[PATCH 3.16 068/114] Minimal fix-up of bad hashing behavior of hash_64()

[Ben Hutchings]

3.16.36-rc1 review patch.  If anyone has any objections, please let me know.

------------------

From: Linus Torvalds <torvalds@xxxxxxxxxxxxxxxxxxxx>

commit 689de1d6ca95b3b5bd8ee446863bf81a4883ea25 upstream.

This is a fairly minimal fixup to the horribly bad behavior of hash_64()
with certain input patterns.

In particular, because the multiplicative value used for the 64-bit hash
was intentionally bit-sparse (so that the multiply could be done with
shifts and adds on architectures without hardware multipliers), some
bits did not get spread out very much.  In particular, certain fairly
common bit ranges in the input (roughly bits 12-20: commonly with the
most information in them when you hash things like byte offsets in files
or memory that have block factors that mean that the low bits are often
zero) would not necessarily show up much in the result.

There's a bigger patch-series brewing to fix up things more completely,
but this is the fairly minimal fix for the 64-bit hashing problem.  It
simply picks a much better constant multiplier, spreading the bits out a
lot better.

NOTE! For 32-bit architectures, the bad old hash_64() remains the same
for now, since 64-bit multiplies are expensive.  The bigger hashing
cleanup will replace the 32-bit case with something better.

The new constants were picked by George Spelvin who wrote that bigger
cleanup series.  I just picked out the constants and part of the comment
from that series.

Cc: George Spelvin <linux@xxxxxxxxxxx>
Cc: Thomas Gleixner <tglx@xxxxxxxxxxxxx>
Signed-off-by: Linus Torvalds <torvalds@xxxxxxxxxxxxxxxxxxxx>
Signed-off-by: Ben Hutchings <ben@xxxxxxxxxxxxxxx>
---
 include/linux/hash.h | 20 ++++++++++++++++++--
 1 file changed, 18 insertions(+), 2 deletions(-)

--- a/include/linux/hash.h
+++ b/include/linux/hash.h
@@ -33,12 +33,28 @@
 #error Wordsize not 32 or 64
 #endif
 
+/*
+ * The above primes are actively bad for hashing, since they are
+ * too sparse. The 32-bit one is mostly ok, the 64-bit one causes
+ * real problems. Besides, the "prime" part is pointless for the
+ * multiplicative hash.
+ *
+ * Although a random odd number will do, it turns out that the golden
+ * ratio phi = (sqrt(5)-1)/2, or its negative, has particularly nice
+ * properties.
+ *
+ * These are the negative, (1 - phi) = (phi^2) = (3 - sqrt(5))/2.
+ * (See Knuth vol 3, section 6.4, exercise 9.)
+ */
+#define GOLDEN_RATIO_32 0x61C88647
+#define GOLDEN_RATIO_64 0x61C8864680B583EBull
+
 static __always_inline u64 hash_64(u64 val, unsigned int bits)
 {
 	u64 hash = val;
 
-#if defined(CONFIG_ARCH_HAS_FAST_MULTIPLIER) && BITS_PER_LONG == 64
-	hash = hash * GOLDEN_RATIO_PRIME_64;
+#if BITS_PER_LONG == 64
+	hash = hash * GOLDEN_RATIO_64;
 #else
 	/*  Sigh, gcc can't optimise this alone like it does for 32 bits. */
 	u64 n = hash;