Define bash function which does not show up in xtrace (set -x)

You cannot change how the function is invoked from inside the function, but you could define the function to invoke a subshell which then immediately turns off tracing; notice the parenthesis surrounding the body instead of the typical braces:

log() (
  set +x
  # rest of log()
)

Invoking log() then generates only the call itself (from the existing set -x code) and the set +x call, not the rest of the subsequent commands in the function. The existing set -x setting is restored once the function exits.

A quick and dirty hack that should work in all shells is to (temporarily) make your log an external script instead of a function.

In bash you could also use a trap '...' DEBUG and shopt -s extdebug combination, which is much more versatile than set -x. Example:

debug() {
        local f=${FUNCNAME[1]} d=${#FUNCNAME[@]} c=$BASH_COMMAND
        if [ "$NOTRACE" ]; then
                case $debug_skip in ''|$d) debug_skip=;; *) return;; esac
                eval "case \$c in $NOTRACE) debug_skip=\$d; return; esac"
        fi

        # before the 1st command in a function XXX
        case $c in $f|"$f "*) return;; esac

        printf >&2 "%*s(%s) %s\n" $((d * 2 - 4)) "" "$f" "$c"
}

(Of course, you can dispense with the strange format + indenting and make it completely set-x-like; you can also redirect it to another file instead of mixed with the stderr from commands.)

Then:

NOTRACE='"log "*'
shopt -s extdebug
trap debug DEBUG

log(){ log1 "$@"; }; log1(){ log2 "$@"; }
log2(){ log3 "$@"; }; log3(){ echo "$@"; }

foo(){ foo1 "$@"; }; foo1(){ foo2 "$@"; }
foo2(){ foo3 "$@"; }; foo3(){ echo "$@"; }

bar(){ case $# in 0) ;; *) echo "$1"; shift; bar "$@";; esac; }

foo 1 2 3
log 7 8 9
bar 1 2 3 4

will result in:

(main) foo 1 2 3
  (foo) foo1 "$@"
    (foo1) foo2 "$@"
      (foo2) foo3 "$@"
        (foo3) echo "$@"
1 2 3
7 8 9
(main) bar 1 2 3 4
  (bar) case $# in
  (bar) echo "$1"
1
  (bar) shift
    (bar) case $# in
    (bar) echo "$1"
2
    (bar) shift
      (bar) case $# in
      (bar) echo "$1"
3
      (bar) shift
        (bar) case $# in
        (bar) echo "$1"
4
        (bar) shift
          (bar) case $# in