diff --git a/crystal.cpp b/crystal.cpp
index ca942aa0..a03b49dc 100644
--- a/crystal.cpp
+++ b/crystal.cpp
@@ -20,7 +20,14 @@ struct coord : public array<int, MAXDIM> {
 
 static const coord c0 = {};
 
-typedef array<ld, MAXDIM> ldcoord;
+struct ldcoord : public array<ld, MAXDIM> {
+  friend ldcoord operator + (ldcoord a, ldcoord b) { ldcoord r; for(int i=0; i<MAXDIM; i++) r[i] = a[i] + b[i]; return r; }
+  friend ldcoord operator - (ldcoord a, ldcoord b) { ldcoord r; for(int i=0; i<MAXDIM; i++) r[i] = a[i] - b[i]; return r; }
+  friend ldcoord operator * (ldcoord a, ld v) { ldcoord r; for(int i=0; i<MAXDIM; i++) r[i] = a[i] * v; return r; }
+  friend ldcoord operator / (ldcoord a, ld v) { ldcoord r; for(int i=0; i<MAXDIM; i++) r[i] = a[i] / v; return r; }
+  friend ld operator | (ldcoord a, ldcoord b) { ld r=0; for(int i=0; i<MAXDIM; i++) r += a[i] * b[i]; return r; }
+  };
+
 static const ldcoord ldc0 = {};
 #endif
 
@@ -46,13 +53,6 @@ ldcoord told(coord c) { ldcoord a; for(int i=0; i<MAXDIM; i++) a[i] = c[i]; retu
 // strange number to prevent weird acting in case of precision errors
 coord roundcoord(ldcoord c) { coord a; for(int i=0; i<MAXDIM; i++) a[i] = floor(c[i] + .5136); return a; }
 
-ldcoord operator + (ldcoord a, ldcoord b) { ldcoord r; for(int i=0; i<MAXDIM; i++) r[i] = a[i] + b[i]; return r; }
-ldcoord operator - (ldcoord a, ldcoord b) { ldcoord r; for(int i=0; i<MAXDIM; i++) r[i] = a[i] - b[i]; return r; }
-ldcoord operator * (ldcoord a, ld v) { ldcoord r; for(int i=0; i<MAXDIM; i++) r[i] = a[i] * v; return r; }
-ldcoord operator / (ldcoord a, ld v) { ldcoord r; for(int i=0; i<MAXDIM; i++) r[i] = a[i] / v; return r; }
-
-ld operator | (ldcoord a, ldcoord b) { ld r=0; for(int i=0; i<MAXDIM; i++) r += a[i] * b[i]; return r; }
-
 EX ld compass_probability = 1;
 
 int tocode(int cname) { return (1 << (cname >> 1)); }