diff --git a/.github/workflows/pull_request.yml b/.github/workflows/pull_request.yml
index a92c6416..bf0ce917 100644
--- a/.github/workflows/pull_request.yml
+++ b/.github/workflows/pull_request.yml
@@ -8,6 +8,9 @@ jobs:
   tests:
     name: Test
     uses: swiftlang/github-workflows/.github/workflows/swift_package_test.yml@main
+    with:
+      enable_wasm_sdk_build: true
+      wasm_sdk_build_command: swift build --target Numerics
   soundness:
     name: Soundness
     uses: swiftlang/github-workflows/.github/workflows/soundness.yml@main
diff --git a/Sources/RealModule/Float16+Real.swift b/Sources/RealModule/Float16+Real.swift
index 6781683e..98e97e89 100644
--- a/Sources/RealModule/Float16+Real.swift
+++ b/Sources/RealModule/Float16+Real.swift
@@ -173,6 +173,10 @@ extension Float16: Real {
   }
   #endif
   
+  #if !arch(wasm32)
+  // WASM doesn't have _Float16 on the C side, so we can't define the C hooks
+  // that these use. TODO: implement these as Swift builtins instead.
+  
   @_transparent
   public static func _relaxedAdd(_ a: Float16, _ b: Float16) -> Float16 {
     _numerics_relaxed_addf16(a, b)
@@ -182,6 +186,7 @@ extension Float16: Real {
   public static func _relaxedMul(_ a: Float16, _ b: Float16) -> Float16 {
     _numerics_relaxed_mulf16(a, b)
   }
+  #endif
 }
 
 #endif
diff --git a/Sources/_NumericsShims/include/_NumericsShims.h b/Sources/_NumericsShims/include/_NumericsShims.h
index 0cf3c191..8b7bf995 100644
--- a/Sources/_NumericsShims/include/_NumericsShims.h
+++ b/Sources/_NumericsShims/include/_NumericsShims.h
@@ -389,6 +389,7 @@ HEADER_SHIM long double libm_lgammal(long double x, int *signp) {
 // MARK: - math inlines with relaxed semantics to support optimization.
 #define CLANG_RELAX_FP _Pragma("clang fp reassociate(on) contract(fast)")
 
+#if !defined __wasm__ // No _Float16 on wasm
 /// a + b with the "allow reassociation" and "allow FMA formation" flags
 /// set in the IR.
 HEADER_SHIM _Float16 _numerics_relaxed_addf16(_Float16 a, _Float16 b) {
@@ -402,6 +403,7 @@ HEADER_SHIM _Float16 _numerics_relaxed_mulf16(_Float16 a, _Float16 b) {
   CLANG_RELAX_FP
   return a * b;
 }
+#endif
 
 /// a + b with the "allow reassociation" and "allow FMA formation" flags
 /// set in the IR.