diff --git a/.gitignore b/.gitignore
index f71c7c7..707f265 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,3 +1,9 @@
 /3.5.1.tar.gz
 /sleef-3.5.1.tar.gz
 /sleef-3.5.1-filtered.tar.xz
+/sleef-3.5.1-filtered.tar.zst
+/sleef-3.6-filtered.tar.zst
+/sleef-3.6.1-filtered.tar.zst
+/sleef-3.7-filtered.tar.zst
+/sleef-3.8-filtered.tar.zst
+/sleef-3.9.0-filtered.tar.zst
diff --git a/471.patch b/471.patch
deleted file mode 100644
index 4849399..0000000
--- a/471.patch
+++ /dev/null
@@ -1,48 +0,0 @@
-From 1f27275c72c31451d8f458a4ddec01609830bc5f Mon Sep 17 00:00:00 2001
-From: "Benjamin A. Beasley" <code@musicinmybrain.net>
-Date: Wed, 4 Oct 2023 16:28:49 -0400
-Subject: [PATCH] Do not define our own mpfr_sinpi/mpfr_cospi for mpfr 4.2.0
- and later
-
-These two functions were added to the MPFR API.
-
-Fixes #458.
----
- src/libm-tester/testerutil.c | 2 ++
- src/libm-tester/testerutil.h | 2 ++
- 2 files changed, 4 insertions(+)
-
-diff --git a/src/libm-tester/testerutil.c b/src/libm-tester/testerutil.c
-index 8e8b8936..688642ca 100644
---- a/src/libm-tester/testerutil.c
-+++ b/src/libm-tester/testerutil.c
-@@ -289,6 +289,7 @@ double countULP2sp(float d, mpfr_t c0) {
- 
- //
- 
-+#if MPFR_VERSION < MPFR_VERSION_NUM(4, 2, 0)
- void mpfr_sinpi(mpfr_t ret, mpfr_t arg, mpfr_rnd_t rnd) {
-   mpfr_t frpi, frd;
-   mpfr_inits(frpi, frd, NULL);
-@@ -314,6 +315,7 @@ void mpfr_cospi(mpfr_t ret, mpfr_t arg, mpfr_rnd_t rnd) {
- 
-   mpfr_clears(frpi, frd, NULL);
- }
-+#endif
- 
- void mpfr_lgamma_nosign(mpfr_t ret, mpfr_t arg, mpfr_rnd_t rnd) {
-   int s;
-diff --git a/src/libm-tester/testerutil.h b/src/libm-tester/testerutil.h
-index 7f371414..313bf7b2 100644
---- a/src/libm-tester/testerutil.h
-+++ b/src/libm-tester/testerutil.h
-@@ -90,7 +90,9 @@ int cmpDenormsp(float x, mpfr_t fry);
- double countULPsp(float d, mpfr_t c);
- double countULP2sp(float d, mpfr_t c);
- 
-+#if MPFR_VERSION < MPFR_VERSION_NUM(4, 2, 0)
- void mpfr_sinpi(mpfr_t ret, mpfr_t arg, mpfr_rnd_t rnd);
- void mpfr_cospi(mpfr_t ret, mpfr_t arg, mpfr_rnd_t rnd);
-+#endif
- void mpfr_lgamma_nosign(mpfr_t ret, mpfr_t arg, mpfr_rnd_t rnd);
- #endif
diff --git a/get_source.sh b/get_source.sh
index d17508c..3745066 100755
--- a/get_source.sh
+++ b/get_source.sh
@@ -11,7 +11,7 @@ Usage: $1 VERSION
 
 Generate a source archive for sleef with src/gencoef/ removed, since the code
 therein is licensed CC-BY-4.0, but this license is not approved for code in
-Fedora.  The result will be named sleef-\${VERSION}-filtered.tar.xz and will be
+Fedora. The result will be named sleef-\${VERSION}-filtered.tar.zst and will be
 written into the current working directory.
 EOF
 }
@@ -31,22 +31,36 @@ VERSION="${1}"
 SOURCE0="${FORGEURL}/archive/${VERSION}/sleef-${VERSION}.tar.gz"
 TARNAME="$(basename "${SOURCE0}")"
 TARDIR="$(basename "${SOURCE0}" '.tar.gz')"
-NEWTAR="${TARDIR}-filtered.tar.xz"
+NEWTAR="${TARDIR}-filtered.tar.zst"
 
 SAVEDIR="${PWD}"
 XDIR="$(mktemp -d)"
-trap "rm -rvf '${XDIR}'" INT TERM EXIT
+trap "rm -rf '${XDIR}'" INT TERM EXIT
 
 cd "${XDIR}"
 curl -L -O "${SOURCE0}"
-tar -xzvf "${TARNAME}"
+tar -xzf "${TARNAME}"
+MTIME="$(stat -c '%Y' "${TARDIR}")"
 rm -rvf "${TARDIR}/src/gencoef/"
 if grep -ErinI 'Attribution 4\.0' .
 then
 	echo 'ERROR: did not properly remove problematic content' 1>&2
 	exit 1
 fi
-tar -cv "${TARDIR}/" | xz -9e > "${NEWTAR}"
+# https://www.gnu.org/software/tar/manual/html_section/Reproducibility.html
+# We reset all mtimes to that of the top-level extracted directory; since git
+# archives don’t have meaningful per-file mtimes, nothing useful is lost.
+TZ=UTC LC_ALL=C tar \
+    --create \
+    --sort=name \
+    --format=posix \
+    --numeric-owner --owner=0 --group=0 \
+    --mode=go+u,go-w \
+    --pax-option='delete=atime,delete=ctime' \
+    --clamp-mtime --mtime="@${MTIME}" \
+    "${TARDIR}/" |
+  zstdmt --ultra -22 > "${NEWTAR}"
+touch -d @"${MTIME}" "${NEWTAR}"
 
 cd "${SAVEDIR}"
 mv -v "${XDIR}/${NEWTAR}" .
diff --git a/sleef.rpmlintrc b/sleef.rpmlintrc
index 0e0dc24..7a1f9b5 100644
--- a/sleef.rpmlintrc
+++ b/sleef.rpmlintrc
@@ -1,2 +1,12 @@
 # These are not real spelling errors...
-addFilter(r'spelling-error .*(\(en_US\)| en_US) ([Vv]ectorized) ')
+addFilter(r"sleef-gnuabi\..*: spelling-error \('(lib(sleefgnuabi|mvec)|glibc)', ")
+# All of the documentation is in the -doc subpackage.
+addFilter(r" no-documentation")
+# This Source cannot be a URL because we must filter out certain files.
+addFilter(r" invalid-url Source[0-9]+: sleef-.*-filtered\.tar\.zst")
+# Bogus; it is a perfectly fine zstandard file.
+addFilter(r" inconsistent-file-extension sleef-.*-filtered\.tar\.zst")
+# We are not sure why some files from docs/ are duplicated in docs/src/. The
+# files are small compared to the documentation overall, so it does not seem
+# worth too much investigation, and hardlinking them would be a little tedious.
+addFilter(r" files-duplicate /.*/docs/src/")
diff --git a/sleef.spec b/sleef.spec
index 5a69c1d..ea7b1d4 100644
--- a/sleef.spec
+++ b/sleef.spec
@@ -1,23 +1,17 @@
-# We do not ship the DFT library since it has undiagnosed test failures on
-# Fedora at -O2, and is not well-supported upstream. Additionally, it uses
-# illegal instructions on ARM and s390x, at least on the Fedora build machines.
-# See https://github.com/shibatch/sleef/issues/214.
-%bcond dft 0
-# We would like to ship the quad-precision library, but since it is still
-# considered experimental, it may have breaking ABI or API changes without an
-# soversion bump, which is a no-no in Fedora. Rather than contorting ourselves
-# to accommodate this, we disable it until it stabilizes or some dependent
-# package appears.
-%bcond quad 0
-# Similarly, Fedora packages should not ship static libraries unless absolutely
-# required. Some software, like pytorch, really does rely on the inline headers
-# and accompanying static support library for exceptional performance
-# requirements, but no such software exists in Fedora at the moment. We will
-# leave this feature disabled until someone asks for it.
+%bcond dft 1
+%bcond quad 1
+# Fedora packages should not ship static libraries unless absolutely required.
+# Some software may really rely on the inline headers and accompanying static
+# support library for exceptional performance requirements, but we will leave
+# this feature disabled until someone asks for it.
 %bcond static 0
 
+# Adds a BuildRequires on tlfloat and enables more tests
+%bcond tlfloat 1
+
 Name:           sleef
-Version:        3.5.1
+Version:        3.9.0
+%global tag %{version}
 %global so_version 3
 Release:        %autorelease
 Summary:        Vectorized math library
@@ -35,34 +29,48 @@ Summary:        Vectorized math library
 License:        BSL-1.0
 URL:            https://sleef.org
 # This is a filtered version of:
-#   https://github.com/shibatch/sleef/archive/%%{version}/sleef-%%{version}.tar.gz
+#   https://github.com/shibatch/sleef/archive/%%{tag}/sleef-%%{tag}.tar.gz
 # See the comment above License for why this is necessary. The archive is
 # produced by using the script in Source1:
 #   ./get_source.sh ${VERSION}
-Source0:        sleef-%{version}-filtered.tar.xz
+Source0:        sleef-%{tag}-filtered.tar.zst
 Source1:        get_source.sh
 
-# Do not define our own mpfr_sinpi/mpfr_cospi for mpfr 4.2.0 and later
-# https://github.com/shibatch/sleef/pull/471
-#
-#   This is similar to:
-#
-# mpfr-4.2 add mpfr_cospi and mpfr_sinpi
-# https://github.com/shibatch/sleef/pull/462
-#
-#   ...but maintains backwards-compatibility with mpfr version before 4.2.0.
-#
-#   Fixes:
-#
-# Compilation fails (conflicting types) if mpfr-devel 4.2.0 is provided
-# https://github.com/shibatch/sleef/issues/458
-Patch:          https://github.com/shibatch/sleef/pull/471.patch
-
 # https://fedoraproject.org/wiki/Changes/EncourageI686LeafRemoval
 ExcludeArch:    %{ix86}
 
+# On aarch64, since 3.9.0, we cannot link at least bin/tester3svenofma when LTO
+# is enabled, due to confusion about SVE.
+#
+#   /builddir/build/BUILD/sleef-3.9.0-build/sleef-3.9.0/src/common/testerutil.c:
+#   In function ‘memrand.constprop’:
+#   /builddir/build/BUILD/sleef-3.9.0-build/sleef-3.9.0/src/common/testerutil.c:101:6:
+#   error: this operation requires the SVE ISA extension
+#     101 | void memrand(void *p, int size) {
+#         |      ^
+#   /builddir/build/BUILD/sleef-3.9.0-build/sleef-3.9.0/src/common/testerutil.c:101:6:
+#   note: you can enable SVE using the command-line option ‘-march’, or by
+#   using the ‘target’ attribute or pragma
+#   /builddir/build/BUILD/sleef-3.9.0-build/sleef-3.9.0/src/common/testerutil.c:101:
+#   confused by earlier errors, bailing out
+#
+# This might be an upstream bug, but it is hard to understand. Upstream
+# provides their own LTO option, SLEEF_ENABLE_LTO, but for does not support it
+# in combination with shared libraries.
+#
+# - We could still build the library with LTO and not test it
+#   (-DSLEEF_BUILD_TESTS:BOOL=FALSE) on aarch64.
+# - It’s not clear how we could disable LTO *only for the tests*.
+# - We choose to disable LTO entirely on aarch64, because we really want to run
+#   the tests. We hope that the performance impact is not significant. It
+#   currently does not seem necessary to disable LTO on other architectures.
+%ifarch %{arm64}
+%global _lto_cflags %{nil}
+%endif
+
 BuildRequires:  cmake >= 3.4.3
 BuildRequires:  gcc
+BuildRequires:  gcc-c++
 BuildRequires:  ninja-build
 # For tests only:
 BuildRequires:  pkgconfig(mpfr)
@@ -72,10 +80,13 @@ BuildRequires:  pkgconfig(libcrypto)
 %if %{with dft}
 BuildRequires:  pkgconfig(fftw3)
 %endif
+%if %{with tlfloat}
+BuildRequires:  pkgconfig(tlfloat)
+%endif
 
 # See https://sleef.org/additional.xhtml#gnuabi. The gnuabi version of the
 # library only applies to these architectures.
-%global gnuabi_arches %{ix86} x86_64 aarch64
+%global gnuabi_arches %{ix86} %{x86_64} %{arm64}
 # See https://github.com/shibatch/sleef/pull/283.
 %if %{with static}
 %global inline_enabled 1
@@ -191,18 +202,16 @@ developing applications that use sleef-quad.
 
 
 %prep
-%autosetup -p1
-# The gencoef tool sources are licensed CC-BY-4.0, which is allowed for content
-# but not for code. Remove them to prove that they are not used in the build.
-rm -vrf src/gencoef
+%autosetup -n sleef-%{tag} -p1
+# Remove an unwanted hidden file from the docs
+find docs/ -type f -name .nojekyll -print -delete
 
 
-%build
-# -GNinja: Upstream prominently states that parallel build is only supported
-# with the Ninja generator for cmake, not with the make one. See
-# https://sleef.org/compile.xhtml.
+%conf
+# -GNinja: This used to be required for parallel builds; it is still faster.
 #
 # -DENFORCE_TESTER3: The build should fail if we cannot build all tests.
+# -DENFORCE_TESTER4: Likewise, except that tester4 requires tlfloat.
 #
 # -DBUILD_INLINE_HEADERS: Do not build the “inline” headers. This would provide
 #   an arch-specific collection of sleefinline_*.h headers in _includedir, as
@@ -211,13 +220,30 @@ rm -vrf src/gencoef
 #   and would thus also be treated as a static library in the Fedora
 #   guidelines) should be omitted unless something in Fedora absolutely
 #   requires them.
+#
+# -DSLEEFDFT_ENABLE_STREAM: The author writes, “The recommended value for
+#   SLEEFDFT_ENABLE_STREAM depends on the architecture, and it is only
+#   recommended to be turned on on x86_64.”
+#   https://github.com/shibatch/sleef/discussions/654#discussioncomment-12860550
 %cmake \
     -GNinja \
-    -DENFORCE_TESTER3:BOOL=TRUE \
-    -DBUILD_INLINE_HEADERS:BOOL=%{?inline_enabled:TRUE}%{?!inline_enabled:FALSE} \
-    -DBUILD_GNUABI_LIBS:BOOL=%{?gnuabi_enabled:TRUE}%{?!gnuabi_enabled:FALSE} \
-    -DBUILD_DFT:BOOL=%{?with_dft:TRUE}%{?!with_dft:FALSE} \
-    -DBUILD_QUAD:BOOL=%{?with_quad:TRUE}%{?!with_quad:FALSE}
+    -DSLEEF_BUILD_DFT:BOOL=%{?with_dft:TRUE}%{?!with_dft:FALSE} \
+    -DSLEEF_ENFORCE_DFT:BOOL=%{?with_dft:TRUE}%{?!with_dft:FALSE} \
+%ifarch %{x86_64}
+    -DSLEEFDFT_ENABLE_STREAM:BOOL=TRUE \
+%else
+    -DSLEEFDFT_ENABLE_STREAM:BOOL=FALSE \
+%endif
+    -DSLEEF_BUILD_GNUABI_LIBS:BOOL=%{?gnuabi_enabled:TRUE}%{?!gnuabi_enabled:FALSE} \
+    -DSLEEF_BUILD_INLINE_HEADERS:BOOL=%{?inline_enabled:TRUE}%{?!inline_enabled:FALSE} \
+    -DSLEEF_BUILD_QUAD:BOOL=%{?with_quad:TRUE}%{?!with_quad:FALSE} \
+    -DSLEEF_BUILD_SHARED_LIBS:BOOL=TRUE \
+    -DSLEEF_ENFORCE_TESTER3:BOOL=TRUE \
+    -DSLEEF_ENFORCE_TESTER4:BOOL=%{?with_tlfloat:TRUE}%{?!with_tlfloat:FALSE} \
+    -DSLEEF_ENABLE_TLFLOAT:BOOL=%{?with_tlfloat:TRUE}%{?!with_tlfloat:FALSE}
+
+
+%build
 %cmake_build
 
 
@@ -226,27 +252,41 @@ rm -vrf src/gencoef
 
 
 %check
+# Logging CPU features is helpful for debugging, especially in COPR builds
+# where the builder hardware information is not necessarily logged separately.
+echo '==== Build host CPU features ===='
+cat /proc/cpuinfo
+
 skips='^($.'
 
-# https://github.com/shibatch/sleef/issues/439
-%ifarch x86_64 %{arm64} ppc64le s390x
-skips="${skips}|iuty?purecfma_scalar"
+%ifarch %{arm64}
+# Some tests are specifically for SVE code. We can only run these tests on
+# builder hardware that has the SVE extensions, which are not part of the
+# aarch64 baseline.
+if ! grep -E '[Ff](lags|eatures).*\bsve\b' /proc/cpuinfo >/dev/null
+then
+  skips="${skips}|gnuabi_compatibility_SVE(_masked)?|qiutsve"
+fi
 %endif
-%ifarch %{arm64} ppc64le s390x
-skips="${skips}|iuty?purec_scalar"
-%endif
-%ifarch s390x
-skips="${skips}|iuty?zvector2(nofma)?"
+%ifarch %{power64}
+# Some tests are specifically for VSX3 code. We can only run these tests on
+# builder hardware that has the VSX3 extensions (POWER 9 or later), which are
+# not part of the ppc64le baseline (POWER 8).
+if grep -E -i '\bPOWER8\b' /proc/cpuinfo >/dev/null
+then
+  skips="${skips}|.*vsx3(nofma)?"
+fi
 %endif
 
-%if %{with dft}
-# The DFT library has known test failures
-# (https://github.com/shibatch/sleef/issues/214).
-skips="${skips}|fftwtest2d[ds]p_(4_4|8_8|10_10|5_15)"
-%ifarch aarch64 s390x
-# Plus, it uses illegal instructions:
-skips="${skips}|naivetest[ds]p_([2345]|10)"
-skips="${skips}|fftwtest(1d[ds]p_1[26]|2d[ds]p_2_2)"
+%ifarch %{x86_64}
+%if %{undefined fc43} && %{undefined fc42} && %{undefined el10}
+# At least one test within this executable fails since GCC 16 landed in Fedora
+# 44. It’s not very easy to tell exactly what is going wrong, and upstream is
+# not likely to be interested since (as determined by bisection) the failure
+# was resolved upstream by the removal of no-FMA helpers in
+# https://github.com/shibatch/sleef/pull/685. Let’s just skip this while we
+# await the next upstream release.
+skips="${skips}|tester4ypurec_scalar"
 %endif
 %endif
 
@@ -264,6 +304,7 @@ skips="${skips})$"
 %{_includedir}/sleef.h
 %{_libdir}/libsleef.so
 %{_libdir}/pkgconfig/sleef.pc
+%{_libdir}/cmake/sleef/
 
 
 %if 0%{?inline_enabled}
@@ -276,9 +317,8 @@ skips="${skips})$"
 %files doc
 %license LICENSE.txt
 %doc CHANGELOG.md
-%doc CONTRIBUTORS.md
-%doc README.md
-%doc doc/html/
+%doc README.adoc
+%doc docs/
 
 
 %ifarch %{gnuabi_arches}
diff --git a/sources b/sources
index 7a04a36..a0b715a 100644
--- a/sources
+++ b/sources
@@ -1 +1 @@
-SHA512 (sleef-3.5.1-filtered.tar.xz) = a40e9292bc7164ad0b9a4a718fbe78cccb04a19a4b824d34d7991fd75656be9f9336a5f226b0004e88e01c1c8592b420e789e63a88ff3810a68cf08d6617c1bf
+SHA512 (sleef-3.9.0-filtered.tar.zst) = 4c55c310795569debed8c771cf0251a126e8291515bf562e6ac4b611dafe6df5fd0024d129dbeaf2c6bce39112bb8a826acabd762beebdd17de86259394b5933