How does \delimiter work? How does it convert its argument into character(s?) and why?

Question

studying the definition of \lvert (which just made me finally understand what does mean \@xp\@gobble and how it works \o/), I found the \delimiter command, with a numeric argument advanced by 0x1000000… So if I well understood delimiter translates into one character according its numerical argument… with something depending wether we’re inside mathmode or not… Well how does this number translate into something (where’s the translation table?), how is it related with mathmode and what does thi advancement by 0x1000000 mean/implies? And finally what’s the purpose of \delimiter?

Answer 1

\vert in latex is defined by

\DeclareMathDelimiter{\vert}
   {\mathord}{symbols}{"6A}{largesymbols}{"0C}

which says that it is an ordinary delimiter (not open or close) that at its natural size is taken from the symbol fonts (starting at) position hex 6A with larger sizes taken from the largesymbol font (starting at) position hex 0C.

We can look at the plain TeX definition of the same.

\def\vert{\delimiter"26A30C }

which is more compact but perhaps less readable.

\delimiter is a number which packs a bit code which we can decode by splitting up the hex digits

0 (not shown) = \mathord

2 = symbol font

6A = symbol font slot

3 = extension (large symbol) font

0C = Slot in large symbol font.

amsmath defines lvert to be an "opening" version of vert which could have been

\DeclareMathDelimiter{\lvert}
   {\mathopen}{symbols}{"6A}{largesymbols}{"0C}

but to allow for possible different font encodings it uses the primitive syntax and just adds "4000000 so the leading hex digit is 4 not 0 denoting a mathopen.

the tfm font metrics associate with the math fonts specify how delimiters stretch, starting from the specified slots the metrics chain together a sequence of larger glyphs then finally how to build an arbitrarily large character by stacking top bottom (possibly middle, for {) and repeatable segments.

To see the metric information taking an example and the plain tex versions the 3 means \fam3 which is defined by

\textfont3=\tenex

which says fam3 is \tenex which is defined by

\font\tenex=cmex10 % math extension

so we can look at the metrics of cmex10 using the comand

 tftopl cmex10.tfm > cmex10.pl

the .pl property list being a readable form of the font metrics.

hex OC is Octal 12 and in the pl file you see

(CHARACTER O 12
   (CHARWD R 0.472224)
   (CHARHT R 0.039999)
   (CHARDP R 1.160013)
   (NEXTLARGER O 104)
   )

which tells you, apart from the usual height, depth, width, that this character is part of a chain of characters implementing an extendable delimiter and if this one is too small try character octal 104.