18
			| ((p->uri[1] & 0x3F) << 12)
			| ((p->uri[2] & 0x3F) << 6)
			| ((p->uri[3] & 0x3F));
		p->uri += 3;
	} else
		return 0;

	return (((0x080 <= c) && (c <= 0x7FF))
	    || (((0x800 <= c) && (c <= 0xFFFF)))
	    || (((0x10000 <= c) && (c <= 0x10FFFF))));

Oh my, this is starting to become ugly, isn’t it? Well, at least we can be sure that this handle everything and move on.

Except that even this version is not complete. Sure, we know that we’ve read a valid UNICODE codepoint, but here’s the twist: overlong sequences.

In UTF-8 sometimes you can encode the same character in multiple ways. The classic example, the one that various RFCs mentions, is the case of 0xC080.

 C    0    8    0       hexadecimal
1100 0000 1000 0000     binary
 12   0    8    0       decimal

This looks like a legit UTF-8 two-byte characters, but it gets encoded to NUL, U+0000.

In RFC3629 — “UTF-8, a transformation format of ISO 10646” — explicitly warns implementors about this issue:

Implementations of the decoding algorithm above MUST protect against decoding invalid sequences. For instance, a naive implementation may decode the overlong UTF-8 sequence C0 80 into the character U+0000, or the surrogate pair ED A1 8C ED BE B4 into U+233B4. Decoding invalid sequences may have security consequences or cause other problems. See Security Considerations (Section 10) below.
— RFC3629, 3. “UTF-8 definition”

Well, we could reverse the logic and have the various checks in every if-else branch but, honestly, this is becoming even messier. Magic numbers everywhere, long checks, etc; if only there were a simpler decoder…

Introducing the “Flexible and Economical UTF-8 decoder”, by Björn Höhrmann.

The decoder goes as follows:

// Copyright (c) 2008-2009 Bjoern Hoehrmann <bjoern@hoehrmann.de>
// See http://bjoern.hoehrmann.de/utf-8/decoder/dfa/ for details.

#define UTF8_ACCEPT 0
#define UTF8_REJECT 1

static const uint8_t utf8d[] = {
  /* lots of data */

uint32_t inline
decode(uint32_t* state, uint32_t* codep, uint32_t byte) {
  uint32_t type = utf8d[byte];

  *codep = (*state != UTF8_ACCEPT) ?
    (byte & 0x3fu) | (*codep << 6) :
    (0xff >> type) & (byte);

  *state = utf8d[256 + *state*16 + type];
  return *state;

The beauty of this decoder lies in the technique used: a state machine. I love state machines: they’re easy to design and reason about, fun and compact to implement and require only a small fixed amount of resources.

valid_multibyte_utf8 can now be built on top of decode easily as follows:

valid_multibyte_utf8(struct parser *p)
	uint32_t cp = 0, state = 0;

        for (; *p->uri; p->uri++)
		if (!utf8_decode(&state, &cp, *p->uri))

	/* reject also the ASCII range */
        return !state && cp > 0x7F

That’s all about it. I found interesting to study these various techniques to decode UTF-8. Also, if you don’t know the story behind how Ken Thompson designed it on a placemat, go read it, it’s fascinating!