Optimize `absl::Hash` by making `LowLevelHash` faster.

Throughput of the 64 byte chunk loop inside `LowLevelHash` (or now in `LowLevelHashLenGt16`) gets limited by the loop carried dependency on `current_state`. By using 4 states instead of 2, we can reduce this duration by 1 cycle. On Skylake, it is reduced from 9 cycles to 8 cycles (12.5% faster asymptotically).

To see the reduction in a simplified version of `LowLevelHash` implementation on Skylake:
* Before: https://godbolt.org/z/Tcj9vsGax, llvm-mca (https://godbolt.org/z/3o78Msr63) shows 9 cycles / iteration.
* After: https://godbolt.org/z/q4GM4EjPr, llvm-mca (https://godbolt.org/z/W5d1KEMzq) shows 8 cycles / iteration.
* This CL is removing 1 xor (1 cycle) per iteration from the critical path.

A block for 32 byte chunk is also added.

Finally, just before returning, `Mix` is called 1 time instead of twice.

PiperOrigin-RevId: 605090653
Change-Id: Ib7517ebb8bef7484066cd14cf41a943953e93377

4 files changed, 154 insertions, 116 deletions

diff --git a/absl/hash/internal/hash.cc b/absl/hash/internal/hash.cc
index 11451e57..93906ef8 100644
--- a/absl/hash/internal/hash.cc
+++ b/absl/hash/internal/hash.cc
@@ -61,7 +61,7 @@ constexpr uint64_t kHashSalt[5] = {
 
 uint64_t MixingHashState::LowLevelHashImpl(const unsigned char* data,
                                            size_t len) {
-  return LowLevelHash(data, len, Seed(), kHashSalt);
+  return LowLevelHashLenGt16(data, len, Seed(), kHashSalt);
 }
 
 }  // namespace hash_internal
diff --git a/absl/hash/internal/low_level_hash.cc b/absl/hash/internal/low_level_hash.cc
index b5db0b89..43de6729 100644
--- a/absl/hash/internal/low_level_hash.cc
+++ b/absl/hash/internal/low_level_hash.cc
@@ -14,6 +14,9 @@
 
 #include "absl/hash/internal/low_level_hash.h"
 
+#include <cstddef>
+#include <cstdint>
+
 #include "absl/base/internal/unaligned_access.h"
 #include "absl/base/prefetch.h"
 #include "absl/numeric/int128.h"
@@ -28,8 +31,8 @@ static uint64_t Mix(uint64_t v0, uint64_t v1) {
   return absl::Uint128Low64(p) ^ absl::Uint128High64(p);
 }
 
-uint64_t LowLevelHash(const void* data, size_t len, uint64_t seed,
-                      const uint64_t salt[5]) {
+uint64_t LowLevelHashLenGt16(const void* data, size_t len, uint64_t seed,
+                             const uint64_t salt[5]) {
   // Prefetch the cacheline that data resides in.
   PrefetchToLocalCache(data);
   const uint8_t* ptr = static_cast<const uint8_t*>(data);
@@ -40,7 +43,9 @@ uint64_t LowLevelHash(const void* data, size_t len, uint64_t seed,
     // If we have more than 64 bytes, we're going to handle chunks of 64
     // bytes at a time. We're going to build up two separate hash states
     // which we will then hash together.
-    uint64_t duplicated_state = current_state;
+    uint64_t duplicated_state0 = current_state;
+    uint64_t duplicated_state1 = current_state;
+    uint64_t duplicated_state2 = current_state;
 
     do {
       // Always prefetch the next cacheline.
@@ -55,24 +60,39 @@ uint64_t LowLevelHash(const void* data, size_t len, uint64_t seed,
       uint64_t g = absl::base_internal::UnalignedLoad64(ptr + 48);
       uint64_t h = absl::base_internal::UnalignedLoad64(ptr + 56);
 
-      uint64_t cs0 = Mix(a ^ salt[1], b ^ current_state);
-      uint64_t cs1 = Mix(c ^ salt[2], d ^ current_state);
-      current_state = (cs0 ^ cs1);
+      current_state = Mix(a ^ salt[1], b ^ current_state);
+      duplicated_state0 = Mix(c ^ salt[2], d ^ duplicated_state0);
 
-      uint64_t ds0 = Mix(e ^ salt[3], f ^ duplicated_state);
-      uint64_t ds1 = Mix(g ^ salt[4], h ^ duplicated_state);
-      duplicated_state = (ds0 ^ ds1);
+      duplicated_state1 = Mix(e ^ salt[3], f ^ duplicated_state1);
+      duplicated_state2 = Mix(g ^ salt[4], h ^ duplicated_state2);
 
       ptr += 64;
       len -= 64;
     } while (len > 64);
 
-    current_state = current_state ^ duplicated_state;
+    current_state = (current_state ^ duplicated_state0) ^
+                    (duplicated_state1 + duplicated_state2);
   }
 
   // We now have a data `ptr` with at most 64 bytes and the current state
   // of the hashing state machine stored in current_state.
-  while (len > 16) {
+  if (len > 32) {
+    uint64_t a = absl::base_internal::UnalignedLoad64(ptr);
+    uint64_t b = absl::base_internal::UnalignedLoad64(ptr + 8);
+    uint64_t c = absl::base_internal::UnalignedLoad64(ptr + 16);
+    uint64_t d = absl::base_internal::UnalignedLoad64(ptr + 24);
+
+    uint64_t cs0 = Mix(a ^ salt[1], b ^ current_state);
+    uint64_t cs1 = Mix(c ^ salt[2], d ^ current_state);
+    current_state = cs0 ^ cs1;
+
+    ptr += 32;
+    len -= 32;
+  }
+
+  // We now have a data `ptr` with at most 32 bytes and the current state
+  // of the hashing state machine stored in current_state.
+  if (len > 16) {
     uint64_t a = absl::base_internal::UnalignedLoad64(ptr);
     uint64_t b = absl::base_internal::UnalignedLoad64(ptr + 8);
 
@@ -82,13 +102,33 @@ uint64_t LowLevelHash(const void* data, size_t len, uint64_t seed,
     len -= 16;
   }
 
-  // We now have a data `ptr` with at most 16 bytes.
+  // We now have a data `ptr` with at least 1 and at most 16 bytes. But we can
+  // safely read from `ptr + len - 16`.
+  uint64_t a = absl::base_internal::UnalignedLoad64(ptr + len - 16);
+  uint64_t b = absl::base_internal::UnalignedLoad64(ptr + len - 8);
+
+  return Mix(a ^ salt[1] ^ starting_length, b ^ current_state);
+}
+
+uint64_t LowLevelHash(const void* data, size_t len, uint64_t seed,
+                      const uint64_t salt[5]) {
+  if (len > 16) return LowLevelHashLenGt16(data, len, seed, salt);
+
+  // Prefetch the cacheline that data resides in.
+  PrefetchToLocalCache(data);
+  const uint8_t* ptr = static_cast<const uint8_t*>(data);
+  uint64_t starting_length = static_cast<uint64_t>(len);
+  uint64_t current_state = seed ^ salt[0];
+  if (len == 0) return current_state;
+
   uint64_t a = 0;
   uint64_t b = 0;
+
+  // We now have a data `ptr` with at least 1 and at most 16 bytes.
   if (len > 8) {
     // When we have at least 9 and at most 16 bytes, set A to the first 64
-    // bits of the input and B to the last 64 bits of the input. Yes, they will
-    // overlap in the middle if we are working with less than the full 16
+    // bits of the input and B to the last 64 bits of the input. Yes, they
+    // will overlap in the middle if we are working with less than the full 16
     // bytes.
     a = absl::base_internal::UnalignedLoad64(ptr);
     b = absl::base_internal::UnalignedLoad64(ptr + len - 8);
@@ -97,20 +137,14 @@ uint64_t LowLevelHash(const void* data, size_t len, uint64_t seed,
     // bits and B to the last 32 bits.
     a = absl::base_internal::UnalignedLoad32(ptr);
     b = absl::base_internal::UnalignedLoad32(ptr + len - 4);
-  } else if (len > 0) {
-    // If we have at least 1 and at most 3 bytes, read all of the provided
-    // bits into A, with some adjustments.
-    a = static_cast<uint64_t>((ptr[0] << 16) | (ptr[len >> 1] << 8) |
-                              ptr[len - 1]);
-    b = 0;
   } else {
-    a = 0;
-    b = 0;
+    // If we have at least 1 and at most 3 bytes, read 2 bytes into A and the
+    // other byte into B, with some adjustments.
+    a = static_cast<uint64_t>((ptr[0] << 8) | ptr[len - 1]);
+    b = static_cast<uint64_t>(ptr[len >> 1]);
   }
 
-  uint64_t w = Mix(a ^ salt[1], b ^ current_state);
-  uint64_t z = salt[1] ^ starting_length;
-  return Mix(w, z);
+  return Mix(a ^ salt[1] ^ starting_length, b ^ current_state);
 }
 
 }  // namespace hash_internal
diff --git a/absl/hash/internal/low_level_hash.h b/absl/hash/internal/low_level_hash.h
index 439968aa..d460e351 100644
--- a/absl/hash/internal/low_level_hash.h
+++ b/absl/hash/internal/low_level_hash.h
@@ -43,6 +43,10 @@ namespace hash_internal {
 uint64_t LowLevelHash(const void* data, size_t len, uint64_t seed,
                       const uint64_t salt[5]);
 
+// Same as above except the length must be greater than 16.
+uint64_t LowLevelHashLenGt16(const void* data, size_t len, uint64_t seed,
+                             const uint64_t salt[5]);
+
 }  // namespace hash_internal
 ABSL_NAMESPACE_END
 }  // namespace absl
diff --git a/absl/hash/internal/low_level_hash_test.cc b/absl/hash/internal/low_level_hash_test.cc
index 589a3d8f..ea781dd9 100644
--- a/absl/hash/internal/low_level_hash_test.cc
+++ b/absl/hash/internal/low_level_hash_test.cc
@@ -406,99 +406,99 @@ TEST(LowLevelHashTest, VerifyGolden) {
 
 #if defined(ABSL_IS_BIG_ENDIAN)
   constexpr uint64_t kGolden[kNumGoldenOutputs] = {
-      0xe5a40d39ab796423, 0x1766974bf7527d81, 0x5c3bbbe230db17a8,
-      0xa6630143a7e6aa6f, 0x17645cb7318b86b,  0x218b175f30ba61f8,
-      0xa6564b468248c683, 0xef192f401b116e1c, 0xbe8dc0c54617639d,
-      0xe7b01610fc22dbb8, 0x99d9f694404af913, 0xf4eecd37464b45c5,
-      0x7d2c653d63596d9b, 0x3f15c8544ec5393a, 0x6b9dc0c1704f796c,
-      0xf1ded7a7eae5ed5a, 0x2db2fd7c6dd4641b, 0x151ca2d3d4cd33ab,
-      0xa5af5994ac2ccd64, 0x2b2a4ca3191d2fce, 0xf89e68c9364e7c05,
-      0x71724c70b799c21,  0x70536fabfd157369, 0xdee92794c3c3082b,
-      0xac033a6743d3b3eb, 0xed2956b506cd5151, 0xbd669644755264b6,
-      0x6ab1ff5d5f549a63, 0xf6bd551a2e3e04e,  0x7b5a8cef6875ea73,
-      0x22bccf4d4db0a91c, 0x4f2bc07754c7c7eb, 0xfb6b8342a86725db,
-      0x13a1a0d4c5854da,  0x5f6e44655f7dedac, 0x54a9198dff2bdf85,
-      0xdb17e6915d4e4042, 0xa69926cf5c3b89f,  0xf77f031bfd74c096,
-      0x1d6f916fdd50ec3c, 0x334ac76013ade393, 0x99370f899111de15,
-      0x352457a03ada6de,  0x341974d4f42d854d, 0xda89ab02872aeb5,
-      0x6ec2b74e143b10d9, 0x6f284c0b5cd60522, 0xf9670de353438f88,
-      0xde920913adf0a2b4, 0xb7a07d7c0c17a8ec, 0x879a69f558ba3a98,
-      0x360cf6d802df20f9, 0x53530f8046673738, 0xbd8f5f2bcf35e483,
-      0x3f171f047144b983, 0x644d04e820823465, 0x50e44773a20b2702,
-      0xe584ed4c05c745dd, 0x9a825c85b95ab6c0, 0xbce2931deb74e775,
-      0x10468e9e705c7cfe, 0x12e01de3104141e2, 0x5c11ae2ee3713abd,
-      0x6ac5ffb0860319e6, 0xc1e6da1849d30fc9, 0xa0e4d247a458b447,
-      0x4530d4615c32b89b, 0x116aa09107a76505, 0xf941339d00d9bb73,
-      0x573a0fc1615afb33, 0xa975c81dc868b258, 0x3ab2c5250ab54bda,
-      0x37f99f208a3e3b11, 0x4b49b0ff706689d,  0x30bafa0b8f0a87fe,
-      0xea6787a65cc20cdd, 0x55861729f1fc3ab8, 0xea38e009c5be9b72,
-      0xcb8522cba33c3c66, 0x352e77653fe306f3, 0xe0bb760793bac064,
-      0xf66ec59322662956, 0x637aa320455d56f8, 0x46ee546be5824a89,
-      0x9e6842421e83d8a4, 0xf98ac2bc96b9fb8c, 0xf2c1002fd9a70b99,
-      0x4c2b62b1e39e9405, 0x3248555fa3ade9c4, 0xd4d04c37f6417c21,
-      0xf40cd506b1bf5653, 0x6c45d6005c760d2f, 0x61d88a7e61ff0d7e,
-      0x131591e8a53cc967, 0xdae85cb9bc29bab6, 0xe98835334905e626,
-      0x7cce50a2b66b8754, 0x5b0b3d0c5ac498ae, 0xd35a218c974d1756,
-      0xfce436ddc1d003c,  0xd183901de90bb741, 0x9378f8f34974a66,
-      0x21f11ae0a0402368, 0xf2fbd7c94ef89cb6, 0xc329c69d0f0d080b,
-      0xf2841cba16216a61, 0x47aba97b44916df1, 0x724d4e00a8019fcf,
-      0x2df9005c2a728d63, 0xc788892a1a5d7515, 0x9e993a65f9df0480,
-      0x76876721ff49f969, 0xbe7a796cfba15bf5, 0xa4c8bd54586f5488,
-      0xb390a325275501ab, 0x893f11317427ccf1, 0x92f2bb57da5695b9,
-      0x30985b90da88269f, 0x2c690e268e086de8, 0x1c02df6097997196,
-      0x1f9778f8bbdf6455, 0x7d57378c7bf8416d, 0xba8582a5f8d84d38,
-      0xe8ca43b85050be4e, 0x5048cf6bed8a5d9f, 0xfbc5ba80917d0ea4,
-      0x8011026525bf1691, 0x26b8dc6aed9fb50d, 0x191f5bfee77c1fe3,
-      0xdd497891465a2cc1, 0x6f1fe8c57a33072e, 0x2c9f4ec078c460c0,
-      0x9a725bde8f6a1437, 0x6ce545fa3ef61e4d,
+      0x4c34aacf38f6eee4, 0x88b1366815e50b88, 0x1a36bd0c6150fb9c,
+      0xa783aba8a67366c7, 0x5e4a92123ae874f2, 0x0cc9ecf27067ee9a,
+      0xbe77aa94940527f9, 0x7ea5c12f2669fe31, 0xa33eed8737d946b9,
+      0x310aec5b1340bb36, 0x354e400861c5d8ff, 0x15be98166adcf42f,
+      0xc51910b62a90ae51, 0x539d47fc7fdf6a1f, 0x3ebba9daa46eef93,
+      0xd96bcd3a9113c17f, 0xc78eaf6256ded15a, 0x98902ed321c2f0d9,
+      0x75a4ac96414b954a, 0x2cb90e00a39e307b, 0x46539574626c3637,
+      0x186ec89a2be3ff45, 0x972a3bf7531519d2, 0xa14df0d25922364b,
+      0xa351e19d22752109, 0x08bd311d8fed4f82, 0xea2b52ddc6af54f9,
+      0x5f20549941338336, 0xd43b07422dc2782e, 0x377c68e2acda4835,
+      0x1b31a0a663b1d7b3, 0x7388ba5d68058a1a, 0xe382794ea816f032,
+      0xd4c3fe7889276ee0, 0x2833030545582ea9, 0x554d32a55e55df32,
+      0x8d6d33d7e17b424d, 0xe51a193d03ae1e34, 0xabb6a80835bd66b3,
+      0x0e4ba5293f9ce9b7, 0x1ebd8642cb762cdf, 0xcb54b555850888ee,
+      0x1e4195e4717c701f, 0x6235a13937f6532a, 0xd460960741e845c0,
+      0x2a72168a2d6af7b1, 0x6be38fbbfc5b17de, 0x4ee97cffa0d0fb39,
+      0xfdf1119ad5e71a55, 0x0dff7f66b3070727, 0x812d791d6ed62744,
+      0x60962919074b70b8, 0x956fa5c7d6872547, 0xee892daa58aae597,
+      0xeeda546e998ee369, 0x454481f5eb9b1fa8, 0x1054394634c98b1b,
+      0x55bb425415f591fb, 0x9601fa97416232c4, 0xd7a18506519daad7,
+      0x90935cb5de039acf, 0xe64054c5146ed359, 0xe5b323fb1e866c09,
+      0x10a472555f5ba1bc, 0xe3c0cd57d26e0972, 0x7ca3db7c121da3e8,
+      0x7004a89c800bb466, 0x865f69c1a1ff7f39, 0xbe0edd48f0cf2b99,
+      0x10e5e4ba3cc400f5, 0xafc2b91a220eef50, 0x6f04a259289b24f1,
+      0x2179a8070e880ef0, 0xd6a9a3d023a740c2, 0x96e6d7954755d9b8,
+      0xc8e4bddecce5af9f, 0x93941f0fbc724c92, 0xbef5fb15bf76a479,
+      0x534dca8f5da86529, 0x70789790feec116b, 0x2a296e167eea1fe9,
+      0x54cb1efd2a3ec7ea, 0x357b43897dfeb9f7, 0xd1eda89bc7ff89d3,
+      0x434f2e10cbb83c98, 0xeec4cdac46ca69ce, 0xd46aafd52a303206,
+      0x4bf05968ff50a5c9, 0x71c533747a6292df, 0xa40bd0d16a36118c,
+      0x597b4ee310c395ab, 0xc5b3e3e386172583, 0x12ca0b32284e6c70,
+      0xb48995fadcf35630, 0x0646368454cd217d, 0xa21c168e40d765b5,
+      0x4260d3811337da30, 0xb72728a01cff78e4, 0x8586920947f4756f,
+      0xc21e5f853cae7dc1, 0xf08c9533be9de285, 0x72df06653b4256d6,
+      0xf7b7f937f8db1779, 0x976db27dd0418127, 0x9ce863b7bc3f9e00,
+      0xebb679854fcf3a0a, 0x2ccebabbcf1afa99, 0x44201d6be451dac5,
+      0xb4af71c0e9a537d1, 0xad8fe9bb33ed2681, 0xcb30128bb68df43b,
+      0x154d8328903e8d07, 0x5844276dabeabdff, 0xd99017d7d36d930b,
+      0xabb0b4774fb261ca, 0x0a43f075d62e67e0, 0x8df7b371355ada6b,
+      0xf4c7a40d06513dcf, 0x257a3615955a0372, 0x987ac410bba74c06,
+      0xa011a46f25a632a2, 0xa14384b963ddd995, 0xf51b6b8cf9d50ba7,
+      0x3acdb91ee3abf18d, 0x34e799be08920e8c, 0x8766748a31304b36,
+      0x0aa239d5d0092f2e, 0xadf473ed26628594, 0xc4094b798eb4b79b,
+      0xe04ee5f33cd130f4, 0x85045d098c341d46, 0xf936cdf115a890ec,
+      0x51d137b6d8d2eb4f, 0xd10738bb2fccc1ef,
   };
 #else
   constexpr uint64_t kGolden[kNumGoldenOutputs] = {
-      0xe5a40d39ab796423, 0x1766974bf7527d81, 0x5c3bbbe230db17a8,
-      0xa6630143a7e6aa6f, 0x8787cb2d04b0c984, 0x33603654ff574ac2,
-      0xa6564b468248c683, 0xef192f401b116e1c, 0xbe8dc0c54617639d,
-      0x93d7f665b5521c8e, 0x646d70bb42445f28, 0x96a7b1e3cc9bd426,
-      0x76020289ab0790c4, 0x39f842e4133b9b44, 0x2b8d7047be4bcaab,
-      0x99628abef6716a97, 0x4432e02ba42b2740, 0x74d810efcad7918a,
-      0x88c84e986002507f, 0x4f99acf193cf39b9, 0xd90e7a3655891e37,
-      0x3bb378b1d4df8fcf, 0xf78e94045c052d47, 0x26da0b2130da6b40,
-      0x30b4d426af8c6986, 0x5413b4aaf3baaeae, 0x756ab265370a1597,
-      0xdaf5f4b7d09814fb, 0x8f874ae37742b75e, 0x8fecd03956121ce8,
-      0x229c292ea7a08285, 0x0bb4bf0692d14bae, 0x207b24ca3bdac1db,
-      0x64f6cd6745d3825b, 0xa2b2e1656b58df1e, 0x0d01d30d9ee7a148,
-      0x1cb4cd00ab804e3b, 0x4697f2637fd90999, 0x8383a756b5688c07,
-      0x695c29cb3696a975, 0xda2e5a5a5e971521, 0x7935d4befa056b2b,
-      0x38dd541ca95420fe, 0xcc06c7a4963f967f, 0xbf0f6f66e232fb20,
-      0xf7efb32d373fe71a, 0xe2e64634b1c12660, 0x285b8fd1638e306d,
-      0x658e8a4e3b714d6c, 0xf391fb968e0eb398, 0x744a9ea0cc144bf2,
-      0x12636f2be11012f1, 0x29c57de825948f80, 0x58c6f99ab0d1c021,
-      0x13e7b5a7b82fe3bb, 0x10fbc87901e02b63, 0xa24c9184901b748b,
-      0xcac4fd4c5080e581, 0xc38bdb7483ba68e1, 0xdb2a8069b2ceaffa,
-      0xdf9fe91d0d1c7887, 0xe83f49e96e2e6a08, 0x0c69e61b62ca2b62,
-      0xb4a4f3f85f8298fe, 0x167a1b39e1e95f41, 0xf8a2a5649855ee41,
-      0x27992565b595c498, 0x3e08cca5b71f9346, 0xad406b10c770a6d2,
-      0xd1713ce6e552bcf2, 0x753b287194c73ad3, 0x5ae41a95f600af1c,
-      0x4a61163b86a8bb4c, 0x42eeaa79e760c7e4, 0x698df622ef465b0a,
-      0x157583111e1a6026, 0xaa1388f078e793e0, 0xf10d68d0f3309360,
-      0x2af056184457a3de, 0x6d0058e1590b2489, 0x638f287f68817f12,
-      0xc46b71fecefd5467, 0x2c8e94679d964e0a, 0x8612b797ce22503a,
-      0x59f929babfba7170, 0x9527556923fb49a0, 0x1039ab644f5e150b,
-      0x7816c83f3aa05e6d, 0xf51d2f564518c619, 0x67d494cff03ac004,
-      0x2802d636ced1cfbb, 0xf64e20bad771cb12, 0x0b9a6cf84a83e15e,
-      0x8da6630319609301, 0x40946a86e2a996f3, 0xcab7f5997953fa76,
-      0x39129ca0e04fc465, 0x5238221fd685e1b8, 0x175130c407dbcaab,
-      0x02f20e7536c0b0df, 0x2742cb488a04ad56, 0xd6afb593879ff93b,
-      0xf50ad64caac0ca7f, 0x2ade95c4261364ae, 0x5c4f3299faacd07a,
-      0xfffe3bff0ae5e9bc, 0x1db785c0005166e4, 0xea000d962ad18418,
-      0xe42aef38359362d9, 0xc8e95657348a3891, 0xc162eca864f238c6,
-      0xbe1fb373e20579ad, 0x628a1d4f40aa6ffd, 0xa87bdb7456340f90,
-      0x5960ef3ba982c801, 0x5026586df9a431ec, 0xfe4b8a20fdf0840b,
-      0xdcb761867da7072f, 0xc10d4653667275b7, 0x727720deec13110b,
-      0x710b009662858dc9, 0xfbf8f7a3ecac1eb7, 0xb6fc4fcd0722e3df,
-      0x7cb86dcc55104aac, 0x19e71e9b45c3a51e, 0x51de38573c2bea48,
-      0xa73ab6996d6df158, 0x55ef2b8c930817b2, 0xb2850bf5fae87157,
-      0xecf3de1acd04651f, 0xcc0a40552559ff32, 0xc385c374f20315b1,
-      0xb90208a4c7234183, 0x58aa1ca7a4c075d9,
+      0x4c34aacf38f6eee4, 0x88b1366815e50b88, 0x1a36bd0c6150fb9c,
+      0xa783aba8a67366c7, 0xbc89ebdc622314e4, 0x632bc3cfcc7544d8,
+      0xbe77aa94940527f9, 0x7ea5c12f2669fe31, 0xa33eed8737d946b9,
+      0x74d832ea11fd18ab, 0x49c0487486246cdc, 0x3fdd986c87ddb0a0,
+      0xac3fa52a64d7c09a, 0xbff0e330196e7ed2, 0x8c8138d3ad7d3cce,
+      0x968c7d4b48e93778, 0xa04c78d3a421f529, 0x8854bc9c3c3c0241,
+      0xcccfcdf5a41113fe, 0xe6fc63dc543d984d, 0x00a39ff89e903c05,
+      0xaf7e9da25f9a26f9, 0x6e269a13d01a43df, 0x846d2300ce2ecdf8,
+      0xe7ea8c8f08478260, 0x9a2db0d62f6232f3, 0x6f66c761d168c59f,
+      0x55f9feacaae82043, 0x518084043700f614, 0xb0c8cfc11bead99f,
+      0xe4a68fdab6359d80, 0x97b17caa8f92236e, 0x96edf5e8363643dc,
+      0x9b3fbcd8d5b254cd, 0x22a263621d9b3a8b, 0xde90bf6f81800a6d,
+      0x1b51cae38c2e9513, 0x689215b3c414ef21, 0x064dc85afae8f557,
+      0xa2f3a8b51f408378, 0x6907c197ec1f6a3b, 0xfe83a42ef5c1cf13,
+      0x9b8b1d8f7a20cc13, 0x1f1681d52ca895d0, 0xd7b1670bf28e0f96,
+      0xb32f20f82d8b038a, 0x6a61d030fb2f5253, 0x8eb2bb0bc29ebb39,
+      0x144f36f7a9eef95c, 0xe77aa47d29808d8c, 0xf14d34c1fc568bad,
+      0x9796dcd4383f3c73, 0xa2f685fc1be7225b, 0xf3791295b16068b1,
+      0xb6b8f63424618948, 0x8ac4fd587045db19, 0x7e2aec2c34feb72e,
+      0x72e135a6910ccbb1, 0x661ff16f3c904e6f, 0xdf92cf9d67ca092d,
+      0x98a9953d79722eef, 0xe0649ed2181d1707, 0xcd8b8478636a297b,
+      0x9516258709c8471b, 0xc703b675b51f4394, 0xdb740eae020139f3,
+      0x57d1499ac4212ff2, 0x355cc03713d43825, 0x0e71ac9b8b1e101e,
+      0x8029fa72258ff559, 0xa2159726b4c16a50, 0x04e61582fba43007,
+      0xdab25af835be8cce, 0x13510b1b184705ee, 0xabdbc9e53666fdeb,
+      0x94a788fcb8173cef, 0x750d5e031286e722, 0x02559e72f4f5b497,
+      0x7d6e0e5996a646fa, 0x66e871b73b014132, 0x2ec170083f8b784f,
+      0x34ac9540cfce3fd9, 0x75c5622c6aad1295, 0xf799a6bb2651acc1,
+      0x8f6bcd3145bdc452, 0xddd9d326eb584a04, 0x5411af1e3532f8dc,
+      0xeb34722f2ad0f509, 0x835bc952a82298cc, 0xeb3839ff60ea92ad,
+      0x70bddf1bcdc8a4bc, 0x4bfb3ee86fcde525, 0xc7b3b93b81dfa386,
+      0xe66db544d57997e8, 0xf68a1b83fd363187, 0xe9b99bec615b171b,
+      0x093fba04d04ad28a, 0xba6117ed4231a303, 0x594bef25f9d4e206,
+      0x0a8cba60578b8f67, 0x88f6c7ca10b06019, 0x32a74082aef17b08,
+      0xe758222f971e22df, 0x4af14ff4a593e51e, 0xdba651e16cb09044,
+      0x3f3ac837d181eaac, 0xa5589a3f89610c01, 0xd409a7c3a18d5643,
+      0x8a89444f82962f26, 0x22eb62a13b9771b9, 0xd3a617615256ddd8,
+      0x7089b990c4bba297, 0x7d752893783eac4f, 0x1f2fcbb79372c915,
+      0x67a4446b17eb9839, 0x70d11df5cae46788, 0x52621e1780b47d0f,
+      0xcf63b93a6e590ee6, 0xb6bc96b58ee064b8, 0x2587f8d635ca9c75,
+      0xc6bddd62ec5e5d01, 0x957398ad3009cdb7, 0x05b6890b20bcd0d3,
+      0xbe6e965ff837222e, 0x47383a87d2b04b1a, 0x7d42207e6d8d7950,
+      0x7e981ed12a7f4aa3, 0xdebb05b30769441a, 0xaac5d86f4ff76c49,
+      0x384f195ca3248331, 0xec4c4b855e909ca1, 0x6a7eeb5a657d73d5,
+      0x9efbebe2fa9c2791, 0x19e7fa0546900c4d,
   };
 #endif