function popd {      # pop directory off the stack, cd to new top
    if [ $(echo $1 | grep '^+[0-9][0-9]*$') ]; then

        # case of popd +n: delete n-th directory from stack
        let num=${1#+}
        getNdirs $num
        DIRSTACK="$stackfront$DIRSTACK"
        cd ${DIRSTACK%% *}
        echo "$PWD"

    else

        # normal case of popd without argument
        if [ -n "$DIRSTACK" ]; then
            DIRSTACK=${DIRSTACK#* }
            cd ${DIRSTACK%% *}
            echo "$PWD"
        else
            echo "stack empty, still in $PWD."
        fi
    fi
}

function getNdirs {
    stackfront=''
    let count=0
    while [ $count -le $1 ]; do
        target=${DIRSTACK%${DIRSTACK#* }}
        stackfront="$stackfront$target"
        DIRSTACK=${DIRSTACK#$target}
        let count=count+1
    done

    stackfront=${stackfront%$target}
}

function pud {
    if [ $(echo $1 | grep '^+[0-9][0-9]*$') ]; then
        # case of pushd +n: rotate n-th directory to top
        let num=${1#+}
        getNdirs $num

        DIRSTACK="$target$stackfront$DIRSTACK"
        cd $target
        echo "$DIRSTACK"

    elif [ -z $1 ]; then
        # case of pushd without args; swap top two directories
        firstdir=${DIRSTACK%% *}
        DIRSTACK=${DIRSTACK#* }
        seconddir=${DIRSTACK%% *}
        DIRSTACK=${DIRSTACK#* }
        DIRSTACK="$seconddir $firstdir $DIRSTACK"
        cd $seconddir

    else
        # normal case of pushd dirname
        dirname=$1
        if [ \( -d $dirname \) -a \( -x $dirname \) ]; then
            DIRSTACK="$dirname ${DIRSTACK:-$PWD" "}"
            cd $dirname
            echo "$DIRSTACK"
        else
            echo still in "$PWD."
        fi
    fi
}