According to a post by Alex Deucher, the canonical way to build the ATI driver with TV Out support that he maintains is:

1. First make sure you back up the existing radeon (radeon_drv.so) and ati (ati_drv.so) drivers.
2. install the xorg-dev, mesa-dev, libdrm-dev and xserver-dev packages for your distro. The usual build tools are needed too (autoconf, automake, libtool, gcc and others)
3. git-clone https://gitlab.freedesktop.org/xorg/driver/xf86-video-ati.git
4. cd xf86-video-ati
5. ./autogen.sh --prefix=/usr
6. make
7. sudo make install or make install as root

If you get this error after running autogen.sh, you forgot to install libtool:

configure.ac:38: error: possibly undefined macro: AC_DISABLE_STATIC
      If this token and others are legitimate, please use m4_pattern_allow.
      See the Autoconf documentation.
configure.ac:39: error: possibly undefined macro: AC_PROG_LIBTOOL
autoreconf: /usr/bin/autoconf failed with exit status: 1