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// <!--
// The MIT License (MIT)
//
// Copyright (c) 2024 Kris Jusiak <[email protected]>
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
//
#if 0
// -->
[Overview](#Overview) / [Examples](#Examples) / [API](#API) / [FAQ](#FAQ)
## MPH: [Minimal] Static perfect hash library
> https://en.wikipedia.org/wiki/Perfect_hash_function
[](https://opensource.org/license/mit)
[](https://github.com/qlibs/mph/releases)
[](https://godbolt.org/z/MsE4nnhvc)
[](https://godbolt.org/z/jcPPsbEvK)
### Use case
> A static perfect hash function maps a set of keys known in advance to a set of values with no collisions.
### Features
- Single header (https://raw.githubusercontent.com/qlibs/mph/main/mph - for integration see [FAQ](#faq))
- Self verification upon include (can be disabled by `-DNTEST` - see [FAQ](#faq))
- Compiles cleanly with ([`-Wall -Wextra -Werror -pedantic -pedantic-errors -fno-exceptions -fno-rtti`](https://godbolt.org/z/WraE4q1dE))
- Minimal [API](#api)
- Optimized run-time execution (see [performance](#performance) / [benchmarks](#benchmarks))
- Fast compilation times (see [compilation](#compilation))
- Trade-offs (see [FAQ](#faq))
### Requirements
- C++20 ([gcc-12+, clang-15+](https://godbolt.org/z/WraE4q1dE)) / [optional] ([bmi2](https://en.wikipedia.org/wiki/X86_Bit_manipulation_instruction_set)), [optional] ([simd](https://en.wikipedia.org/wiki/Single_instruction,_multiple_data)),
### Overview
> Hello world (https://godbolt.org/z/dzd6o3Pxo)
```cpp
enum class color { red, green, blue };
constexpr auto colors = std::array{
std::pair{"red"sv, color::red},
std::pair{"green"sv, color::green},
std::pair{"blue"sv, color::blue},
};
static_assert(color::green == mph::lookup<colors>("green"));
static_assert(color::red == mph::lookup<colors>("red"));
static_assert(color::blue == mph::lookup<colors>("blue"));
std::print("{}", mph::lookup<colors>("green"sv)); // prints 1
```
> `mph::lookup` assumes only valid input and returns mapped value direclty.
```cpp
static_assert(not mph::find<colors>("unknown"));
static_assert(mph::find<colors>("green"));
static_assert(mph::find<colors>("red"));
static_assert(mph::find<colors>("blue"));
std::print("{}", *mph::find<colors>("green"sv)); // prints 1
```
> `mph::find` doesnt assume valid input and returns optional of mapped value.
---
<a name="performance"></a>
> Performance (https://godbolt.org/z/rqYj9a1cr)
```cpp
int lookup(int id) {
static constexpr std::array ids{
std::pair{54u, 91u},
std::pair{64u, 324u},
std::pair{91u, 234u},
};
return mph::lookup<ids>(id);
}
```
```cpp
lookup: // g++ -DNDEBUG -std=c++20 -O3
imull $1275516394, %edi, %eax
shrl $23, %eax
movl $24029728, %ecx
shrxl %eax, %ecx, %eax
andl $511, %eax
retq
```
> Performance (https://godbolt.org/z/vv6W4nGfb)
```cpp
int lookup(int id) {
static constexpr std::array ids{
std::pair{54u, 91u},
std::pair{324u, 54u},
std::pair{64u, 324u},
std::pair{234u, 64u},
std::pair{91u, 234u},
};
return mph::lookup<ids>(id);
}
```
```cpp
lookup: // g++ -DNDEBUG -std=c++20 -O3
andl $7, %edi
leaq lookup(%rip), %rax
movl (%rax,%rdi,4), %eax
retq
lookup:
.long 324
.long 0
.long 64
.long 234
.long 54
.long 0
.long 91
```
> Performance (https://godbolt.org/z/qMzxKK4sd)
```cpp
int find(int id) {
static constexpr std::array ids{
std::pair{27629, 1},
std::pair{6280, 2},
// 1..128 pairs...
std::pair{33691, 128},
};
return *mph::find<ids>(id);
}
```
```cpp
find: // g++ -DNDEBUG -std=c++20 -O3 -mbmi2 -mavx512f
vpbroadcastd %edi, %zmm0
shll $4, %edi
movzbl %dil, %ecx
leaq find
vpcmpeqd (%rdx,%rcx,4), %zmm0, %k0
kmovw %k0, %esi
kortestw %k0, %k0
rep bsfq %rax, %rax
movl $64, %eax
addl %eax, %ecx
xorl %eax, %eax
testw %si, %si
cmovnel 1024(%rdx,%rcx,4), %eax
vzeroupper
retq
find:
... // see godbolt
```
---
> Performance (https://godbolt.org/z/KaKzf7Pax)
```cpp
int find(std::span<const char, 8> str) {
static constexpr auto symbols = std::array{
std::pair{"AMZN "sv, 1},
std::pair{"AAPL "sv, 2},
std::pair{"GOOGL "sv, 3},
std::pair{"META "sv, 4},
std::pair{"MSFT "sv, 5},
std::pair{"NVDA "sv, 6},
std::pair{"TSLA "sv, 7},
};
return *mph::find<symbols>(str);
}
```
```cpp
find: // g++ -DNDEBUG -std=c++20 -O3 -mbmi2
movq 8(%rsi), %rax
movl $1031, %ecx
leaq find(%rip), %rdx
xorl %esi, %esi
movq (%rax), %rax
pextq %rcx, %rax, %rcx
shll $4, %ecx
cmpq (%rcx,%rdx), %rax
movzbl 8(%rcx,%rdx), %eax
cmovnel %esi, %eax
retq
find:
... // see godbolt
```
> Performance (https://godbolt.org/z/fdMPsYWjE)
```cpp
int find(std::string_view str) {
using std::literals::operator""sv;
// values assigned from 0..N-1
static constexpr std::array symbols{
"BTC "sv, "ETH "sv, "BNB "sv,
"SOL "sv, "XRP "sv, "DOGE"sv,
"TON "sv, "ADA "sv, "SHIB"sv,
"AVAX"sv, "LINK"sv, "BCH "sv,
};
return *mph::find<symbols>(str);
}
```
```cpp
find: // g++ -DNDEBUG -std=c++20 -O3 -mbmi2
shll $3, %edi
bzhil %edi, (%rsi), %eax
movl $789, %ecx
pextl %ecx, %eax, %ecx
leaq find(%rip), %rdx
xorl %esi, %esi
cmpl (%rdx,%rcx,8), %eax
movzbl 4(%rdx,%rcx,8), %eax
cmovnel %esi, %eax
retq
find:
... // see godbolt
```
---
### Examples
- [feature] `lookup/find` customization point - https://godbolt.org/z/enqeGxKK9
- [feature] `to` customization point - https://godbolt.org/z/jTMx4n6j3
- [example] `branchless dispatcher` - https://godbolt.org/z/5PTE3ercE
- [performance - https://wg21.link/P2996] `enum_to_string` - https://godbolt.org/z/ojohP6j7f
- [performance - https://wg21.link/P2996] `string_to_enum` - https://godbolt.org/z/83vGhY7M8
---
<a name="benchmarks"></a>
### Benchmarks (https://github.com/qlibs/mph/tree/benchmark)
> `clang++ -std=c++20 -O3 -DNDEBUG -mbmi2 benchmark.cpp`
```
| ns/op | op/s | err% |total | benchmark
|------:|---------------:|-----:|-----:|:----------
| 12.25 | 81,602,449.70 | 0.3% | 0.15 | `random_strings_5_len_4.std.map`
| 5.56 | 179,750,906.50 | 0.2% | 0.07 | `random_strings_5_len_4.std.unordered_map`
| 9.17 | 109,096,850.98 | 0.2% | 0.11 | `random_strings_5_len_4.boost.unordered_map`
| 13.48 | 74,210,250.54 | 0.3% | 0.16 | `random_strings_5_len_4.boost.flat_map`
| 7.70 | 129,942,965.18 | 0.3% | 0.09 | `random_strings_5_len_4.gperf`
| 1.61 | 621,532,188.81 | 0.1% | 0.02 | `random_strings_5_len_4.mph`
| 14.66 | 68,218,086.71 | 0.8% | 0.18 | `random_strings_5_len_8.std.map`
| 13.45 | 74,365,239.56 | 0.2% | 0.16 | `random_strings_5_len_8.std.unordered_map`
| 9.68 | 103,355,605.09 | 0.2% | 0.12 | `random_strings_5_len_8.boost.unordered_map`
| 16.00 | 62,517,180.19 | 0.4% | 0.19 | `random_strings_5_len_8.boost.flat_map`
| 7.70 | 129,809,356.36 | 0.3% | 0.09 | `random_strings_5_len_8.gperf`
| 1.58 | 633,084,194.24 | 0.1% | 0.02 | `random_strings_5_len_8.mph`
| 17.21 | 58,109,576.87 | 0.3% | 0.21 | `random_strings_6_len_2_5.std.map`
| 15.28 | 65,461,167.99 | 0.2% | 0.18 | `random_strings_6_len_2_5.std.unordered_map`
| 12.21 | 81,931,391.20 | 0.4% | 0.15 | `random_strings_6_len_2_5.boost.unordered_map`
| 17.15 | 58,323,741.08 | 0.5% | 0.21 | `random_strings_6_len_2_5.boost.flat_map`
| 7.94 | 125,883,197.55 | 0.5% | 0.09 | `random_strings_6_len_2_5.gperf`
| 6.05 | 165,239,616.00 | 0.5% | 0.07 | `random_strings_6_len_2_5.mph`
| 31.61 | 31,631,402.94 | 0.2% | 0.38 | `random_strings_100_len_8.std.map`
| 15.32 | 65,280,594.09 | 0.2% | 0.18 | `random_strings_100_len_8.std.unordered_map`
| 17.13 | 58,383,850.20 | 0.3% | 0.20 | `random_strings_100_len_8.boost.unordered_map`
| 31.42 | 31,822,519.67 | 0.2% | 0.38 | `random_strings_100_len_8.boost.flat_map`
| 8.04 | 124,397,773.85 | 0.2% | 0.10 | `random_strings_100_len_8.gperf`
| 1.58 | 632,813,481.73 | 0.1% | 0.02 | `random_strings_100_len_8.mph`
| 32.62 | 30,656,015.03 | 0.3% | 0.39 | `random_strings_100_len_1_8.std.map`
| 19.34 | 51,697,107.73 | 0.5% | 0.23 | `random_strings_100_len_1_8.std.unordered_map`
| 19.51 | 51,254,525.17 | 0.3% | 0.23 | `random_strings_100_len_1_8.boost.unordered_map`
| 33.58 | 29,780,574.17 | 0.6% | 0.40 | `random_strings_100_len_1_8.boost.flat_map`
| 13.06 | 76,577,037.07 | 0.7% | 0.16 | `random_strings_100_len_1_8.gperf`
| 6.02 | 166,100,665.07 | 0.2% | 0.07 | `random_strings_100_len_1_8.mph`
| 1.28 | 778,723,795.75 | 0.1% | 0.02 | `random_uints_5.mph`
```
> `g++ -std=c++20 -O3 -DNDEBUG -mbmi2 benchmark.cpp`
```cpp
| ns/op | op/s | err% |total | benchmark
|------:|---------------:|-----:|-----:|:----------
| 12.28 | 81,460,330.38 | 0.9% | 0.15 | `random_strings_5_len_4.std.map`
| 5.29 | 188,967,241.90 | 0.3% | 0.06 | `random_strings_5_len_4.std.unordered_map`
| 9.69 | 103,163,192.67 | 0.2% | 0.12 | `random_strings_5_len_4.boost.unordered_map`
| 13.56 | 73,756,333.08 | 0.4% | 0.16 | `random_strings_5_len_4.boost.flat_map`
| 7.69 | 130,055,662.66 | 0.6% | 0.09 | `random_strings_5_len_4.gperf`
| 1.39 | 718,910,252.82 | 0.1% | 0.02 | `random_strings_5_len_4.mph`
| 14.26 | 70,103,007.82 | 2.4% | 0.17 | `random_strings_5_len_8.std.map`
| 13.36 | 74,871,047.51 | 0.4% | 0.16 | `random_strings_5_len_8.std.unordered_map`
| 9.82 | 101,802,074.00 | 0.3% | 0.12 | `random_strings_5_len_8.boost.unordered_map`
| 15.97 | 62,621,571.95 | 0.3% | 0.19 | `random_strings_5_len_8.boost.flat_map`
| 7.92 | 126,265,206.30 | 0.3% | 0.09 | `random_strings_5_len_8.gperf`
| 1.40 | 713,596,376.62 | 0.4% | 0.02 | `random_strings_5_len_8.mph`
| 15.98 | 62,576,142.34 | 0.5% | 0.19 | `random_strings_6_len_2_5.std.map`
| 17.56 | 56,957,868.12 | 0.5% | 0.21 | `random_strings_6_len_2_5.std.unordered_map`
| 11.68 | 85,637,378.45 | 0.3% | 0.14 | `random_strings_6_len_2_5.boost.unordered_map`
| 17.25 | 57,965,732.68 | 0.6% | 0.21 | `random_strings_6_len_2_5.boost.flat_map`
| 9.13 | 109,580,632.48 | 0.7% | 0.11 | `random_strings_6_len_2_5.gperf`
| 7.17 | 139,563,745.72 | 0.4% | 0.09 | `random_strings_6_len_2_5.mph`
| 30.20 | 33,117,522.76 | 0.7% | 0.36 | `random_strings_100_len_8.std.map`
| 15.01 | 66,627,962.89 | 0.4% | 0.18 | `random_strings_100_len_8.std.unordered_map`
| 16.79 | 59,559,414.60 | 0.6% | 0.20 | `random_strings_100_len_8.boost.unordered_map`
| 31.36 | 31,884,629.57 | 0.8% | 0.38 | `random_strings_100_len_8.boost.flat_map`
| 7.75 | 128,973,947.61 | 0.7% | 0.09 | `random_strings_100_len_8.gperf`
| 1.50 | 667,041,673.54 | 0.1% | 0.02 | `random_strings_100_len_8.mph`
| 30.92 | 32,340,612.08 | 0.4% | 0.37 | `random_strings_100_len_1_8.std.map`
| 25.35 | 39,450,222.09 | 0.4% | 0.30 | `random_strings_100_len_1_8.std.unordered_map`
| 19.76 | 50,609,820.90 | 0.2% | 0.24 | `random_strings_100_len_1_8.boost.unordered_map`
| 32.39 | 30,878,018.77 | 0.6% | 0.39 | `random_strings_100_len_1_8.boost.flat_map`
| 11.20 | 89,270,687.92 | 0.2% | 0.13 | `random_strings_100_len_1_8.gperf`
| 7.17 | 139,471,159.67 | 0.5% | 0.09 | `random_strings_100_len_1_8.mph`
| 1.93 | 519,047,110.39 | 0.3% | 0.02 | `random_uints_5.mph`
```
<a name="compilation"></a>
### Benchmarks (https://qlibs.github.io/mph/perfect_hashing)
[](https://qlibs.github.io/mph/perfect_hashing)
[](https://qlibs.github.io/mph/perfect_hashing)
---
### API
```cpp
namespace mph {
/**
* Static [minimal] perfect hash lookup function
* @tparam entries constexpr array of keys or key/value pairs
*/
template<const auto& entries>
inline constexpr auto lookup = [](const auto& key) {
if constexpr(constexpr lookup$magic_lut<entries> lookup{}; lookup) {
return lookup(key);
} else {
return lookup$pext<entries>(key);
}
};
/**
* Static perfect hash find function
* @tparam entries constexpr array of keys or key/value pairs
*/
template<const auto& entries>
inline constexpr auto find =
[]<u8 probability = 50u>(const auto& key, const auto& unknown = {}) -> optional {
if constexpr (entries.size() == 0u) {
return unknown;
} else if constexpr (entries.size() <= 64u) {
return find$pext<entries>.operator()<probability>(key, unknown);
} else {
constexpr auto bucket_size = simd_size_v<key_type, simd_abi::native<key_type>>;
return find$simd<entries, bucket_size>.operator()<probability>(key, unknown);
}
};
} // namespace mph
```
---
### FAQ
- Trade-offs?
> `mph` supports different types of key/value pairs and thousands of key/value pairs, but not millions - (see [benchmarks](#benchmarks)).
- All keys have to fit into `uint128_t`, that includes strings.
- If the above criteria are not satisfied `mph` will [SFINAE](https://en.wikipedia.org/wiki/Substitution_failure_is_not_an_error) away `lookup` function.
- In such case different backup policy should be used instead (which can be also used as customization point for user-defined `lookup` implementation), for example:
```cpp
template<const auto& entries> requires (entries.size() > 1'000'000)
inline constexpr auto mph::find =
[](const auto& key, const auto& unknown = {}) -> optional { ... }
```
- How `mph` is working under the hood?
> `mph` takes advantage of knowing the key/value pairs at compile-time as well as the specific hardware instructions.
The following is a pseudo code of the `lookup` algorithm for minimal perfect hash table.
```python
def lookup$magic_lut[entries: array](key : any, max_attempts = 100'000):
# 0. magic and lut for entries [compile-time]
nbits = sizeof(u32) * CHAR_BIT - countl_zero(max(entries.second))
mask = (1u << nbits) - 1u;
shift = sizeof(u32) * CHAR_BIT - nbits;
lut = {};
while max_attempts--:
magic = rand()
for k, v in entries:
lut |= v << (k * magic >> shift);
for k, v in entries:
if (lut >> (k * magic >> shift) & mask) != v:
lut = {}
break
assert magic != 0 and lut != 0 and shift != 0 and mask != 0
# 1. lookup [run-time]
return (lut >> ((key * magic) >> shift)) & mask;
```
> The following is a pseudo code of the `find` algorithm for perfect hash table.
```python
# word: 00101011
# mask: 11100001
# &: 000____1
# pext: ____0001 # intel/intrinsics-guide/index.html#text=pext
def pext(a : uN, mask : uN):
dst, m, k = ([], 0, 0)
while m < nbits(a):
if mask[m] == 1:
dst.append(a[m])
k += 1
m += 1
return uN(dst)
```
```python
def find$pext[entries: array](key : any, unknown: any):
# 0. find mask which uniquely identifies all keys [compile-time]
mask = 0b111111...
for i in range(nbits(mask)):
masked = []
mask.unset(i)
for k, v in entries:
masked.append(k & mask)
if not unique(masked):
mask.set(i)
assert unique(masked)
assert mask != ~mask{}
# 1. create lookup table [compile-time]
lookup = array(typeof(entries[0]), 2**popcount(mask))
for k, v in entries:
lookup[pext(k, mask)] = (k, v)
# 2. lookup [run-time] # if key is a string convert to integral first (memcpy)
k, v = lookup[pext(key, mask)]
if k == key: # cmove
return v
else:
return unknown
```
```python
def find$simd[entries: array](key : any, unknown: any):
# 0. find mask which uniquely identifies all keys [compile-time]
mask = 0b111111...
bucket_size = simd_size_v<entries[0].first, native>
for i in range(nbits(mask)):
masked = []
mask.unset(i)
for k, v in entries:
masked.append(k & mask)
if not unique(masked, bucket_size):
mask.set(i)
assert unique(masked, bucket_size)
assert mask != ~mask{}
# 1. create lookup table [compile-time]
keys = array(typeof(entries[0].first), bucket_size * 2**popcount(mask))
values = array(typeof(entries[0].second), bucket_size * 2**popcount(mask))
for k, v in entries:
slot = pext(k, mask)
while (keys[slot]) slot++;
keys[slot] = k
values[slot] = v
# 2. lookup [run-time] # if key is a string convert to integral first (memcpy)
index = bucket_size * pext(key, mask)
match = k == keys[&index] # simd element-wise comparison
if any_of(match):
return values[index + find_first_set(match)]
else:
return unknown
```
> [More information](https://krzysztof-jusiak.github.io/talks/cpponsea-2024)
- How to tweak `lookup/find` performance for my data/use case?
> Always measure!
- [[bmi2](https://en.wikipedia.org/wiki/X86_Bit_manipulation_instruction_set) ([Intel Haswell](Intel)+, [AMD Zen3](https://en.wikipedia.org/wiki/Zen_3)+)] hardware instruction acceleration is faster than software emulation. (AMD Zen2 pext takes 18 cycles, is worth disabling hardware accelerated version)
- For integral keys, use u32 or u64.
- For strings, consider aligning the input data and passing it with compile-time size via `span`, `array`.
- If all strings length is less than 4 that will be more optimized than if all string length will be less than 8 and 16. That will make the lookup table smaller and getting the value will have one instruction less.
- Experiment with different `probability` values to optimize lookups. Especially benefitial if its known that input keys are always coming from predefined `entries` (probability = 100) as it will avoid the comparison.
- Consider passing cache size alignment (`hardware_destructive_interference_size` - usually `64u`) to the `lookup/find`. That will align the underlying lookup table.
- How to fix compilation error `constexpr evaluation hit maximum step limit`?
> The following options can be used to increase the limits, however, compilation-times should be monitored.
```
gcc: -fconstexpr-ops-limit=N
clang: -fconstexpr-steps=N
```
- Is support for [bmi2](https://en.wikipedia.org/wiki/X86_Bit_manipulation_instruction_set) instructions required?
> `mph` works on platforms without `bmi2` instructions which can be emulated with some limitations (*).
```cpp
// bmi2
mov ecx, 789
pext ecx, eax, ecx
```
> [intel.com/pext](https://www.intel.com/content/www/us/en/docs/intrinsics-guide/index.html#text=pext) / [uops.info/pext](https://uops.info/table.html?search=PEXT%20(R64%2C%20R64%2C%20R64)&cb_lat=on&cb_HSW=on&cb_BDW=on&cb_SKL=on&cb_CFL=on&cb_CLX=on&cb_ICL=on&cb_TGL=on&cb_RKL=on&cb_ZEN2=on&cb_ZEN3=on&cb_ZEN4=on&cb_measurements=on&cb_bmi=on)
```cpp
// no bmi2
mov ecx, eax
and ecx, 789
imul ecx, ecx, 57
shr ecx, 2
and ecx, 248
```
> https://stackoverflow.com/questions/14547087/extracting-bits-with-a-single-multiplication (*)
- How to disable `cmov` generation?
> Set `probability` value to something else than `50u` (default) - it means that the input data is predictable in some way and `jmp` will be generated instead. Additionaly the following compiler options can be used.
```
clang: -mllvm -x86-cmov-converter=false
```
- How to disable running tests at compile-time?
> When `-DNTEST` is defined static_asserts tests wont be executed upon inclusion.
Note: Use with caution as disabling tests means that there are no gurantees upon inclusion that given compiler/env combination works as expected.
- How to integrate with [CMake.FetchContent](https://cmake.org/cmake/help/latest/module/FetchContent.html)?
```
include(FetchContent)
FetchContent_Declare(
qlibs.mph
GIT_REPOSITORY https://github.com/qlibs/mph
GIT_TAG v5.0.5
)
FetchContent_MakeAvailable(qlibs.mph)
```
```
target_link_libraries(${PROJECT_NAME} PUBLIC qlibs.mph);
```
- Similar projects?
> [gperf](https://www.gnu.org/software/gperf), [frozen](https://github.com/serge-sans-paille/frozen), [nbperf](https://github.com/rurban/nbperf), [cmph](https://cmph.sourceforge.net), [perfecthash](https://github.com/tpn/perfecthash), [lemonhash](https://github.com/ByteHamster/LeMonHash), [pthash](https://github.com/jermp/pthash), [shockhash](https://github.com/ByteHamster/ShockHash), [burr](https://github.com/lorenzhs/BuRR), [hash-prospector](https://github.com/skeeto/hash-prospector)
- Acknowledgments
> https://lemire.me/blog, http://0x80.pl, https://easyperf.net, https://www.jabperf.com, https://johnnysswlab.com, [pefect-hashing](https://github.com/tpn/pdfs/tree/master/Perfect%20Hashing), [gperf](https://www.dre.vanderbilt.edu/~schmidt/PDF/C++-USENIX-90.pdf), [cmph](https://cmph.sourceforge.net/papers), [smasher](https://github.com/rurban/smhasher), [minimal perfect hashing](http://stevehanov.ca/blog/index.php?id=119), [hash functions](https://nullprogram.com/blog/2018/07/31)
<!--
#endif
#pragma once
#pragma GCC system_header
#if __has_include(<experimental/simd>)
#include <experimental/simd>
#endif
namespace mph::inline v5_0_5 {
using i8 = __INT8_TYPE__;
using u8 = __UINT8_TYPE__;
using i16 = __INT16_TYPE__;
using u16 = __UINT16_TYPE__;
using i32 = __INT32_TYPE__;
using u32 = __UINT32_TYPE__;
using i64 = __INT64_TYPE__;
using u64 = __UINT64_TYPE__;
#if defined(__SIZEOF_INT128__)
using i128 = __int128;
using u128 = unsigned __int128;
#endif
namespace utility {
template<class T1, class T2>
struct compressed_pair {
using first_type = T1;
using second_type = T2;
[[no_unique_address]] T1 first;
[[no_unique_address]] T2 second;
};
template<class... Ts> compressed_pair(Ts...) -> compressed_pair<Ts...>;
template<class T, u32 Size>
struct array {
using value_type = T;
[[nodiscard]] constexpr const T* data() const noexcept { return data_; }
[[nodiscard]] constexpr T* data() noexcept { return data_; }
[[nodiscard]] constexpr auto begin() const noexcept { return &data_[0]; }
[[nodiscard]] constexpr auto begin() noexcept { return &data_[0]; }
[[nodiscard]] constexpr auto end() const noexcept { return &data_[0] + Size; }
[[nodiscard]] constexpr auto end() noexcept { return &data_[0] + Size; }
[[nodiscard]] constexpr auto size() const noexcept { return Size; }
[[nodiscard]] constexpr const auto& operator[](u32 i) const noexcept { return data_[i]; }
[[nodiscard]] constexpr auto& operator[](u32 i) noexcept { return data_[i]; }
constexpr void fill(const T& value) noexcept { for (auto i = 0u; i < Size; ++i) { data_[i] = value; } }
T data_[Size];
};
template<class T, class... Ts> array(T, Ts...) -> array<T, 1u + sizeof...(Ts)>;
} // namespace utility
namespace type_traits {
namespace detail {
template<bool> struct conditional;
template<> struct conditional<false> { template <class, class T> using fn = T; };
template<> struct conditional<true> { template <class T, class> using fn = T; };
template<class T> auto value_type(const T&) -> typename T::value_type;
} // namespace detail
template<bool B, class T, class F>
using conditional_t = typename detail::conditional<B>::template fn<T, F>;
template<const auto& v>
using value_type_t = decltype(detail::value_type(v));
template<auto v> struct constant {
static constexpr auto value = v;
constexpr operator auto() const noexcept { return value; }
};
template<auto v> inline constexpr constant<v> constant_v{};
template<class T> struct constant_t { static constexpr T value{}; };
} // namespace type_traits
namespace random {
// https://www.pcg-random.org
struct pcg {
[[nodiscard]] constexpr auto operator()() noexcept -> u32 {
u64 old_state = state;
state = old_state * 6364136223846793005u + increment;
u32 xor_shifted = ((old_state >> 18u) ^ old_state) >> 27u;
u32 rot = u32(old_state >> 59u);
return (xor_shifted >> rot) | (xor_shifted << ((-rot) & 31u));
}
u64 increment{1442695040888963407u};
u64 state{5573589319906701683u + increment};
};
} // namespace random
template<u8 probability> requires (probability >= 0u and probability <= 100u)
inline constexpr auto conditional =
[]<class T>([[maybe_unused]] const bool cond, [[maybe_unused]] const T lhs, [[maybe_unused]] const T rhs) {
if constexpr (probability == 0u) {
return rhs;
} else if constexpr (probability == 100u) {
return lhs;
} else if constexpr (probability == 50u) {
#if __has_builtin(__builtin_unpredictable)
if (__builtin_is_constant_evaluated()) {
return cond ? lhs : rhs;
} else if (__builtin_unpredictable(cond)) {
return lhs;
} else {
return rhs;
}
#else
constexpr auto underlying = [](const auto value) {
if constexpr (__is_enum(decltype(value))) {
return static_cast<__underlying_type(decltype(value))>(value);
} else {
return value;
}
};
if constexpr (requires { T(cond * underlying(lhs.value), cond); }) {
return T(cond * underlying(lhs.value), cond);
} else if constexpr (requires { T(cond * underlying(lhs)); }) {
return T(cond * underlying(lhs));
} else {
return __builtin_expect_with_probability(cond, 1, .5f) ? lhs : rhs;
}
#endif
} else {
return __builtin_expect_with_probability(cond, 1,
[] { return float(probability) / float(100u); }()) ? lhs : rhs;
}
};
template<class T>
[[nodiscard]] [[gnu::always_inline]] constexpr auto to(const auto& data) noexcept -> T {
if (__builtin_is_constant_evaluated()) {
if constexpr (requires { data.data(); data.size(); }) {
T t{};
for (auto i = 0u; i < data.size(); ++i) {
t = (t << __CHAR_BIT__) | data.data()[data.size() - i - 1u];
}
return t;
} else if constexpr (requires(u32 n) { data[n]; }) {
u32 size{};
auto ptr = data;
while (*ptr++) size++;
T t{};
for (auto i = 0u; i < size; ++i) {
t = (t << __CHAR_BIT__) | data[size - i - 1u];
}
return t;
} else {
return static_cast<T>(data);
}
} else if constexpr (requires { static_cast<T>(data); } ) {
return static_cast<T>(data);
} else if constexpr (requires { data.data(); data.size(); }) {
if constexpr (requires { []<template<class, auto> class T_, class _, auto size>(T_<_, size>){}(data); }) {
return [&]<template<class, auto> class T_, class _, auto size>(T_<_, size>) {
if constexpr (not size) {
return T{};
} else if constexpr (size == sizeof(T)) {
return *__builtin_bit_cast(const T*, data.data());
} else if constexpr (size <= sizeof(T)) {
T t{};
__builtin_memcpy(&t, data.data(), size);
return t;
}
}(data);
} else {
#if defined (MPH_PAGE_SIZE)
// https://github.com/bminor/glibc/blob/master/sysdeps/generic/memcopy.h#L162
if ((u64(data.data()) & (MPH_PAGE_SIZE - 1ul)) > (MPH_PAGE_SIZE - sizeof(T))) [[unlikely]] {
return [&data] [[gnu::cold]] {
T t{};
__builtin_memcpy(&t, data.data(), data.size());
return t;
}();
}
#endif
T t{};
__builtin_memcpy(&t, data.data(), data.size() < sizeof(t) ? data.size() : sizeof(t));
const auto index = T(data.size() * __CHAR_BIT__);
#ifdef __BMI2__
if constexpr (sizeof(t) <= sizeof(u32)) {
return __builtin_ia32_bzhi_si(t, index);
} else if constexpr (sizeof(t) <= sizeof(u64)) {
return __builtin_ia32_bzhi_di(t, index);
} else {
#endif
constexpr T size = sizeof(T) * __CHAR_BIT__;
return index >= size ? t : t & ((T(1) << index) - T(1));
#ifdef __BMI2__
}
#endif
}
} else { // unsafe
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Warray-bounds"
return *reinterpret_cast<const T*>(data);
#pragma GCC diagnostic pop
}
__builtin_unreachable();
}
namespace detail {
template<class T, T size = sizeof(T) * __CHAR_BIT__>
[[nodiscard]] [[gnu::always_inline]] constexpr auto pext(const T a, const auto mask) noexcept -> T {
#ifdef __BMI2__
// https://www.intel.com/content/www/us/en/docs/intrinsics-guide/index.html#text=pext
if (__builtin_is_constant_evaluated()) {
T result{};
T m = mask;
auto k = 0u;
for (T i{}; i < size; ++i) {
if (m & 1) result |= ((a >> i) & 1) << k++;
m >>= 1;
}
return result;
}
else if constexpr (requires { u32{mask}; }) { return __builtin_ia32_pext_si(a, mask); }
else if constexpr (requires { u64{mask}; }) { return __builtin_ia32_pext_di(a, mask); }
else
#endif
if constexpr (requires { mask.value; }) {
// https://stackoverflow.com/questions/14547087/extracting-bits-with-a-single-multiplication
// https://github.com/intel/compile-time-init-build/blob/main/include/lookup/pseudo_pext_lookup.hpp
constexpr auto clz = [](auto x) {
decltype(x) n{sizeof(x) * __CHAR_BIT__ - 1};
if (not x) return decltype(x)(sizeof(x) * __CHAR_BIT__);
while (x >>= 1u) n--;
return n;
};
constexpr auto mbits = __builtin_popcountl(mask);
constexpr auto nbits = size - mbits - clz(mask.value);
constexpr auto coefficient = [&] {
auto set = false;
auto dst = nbits;
T result{};
for (auto i = 0u; i < size; ++i) {
const auto curr = ((T(1) << i) & mask) != T();
if (curr and not set) result = result | (T(1) << (dst - i));
dst += curr;
set = curr;
}
return result;
}();
if constexpr(constexpr auto final_mask = ((T(1) << mbits) - T(1));
((((mask) * coefficient) >> nbits) & final_mask) == final_mask) {
return (((a & mask) * coefficient) >> nbits) & final_mask;
}
}
T result{};
T m = mask;
auto k = 0u;
for (T i{}; i < size; ++i) {
if (m & 1) result |= ((a >> i) & 1) << k++;
m >>= 1;
}
return result;
}
template<class T, u32 N = 1u>
[[nodiscard]] constexpr auto mask(const auto& entries) noexcept -> T {
utility::array<T, decltype(entries){}.size()> vs;
T max{};
for (auto i = 0u; i < vs.size(); ++i) {
if (vs[i] = entries[i].first; vs[i] > max) max = vs[i];
}
constexpr auto H = (N * vs.size()) << 1u;
constexpr auto N_ = N - 1u;
const auto lz = sizeof(max) <= sizeof(u32) ? __builtin_clz(max) : __builtin_clzl(max);
const auto nbits = sizeof(T) * __CHAR_BIT__ - lz - 1u;
utility::array<T, H> hashed;
T mask = ((T(1) << nbits) - 1u);
for (int i = nbits; i >= 0; --i) {
mask &= ~(T(1) << i);
hashed = {};
for (auto j = 0u; j < vs.size(); ++j) {
const T masked = (vs[j] & mask) + 1u;
auto slot = masked % H;
auto n = N_;
auto found = false;
while (hashed[slot]) {
if (hashed[slot] == masked and not n--) {
found = true;
break;
}
slot = (slot + 1u) % H;
}
if (found) {
mask |= (T(1) << i);
break;
}
hashed[slot] = masked;
}
}
return mask;
}
template<const auto& entries>
struct traits {
static constexpr auto mappings = [] {
if constexpr (requires { entries[0].size(); }) { // array{"a"sv, "b"sv, ...}
constexpr auto max_len = [] {
u32 len{};
for (const auto& entry : entries) { if (entry.size() > len) { len = entry.size(); } }
return len;
}();
using key_type = decltype([] {
if constexpr (max_len <= sizeof(u8)) { return u8{}; }
else if constexpr (max_len <= sizeof(u16)) { return u16{}; }
else if constexpr (max_len <= sizeof(u32)) { return u32{}; }
else if constexpr (max_len <= sizeof(u64)) { return u64{}; }
#if defined(__SIZEOF_INT128__)
else if constexpr (max_len <= sizeof(u128)) { return u128{}; }
#endif
}());
using mapped_type = decltype([] {
if constexpr (entries.size() < u8(u8{}-1u)) { return u8{}; }
else if constexpr (entries.size() < u16(u16{}-1u)) { return u16{}; }
else if constexpr (entries.size() < u32(u32{}-1u)) { return u32{}; }
else if constexpr (entries.size() < u64(u64{}-1u)) { return u64{}; }
#if defined(__SIZEOF_INT128__)
else if constexpr (entries.size() < u128(u128{}-1u)) { return u128{}; }
#endif
}());
utility::array<utility::compressed_pair<key_type, mapped_type>, entries.size()> entries_;
for (mapped_type i{}; i < entries.size(); ++i) {
entries_[i] = {to<key_type>(entries[i]), mapped_type(i)};
}
return entries_;
} else if constexpr (requires (u32 n) { entries[n].first.size(); entries[n].second; }) { // array{pair{"a"sv, 1}, ...}
constexpr auto max_len = [] {
u32 len{};
for (const auto& entry : entries) { if (entry.first.size() > len) { len = entry.first.size(); } }
return len;
}();
using key_type = decltype([] {
if constexpr (max_len <= sizeof(u8)) { return u8{}; }
else if constexpr (max_len <= sizeof(u16)) { return u16{}; }
else if constexpr (max_len <= sizeof(u32)) { return u32{}; }
else if constexpr (max_len <= sizeof(u64)) { return u64{}; }
#if defined(__SIZEOF_INT128__)
else if constexpr (max_len <= sizeof(u128)) { return u128{}; }
#endif
}());
using mapped_type = typename type_traits::value_type_t<entries>::second_type;
utility::array<utility::compressed_pair<key_type, mapped_type>, entries.size()> entries_;
for (auto i = 0u; i < entries.size(); ++i) {
entries_[i] = {to<key_type>(entries[i].first), entries[i].second};
}
return entries_;
} else if constexpr (not requires (u32 n) { entries[n].first; entries[n].second; }) { // array{1, 2, 3, ...}
using key_type = type_traits::value_type_t<entries>;
using mapped_type = decltype([] {
if constexpr (entries.size() < u8(u8{}-1u)) { return u8{}; }
else if constexpr (entries.size() < u16(u16{}-1u)) { return u16{}; }
else if constexpr (entries.size() < u32(u32{}-1u)) { return u32{}; }
else if constexpr (entries.size() < u64(u64{}-1u)) { return u64{}; }
#if defined(__SIZEOF_INT128__)
else if constexpr (entries.size() < u128(u128{}-1u)) { return u128{}; }
#endif
}());
utility::array<utility::compressed_pair<key_type, mapped_type>, entries.size()> entries_;
for (auto i = 0u; i < entries.size(); ++i) {
entries_[i] = {entries[i], mapped_type(i)};
}
return entries_;
} else if constexpr (__is_enum(typename type_traits::value_type_t<entries>::first_type)) {
using key_type = __underlying_type(typename type_traits::value_type_t<entries>::first_type);
using mapped_type = typename type_traits::value_type_t<entries>::second_type;
utility::array<utility::compressed_pair<key_type, mapped_type>, entries.size()> entries_;
for (auto i = 0u; i < entries.size(); ++i) {
entries_[i] = {static_cast<key_type>(entries[i].first), entries[i].second};
}
return entries_;
} else { // array{pair{1, 2}, ...}
return entries;
}
}();
using key_type = typename type_traits::value_type_t<mappings>::first_type;
using mapped_type = typename type_traits::value_type_t<mappings>::second_type;
using key_mapped_type = utility::compressed_pair<key_type, mapped_type>;
};
} // namespace detail
template<class T>
struct optional {
using value_type = T;
constexpr optional() noexcept = default;
constexpr optional(const value_type value, const bool flag = true) noexcept
: value(value), flag(flag)
{ }
[[nodiscard]] constexpr operator bool() const noexcept { return flag; }