Why does CDPATH not work as documented in the manuals?

Question

The Bourne Again shell manual says, of cd dir:

[…] each directory name in CDPATH is searched for dir. […] If dir begins with a slash (/), then CDPATH is not used.

The Z shell manual says, of cd arg:

Otherwise, if arg begins with a slash, attempt to change to the directory given by arg.

If arg does not begin with a slash, the behaviour depends on whether the current directory . occurs in the list of directories contained in the shell parameter cdpath. […] If . occurs in cdpath, then cdpath is searched strictly in order so that . is only tried at the appropriate point.

The POSIX Ordinary shell manual says, of CDPATH:

Works the same way as PATH for those directories not beginning with / in cd commands.

The Debian Almquist shell manual says, of cd:

If […] the shell variable CDPATH is set and the directory name does not begin with a slash, then the directories listed in CDPATH will be searched for the specified directory.

The '93 Korn shell manual says, of cd arg:

If arg begins with a / then the search path is not used. Otherwise, each directory in the path is searched for arg.

The MirBSD Korn shell manual says, of CDPATH:

It works the same way as PATH for those directories not beginning with / in cd commands.

With the single exception of the '93 Korn shell, none of these are actually the case:

% export CDPATH=/tmp:
% mkdir wibble /tmp/wibble
% ksh93 -c 'cd ./wibble'
/tmp/wibble
% dash -c 'cd ./wibble ; pwd'
/home/JdeBP/wibble
% bash -c 'cd ./wibble ; pwd'
/home/JdeBP/wibble
% mksh -c 'cd ./wibble ; pwd'
/home/JdeBP/wibble
% lksh -c 'cd ./wibble ; pwd'
/home/JdeBP/wibble
% posh -c 'cd ./wibble ; pwd'
/home/JdeBP/wibble
% zsh -c 'cd ./wibble ; pwd'
/home/JdeBP/wibble
% 

/tmp/./wibble exists and is a directory, but only the '93 Korn shell is searching CDPATH and finding it. The rest are not.

Why not?

Answer 1

Because the manuals are wrong.

The '93 Korn shell is wrong, too.

The 1997 Single Unix Specification says:

If the directory operand does not begin with a slash (/) character, and the first component is not dot or dot-dot, cd will search for directory relative to each directory named in the CDPATH variable, in the order listed.

The 2016 Single Unix Specification says the same in a different, and slightly redundant, way:

3. If the directory operand begins with a <slash> character, set curpath to the operand and proceed to step 7.

4. If the first component of the directory operand is dot or dot-dot, proceed to step 6.

[…]

6. Set curpath to the directory operand.

None of the manuals mention the part about . and .., but that is what every shell apart from the '93 Korn shell is actually doing, despite what their manuals say:

% export CDPATH=/tmp:
% lksh -c 'cd wibble'
/tmp/wibble
% dash -c 'cd wibble'
/tmp/wibble
% posh -c 'cd wibble'
/tmp/wibble
% bash -c 'cd wibble'
/tmp/wibble
% mksh -c 'cd wibble'
/tmp/wibble
% zsh -c 'cd wibble ; pwd'
/tmp/wibble
%