kernel: rewrite (C)Log2Int using compiler builtins

Compared to the old CLog2Int code, on my machine the new code using
compiler builtins is between 5 and 10 times faster, and the new generic
code is still 1.2 to 4 times faster.

The new FuncLog2Int calls CLog2Int (or rather, the new static inline
function CLog2UInt which expects an unsigned argument), and thus
benefits from the optimizations as well (though not by as much).

Some micro benchmarks, using the old code:

gap> x:=2^0;; for a in [0..2^25] do Log2Int(x); od; time;
998
gap> x:=2^50;; for a in [0..2^25] do Log2Int(x); od; time;
1916
gap> x:=2^60;; for a in [0..2^25] do Log2Int(x); od; time;
1312
gap> x:=2^80;; for a in [0..2^25] do Log2Int(x); od; time;
2773
gap> x:=2^180;; for a in [0..2^25] do Log2Int(x); od; time;
1504

New code:

gap> x:=2^0;; for a in [0..2^25] do Log2Int(x); od; time;
955
gap> x:=2^50;; for a in [0..2^25] do Log2Int(x); od; time;
970
gap> x:=2^60;; for a in [0..2^25] do Log2Int(x); od; time;
1045
gap> x:=2^80;; for a in [0..2^25] do Log2Int(x); od; time;
1020
gap> x:=2^180;; for a in [0..2^25] do Log2Int(x); od; time;
1007

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

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]);
 
 
 #

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;
 
 

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)",