diff --git a/src/arch/i386/include/bits/strings.h b/src/arch/i386/include/bits/strings.h
new file mode 100644
index 00000000..092bcb59
--- /dev/null
+++ b/src/arch/i386/include/bits/strings.h
@@ -0,0 +1,50 @@
+#ifndef _BITS_STRINGS_H
+#define _BITS_STRINGS_H
+
+FILE_LICENCE ( GPL2_OR_LATER );
+
+/**
+ * Find last (i.e. most significant) set bit
+ *
+ * @v value		Value
+ * @ret msb		Most significant bit set in value (LSB=1), or zero
+ */
+static inline __attribute__ (( always_inline )) int __flsl ( long value ) {
+	long msb_minus_one;
+
+	/* If the input value is zero, the BSR instruction returns
+	 * ZF=1 and leaves an undefined value in the output register.
+	 * Perform this check in C rather than asm so that it can be
+	 * omitted in cases where the compiler is able to prove that
+	 * the input is non-zero.
+	 */
+	if ( value ) {
+		__asm__ ( "bsrl %1, %0"
+			  : "=r" ( msb_minus_one )
+			  : "rm" ( value ) );
+		return ( msb_minus_one + 1 );
+	} else {
+		return 0;
+	}
+}
+
+/**
+ * Find last (i.e. most significant) set bit
+ *
+ * @v value		Value
+ * @ret msb		Most significant bit set in value (LSB=1), or zero
+ */
+static inline __attribute__ (( always_inline )) int __flsll ( long long value ){
+	unsigned long high = ( value >> 32 );
+	unsigned long low = ( value >> 0 );
+
+	if ( high ) {
+		return ( 32 + __flsl ( high ) );
+	} else if ( low ) {
+		return ( __flsl ( low ) );
+	} else {
+		return 0;
+	}
+}
+
+#endif /* _BITS_STRINGS_H */
diff --git a/src/arch/x86/include/bits/strings.h b/src/arch/x86_64/include/bits/strings.h
similarity index 70%
rename from src/arch/x86/include/bits/strings.h
rename to src/arch/x86_64/include/bits/strings.h
index 62e0fbfb..6ee99a50 100644
--- a/src/arch/x86/include/bits/strings.h
+++ b/src/arch/x86_64/include/bits/strings.h
@@ -9,8 +9,8 @@ FILE_LICENCE ( GPL2_OR_LATER );
  * @v value		Value
  * @ret msb		Most significant bit set in value (LSB=1), or zero
  */
-static inline __attribute__ (( always_inline )) int __flsl ( long value ) {
-	long msb_minus_one;
+static inline __attribute__ (( always_inline )) int __flsll ( long long value ){
+	long long msb_minus_one;
 
 	/* If the input value is zero, the BSR instruction returns
 	 * ZF=1 and leaves an undefined value in the output register.
@@ -19,7 +19,7 @@ static inline __attribute__ (( always_inline )) int __flsl ( long value ) {
 	 * the input is non-zero.
 	 */
 	if ( value ) {
-		__asm__ ( "bsr %1, %0"
+		__asm__ ( "bsrq %1, %0"
 			  : "=r" ( msb_minus_one )
 			  : "rm" ( value ) );
 		return ( msb_minus_one + 1 );
@@ -28,4 +28,15 @@ static inline __attribute__ (( always_inline )) int __flsl ( long value ) {
 	}
 }
 
+/**
+ * Find last (i.e. most significant) set bit
+ *
+ * @v value		Value
+ * @ret msb		Most significant bit set in value (LSB=1), or zero
+ */
+static inline __attribute__ (( always_inline )) int __flsl ( long value ) {
+
+	return __flsll ( value );
+}
+
 #endif /* _BITS_STRINGS_H */
diff --git a/src/include/strings.h b/src/include/strings.h
index 924a084f..6912a1e4 100644
--- a/src/include/strings.h
+++ b/src/include/strings.h
@@ -8,15 +8,13 @@ FILE_LICENCE ( GPL2_OR_LATER );
 #include <bits/strings.h>
 
 static inline __attribute__ (( always_inline )) int
-__constant_flsl ( unsigned long x ) {
+__constant_flsll ( unsigned long long x ) {
 	int r = 0;
 
-#if ULONG_MAX > 0xffffffff
-	if ( x & 0xffffffff00000000UL ) {
+	if ( x & 0xffffffff00000000ULL ) {
 		x >>= 32;
 		r += 32;
 	}
-#endif
 	if ( x & 0xffff0000UL ) {
 		x >>= 16;
 		r += 16;
@@ -43,8 +41,17 @@ __constant_flsl ( unsigned long x ) {
 	return r;
 }
 
+static inline __attribute__ (( always_inline )) int
+__constant_flsl ( unsigned long x ) {
+	return __constant_flsll ( x );
+}
+
+int __flsll ( long long x );
 int __flsl ( long x );
 
+#define flsll( x ) \
+	( __builtin_constant_p ( x ) ? __constant_flsll ( x ) : __flsll ( x ) )
+
 #define flsl( x ) \
 	( __builtin_constant_p ( x ) ? __constant_flsl ( x ) : __flsl ( x ) )
 
diff --git a/src/tests/math_test.c b/src/tests/math_test.c
index 96cf050b..e12b7939 100644
--- a/src/tests/math_test.c
+++ b/src/tests/math_test.c
@@ -44,6 +44,16 @@ __attribute__ (( noinline )) int flsl_var ( long value ) {
 	return flsl ( value );
 }
 
+/**
+ * Force a call to the non-constant implementation of flsll()
+ *
+ * @v value		Value
+ * @ret msb		Most significant bit set in value (LSB=1), or zero
+ */
+__attribute__ (( noinline )) int flsll_var ( long long value ) {
+	return flsll ( value );
+}
+
 /**
  * Check current stack pointer
  *
@@ -181,6 +191,25 @@ flsl_okx ( long value, int msb, const char *file, unsigned int line ) {
 }
 #define flsl_ok( value, msb ) flsl_okx ( value, msb, __FILE__, __LINE__ )
 
+/**
+ * Report a flsll() test result
+ *
+ * @v value		Value
+ * @v msb		Expected MSB
+ * @v file		Test code file
+ * @v line		Test code line
+ */
+static inline __attribute__ (( always_inline )) void
+flsll_okx ( long long value, int msb, const char *file, unsigned int line ) {
+
+	/* Verify as a constant (requires to be inlined) */
+	okx ( flsll ( value ) == msb, file, line );
+
+	/* Verify as a non-constant */
+	okx ( flsll_var ( value ) == msb, file, line );
+}
+#define flsll_ok( value, msb ) flsll_okx ( value, msb, __FILE__, __LINE__ )
+
 /**
  * Report a 64-bit unsigned integer division test result
  *
@@ -251,6 +280,14 @@ static void math_test_exec ( void ) {
 	flsl_ok ( -1U, ( 8 * sizeof ( int ) ) );
 	flsl_ok ( -1UL, ( 8 * sizeof ( long ) ) );
 
+	/* Test flsll() */
+	flsll_ok ( 0, 0 );
+	flsll_ok ( 1, 1 );
+	flsll_ok ( 0x6d63623330ULL, 39 );
+	flsll_ok ( -1U, ( 8 * sizeof ( int ) ) );
+	flsll_ok ( -1UL, ( 8 * sizeof ( long ) ) );
+	flsll_ok ( -1ULL, ( 8 * sizeof ( long long ) ) );
+
 	/* Test 64-bit arithmetic
 	 *
 	 * On a 64-bit machine, these tests are fairly meaningless.