diff --git a/maths.cpp b/maths.cpp
index 2738af6a..b33c64c7 100644
--- a/maths.cpp
+++ b/maths.cpp
@@ -19,6 +19,8 @@
 
 #include "maths.hpp"
 
+#include "debug.hpp"
+
 #include "float.hpp"
 
 #include <cmath>
@@ -174,3 +176,11 @@ sign (double val) {
 
 template int sign (int);
 
+
+//-----------------------------------------------------------------------------
+// Simple instantiations. Some functions aren't used internally to the library
+// so it's easier to instantiate early and check for broken code at library
+// build time.
+
+template float smoothstep (float, float, float);
+template double smoothstep (double, double, double);
diff --git a/maths.hpp b/maths.hpp
index d0c5b128..a7c5b756 100644
--- a/maths.hpp
+++ b/maths.hpp
@@ -20,6 +20,8 @@
 #ifndef __MATHS_HPP
 #define __MATHS_HPP
 
+#include "debug.hpp"
+
 #include <cstdint>
 #include <type_traits>
 #include <utility>
@@ -284,6 +286,17 @@ limit [[gnu::pure]] (const T val, const U hi, const V lo)
 }
 
 
+// clamped cubic hermite interpolation
+template <typename T>
+T
+smoothstep [[gnu::pure]] (T a, T b, T x)
+{
+    CHECK_LE(a, b);
+    x = limit ((x - a) / (b - a), T{0}, T{1});
+    return x * x * (3 - 2 * x);
+}
+
+
 #include "maths.ipp"
 
 #endif // __MATHS_HPP