diff --git a/eclass/python-utils-r1.eclass b/eclass/python-utils-r1.eclass
index 368b268..f95981a 100644
--- a/eclass/python-utils-r1.eclass
+++ b/eclass/python-utils-r1.eclass
@@ -1,4 +1,4 @@
-# Copyright 1999-2018 Gentoo Foundation
+# Copyright 1999-2019 Gentoo Authors
 # Distributed under the terms of the GNU General Public License v2
 
 # @ECLASS: python-utils-r1.eclass
@@ -7,7 +7,7 @@
 # @AUTHOR:
 # Author: Michał Górny <mgorny@gentoo.org>
 # Based on work of: Krzysztof Pawlik <nelchael@gentoo.org>
-# @SUPPORTED_EAPIS: 0 1 2 3 4 5 6 7
+# @SUPPORTED_EAPIS: 5 6 7
 # @BLURB: Utility functions for packages with Python parts.
 # @DESCRIPTION:
 # A utility eclass providing functions to query Python implementations,
@@ -20,11 +20,9 @@
 # https://wiki.gentoo.org/wiki/Project:Python/python-utils-r1
 
 case "${EAPI:-0}" in
-	0|1|2|3|4|5|6|7)
-		;;
-	*)
-		die "Unsupported EAPI=${EAPI} (unknown) for ${ECLASS}"
-		;;
+	[0-4]) die "Unsupported EAPI=${EAPI:-0} (too old) for ${ECLASS}" ;;
+	[5-7]) ;;
+	*)     die "Unsupported EAPI=${EAPI} (unknown) for ${ECLASS}" ;;
 esac
 
 if [[ ${_PYTHON_ECLASS_INHERITED} ]]; then
@@ -33,7 +31,7 @@
 
 if [[ ! ${_PYTHON_UTILS_R1} ]]; then
 
-[[ ${EAPI:-0} == [012345] ]] && inherit eutils multilib
+[[ ${EAPI} == 5 ]] && inherit eutils multilib
 inherit toolchain-funcs
 
 # @ECLASS-VARIABLE: _PYTHON_ALL_IMPLS
@@ -41,10 +39,9 @@
 # @DESCRIPTION:
 # All supported Python implementations, most preferred last.
 _PYTHON_ALL_IMPLS=(
-	jython2_7
-	pypy pypy3
+	pypy3
 	python2_7
-	python3_4 python3_5 python3_6 python3_7
+	python3_6 python3_7 python3_8
 )
 readonly _PYTHON_ALL_IMPLS
 
@@ -80,17 +77,12 @@
 	# keep in sync with _PYTHON_ALL_IMPLS!
 	# (not using that list because inline patterns shall be faster)
 	case "${impl}" in
-		python2_7|python3_[4567]|jython2_7)
+		python2_7|python3_[678]|pypy3)
 			return 0
 			;;
-		pypy1_[89]|pypy2_0|python2_[56]|python3_[123])
+		jython2_7|pypy|pypy1_[89]|pypy2_0|python2_[56]|python3_[12345])
 			return 1
 			;;
-		pypy|pypy3)
-			if [[ ${EAPI:-0} == [01234] ]]; then
-				die "PyPy is supported in EAPI 5 and newer only."
-			fi
-			;;
 		*)
 			[[ ${PYTHON_COMPAT_NO_STRICT} ]] && return 1
 			die "Invalid implementation in PYTHON_COMPAT: ${impl}"
@@ -164,11 +156,12 @@
 }
 
 # @FUNCTION: _python_impl_matches
-# @USAGE: <impl> <pattern>...
+# @USAGE: <impl> [<pattern>...]
 # @INTERNAL
 # @DESCRIPTION:
 # Check whether the specified <impl> matches at least one
 # of the patterns following it. Return 0 if it does, 1 otherwise.
+# Matches if no patterns are provided.
 #
 # <impl> can be in PYTHON_COMPAT or EPYTHON form. The patterns can be
 # either:
@@ -176,17 +169,17 @@
 # b) '-2' to indicate all Python 2 variants (= !python_is_python3)
 # c) '-3' to indicate all Python 3 variants (= python_is_python3)
 _python_impl_matches() {
-	[[ ${#} -ge 2 ]] || die "${FUNCNAME}: takes at least 2 parameters"
+	[[ ${#} -ge 1 ]] || die "${FUNCNAME}: takes at least 1 parameter"
+	[[ ${#} -eq 1 ]] && return 0
 
 	local impl=${1} pattern
 	shift
 
 	for pattern; do
 		if [[ ${pattern} == -2 ]]; then
-			! python_is_python3 "${impl}"
-			return
+			python_is_python3 "${impl}" || return 0
 		elif [[ ${pattern} == -3 ]]; then
-			python_is_python3 "${impl}"
+			python_is_python3 "${impl}" && return 0
 			return
 		# unify value style to allow lax matching
 		elif [[ ${impl/./_} == ${pattern/./_} ]]; then
@@ -479,9 +472,9 @@
 					python*)
 						PYTHON_PKG_DEP="dev-lang/python:${impl#python}";;
 					pypy)
-						PYTHON_PKG_DEP='>=virtual/pypy-5:0=';;
+						PYTHON_PKG_DEP='>=dev-python/pypy-5:0=';;
 					pypy3)
-						PYTHON_PKG_DEP='>=virtual/pypy3-5:0=';;
+						PYTHON_PKG_DEP='>=dev-python/pypy3-5:0=';;
 					jython2.7)
 						PYTHON_PKG_DEP='dev-java/jython:2.7';;
 					*)
@@ -692,7 +685,7 @@
 			if [[ ${f} == /* && -d ${D%/}${f} ]]; then
 				set -- "${D%/}${f}" "${@}"
 			fi
-		done < <("${PYTHON}" -c 'import sys; print("\0".join(sys.path))' || die)
+		done < <("${PYTHON}" -c 'import sys; print("".join(x + "\0" for x in sys.path))' || die)
 
 		debug-print "${FUNCNAME}: using sys.path: ${*/%/;}"
 	fi
@@ -775,9 +768,6 @@
 
 	[[ ${EPYTHON} ]] || die 'No Python implementation set (EPYTHON is null).'
 	[[ ${#} -eq 2 ]] || die "Usage: ${FUNCNAME} <path> <new-name>"
-	if [[ ${EAPI:-0} == [0123] ]]; then
-		die "python_do* and python_new* helpers are banned in EAPIs older than 4."
-	fi
 
 	local wrapd=${python_scriptroot:-/usr/bin}
 
@@ -905,9 +895,6 @@
 	debug-print-function ${FUNCNAME} "${@}"
 
 	[[ ${EPYTHON} ]] || die 'No Python implementation set (EPYTHON is null).'
-	if [[ ${EAPI:-0} == [0123] ]]; then
-		die "python_do* and python_new* helpers are banned in EAPIs older than 4."
-	fi
 
 	local d
 	if [[ ${python_moduleroot} == /* ]]; then
@@ -947,9 +934,6 @@
 	debug-print-function ${FUNCNAME} "${@}"
 
 	[[ ${EPYTHON} ]] || die 'No Python implementation set (EPYTHON is null).'
-	if [[ ${EAPI:-0} == [0123] ]]; then
-		die "python_do* and python_new* helpers are banned in EAPIs older than 4."
-	fi
 
 	local d PYTHON_INCLUDEDIR=${PYTHON_INCLUDEDIR}
 	[[ ${PYTHON_INCLUDEDIR} ]] || python_export PYTHON_INCLUDEDIR
@@ -1092,10 +1076,7 @@
 	[[ ${impl} ]] || die "${FUNCNAME}: no impl nor EPYTHON"
 	local hasv_args=()
 
-	case ${EAPI:-0} in
-		0|1|2|3|4)
-			local -x ROOT=/
-			;;
+	case ${EAPI} in
 		5|6)
 			hasv_args+=( --host-root )
 			;;
@@ -1264,7 +1245,7 @@
 
 		if [[ ! ${any_fixed} ]]; then
 			local cmd=eerror
-			[[ ${EAPI:-0} == [012345] ]] && cmd=eqawarn
+			[[ ${EAPI} == 5 ]] && cmd=eqawarn
 
 			"${cmd}" "QA warning: ${FUNCNAME}, ${path#${D%/}} did not match any fixable files."
 			if [[ ${any_correct} ]]; then
@@ -1344,6 +1325,31 @@
 	return 0
 }
 
+# @FUNCTION: build_sphinx
+# @USAGE: <directory>
+# @DESCRIPTION:
+# Build HTML documentation using dev-python/sphinx in the specified
+# <directory>.  Takes care of disabling Intersphinx and appending
+# to HTML_DOCS.
+#
+# If <directory> is relative to the current directory, care needs
+# to be taken to run einstalldocs from the same directory
+# (usually ${S}).
+build_sphinx() {
+	debug-print-function ${FUNCNAME} "${@}"
+	[[ ${#} -eq 1 ]] || die "${FUNCNAME} takes 1 arg: <directory>"
+
+	local dir=${1}
+
+	sed -i -e 's:^intersphinx_mapping:disabled_&:' \
+		"${dir}"/conf.py || die
+	# not all packages include the Makefile in pypi tarball
+	sphinx-build -b html -d "${dir}"/_build/doctrees "${dir}" \
+		"${dir}"/_build/html || die
+
+	HTML_DOCS+=( "${dir}/_build/html/." )
+}
+
 # -- python.eclass functions --
 
 _python_check_dead_variables() {