Message-ID: <20160525073103.5526.qmail@ns.sciencehorizons.net>
Date:	25 May 2016 03:31:03 -0400
From:	"George Spelvin" <linux@...encehorizons.net>
To:	linux-kernel@...r.kernel.org, torvalds@...ux-foundation.org
Cc:	linux@...encehorizons.net, tglx@...utronix.de
Subject: [PATCH 06/10] fs/namei.c: Improve dcache hash function

Patch 0fed3ac866 improved the hash mixing, but the function is slower
than necessary; there's a 7-instruction dependency chain (10 on x86)
each loop iteration.

Word-at-a-time access is a very tight loop (which is good, because
link_path_walk() is one of the hottest code paths in the entire kernel),
and the hash mixing function must not have a longer latency to avoid
slowing it down.

There do not appear to be any published fast hash functions that:
1) Operate on the input a word at a time, and
2) Don't need to know the length of the input beforehand, and
3) Have a single iterated mixing function, not needing conditional
   branches or unrolling to distinguish different loop iterations.

One of the algorithms which comes closest is Yann Collet's xxHash, but
that's two dependent multiplies per word, which is too much.

The key insights in this design are:

1) Except for multiplies, to diffuse one input bit across 64 bits of hash
   state takes at least log2(64) = 6 sequentially dependent instructions.
   That is more cycles than we'd like.
2) An operation like "hash ^= hash << 13" requires a second temporary
   register anyway, and on a 2-operand machine like x86, it's three
   instructions.
3) A better use of a second register is to hold a two-word hash state.
   With careful design, no temporaries are needed at all, so it doesn't
   increase register pressure.  And this gets rid of register copying
   on 2-operand machines, so the code is smaller and faster.
4) Using two words of state weakens the requriement for one-round mixing;
   we now have two rounds of mixing before cancellation is possible.
5) A two-word hash state also allows operations on both halves to be
   done in parallel, so on a superscalar processor we get more mixing
   in fewer cycles.

I ended up using a mixing function inspired by the ChaCha and Speck
round functions.  It is 6 simple instructions and 3 cycles per iteration
(assuming mutliply by 9 can be done by an "lea" isntruction):

		x ^= *input++;
	y ^= x;	x = ROL(x, K1);
	x += y;	y = ROL(y, K2);
	y *= 9;

Not only is this reversible, two consecutive rounds are reversible:
if you are given the initial and final states, but not the intermediate
state, it is possible to compute both input words.  This means that at
least 3 words of input are required to create a collision.

(It also has the property, used by hash_name() to avoid a branch, that
it hashes all-zero to all-zero.)

The rotate constants K1 and K2 were found by experiment.  The search took
a sample of random initial states (I used 1023) and considered the effect
of flipping each of the 64 input bits on each of the 128 output bits two
rounds later.  Each of the 8192 pairs can be considered a biased coin, and
adding up the Shannon entropy of all of them produces a score.

The best-scoring shifts also did well in other tests (flipping bits in y,
trying 3 or 4 rounds of mixing, flipping all 64*63/2 pairs of input bits),
so the choice was made with the additional constraint that the sum of the
shifts is odd and not too close to the word size.

The final state is then folded into a 32-bit hash value by a less carefully
optimized multiply-based scheme.  This also has to be fast, as pathname
components tend to be short (the most common case is one iteration!), but
there's some room for latency, as there is a fair bit of intervening logic
before the hash value is used for anything.

(Performance verified with "bonnie++ -s 0 -n 1536:-2" on tmpfs.  I need
a better benchmark; the numbers seem to show a slight dip in performance
between 4.6.0 and this patch, but they're too noisy to quote.)

Signed-off-by: George Spelvin <linux@...encehorizons.net>
---
 fs/namei.c | 110 ++++++++++++++++++++++++++++++++++++++++---------------------
 1 file changed, 73 insertions(+), 37 deletions(-)

diff --git a/fs/namei.c b/fs/namei.c
index ce640d65..2b8d0650 100644
--- a/fs/namei.c
+++ b/fs/namei.c
@@ -35,6 +35,7 @@
 #include <linux/fs_struct.h>
 #include <linux/posix_acl.h>
 #include <linux/hash.h>
+#include <linux/bitops.h>
 #include <asm/uaccess.h>
 
 #include "internal.h"
@@ -1788,36 +1789,75 @@ static int walk_component(struct nameidata *nd, int flags)
 #include <asm/word-at-a-time.h>
 
 #ifdef CONFIG_64BIT
-
-static inline unsigned int fold_hash(unsigned long hash)
-{
-	return hash_64(hash, 32);
-}
+/*
+ * Register pressure in the mixing function is an issue, particularly
+ * on 32-bit x86, but almost any function requires one state value and
+ * one temporary.  Instead, use a function designed for two state values
+ * and no temporaries.
+ *
+ * This function cannot create a collision in only two iterations, so
+ * we have two iterations to achieve avalanche.  In those two iterations,
+ * we have six layers of mixing, which is enough to spread one bit's
+ * influence out to 2^6 = 64 state bits.
+ *
+ * Rotate constants are scored by considering either 64 one-bit input
+ * deltas or 64*63/2 = 2016 two-bit input deltas, and finding the
+ * probability of that delta causing a change to each of the 128 output
+ * bits, using a sample of random initial states.
+ *
+ * The Shannon entropy of the computed probabilities is then summed
+ * to produce a score.  Ideally, any input change has a 50% chance of
+ * toggling any given output bit.
+ *
+ * Mixing scores (in bits) for (12,45):
+ * Input delta: 1-bit      2-bit
+ * 1 round:     713.3    42542.6
+ * 2 rounds:   2753.7   140389.8
+ * 3 rounds:   5954.1   233458.2
+ * 4 rounds:   7862.6   256672.2
+ * Perfect:    8192     258048
+ *            (64*128) (64*63/2 * 128)
+ */
+#define HASH_MIX(x, y, a)	\
+	(	x ^= (a),	\
+	y ^= x,	x = rol64(x,12),\
+	x += y,	y = rol64(y,45),\
+	y *= 9			)
 
 /*
- * This is George Marsaglia's XORSHIFT generator.
- * It implements a maximum-period LFSR in only a few
- * instructions.  It also has the property (required
- * by hash_name()) that mix_hash(0) = 0.
+ * Fold two longs into one 32-bit hash value.  This must be fast, but
+ * latency isn't quite as critical, as there is a fair bit of additional
+ * work done before the hash value is used.
  */
-static inline unsigned long mix_hash(unsigned long hash)
+static inline unsigned int fold_hash(unsigned long x, unsigned long y)
 {
-	hash ^= hash << 13;
-	hash ^= hash >> 7;
-	hash ^= hash << 17;
-	return hash;
+	y ^= x * GOLDEN_RATIO_64;
+	y *= GOLDEN_RATIO_64;
+	return y >> 32;
 }
 
 #else	/* 32-bit case */
 
-#define fold_hash(x) (x)
+/*
+ * Mixing scores (in bits) for (7,20):
+ * Input delta: 1-bit      2-bit
+ * 1 round:     330.3     9201.6
+ * 2 rounds:   1246.4    25475.4
+ * 3 rounds:   1907.1    31295.1
+ * 4 rounds:   2042.3    31718.6
+ * Perfect:    2048      31744
+ *            (32*64)   (32*31/2 * 64)
+ */
+#define HASH_MIX(x, y, a)	\
+	(	x ^= (a),	\
+	y ^= x,	x = rol32(x, 7),\
+	x += y,	y = rol32(y,20),\
+	y *= 9			)
 
-static inline unsigned long mix_hash(unsigned long hash)
+static inline unsigned int fold_hash(unsigned long x, unsigned long y)
 {
-	hash ^= hash << 13;
-	hash ^= hash >> 17;
-	hash ^= hash << 5;
-	return hash;
+	/* Use arch-optimized multiply if one exists */
+	return __hash32(y ^ __hash32(x));
 }
 
 #endif
@@ -1825,44 +1865,42 @@ static inline unsigned long mix_hash(unsigned long hash)
 /* Return the hash of a string of known length */
 unsigned int full_name_hash(const char *name, unsigned int len)
 {
-	unsigned long a, hash = 0;
+	unsigned long a, x = 0, y = 0;
 
 	for (;;) {
 		a = load_unaligned_zeropad(name);
 		if (len < sizeof(unsigned long))
 			break;
-		hash = mix_hash(hash + a);
+		HASH_MIX(x, y, a);
 		name += sizeof(unsigned long);
 		len -= sizeof(unsigned long);
 		if (!len)
 			goto done;
 	}
-	hash += a & bytemask_from_count(len);
+	HASH_MIX(x, y, a & bytemask_from_count(len));
 done:
-	return fold_hash(hash);
+	return fold_hash(x, y);
 }
 EXPORT_SYMBOL(full_name_hash);
 
 /* Return the "hash_len" (hash and length) of a null-terminated string */
 u64 hash_string(const char *name)
 {
-	unsigned long a, adata, mask, hash, len;
+	unsigned long a = 0, x = 0, y = 0, adata, mask, len;
 	const struct word_at_a_time constants = WORD_AT_A_TIME_CONSTANTS;
 
-	hash = a = 0;
 	len = -sizeof(unsigned long);
 	do {
-		hash = mix_hash(hash + a);
+		HASH_MIX(x, y, a);
 		len += sizeof(unsigned long);
 		a = load_unaligned_zeropad(name+len);
 	} while (!has_zero(a, &adata, &constants));
 
 	adata = prep_zero_mask(a, adata, &constants);
 	mask = create_zero_mask(adata);
-	hash += a & zero_bytemask(mask);
-	len += find_zero(mask);
+	HASH_MIX(x, y, a & zero_bytemask(mask));
 
-	return hashlen_create(fold_hash(hash), len);
+	return hashlen_create(fold_hash(x, y), len + find_zero(mask));
 }
 EXPORT_SYMBOL(hash_string);
 
@@ -1872,13 +1910,12 @@ EXPORT_SYMBOL(hash_string);
  */
 static inline u64 hash_name(const char *name)
 {
-	unsigned long a, b, adata, bdata, mask, hash, len;
+	unsigned long a = 0, b, x = 0, y = 0, adata, bdata, mask, len;
 	const struct word_at_a_time constants = WORD_AT_A_TIME_CONSTANTS;
 
-	hash = a = 0;
 	len = -sizeof(unsigned long);
 	do {
-		hash = mix_hash(hash + a);
+		HASH_MIX(x, y, a);
 		len += sizeof(unsigned long);
 		a = load_unaligned_zeropad(name+len);
 		b = a ^ REPEAT_BYTE('/');
@@ -1889,12 +1926,11 @@ static inline u64 hash_name(const char *name)
 
 	mask = create_zero_mask(adata | bdata);
 
-	hash += a & zero_bytemask(mask);
-	len += find_zero(mask);
-	return hashlen_create(fold_hash(hash), len);
+	HASH_MIX(x, y, a & zero_bytemask(mask));
+	return hashlen_create(fold_hash(x, y), len + find_zero(mask));
 }
 
-#else
+#else	/* !CONFIG_DCACHE_WORD_ACCESS: Slow, byte-at-a-time version */
 
 /* Return the hash of a string of known length */
 unsigned int full_name_hash(const char *name, unsigned int len)
-- 
2.8.1

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