diff --git a/src/util/rational.h b/src/util/rational.h
index c02a5a2c3..0d8a23e81 100644
--- a/src/util/rational.h
+++ b/src/util/rational.h
@@ -331,22 +331,13 @@ public:
         return target;
     }
 
-    friend inline rational gcd(rational const & r1, rational const & r2) {
-        rational result;
-        m().gcd(r1.m_val, r2.m_val, result.m_val);
-        return result;
-    }
+    friend inline rational gcd(rational const & r1, rational const & r2);
 
     //
     // extended Euclid:
     // r1*a + r2*b = gcd
     //
-    friend inline rational gcd(rational const & r1, rational const & r2, rational & a, rational & b) {
-        rational result;
-        m().gcd(r1.m_val, r2.m_val, a.m_val, b.m_val, result.m_val);
-        return result;
-    }
-
+    friend inline rational gcd(rational const & r1, rational const & r2, rational & a, rational & b);
 
     friend inline rational lcm(rational const & r1, rational const & r2) {
         rational result;
@@ -378,11 +369,7 @@ public:
         return result;
     }
 
-    friend inline rational abs(rational const & r) {
-        rational result(r);
-        m().abs(result.m_val);
-        return result;
-    }
+    friend inline rational abs(rational const & r);
 
     rational to_rational() const { return *this; }
 
@@ -446,5 +433,24 @@ inline rational power(rational const & r, unsigned p) {
     return r.expt(p);
 }
 
+inline rational abs(rational const & r) {
+  rational result(r);
+  rational::m().abs(result.m_val);
+  return result;
+}
+
+inline rational gcd(rational const & r1, rational const & r2) {
+  rational result;
+  rational::m().gcd(r1.m_val, r2.m_val, result.m_val);
+  return result;
+}
+
+inline rational gcd(rational const & r1, rational const & r2, rational & a, rational & b) {
+  rational result;
+  rational::m().gcd(r1.m_val, r2.m_val, a.m_val, b.m_val, result.m_val);
+  return result;
+}
+
+
 #endif /* _RATIONAL_H_ */