diff --git a/cnf/config.hin b/cnf/config.hin
index a27a32c473..dade4ee603 100644
--- a/cnf/config.hin
+++ b/cnf/config.hin
@@ -376,6 +376,15 @@
 /* Define to 1 if you have the `_setjmp' function. */
 #undef HAVE__SETJMP
 
+/* Define to 1 if the system has the `__builtin_clz' built-in function */
+#undef HAVE___BUILTIN_CLZ
+
+/* Define to 1 if the system has the `__builtin_clzl' built-in function */
+#undef HAVE___BUILTIN_CLZL
+
+/* Define to 1 if the system has the `__builtin_clzll' built-in function */
+#undef HAVE___BUILTIN_CLZLL
+
 /* Define to 1 if the system has the `__builtin_smulll_overflow' built-in
    function */
 #undef HAVE___BUILTIN_SMULLL_OVERFLOW
diff --git a/cnf/configure.in b/cnf/configure.in
index 259ec108d3..d99be9c429 100644
--- a/cnf/configure.in
+++ b/cnf/configure.in
@@ -68,6 +68,9 @@ AC_DEFUN([CHECK_COMPILER_BUILTIN],
 CHECK_COMPILER_BUILTIN([__builtin_smul_overflow],[0,0,0]);
 CHECK_COMPILER_BUILTIN([__builtin_smull_overflow],[0,0,0]);
 CHECK_COMPILER_BUILTIN([__builtin_smulll_overflow],[0,0,0]);
+CHECK_COMPILER_BUILTIN([__builtin_clz],[0]);
+CHECK_COMPILER_BUILTIN([__builtin_clzl],[0]);
+CHECK_COMPILER_BUILTIN([__builtin_clzll],[0]);
 
 
 #
diff --git a/cnf/configure.out b/cnf/configure.out
index 02d029b608..474e140778 100755
--- a/cnf/configure.out
+++ b/cnf/configure.out
@@ -4521,6 +4521,102 @@ cat >>confdefs.h <<_ACEOF
 #define HAVE___BUILTIN_SMULLL_OVERFLOW 1
 _ACEOF
 
+fi;
+{ $as_echo "$as_me:${as_lineno-$LINENO}: checking for __builtin_clz" >&5
+$as_echo_n "checking for __builtin_clz... " >&6; }
+    cat confdefs.h - <<_ACEOF >conftest.$ac_ext
+/* end confdefs.h.  */
+
+int
+main ()
+{
+__builtin_clz(0);
+
+
+  ;
+  return 0;
+}
+_ACEOF
+if ac_fn_c_try_link "$LINENO"; then :
+  have___builtin_clz=yes
+else
+  have___builtin_clz=no
+
+fi
+rm -f core conftest.err conftest.$ac_objext \
+    conftest$ac_exeext conftest.$ac_ext
+    { $as_echo "$as_me:${as_lineno-$LINENO}: result: $have___builtin_clz" >&5
+$as_echo "$have___builtin_clz" >&6; }
+    if test yes = $have___builtin_clz; then :
+
+cat >>confdefs.h <<_ACEOF
+#define HAVE___BUILTIN_CLZ 1
+_ACEOF
+
+fi;
+{ $as_echo "$as_me:${as_lineno-$LINENO}: checking for __builtin_clzl" >&5
+$as_echo_n "checking for __builtin_clzl... " >&6; }
+    cat confdefs.h - <<_ACEOF >conftest.$ac_ext
+/* end confdefs.h.  */
+
+int
+main ()
+{
+__builtin_clzl(0);
+
+
+  ;
+  return 0;
+}
+_ACEOF
+if ac_fn_c_try_link "$LINENO"; then :
+  have___builtin_clzl=yes
+else
+  have___builtin_clzl=no
+
+fi
+rm -f core conftest.err conftest.$ac_objext \
+    conftest$ac_exeext conftest.$ac_ext
+    { $as_echo "$as_me:${as_lineno-$LINENO}: result: $have___builtin_clzl" >&5
+$as_echo "$have___builtin_clzl" >&6; }
+    if test yes = $have___builtin_clzl; then :
+
+cat >>confdefs.h <<_ACEOF
+#define HAVE___BUILTIN_CLZL 1
+_ACEOF
+
+fi;
+{ $as_echo "$as_me:${as_lineno-$LINENO}: checking for __builtin_clzll" >&5
+$as_echo_n "checking for __builtin_clzll... " >&6; }
+    cat confdefs.h - <<_ACEOF >conftest.$ac_ext
+/* end confdefs.h.  */
+
+int
+main ()
+{
+__builtin_clzll(0);
+
+
+  ;
+  return 0;
+}
+_ACEOF
+if ac_fn_c_try_link "$LINENO"; then :
+  have___builtin_clzll=yes
+else
+  have___builtin_clzll=no
+
+fi
+rm -f core conftest.err conftest.$ac_objext \
+    conftest$ac_exeext conftest.$ac_ext
+    { $as_echo "$as_me:${as_lineno-$LINENO}: result: $have___builtin_clzll" >&5
+$as_echo "$have___builtin_clzll" >&6; }
+    if test yes = $have___builtin_clzll; then :
+
+cat >>confdefs.h <<_ACEOF
+#define HAVE___BUILTIN_CLZLL 1
+_ACEOF
+
 fi;
 
 
diff --git a/src/gmpints.c b/src/gmpints.c
index aa7cee95c6..90d03812ba 100644
--- a/src/gmpints.c
+++ b/src/gmpints.c
@@ -638,21 +638,55 @@ Obj FuncIntHexString( Obj self,  Obj str )
 /****************************************************************************
 **  
 **  Implementation of Log2Int for C integers.
+**
+**  When available, we try to use GCC builtins. Otherwise, fall back to code
+**  based on https://graphics.stanford.edu/~seander/bithacks.html#IntegerLogLookup.
+**  On a test machine with x86 64bit, the builtins are about 4 times faster
+**  than the generic code.
+**
 */
 
+static Int CLog2UInt(UInt a)
+{
+#if SIZEOF_VOID_P == SIZEOF_INT && HAVE___BUILTIN_CLZ
+  return GMP_LIMB_BITS - 1 - __builtin_clz(a);
+#elif SIZEOF_VOID_P == SIZEOF_LONG && HAVE___BUILTIN_CLZL
+  return GMP_LIMB_BITS - 1 - __builtin_clzl(a);
+#elif SIZEOF_VOID_P == SIZEOF_LONG_LONG && HAVE___BUILTIN_CLZLL
+  return GMP_LIMB_BITS - 1 - __builtin_clzll(a);
+#else
+    static const char LogTable256[256] = {
+       -1, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3,
+        4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
+        5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
+        5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
+        6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
+        6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
+        6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
+        6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
+        7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
+        7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
+        7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
+        7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
+        7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
+        7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
+        7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
+        7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7
+    };
+
+    Int res = 0;
+    UInt b;
+    b = a >> 32; if (b) { res+=32; a=b; }
+    b = a >> 16; if (b) { res+=16; a=b; }
+    b = a >>  8; if (b) { res+= 8; a=b; }
+    return res + LogTable256[a];
+#endif
+}
+
 Int CLog2Int(Int a)
 {
-  Int res, mask;
   if (a < 0) a = -a;
-  if (a < 1) return -1;
-  if (a < 65536) {
-    for(mask = 2, res = 0; ;mask *= 2, res += 1) {
-      if(a < mask) return res;
-    }
-  }
-  for(mask = 65536, res = 15; ;mask *= 2, res += 1) {
-    if(a < mask) return res;
-  }
+  return CLog2UInt(a);
 }
 
 /****************************************************************************
@@ -663,29 +697,22 @@ Int CLog2Int(Int a)
 */
 Obj FuncLog2Int( Obj self, Obj integer)
 {
-  Int d;
-  Int a, len;
-  TypLimb dmask;
-  
-  /* case of small ints                                                    */
-  if (IS_INTOBJ(integer)) {
+  if ( IS_INTOBJ(integer) ) {
     return INTOBJ_INT(CLog2Int(INT_INTOBJ(integer)));
   }
 
-  /* case of long ints                                                     */
   if ( IS_LARGEINT(integer) ) {
-    for (len = SIZE_INT(integer); ADDR_INT(integer)[len-1] == 0; len--);
-    /* Instead of computing 
-          res = len * GMP_LIMB_BITS - d;
-       we keep len and d separate, because on 32 bit systems res may
-       not fit into an Int (and not into an immediate integer).            */
-    d = 1;
-    a = (TypLimb)(ADDR_INT(integer)[len-1]); 
-    for(dmask = (TypLimb)1 << (GMP_LIMB_BITS - 1);
-        (dmask & a) == 0 && dmask != (TypLimb)0;
-        dmask = dmask >> 1, d++);
-    return DiffInt(ProdInt(INTOBJ_INT(len), INTOBJ_INT(GMP_LIMB_BITS)), 
-                   INTOBJ_INT(d));
+    UInt len = SIZE_INT(integer) - 1;
+    UInt a = CLog2UInt( ADDR_INT(integer)[len] );
+
+#ifdef SYS_IS_64_BIT
+    return INTOBJ_INT(len * GMP_LIMB_BITS + a);
+#else
+    /* The final result is len * GMP_LIMB_BITS - d, which may not
+       fit into an immediate integer (at least on a 32bit system) */
+    return SumInt(ProdInt(INTOBJ_INT(len), INTOBJ_INT(GMP_LIMB_BITS)),
+                   INTOBJ_INT(a));
+#endif
   }
   else {
     ErrorReturnObj("Log2Int: argument must be a int, (not a %s)",