Let's try a different approach.

Author: stephentyrone

Package.swift

@@ -50,8 +50,10 @@ let package = Package(
     ),
 
     // MARK: - Implementation details
-    .systemLibrary(
-      name: "_NumericsShims"
+    .target(
+      name: "_NumericsShims",
+      exclude: excludedFilenames,
+      linkerSettings: [.linkedLibrary("m", .when(platforms: [.linux]))]
     ),
 
     .target(

Sources/_NumericsShims/_NumericsShims.c

@@ -0,0 +1,19 @@
+//===--- NumericsShims.c --------------------------------------*- swift -*-===//
+//
+// This source file is part of the Swift Numerics open source project
+//
+// Copyright (c) 2019 Apple Inc. and the Swift Numerics project authors
+// Licensed under Apache License v2.0 with Runtime Library Exception
+//
+// See https://swift.org/LICENSE.txt for license information
+//
+//===----------------------------------------------------------------------===//
+
+// This file exists only to trigger the NumericShims module to build; without
+// it swiftpm won't build anything, and then the shims are not available for
+// the modules that need them.
+
+// If any shims are added that are not pure header inlines, whatever runtime
+// support they require can be added to this file.
+
+#include "_NumericsShims.h"

Sources/_NumericsShims/_NumericsShims.h renamed to Sources/_NumericsShims/include/_NumericsShims.h

@@ -1,4 +1,3 @@
 module _NumericsShims {
   header "_NumericsShims.h"
-  link "m"
 }