diff --git a/src/tests/math_test.c b/src/tests/math_test.c
index 3967e620..fe61e29c 100644
--- a/src/tests/math_test.c
+++ b/src/tests/math_test.c
@@ -43,6 +43,54 @@ __attribute__ (( noinline )) int flsl_var ( long value ) {
 	return flsl ( value );
 }
 
+/**
+ * Force a use of runtime 64-bit unsigned integer division
+ *
+ * @v dividend		Dividend
+ * @v divisor		Divisor
+ * @ret quotient	Quotient
+ */
+__attribute__ (( noinline )) uint64_t u64div_var ( uint64_t dividend,
+						   uint64_t divisor ) {
+	return ( dividend / divisor );
+}
+
+/**
+ * Force a use of runtime 64-bit unsigned integer modulus
+ *
+ * @v dividend		Dividend
+ * @v divisor		Divisor
+ * @ret remainder	Remainder
+ */
+__attribute__ (( noinline )) uint64_t u64mod_var ( uint64_t dividend,
+						   uint64_t divisor ) {
+	return ( dividend % divisor );
+}
+
+/**
+ * Force a use of runtime 64-bit signed integer division
+ *
+ * @v dividend		Dividend
+ * @v divisor		Divisor
+ * @ret quotient	Quotient
+ */
+__attribute__ (( noinline )) int64_t s64div_var ( int64_t dividend,
+						  int64_t divisor ) {
+	return ( dividend / divisor );
+}
+
+/**
+ * Force a use of runtime 64-bit unsigned integer modulus
+ *
+ * @v dividend		Dividend
+ * @v divisor		Divisor
+ * @ret remainder	Remainder
+ */
+__attribute__ (( noinline )) int64_t s64mod_var ( int64_t dividend,
+						  int64_t divisor ) {
+	return ( dividend % divisor );
+}
+
 /**
  * Report a flsl() test result
  *
@@ -62,6 +110,60 @@ 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 64-bit unsigned integer division test result
+ *
+ * @v dividend		Dividend
+ * @v divisor		Divisor
+ * @v quotient		Quotient
+ * @v remainder		Remainder
+ * @v file		Test code file
+ * @v line		Test code line
+ */
+static void u64divmod_okx ( uint64_t dividend, uint64_t divisor,
+			    uint64_t quotient, uint64_t remainder,
+			    const char *file, unsigned int line ) {
+
+	/* Sanity check */
+	okx ( ( ( divisor * quotient ) + remainder ) == dividend, file, line );
+
+	/* Check division */
+	okx ( u64div_var ( dividend, divisor ) == quotient, file, line );
+
+	/* Check modulus */
+	okx ( u64mod_var ( dividend, divisor ) == remainder, file, line );
+}
+#define u64divmod_ok( dividend, divisor, quotient, remainder )	\
+	u64divmod_okx ( dividend, divisor, quotient, remainder,	\
+			__FILE__, __LINE__ )
+
+/**
+ * Report a 64-bit signed integer division test result
+ *
+ * @v dividend		Dividend
+ * @v divisor		Divisor
+ * @v quotient		Quotient
+ * @v remainder		Remainder
+ * @v file		Test code file
+ * @v line		Test code line
+ */
+static void s64divmod_okx ( int64_t dividend, int64_t divisor,
+			    int64_t quotient, int64_t remainder,
+			    const char *file, unsigned int line ) {
+
+	/* Sanity check */
+	okx ( ( ( divisor * quotient ) + remainder ) == dividend, file, line );
+
+	/* Check division */
+	okx ( s64div_var ( dividend, divisor ) == quotient, file, line );
+
+	/* Check modulus */
+	okx ( s64mod_var ( dividend, divisor ) == remainder, file, line );
+}
+#define s64divmod_ok( dividend, divisor, quotient, remainder )	\
+	s64divmod_okx ( dividend, divisor, quotient, remainder,	\
+			__FILE__, __LINE__ )
+
 /**
  * Perform mathematical self-tests
  *
@@ -77,6 +179,26 @@ static void math_test_exec ( void ) {
 	flsl_ok ( 0x69505845, 31 );
 	flsl_ok ( -1U, ( 8 * sizeof ( int ) ) );
 	flsl_ok ( -1UL, ( 8 * sizeof ( long ) ) );
+
+	/* Test 64-bit arithmetic
+	 *
+	 * On a 64-bit machine, these tests are fairly meaningless.
+	 *
+	 * On a 32-bit machine, these tests verify the correct
+	 * operation of our libgcc functions __udivmoddi4()
+	 * etc. (including checking that the implicit calling
+	 * convention assumed by gcc matches our expectations).
+	 */
+	u64divmod_ok ( 0x2b90ddccf699f765ULL, 0xed9f5e73ULL,
+		       0x2eef6ab4ULL, 0x0e12f089ULL );
+	s64divmod_ok ( 0x2b90ddccf699f765ULL, 0xed9f5e73ULL,
+		       0x2eef6ab4ULL, 0x0e12f089ULL );
+	u64divmod_ok ( 0xc09e00dcb9e34b54ULL, 0x35968185cdc744f3ULL,
+		       3, 0x1fda7c4b508d7c7bULL );
+	s64divmod_ok ( -0x3f61ff23461cb4acLL, 0x35968185cdc744f3ULL,
+		       -1LL, -0x9cb7d9d78556fb9LL );
+	u64divmod_ok ( 0, 0x5b2f2737f4ffULL, 0, 0 );
+	s64divmod_ok ( 0, 0xbb00ded72766207fULL, 0, 0 );
 }
 
 /** Mathematical self-tests */