diff --git a/Package.swift b/Package.swift
index 115062e..9d0d165 100644
--- a/Package.swift
+++ b/Package.swift
@@ -17,8 +17,12 @@ let package = Package(
     ],
     targets: [
         .binaryTarget(
-            name: "_Differentiation", 
+            name: "_Differentiation",
             path: "_Differentiation.xcframework"
-        )
+        ),
+        .testTarget(
+            name: "DifferentiationTests",
+            dependencies: ["_Differentiation"]
+        ),
     ]
 )
diff --git a/Tests/DifferentiationTests/DifferentiationTests.swift b/Tests/DifferentiationTests/DifferentiationTests.swift
new file mode 100644
index 0000000..bcb443a
--- /dev/null
+++ b/Tests/DifferentiationTests/DifferentiationTests.swift
@@ -0,0 +1,58 @@
+import XCTest
+import _Differentiation
+
+@differentiable(reverse)
+private func quadratic(_ x: Double) -> Double {
+    x * x + 3 * x + 2
+}
+
+@differentiable(reverse)
+private func weightedPolynomial(_ x: Double, _ y: Double) -> Double {
+    x * x + x * y + y
+}
+
+private struct Scalar: Differentiable, AdditiveArithmetic {
+    var value: Double
+
+    static let zero = Scalar(value: 0)
+
+    static func + (lhs: Scalar, rhs: Scalar) -> Scalar {
+        Scalar(value: lhs.value + rhs.value)
+    }
+
+    static func - (lhs: Scalar, rhs: Scalar) -> Scalar {
+        Scalar(value: lhs.value - rhs.value)
+    }
+
+    mutating func move(by offset: Scalar) {
+        value += offset.value
+    }
+}
+
+@differentiable(reverse)
+private func unwrap(_ scalar: Scalar) -> Double {
+    scalar.value
+}
+
+final class DifferentiationTests: XCTestCase {
+    func testComputesValueWithGradient() {
+        let result = valueWithGradient(at: 4.0, of: quadratic)
+
+        XCTAssertEqual(result.value, 30.0, accuracy: 1e-12)
+        XCTAssertEqual(result.gradient, 11.0, accuracy: 1e-12)
+    }
+
+    func testComputesMultiArgumentGradient() {
+        let result = valueWithGradient(at: 3.0, 5.0, of: weightedPolynomial)
+
+        XCTAssertEqual(result.value, 29.0, accuracy: 1e-12)
+        XCTAssertEqual(result.gradient.0, 11.0, accuracy: 1e-12)
+        XCTAssertEqual(result.gradient.1, 4.0, accuracy: 1e-12)
+    }
+
+    func testCustomDifferentiableTypeCanBeUsedAcrossModuleBoundary() {
+        let gradient = gradient(at: Scalar(value: 7), of: unwrap)
+
+        XCTAssertEqual(gradient.value, 1.0, accuracy: 1e-12)
+    }
+}
diff --git a/Tools/build-library.sh b/Tools/build-library.sh
new file mode 100755
index 0000000..b9cd0ab
--- /dev/null
+++ b/Tools/build-library.sh
@@ -0,0 +1,352 @@
+#!/usr/bin/env bash
+
+set -euo pipefail
+
+MODULE_NAME="_Differentiation"
+ORIGINAL_TARGET_NAME="swift_Differentiation"
+MODULE_LINK_NAME="lib_Differentiation"
+shared_library=0
+
+usage() {
+  cat <<EOF
+Usage:
+  Tools/build-library.sh --swift-source PATH [--shared-library] [--keep-work-dir]
+
+Builds a static ${MODULE_NAME} XCFramework from a swiftlang/swift source tree by
+default. Pass --shared-library to build a dynamic XCFramework instead.
+Replaces ${MODULE_NAME}.xcframework at the repository root.
+
+Options:
+  --swift-source PATH  Path to the swiftlang/swift checkout.
+  --shared-library     Build a shared library (.dylib) instead of a static one (.a).
+  --keep-work-dir      Keep the temporary staging/build directory for inspection.
+  -h, --help           Show this help.
+EOF
+}
+
+die() {
+  echo "error: $*" >&2
+  exit 1
+}
+
+log() {
+  echo "==> $*"
+}
+
+require_tool() {
+  command -v "$1" >/dev/null 2>&1 || die "required tool '$1' was not found on PATH"
+}
+
+absolute_existing_dir() {
+  local path="$1"
+  [[ -d "$path" ]] || die "directory does not exist: $path"
+  cd "$path" >/dev/null
+  pwd -P
+}
+
+absolute_output_path() {
+  local path="$1"
+  local parent
+  local base
+  parent="$(dirname "$path")"
+  base="$(basename "$path")"
+  mkdir -p "$parent"
+  cd "$parent" >/dev/null
+  printf '%s/%s\n' "$(pwd -P)" "$base"
+}
+
+repo_root="$(cd "$(dirname "${BASH_SOURCE[0]}")/.." >/dev/null && pwd -P)"
+swift_source=""
+output_path="${repo_root}/${MODULE_NAME}.xcframework"
+keep_work_dir=0
+library_extension="a"
+build_shared_libs="NO"
+
+while [[ $# -gt 0 ]]; do
+  case "$1" in
+    --swift-source)
+      [[ $# -ge 2 ]] || die "--swift-source requires a path"
+      swift_source="$2"
+      shift 2
+      ;;
+    --swift-source=*)
+      swift_source="${1#*=}"
+      shift
+      ;;
+    --keep-work-dir)
+      keep_work_dir=1
+      shift
+      ;;
+    --shared-library)
+      shared_library=1
+      library_extension="dylib"
+      build_shared_libs="YES"
+      shift
+      ;;
+    -h|--help)
+      usage
+      exit 0
+      ;;
+    *)
+      die "unknown argument: $1"
+      ;;
+  esac
+done
+
+[[ -n "$swift_source" ]] || die "--swift-source is required"
+
+require_tool cmake
+require_tool ninja
+if [[ "$shared_library" -eq 1 ]]; then
+  require_tool install_name_tool
+fi
+
+ORIGINAL_LIBRARY_BASENAME="lib${ORIGINAL_TARGET_NAME}.${library_extension}"
+# Swift turns -module-link-name lib_Differentiation into -llib_Differentiation,
+# so the packaged library must carry the Darwin lib prefix as liblib_Differentiation.
+LIBRARY_BASENAME="lib${MODULE_LINK_NAME}.${library_extension}"
+
+swift_source="$(absolute_existing_dir "$swift_source")"
+
+[[ -f "${swift_source}/Runtimes/Resync.cmake" ]] || die "missing Runtimes/Resync.cmake under ${swift_source}"
+[[ -d "${swift_source}/Runtimes/Supplemental/Differentiation" ]] || die "missing Runtimes/Supplemental/Differentiation under ${swift_source}"
+[[ -d "${swift_source}/stdlib/public/Differentiation" ]] || die "missing stdlib/public/Differentiation under ${swift_source}"
+[[ -x "${swift_source}/utils/gyb" ]] || die "missing executable utils/gyb under ${swift_source}"
+
+work_dir="$(mktemp -d "${TMPDIR:-/tmp}/swift-differentiation-stdlib.XXXXXX")"
+cleanup() {
+  if [[ "$keep_work_dir" -eq 1 ]]; then
+    log "Kept work directory: ${work_dir}"
+  else
+    rm -rf "$work_dir"
+  fi
+}
+trap cleanup EXIT
+
+stage_dir="${work_dir}/swift-stage"
+build_root="${work_dir}/build"
+module_cache="${work_dir}/module-cache"
+staged_differentiation_dir="${stage_dir}/Runtimes/Supplemental/Differentiation"
+staged_cmake_lists="${staged_differentiation_dir}/CMakeLists.txt"
+
+log "Staging swift Runtimes under ${stage_dir}"
+mkdir -p "$stage_dir" "$build_root" "$module_cache"
+cp -R "${swift_source}/Runtimes" "${stage_dir}/Runtimes"
+ln -s "${swift_source}/stdlib" "${stage_dir}/stdlib"
+
+log "Resyncing staged runtime sources"
+cmake -P "${stage_dir}/Runtimes/Resync.cmake"
+
+patch_cmake_lists() {
+  local input="$1"
+  local tmp="${input}.tmp"
+
+  awk -v module_link_name="$MODULE_LINK_NAME" '
+    {
+      print
+      if ($0 ~ /^  Swift_MODULE_NAME _Differentiation\)$/) {
+        print ""
+        print "target_compile_options(swift_Differentiation PRIVATE"
+        print "  \"\$<\$<COMPILE_LANGUAGE:Swift>:SHELL:-module-link-name " module_link_name ">\")"
+        print "target_compile_options(swift_Differentiation PRIVATE"
+        print "  \"\$<\$<COMPILE_LANGUAGE:Swift>:SHELL:-Xfrontend -empty-abi-descriptor>\")"
+      }
+    }
+  ' "$input" > "$tmp"
+
+  if ! grep -q -- "-module-link-name ${MODULE_LINK_NAME}" "$tmp"; then
+    rm -f "$tmp"
+    die "failed to patch ${input} with module link name ${MODULE_LINK_NAME}"
+  fi
+  if ! grep -q -- "-empty-abi-descriptor" "$tmp"; then
+    rm -f "$tmp"
+    die "failed to patch ${input} with -empty-abi-descriptor"
+  fi
+
+  mv "$tmp" "$input"
+}
+
+log "Patching staged CMake to emit -module-link-name ${MODULE_LINK_NAME}"
+patch_cmake_lists "$staged_cmake_lists"
+
+export CLANG_MODULE_CACHE_PATH="$module_cache"
+
+build_slice() {
+  local identifier="$1"
+  local sysroot="$2"
+  local deployment_target="$3"
+  local compiler_target="$4"
+  local build_dir="${build_root}/${identifier}"
+
+  log "Configuring ${identifier}"
+  cmake -G Ninja \
+    -B "$build_dir" \
+    -S "$staged_differentiation_dir" \
+    -DCMAKE_OSX_SYSROOT="$sysroot" \
+    -DCMAKE_OSX_DEPLOYMENT_TARGET="$deployment_target" \
+    -DCMAKE_OSX_ARCHITECTURES=arm64 \
+    -DBUILD_SHARED_LIBS="$build_shared_libs" \
+    -DCMAKE_C_COMPILER_TARGET="$compiler_target" \
+    -DCMAKE_CXX_COMPILER_TARGET="$compiler_target" \
+    -DCMAKE_Swift_COMPILER_TARGET="$compiler_target" \
+    -DCMAKE_BUILD_TYPE=Release \
+    -DSwiftDifferentiation_SWIFTC_SOURCE_DIR="$swift_source" \
+    -DSwiftDifferentiation_ENABLE_LIBRARY_EVOLUTION=YES \
+    -DSwiftDifferentiation_ENABLE_VECTOR_TYPES=YES
+
+  log "Building ${identifier}"
+  cmake --build "$build_dir"
+}
+
+copy_slice() {
+  local build_identifier="$1"
+  local output_identifier="$2"
+  local build_dir="${build_root}/${build_identifier}"
+  local slice_dir="${output_path}/${output_identifier}"
+  local built_library="${build_dir}/${ORIGINAL_LIBRARY_BASENAME}"
+  local built_module_dir="${build_dir}/${MODULE_NAME}.swiftmodule"
+  local packaged_module_dir="${slice_dir}/${MODULE_NAME}.swiftmodule"
+  local packaged_library="${slice_dir}/${LIBRARY_BASENAME}"
+
+  [[ -f "$built_library" ]] || die "missing built library: ${built_library}"
+  [[ -d "$built_module_dir" ]] || die "missing built Swift module directory: ${built_module_dir}"
+
+  mkdir -p "$slice_dir"
+  cp "$built_library" "$packaged_library"
+  if [[ "$shared_library" -eq 1 ]]; then
+    install_name_tool -id "@rpath/${LIBRARY_BASENAME}" "$packaged_library"
+  fi
+  cp -R "$built_module_dir" "$packaged_module_dir"
+
+  # Keep compiler-produced binary module artifacts so consumers using the exact
+  # same compiler release can import the prebuilt module instead of rechecking
+  # the textual interface.
+  find "$packaged_module_dir" -name '*.swiftsourceinfo' -delete
+}
+
+verify_slice() {
+  local identifier="$1"
+  local slice_dir="${output_path}/${identifier}"
+  local packaged_library="${slice_dir}/${LIBRARY_BASENAME}"
+  local found_interface=0
+  local found_binary_module=0
+  local found_swiftdoc=0
+
+  [[ -f "$packaged_library" ]] || die "missing packaged library: ${packaged_library}"
+
+  if [[ "$shared_library" -eq 1 ]]; then
+    if ! otool -D "$packaged_library" | grep -q -- "@rpath/${LIBRARY_BASENAME}"; then
+      die "${packaged_library} does not have @rpath/${LIBRARY_BASENAME} as its install name"
+    fi
+  fi
+
+  while IFS= read -r -d '' interface; do
+    found_interface=1
+    if ! grep -q -- "-module-link-name ${MODULE_LINK_NAME}" "$interface"; then
+      die "${interface} does not contain -module-link-name ${MODULE_LINK_NAME}"
+    fi
+    if grep -q -- "-module-link-name ${ORIGINAL_TARGET_NAME}" "$interface"; then
+      die "${interface} still contains -module-link-name ${ORIGINAL_TARGET_NAME}"
+    fi
+  done < <(find "${slice_dir}/${MODULE_NAME}.swiftmodule" -name '*.swiftinterface' -print0)
+
+  [[ "$found_interface" -eq 1 ]] || die "no textual Swift interfaces found in ${slice_dir}/${MODULE_NAME}.swiftmodule"
+  while IFS= read -r -d '' _; do
+    found_binary_module=1
+  done < <(find "${slice_dir}/${MODULE_NAME}.swiftmodule" -name '*.swiftmodule' -print0)
+  [[ "$found_binary_module" -eq 1 ]] || die "no binary Swift modules found in ${slice_dir}/${MODULE_NAME}.swiftmodule"
+
+  while IFS= read -r -d '' _; do
+    found_swiftdoc=1
+  done < <(find "${slice_dir}/${MODULE_NAME}.swiftmodule" -name '*.swiftdoc' -print0)
+  [[ "$found_swiftdoc" -eq 1 ]] || die "no Swift documentation modules found in ${slice_dir}/${MODULE_NAME}.swiftmodule"
+}
+
+write_info_plist() {
+  cat > "${output_path}/Info.plist" <<EOF
+<?xml version="1.0" encoding="UTF-8"?>
+<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
+<plist version="1.0">
+<dict>
+	<key>AvailableLibraries</key>
+	<array>
+		<dict>
+			<key>BinaryPath</key>
+			<string>${LIBRARY_BASENAME}</string>
+			<key>SwiftModulesPath</key>
+			<string>${MODULE_NAME}.swiftmodule</string>
+			<key>LibraryIdentifier</key>
+			<string>macos-arm64</string>
+			<key>LibraryPath</key>
+			<string>${LIBRARY_BASENAME}</string>
+			<key>SupportedArchitectures</key>
+			<array>
+				<string>arm64</string>
+			</array>
+			<key>SupportedPlatform</key>
+			<string>macos</string>
+		</dict>
+		<dict>
+			<key>BinaryPath</key>
+			<string>${LIBRARY_BASENAME}</string>
+			<key>SwiftModulesPath</key>
+			<string>${MODULE_NAME}.swiftmodule</string>
+			<key>LibraryIdentifier</key>
+			<string>ios-arm64-simulator</string>
+			<key>LibraryPath</key>
+			<string>${LIBRARY_BASENAME}</string>
+			<key>SupportedArchitectures</key>
+			<array>
+				<string>arm64</string>
+			</array>
+			<key>SupportedPlatform</key>
+			<string>ios</string>
+			<key>SupportedPlatformVariant</key>
+			<string>simulator</string>
+		</dict>
+		<dict>
+			<key>BinaryPath</key>
+			<string>${LIBRARY_BASENAME}</string>
+			<key>SwiftModulesPath</key>
+			<string>${MODULE_NAME}.swiftmodule</string>
+			<key>LibraryIdentifier</key>
+			<string>ios-arm64</string>
+			<key>LibraryPath</key>
+			<string>${LIBRARY_BASENAME}</string>
+			<key>SupportedArchitectures</key>
+			<array>
+				<string>arm64</string>
+			</array>
+			<key>SupportedPlatform</key>
+			<string>ios</string>
+		</dict>
+	</array>
+	<key>CFBundlePackageType</key>
+	<string>XFWK</string>
+	<key>XCFrameworkFormatVersion</key>
+	<string>1.0</string>
+</dict>
+</plist>
+EOF
+}
+
+log "Preparing output at ${output_path}"
+rm -rf "$output_path"
+mkdir -p "$output_path"
+
+build_slice macosx macosx 13.0 arm64-apple-macos13.0
+copy_slice macosx macos-arm64
+
+build_slice iphoneos iphoneos 16.0 arm64-apple-ios16.0
+copy_slice iphoneos ios-arm64
+
+build_slice iphonesimulator iphonesimulator 16.0 arm64-apple-ios16.0-simulator
+copy_slice iphonesimulator ios-arm64-simulator
+
+write_info_plist
+
+verify_slice macos-arm64
+verify_slice ios-arm64
+verify_slice ios-arm64-simulator
+
+log "Built ${output_path}"