diff --git a/src/field_impl.h b/src/field_impl.h
index 551a6243e2..1994017ba5 100644
--- a/src/field_impl.h
+++ b/src/field_impl.h
@@ -208,6 +208,16 @@ static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a) {
 }
 
 static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a) {
+#if !defined(USE_FIELD_INV_BUILTIN) && !defined(USE_FIELD_INV_NUM)
+    /* In case no field inverse implementation has been selected,
+       choose one based on num implementation. */
+    #if defined(USE_NUM_GMP)
+        #define USE_FIELD_INV_NUM 1 /* "NUM" implementation requires GMP */
+    #else
+        #define USE_FIELD_INV_BUILTIN 1
+    #endif
+#endif
+
 #if defined(USE_FIELD_INV_BUILTIN)
     secp256k1_fe_inv(r, a);
 #elif defined(USE_FIELD_INV_NUM)
diff --git a/src/scalar_impl.h b/src/scalar_impl.h
index 88ea97de86..ec2d8985a6 100644
--- a/src/scalar_impl.h
+++ b/src/scalar_impl.h
@@ -240,6 +240,16 @@ SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a)
 }
 
 static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *x) {
+#if !defined(USE_SCALAR_INV_BUILTIN) && !defined(USE_SCALAR_INV_NUM)
+    /* In case no scalar inverse implementation has been selected,
+       choose one based on num implementation. */
+    #if defined(USE_NUM_GMP)
+        #define USE_SCALAR_INV_NUM 1 /* "NUM" implementation requires GMP */
+    #else
+        #define USE_SCALAR_INV_BUILTIN 1
+    #endif
+#endif
+
 #if defined(USE_SCALAR_INV_BUILTIN)
     secp256k1_scalar_inverse(r, x);
 #elif defined(USE_SCALAR_INV_NUM)