[PATCH v3 06/10] fs/namei.c: Improve dcache hash function
From: George Spelvin
Date: Sat May 28 2016  15:59:20 EST
Patch 0fed3ac866 improved the hash mixing, but the function is slower
than necessary; there's a 7instruction dependency chain (10 on x86)
each loop iteration.
Wordatatime 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) Barring expensive ops like 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 2operand machine like x86, it's three
instructions.
3) A better use of a second register is to hold a twoword 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 2operand machines, so the code is smaller and faster.
4) Using two words of state weakens the requirement for oneround mixing;
we now have two rounds of mixing before cancellation is possible.
5) A twoword 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 multiply by 9 can be done by an "lea" instruction):
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 allzero to allzero.)
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 bestscoring 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 32bit hash value by a less carefully
optimized multiplybased 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.)
Special thanks to Bruce fields for diligent testing which uncovered a
nasty fencepost error in an earlier version of this patch.
[checkpatch.pl formatting complaints noted and respectfully disagreed with.]
Signedoffby: George Spelvin <linux@xxxxxxxxxxxxxxxxxxx>
Testedby: J. Bruce Fields <bfields@xxxxxxxxxx>

fs/namei.c  121 +++++++++++++++++++++++++++++++++++++++++
1 file changed, 81 insertions(+), 40 deletions()
diff git a/fs/namei.c b/fs/namei.c
index dd98d43a..a49cbd7e 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"
@@ 1788,44 +1789,89 @@ static int walk_component(struct nameidata *nd, int flags)
#include <asm/wordatatime.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 32bit 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 onebit input
+ * deltas or 64*63/2 = 2016 twobit 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: 1bit 2bit
+ * 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 maximumperiod 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 32bit 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 /* 32bit case */
#define fold_hash(x) (x)
+/*
+ * Mixing scores (in bits) for (7,20):
+ * Input delta: 1bit 2bit
+ * 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 archoptimized multiply if one exists */
+ return __hash_32(y ^ __hash_32(x));
}
#endif
/* Return the hash of a string of known length */
+/*
+ * Return the hash of a string of known length. This is carfully
+ * designed to match hash_name(), which is the more critical function.
+ * In particular, we must end by hashing a final word containing 0..7
+ * payload bytes, to match the way that hash_name() iterates until it
+ * finds the delimiter after the name.
+ */
unsigned int full_name_hash(const char *name, unsigned int len)
{
 unsigned long a, hash = 0;
+ unsigned long a, x = 0, y = 0;
for (;;) {
if (!len)
@@ 1833,36 +1879,34 @@ unsigned int full_name_hash(const char *name, unsigned int len)
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);
}
 hash += a & bytemask_from_count(len);
+ x ^= 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 nullterminated string */
u64 hashlen_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);
+ x ^= a & zero_bytemask(mask);
 return hashlen_create(fold_hash(hash), len);
+ return hashlen_create(fold_hash(x, y), len + find_zero(mask));
}
EXPORT_SYMBOL(hashlen_string);
@@ 1872,13 +1916,12 @@ EXPORT_SYMBOL(hashlen_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('/');
@@ 1886,15 +1929,13 @@ static inline u64 hash_name(const char *name)
adata = prep_zero_mask(a, adata, &constants);
bdata = prep_zero_mask(b, bdata, &constants);

mask = create_zero_mask(adata  bdata);
+ x ^= a & zero_bytemask(mask);
 hash += a & zero_bytemask(mask);
 len += find_zero(mask);
 return hashlen_create(fold_hash(hash), len);
+ return hashlen_create(fold_hash(x, y), len + find_zero(mask));
}
#else
+#else /* !CONFIG_DCACHE_WORD_ACCESS: Slow, byteatatime version */
/* Return the hash of a string of known length */
unsigned int full_name_hash(const char *name, unsigned int len)
@@ 1965,7 +2006,7 @@ static int link_path_walk(const char *name, struct nameidata *nd)
int type;
err = may_lookup(nd);
 if (err)
+ if (err)
return err;
hash_len = hash_name(name);

2.8.1