+// Column major (same as OpenGL).
+typedef double Matrix3x3[9];
+
+// Read a file from disk and return its contents.
+// Dies if the file does not exist.
+std::string read_file(const std::string &filename);
+
+// Compile the given GLSL shader (typically a vertex or fragment shader)
+// and return the object number.
+GLuint compile_shader(const std::string &shader_src, GLenum type);
+
+// Compute a * b.
+void multiply_3x3_matrices(const Matrix3x3 a, const Matrix3x3 b, Matrix3x3 result);
+
+// Compute m^-1. Result is undefined if the matrix is singular or near-singular.
+void invert_3x3_matrix(const Matrix3x3 m, Matrix3x3 result);
+
+// Print a 3x3 matrix to standard output. Useful for debugging.
+void print_3x3_matrix(const Matrix3x3 m);
+
+#ifdef NDEBUG
+#define check_error()
+#else
+#define check_error() { int err = glGetError(); if (err != GL_NO_ERROR) { printf("GL error 0x%x at %s:%d\n", err, __FILE__, __LINE__); exit(1); } }
+#endif
+