base on C++ template library for high performance SIMD based sorting algorithms # x86-simd-sort C++ template library for high performance SIMD based sorting routines for built-in integers and floats (16-bit, 32-bit and 64-bit data types) and custom defined C++ objects. The sorting routines are accelerated using AVX-512/AVX2 when available. The library auto picks the best version depending on the processor it is run on. If you are looking for the AVX-512 or AVX2 specific implementations, please see [README](https://github.com/intel/x86-simd-sort/blob/main/src/README.md) file under `src/` directory. The following routines are currently supported: ## Sort an array of custom defined class objects (uses `O(N)` space) ``` cpp template <typename T, typename Func> void x86simdsort::object_qsort(T *arr, uint32_t arrsize, Func key_func) ``` `T` is any user defined struct or class and `arr` is a pointer to the first element in the array of objects of type `T`. `Func` is a lambda function that computes the `key` value for each object which is the metric used to sort the objects. `Func` needs to have the following signature: ```cpp [] (T obj) -> key_t { key_t key; /* compute key for obj */ return key; } ``` Note that the return type of the key `key_t` needs to be one of the following : `[float, uint32_t, int32_t, double, uint64_t, int64_t]`. `object_qsort` has a space complexity of `O(N)`. Specifically, it requires `arrsize * sizeof(key_t)` bytes to store a vector with all the keys and an additional `arrsize * sizeof(uint32_t)` bytes to store the indexes of the object array. For performance reasons, we support `object_qsort` only when the array size is less than or equal to `UINT32_MAX`. An example usage of `object_qsort` is provided in the [examples](#Sort-an-array-of-Points-using-object_qsort) section. Refer to [section](#Performance-of-object_qsort) to get a sense of how fast this is relative to `std::sort`. ## Sort an array of built-in integers and floats ```cpp void x86simdsort::qsort(T* arr, size_t size, bool hasnan, bool descending); void x86simdsort::qselect(T* arr, size_t k, size_t size, bool hasnan, bool descending); void x86simdsort::partial_qsort(T* arr, size_t k, size_t size, bool hasnan, bool descending); ``` Supported datatypes: `T` $\in$ `[_Float16, uint16_t, int16_t, float, uint32_t, int32_t, double, uint64_t, int64_t]` ## Key-value sort routines on pairs of arrays ```cpp void x86simdsort::keyvalue_qsort(T1* key, T2* val, size_t size, bool hasnan, bool descending); void x86simdsort::keyvalue_select(T1* key, T2* val, size_t k, size_t size, bool hasnan, bool descending); void x86simdsort::keyvalue_partial_sort(T1* key, T2* val, size_t k, size_t size, bool hasnan, bool descending); ``` Supported datatypes: `T1`, `T2` $\in$ `[float, uint32_t, int32_t, double, uint64_t, int64_t]` Note that keyvalue sort is not yet supported for 16-bit data types. ## Arg sort routines on arrays ```cpp std::vector<size_t> arg = x86simdsort::argsort(T* arr, size_t size, bool hasnan, bool descending); std::vector<size_t> arg = x86simdsort::argselect(T* arr, size_t k, size_t size, bool hasnan); ``` Supported datatypes: `T` $\in$ `[_Float16, uint16_t, int16_t, float, uint32_t, int32_t, double, uint64_t, int64_t]` ## Build/Install [meson](https://github.com/mesonbuild/meson) is the used build system. Command to build and install the library: ``` meson setup --buildtype release builddir && cd builddir meson compile sudo meson install ``` Once installed, you can use `pkg-config --cflags --libs x86simdsortcpp` to populate the right cflags and ldflags to compile and link your C++ program. This repository also contains a test suite and benchmarking suite which are written using [googletest](https://github.com/google/googletest) and [google benchmark](https://github.com/google/benchmark) frameworks respectively. You can configure meson to build them both by using `-Dbuild_tests=true` and `-Dbuild_benchmarks=true`. ## Example usage #### Sort an array of floats ```cpp #include "x86simdsort.h" int main() { std::vector<float> arr{1000}; x86simdsort::qsort(arr.data(), 1000, true); return 0; } ``` #### Sort an array of Points using object_qsort ```cpp #include "x86simdsort.h" #include <cmath> struct Point { double x, y, z; }; int main() { std::vector<Point> arr{1000}; // Sort an array of Points by its x value: x86simdsort::object_qsort(arr.data(), 1000, [](Point p) { return p.x; }); // Sort an array of Points by its distance from origin: x86simdsort::object_qsort(arr.data(), 1000, [](Point p) { return sqrt(p.x*p.x+p.y*p.y+p.z*p.z); }); return 0; } ``` ## Details - `x86simdsort::qsort` is equivalent to `qsort` in [C](https://www.tutorialspoint.com/c_standard_library/c_function_qsort.htm) or `std::sort` in [C++](https://en.cppreference.com/w/cpp/algorithm/sort). - `x86simdsort::qselect` is equivalent to `std::nth_element` in [C++](https://en.cppreference.com/w/cpp/algorithm/nth_element) or `np.partition` in [NumPy](https://numpy.org/doc/stable/reference/generated/numpy.partition.html). - `x86simdsort::partial_qsort` is equivalent to `std::partial_sort` in [C++](https://en.cppreference.com/w/cpp/algorithm/partial_sort). - `x86simdsort::argsort` is equivalent to `np.argsort` in [NumPy](https://numpy.org/doc/stable/reference/generated/numpy.argsort.html). - `x86simdsort::argselect` is equivalent to `np.argpartition` in [NumPy](https://numpy.org/doc/stable/reference/generated/numpy.argpartition.html). Supported datatypes: `uint16_t, int16_t, _Float16, uint32_t, int32_t, float, uint64_t, int64_t, double`. Note that `_Float16` will require building this library with g++ >= 12.x. All the functions have an optional argument `bool hasnan` set to `false` by default (these are relevant to floating point data types only). If your array has NAN's, the the behaviour of the sorting routine is undefined. If `hasnan` is set to true, NAN's are always sorted to the end of the array. In addition to that, qsort will replace all your NAN's with `std::numeric_limits<T>::quiet_NaN`. The original bit-exact NaNs in the input are not preserved. Also note that the arg methods (argsort and argselect) will not use the SIMD based algorithms if they detect NAN's in the array. You can read details of all the implementations [here](https://github.com/intel/x86-simd-sort/blob/main/src/README.md). ## Performance comparison on AVX-512: `object_qsort` v/s `std::sort` Performance of `object_qsort` can vary significantly depending on the defintion of the custom class and we highly recommend benchmarking before using it. For the sake of illustration, we provide a few examples in [./benchmarks/bench-objsort.hpp](./benchmarks/bench-objsort.hpp) which measures performance of `object_qsort` relative to `std::sort` when sorting an array of 3D points represented by the class: `struct Point {double x, y, z;}` and `struct Point {float x, y, x;}`. We sort these points based on several different metrics: + sort by coordinate `x` + sort by manhanttan distance (relative to origin): `abs(x) + abx(y) + abs(z)` + sort by Euclidean distance (relative to origin): `sqrt(x*x + y*y + z*z)` + sort by Chebyshev distance (relative to origin): `max(abs(x), abs(y), abs(z))` The performance data (shown in the plot below) can be collected by building the benchmarks suite and running `./builddir/benchexe --benchmark_filter==*obj*`. The data plot shown below was collected on a processor with AVX-512. For the simplest of cases where we want to sort an array of struct by one of its members, `object_qsort` can be up-to 5x faster for 32-bit data type and about 4x for 64-bit data type. It tends to do even better when the metric to sort by gets more complicated. Sorting by Euclidean distance can be up-to 10x faster.  ## Downstream projects using x86-simd-sort - NumPy uses this as a [submodule](https://github.com/numpy/numpy/pull/22315) to accelerate `np.sort, np.argsort, np.partition and np.argpartition`. - PyTorch uses this as a [submodule](https://github.com/pytorch/pytorch/pull/127936) to accelerate `torch.sort, torch.argsort`. - A slightly modifed version this library has been integrated into [openJDK](https://github.com/openjdk/jdk/pull/14227). - [GRAPE](https://github.com/alibaba/libgrape-lite.git): C++ library for parallel graph processing. - AVX-512 version of the key-value sort has been submitted to [Oceanbase](https://github.com/oceanbase/oceanbase/pull/1325). 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