### fs/namei.c: Improve dcache hash function

Patch 0fed3ac8 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) 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 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 requirement 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 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 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.) 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.] Signed-off-by: George Spelvin <linux@sciencehorizons.net> Tested-by: J. Bruce Fields <bfields@redhat.com>

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