Add default implementation for determinant so that it works with -target cpu

source/slang/hlsl.meta.slang

@@ -8565,6 +8565,37 @@ T determinant(matrix<T,N,N> m)
         OpExtInst $$T result glsl450 Determinant $m
     };
     case wgsl: __intrinsic_asm "determinant";
+    default:
+        static_assert(N >= 1 && N <= 4, "determinant is only implemented up to 4x4 matrices");
+        if (N == 1)
+        {
+            return m[0][0];
+        }
+        else if (N == 2)
+        {
+            return m[0][0] * m[1][1] - m[0][1] * m[1][0];
+        }
+        else if (N == 3)
+        {
+            return
+                m[0][0] * (m[1][1] * m[2][2] - m[1][2] * m[2][1])
+              - m[0][1] * (m[1][0] * m[2][2] - m[1][2] * m[2][0])
+              + m[0][2] * (m[1][0] * m[2][1] - m[1][1] * m[2][0]);
+        }
+        else// if (N == 4)
+        {
+            T a = m[2][2] * m[3][3] - m[2][3] * m[3][2];
+            T b = m[2][1] * m[3][3] - m[2][3] * m[3][1];
+            T c = m[2][1] * m[3][2] - m[2][2] * m[3][1];
+            T d = m[2][0] * m[3][3] - m[2][3] * m[3][0];
+            T e = m[2][0] * m[3][2] - m[2][2] * m[3][0];
+            T f = m[2][0] * m[3][1] - m[2][1] * m[3][0];
+            return
+                m[0][0] * (m[1][1] * a - m[1][2] * b + m[1][3] * c)
+              - m[0][1] * (m[1][0] * a - m[1][2] * d + m[1][3] * e)
+              + m[0][2] * (m[1][0] * b - m[1][1] * d + m[1][3] * f)
+              - m[0][3] * (m[1][0] * c - m[1][1] * e + m[1][2] * f);
+        }
     }
 }