div64_u64(): improve precision on 32bit platforms

The current implementation of div64_u64 for 32bit systems returns an
approximately correct result when the divisor exceeds 32bits.  Since doing
64bit division using 32bit hardware is a long since solved problem we just
use one of the existing proven methods.

Additionally, add a div64_s64 function to correctly handle doing signed
64bit division.

Addresses https://bugzilla.redhat.com/show_bug.cgi?id=616105

Signed-off-by: Brian Behlendorf <behlendorf1@llnl.gov>
Signed-off-by: Oleg Nesterov <oleg@redhat.com>
Cc: Ben Woodard <bwoodard@llnl.gov>
Cc: Jeremy Fitzhardinge <jeremy@goop.org>
Cc: Mark Grondona <mgrondona@llnl.gov>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>

include/linux/kernel.h

@@ -173,6 +173,11 @@ extern int _cond_resched(void);
 		(__x < 0) ? -__x : __x;		\
 	})
 
+#define abs64(x) ({				\
+		s64 __x = (x);			\
+		(__x < 0) ? -__x : __x;		\
+	})
+
 #ifdef CONFIG_PROVE_LOCKING
 void might_fault(void);
 #else

include/linux/math64.h

@@ -35,6 +35,14 @@ static inline u64 div64_u64(u64 dividend, u64 divisor)
 	return dividend / divisor;
 }
 
+/**
+ * div64_s64 - signed 64bit divide with 64bit divisor
+ */
+static inline s64 div64_s64(s64 dividend, s64 divisor)
+{
+	return dividend / divisor;
+}
+
 #elif BITS_PER_LONG == 32
 
 #ifndef div_u64_rem
@@ -53,6 +61,10 @@ extern s64 div_s64_rem(s64 dividend, s32 divisor, s32 *remainder);
 extern u64 div64_u64(u64 dividend, u64 divisor);
 #endif
 
+#ifndef div64_s64
+extern s64 div64_s64(s64 dividend, s64 divisor);
+#endif
+
 #endif /* BITS_PER_LONG */
 
 /**

lib/div64.c

@@ -77,26 +77,58 @@ s64 div_s64_rem(s64 dividend, s32 divisor, s32 *remainder)
 EXPORT_SYMBOL(div_s64_rem);
 #endif
 
-/* 64bit divisor, dividend and result. dynamic precision */
+/**
+ * div64_u64 - unsigned 64bit divide with 64bit divisor
+ * @dividend:	64bit dividend
+ * @divisor:	64bit divisor
+ *
+ * This implementation is a modified version of the algorithm proposed
+ * by the book 'Hacker's Delight'.  The original source and full proof
+ * can be found here and is available for use without restriction.
+ *
+ * 'http://www.hackersdelight.org/HDcode/newCode/divDouble.c'
+ */
 #ifndef div64_u64
 u64 div64_u64(u64 dividend, u64 divisor)
 {
-	u32 high, d;
+	u32 high = divisor >> 32;
+	u64 quot;
 
-	high = divisor >> 32;
-	if (high) {
-		unsigned int shift = fls(high);
+	if (high == 0) {
+		quot = div_u64(dividend, divisor);
+	} else {
+		int n = 1 + fls(high);
+		quot = div_u64(dividend >> n, divisor >> n);
 
-		d = divisor >> shift;
-		dividend >>= shift;
-	} else
-		d = divisor;
+		if (quot != 0)
+			quot--;
+		if ((dividend - quot * divisor) >= divisor)
+			quot++;
+	}
 
-	return div_u64(dividend, d);
+	return quot;
 }
 EXPORT_SYMBOL(div64_u64);
 #endif
 
+/**
+ * div64_s64 - signed 64bit divide with 64bit divisor
+ * @dividend:	64bit dividend
+ * @divisor:	64bit divisor
+ */
+#ifndef div64_s64
+s64 div64_s64(s64 dividend, s64 divisor)
+{
+	s64 quot, t;
+
+	quot = div64_u64(abs64(dividend), abs64(divisor));
+	t = (dividend ^ divisor) >> 63;
+
+	return (quot ^ t) - t;
+}
+EXPORT_SYMBOL(div64_s64);
+#endif
+
 #endif /* BITS_PER_LONG == 32 */
 
 /*