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// Copyright (c) 2011 Google, Inc.
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// Permission is hereby granted, free of charge, to any person obtaining a copy
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// of this software and associated documentation files (the "Software"), to deal
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// in the Software without restriction, including without limitation the rights
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// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the Software is
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// furnished to do so, subject to the following conditions:
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// The above copyright notice and this permission notice shall be included in
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// all copies or substantial portions of the Software.
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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// CityHash, by Geoff Pike and Jyrki Alakuijala
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// This file provides CityHash64() and related functions.
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// It's probably possible to create even faster hash functions by
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// writing a program that systematically explores some of the space of
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// possible hash functions, by using SIMD instructions, or by
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// compromising on hash quality.
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#include <string.h> // for memcpy and memset
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static uint64 UNALIGNED_LOAD64(const char *p) {
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memcpy(&result, p, sizeof(result));
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static uint32 UNALIGNED_LOAD32(const char *p) {
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memcpy(&result, p, sizeof(result));
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#if !defined(WORDS_BIGENDIAN)
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#define uint32_in_expected_order(x) (x)
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#define uint64_in_expected_order(x) (x)
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#define bswap_32(x) _byteswap_ulong(x)
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#define bswap_64(x) _byteswap_uint64(x)
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#elif defined(__APPLE__)
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// Mac OS X / Darwin features
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#include <libkern/OSByteOrder.h>
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#define bswap_32(x) OSSwapInt32(x)
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#define bswap_64(x) OSSwapInt64(x)
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#define uint32_in_expected_order(x) (bswap_32(x))
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#define uint64_in_expected_order(x) (bswap_64(x))
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#endif // WORDS_BIGENDIAN
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#if HAVE_BUILTIN_EXPECT
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#define LIKELY(x) (__builtin_expect(!!(x), 1))
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static uint64 Fetch64(const char *p) {
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return uint64_in_expected_order(UNALIGNED_LOAD64(p));
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static uint32 Fetch32(const char *p) {
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return uint32_in_expected_order(UNALIGNED_LOAD32(p));
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// Some primes between 2^63 and 2^64 for various uses.
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static const uint64 k0 = 0xc3a5c85c97cb3127ULL;
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static const uint64 k1 = 0xb492b66fbe98f273ULL;
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static const uint64 k2 = 0x9ae16a3b2f90404fULL;
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static const uint64 k3 = 0xc949d7c7509e6557ULL;
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// Bitwise right rotate. Normally this will compile to a single
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// instruction, especially if the shift is a manifest constant.
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static uint64 Rotate(uint64 val, int shift) {
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// Avoid shifting by 64: doing so yields an undefined result.
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return shift == 0 ? val : ((val >> shift) | (val << (64 - shift)));
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// Equivalent to Rotate(), but requires the second arg to be non-zero.
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// On x86-64, and probably others, it's possible for this to compile
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// to a single instruction if both args are already in registers.
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static uint64 RotateByAtLeast1(uint64 val, int shift) {
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return (val >> shift) | (val << (64 - shift));
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static uint64 ShiftMix(uint64 val) {
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return val ^ (val >> 47);
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static uint64 HashLen16(uint64 u, uint64 v) {
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return Hash128to64(uint128(u, v));
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static uint64 HashLen0to16(const char *s, size_t len) {
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uint64 a = Fetch64(s);
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uint64 b = Fetch64(s + len - 8);
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return HashLen16(a, RotateByAtLeast1(b + len, len)) ^ b;
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uint64 a = Fetch32(s);
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return HashLen16(len + (a << 3), Fetch32(s + len - 4));
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uint8 b = s[len >> 1];
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uint8 c = s[len - 1];
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uint32 y = static_cast<uint32>(a) + (static_cast<uint32>(b) << 8);
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uint32 z = len + (static_cast<uint32>(c) << 2);
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return ShiftMix(y * k2 ^ z * k3) * k2;
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// This probably works well for 16-byte strings as well, but it may be overkill
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static uint64 HashLen17to32(const char *s, size_t len) {
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uint64 a = Fetch64(s) * k1;
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uint64 b = Fetch64(s + 8);
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uint64 c = Fetch64(s + len - 8) * k2;
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uint64 d = Fetch64(s + len - 16) * k0;
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return HashLen16(Rotate(a - b, 43) + Rotate(c, 30) + d,
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a + Rotate(b ^ k3, 20) - c + len);
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// Return a 16-byte hash for 48 bytes. Quick and dirty.
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// Callers do best to use "random-looking" values for a and b.
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static pair<uint64, uint64> WeakHashLen32WithSeeds(
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uint64 w, uint64 x, uint64 y, uint64 z, uint64 a, uint64 b) {
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b = Rotate(b + a + z, 21);
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return make_pair(a + z, b + c);
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// Return a 16-byte hash for s[0] ... s[31], a, and b. Quick and dirty.
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static pair<uint64, uint64> WeakHashLen32WithSeeds(
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const char* s, uint64 a, uint64 b) {
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return WeakHashLen32WithSeeds(Fetch64(s),
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// Return an 8-byte hash for 33 to 64 bytes.
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static uint64 HashLen33to64(const char *s, size_t len) {
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uint64 z = Fetch64(s + 24);
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uint64 a = Fetch64(s) + (len + Fetch64(s + len - 16)) * k0;
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uint64 b = Rotate(a + z, 52);
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uint64 c = Rotate(a, 37);
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a += Fetch64(s + 16);
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uint64 vs = b + Rotate(a, 31) + c;
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a = Fetch64(s + 16) + Fetch64(s + len - 32);
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z = Fetch64(s + len - 8);
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b = Rotate(a + z, 52);
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a += Fetch64(s + len - 24);
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a += Fetch64(s + len - 16);
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uint64 ws = b + Rotate(a, 31) + c;
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uint64 r = ShiftMix((vf + ws) * k2 + (wf + vs) * k0);
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return ShiftMix(r * k0 + vs) * k2;
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uint64 CityHash64(const char *s, size_t len) {
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return HashLen0to16(s, len);
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return HashLen17to32(s, len);
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} else if (len <= 64) {
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return HashLen33to64(s, len);
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// For strings over 64 bytes we hash the end first, and then as we
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// loop we keep 56 bytes of state: v, w, x, y, and z.
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uint64 x = Fetch64(s + len - 40);
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uint64 y = Fetch64(s + len - 16) + Fetch64(s + len - 56);
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uint64 z = HashLen16(Fetch64(s + len - 48) + len, Fetch64(s + len - 24));
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pair<uint64, uint64> v = WeakHashLen32WithSeeds(s + len - 64, len, z);
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pair<uint64, uint64> w = WeakHashLen32WithSeeds(s + len - 32, y + k1, x);
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x = x * k1 + Fetch64(s);
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// Decrease len to the nearest multiple of 64, and operate on 64-byte chunks.
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len = (len - 1) & ~static_cast<size_t>(63);
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x = Rotate(x + y + v.first + Fetch64(s + 8), 37) * k1;
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y = Rotate(y + v.second + Fetch64(s + 48), 42) * k1;
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y += v.first + Fetch64(s + 40);
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z = Rotate(z + w.first, 33) * k1;
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v = WeakHashLen32WithSeeds(s, v.second * k1, x + w.first);
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w = WeakHashLen32WithSeeds(s + 32, z + w.second, y + Fetch64(s + 16));
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return HashLen16(HashLen16(v.first, w.first) + ShiftMix(y) * k1 + z,
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HashLen16(v.second, w.second) + x);
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uint64 CityHash64WithSeed(const char *s, size_t len, uint64 seed) {
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return CityHash64WithSeeds(s, len, k2, seed);
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uint64 CityHash64WithSeeds(const char *s, size_t len,
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uint64 seed0, uint64 seed1) {
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return HashLen16(CityHash64(s, len) - seed0, seed1);
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// A subroutine for CityHash128(). Returns a decent 128-bit hash for strings
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// of any length representable in signed long. Based on City and Murmur.
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static uint128 CityMurmur(const char *s, size_t len, uint128 seed) {
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uint64 a = Uint128Low64(seed);
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uint64 b = Uint128High64(seed);
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signed long l = len - 16;
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if (l <= 0) { // len <= 16
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a = ShiftMix(a * k1) * k1;
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c = b * k1 + HashLen0to16(s, len);
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d = ShiftMix(a + (len >= 8 ? Fetch64(s) : c));
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c = HashLen16(Fetch64(s + len - 8) + k1, a);
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d = HashLen16(b + len, c + Fetch64(s + len - 16));
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a ^= ShiftMix(Fetch64(s) * k1) * k1;
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c ^= ShiftMix(Fetch64(s + 8) * k1) * k1;
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return uint128(a ^ b, HashLen16(b, a));
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uint128 CityHash128WithSeed(const char *s, size_t len, uint128 seed) {
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return CityMurmur(s, len, seed);
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// We expect len >= 128 to be the common case. Keep 56 bytes of state:
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// v, w, x, y, and z.
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pair<uint64, uint64> v, w;
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uint64 x = Uint128Low64(seed);
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uint64 y = Uint128High64(seed);
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v.first = Rotate(y ^ k1, 49) * k1 + Fetch64(s);
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v.second = Rotate(v.first, 42) * k1 + Fetch64(s + 8);
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w.first = Rotate(y + z, 35) * k1 + x;
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w.second = Rotate(x + Fetch64(s + 88), 53) * k1;
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// This is the same inner loop as CityHash64(), manually unrolled.
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x = Rotate(x + y + v.first + Fetch64(s + 8), 37) * k1;
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y = Rotate(y + v.second + Fetch64(s + 48), 42) * k1;
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y += v.first + Fetch64(s + 40);
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z = Rotate(z + w.first, 33) * k1;
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v = WeakHashLen32WithSeeds(s, v.second * k1, x + w.first);
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w = WeakHashLen32WithSeeds(s + 32, z + w.second, y + Fetch64(s + 16));
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x = Rotate(x + y + v.first + Fetch64(s + 8), 37) * k1;
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y = Rotate(y + v.second + Fetch64(s + 48), 42) * k1;
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y += v.first + Fetch64(s + 40);
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z = Rotate(z + w.first, 33) * k1;
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v = WeakHashLen32WithSeeds(s, v.second * k1, x + w.first);
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w = WeakHashLen32WithSeeds(s + 32, z + w.second, y + Fetch64(s + 16));
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} while (LIKELY(len >= 128));
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x += Rotate(v.first + z, 49) * k0;
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z += Rotate(w.first, 37) * k0;
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// If 0 < len < 128, hash up to 4 chunks of 32 bytes each from the end of s.
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for (size_t tail_done = 0; tail_done < len; ) {
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y = Rotate(x + y, 42) * k0 + v.second;
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w.first += Fetch64(s + len - tail_done + 16);
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x = x * k0 + w.first;
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z += w.second + Fetch64(s + len - tail_done);
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v = WeakHashLen32WithSeeds(s + len - tail_done, v.first + z, v.second);
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// At this point our 56 bytes of state should contain more than
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// enough information for a strong 128-bit hash. We use two
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// different 56-byte-to-8-byte hashes to get a 16-byte final result.
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x = HashLen16(x, v.first);
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y = HashLen16(y + z, w.first);
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return uint128(HashLen16(x + v.second, w.second) + y,
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HashLen16(x + w.second, y + v.second));
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uint128 CityHash128(const char *s, size_t len) {
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return CityHash128WithSeed(s + 16,
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uint128(Fetch64(s) ^ k3,
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} else if (len >= 8) {
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return CityHash128WithSeed(NULL,
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uint128(Fetch64(s) ^ (len * k0),
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Fetch64(s + len - 8) ^ k1));
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return CityHash128WithSeed(s, len, uint128(k0, k1));
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#if 0 // #ifdef __SSE4_2__
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#include <nmmintrin.h>
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// Requires len >= 240.
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static void CityHashCrc256Long(const char *s, size_t len,
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uint32 seed, uint64 *result) {
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uint64 a = Fetch64(s + 56) + k0;
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uint64 b = Fetch64(s + 96) + k0;
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uint64 c = result[0] = HashLen16(b, len);
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uint64 d = result[1] = Fetch64(s + 120) * k0 + len;
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uint64 e = Fetch64(s + 184) + seed;
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// 240 bytes of input per iter.
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size_t iters = len / 240;
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#define CHUNK(multiplier, z) \
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a = Rotate(b, 41 ^ z) * multiplier + Fetch64(s); \
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b = Rotate(c, 27 ^ z) * multiplier + Fetch64(s + 8); \
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c = Rotate(d, 41 ^ z) * multiplier + Fetch64(s + 16); \
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d = Rotate(e, 33 ^ z) * multiplier + Fetch64(s + 24); \
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e = Rotate(t, 25 ^ z) * multiplier + Fetch64(s + 32); \
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f = _mm_crc32_u64(f, a); \
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g = _mm_crc32_u64(g, b); \
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h = _mm_crc32_u64(h, c); \
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i = _mm_crc32_u64(i, d); \
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j = _mm_crc32_u64(j, e); \
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CHUNK(1, 1); CHUNK(k0, 0);
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CHUNK(1, 1); CHUNK(k0, 0);
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CHUNK(1, 1); CHUNK(k0, 0);
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} while (--iters > 0);
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c = HashLen16(c, f) + i;
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d = HashLen16(d, e + result[0]);
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i += HashLen16(h, t);
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e = HashLen16(a, d) + j;
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f = HashLen16(b, c) + a;
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g = HashLen16(j, i) + c;
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result[0] = e + f + g + h;
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a = ShiftMix((a + g) * k0) * k0 + b;
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result[1] += a + result[0];
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a = ShiftMix(a * k0) * k0 + c;
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result[2] = a + result[1];
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a = ShiftMix((a + e) * k0) * k0;
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result[3] = a + result[2];
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// Requires len < 240.
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static void CityHashCrc256Short(const char *s, size_t len, uint64 *result) {
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memset(buf + len, 0, 240 - len);
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CityHashCrc256Long(buf, 240, ~static_cast<uint32>(len), result);
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void CityHashCrc256(const char *s, size_t len, uint64 *result) {
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if (LIKELY(len >= 240)) {
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CityHashCrc256Long(s, len, 0, result);
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CityHashCrc256Short(s, len, result);
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uint128 CityHashCrc128WithSeed(const char *s, size_t len, uint128 seed) {
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return CityHash128WithSeed(s, len, seed);
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CityHashCrc256(s, len, result);
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uint64 u = Uint128High64(seed) + result[0];
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uint64 v = Uint128Low64(seed) + result[1];
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return uint128(HashLen16(u, v + result[2]),
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HashLen16(Rotate(v, 32), u * k0 + result[3]));
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uint128 CityHashCrc128(const char *s, size_t len) {
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return CityHash128(s, len);
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CityHashCrc256(s, len, result);
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return uint128(result[2], result[3]);